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Optical studies of precipitation in dilute copper-cobalt alloys using differential reflectometry

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Optical studies of precipitation in dilute copper-cobalt alloys using differential reflectometry
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Goho, William Michael, 1954-
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xi, 132 leaves : ill. ; 28 cm.

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Alloys ( jstor )
Cobalt ( jstor )
Hardness ( jstor )
Optical properties ( jstor )
Precipitates ( jstor )
Precipitation ( jstor )
Precipitation hardening ( jstor )
Reflectance ( jstor )
Signals ( jstor )
Solutes ( jstor )
Copper alloys ( lcsh )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis Ph. D
Reflectometer ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1986.
Bibliography:
Includes bibliographical references (leaves 127-131).
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Also available online.
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Typescript.
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Vita.
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by William Michael Goho.

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OPTICAL STUDIES OF PRECIPITATION
IN DILUTE COPPER-COBALT ALLOYS
USING DIFFERENTIAL REFLECTOMETRY













By

WILLIAM MICHAEL GOHO












A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY





UNIVERSITY OF FLORIDA






1986















ACKNOWLEDGEMENTS


The author wishes to recognize the contributions of the following people, without whose efforts this work could not have been completed.

The typing of this dissertation was done by Susan Matts Goho. This enormous task represents a tiny fraction of the support which she has provided. She has provided me with the technical, academic, and emotional means with which to bring this long process to an end. This accomplishment must be shared equally with her.

The author is grateful to Dr. R. E. Hummel for his

unique attitude in helping his students in all aspects of their concerns as well as for his technical advice. 1 have benefitted greatly from his tutelage and aspire to be as good a teacher as he.

Dr. P. H. Holloway has provided many hours of helpful discussions on matters of concern to this dissertation. He has also provided much needed encouragement at crucial times during the writing of this work.

The author wishes to thank all the members of the dissertation committee for their efforts.

















TABLE OF CONTENTS

Page

ACKNOWLEGDEMENTS...........................................1ii


LIST OF TABLES.............................................. v


LIST OF FIGURES............................................ vi


ABSTRACT................................................... A


CHAPTER 1. INTRODUCTION................................... 1


CHAPTER 2. OBSERVATIONS CONCERNING PRECIPITATION
AND OPTICAL PROPERTIES OF ALLOYS.............. 4

2.1 Precipitation: General.................... 4
2.2 Precipitation in Dilute CopperCobalt Alloys............................ 17
2.3 Optical Properties of Copper and
Copper Alloys............................ 30


CHAPTER 3. EXPERIMENTAL PROCEDURE........................ 43

3.1 Experimental Approach.................... 43
3.2 Alloy Preparation........................ 44
3.3 Differential Reflectometer.............. 47
3.4 Polishing Procedure...................... 50
3.5 Aging.................................... 51
3.6 Microhardness Tests...................... 52


CHAPTER 4. EXPERIMENTAL RESULTS AND DISCUSSION ..........54

4.1 Microhardness Tests: Results and
Discussion............................... 54
4.2 Compositional Modulation: Results
and Discussion........................... 66
4.3 Aging Experiments........................ 82
4.4 The Kinetics of the Precipitation
Reaction................................ 109

iii
















TABLE OF CONTENTS (continued)

Page

4.5 Comparison of Microhardness and
Optical Results ....................... 116


CHAPTER 5. SUMMARY .................................... 124


REFERENCES ............................................. 127


BIOGRAPHICAL SKETCH .................................... 132





































iv















LlST OF TABLES


Page


Table 2-1. Time to Peak Property for Copper-Cobalt
Precipitation ............................... 28

Table 3-1. Alloys Used in Composition Modulation
Experiments ................................. 46

Table 3-2. Alloys Used in Aging Experiments ............ 46

Table 4-1. Radius of Precipitate at Peak Property for
Copper-Cobalt System ........................ 65

Table 4-2. Functional Dependency, n, of the Exponent
in the Avrami Equation ..................... 114
































v
















LIST OF FIGURES

Page

Figure 2-1. Phase Diagram of Hypothetiacl Precipitation
Hardenable Alloy and Corresponding Free
Energy Diagram .............................. 7

Figure 2-2. Composite Hardness Curve ................... 13

Figure 2-3. Composite Curve showing the Effect of
Precipitation on Electrical Resistivity .... 18 Figure 2-4. Phase Diagram of Copper-Cobalt System ...... 19 Figure 2-5. Hardness versus Time for Cu-2.0% Co
Aged at 6000C .............................. 25

Figure 2-6. Yield Strength and Hardness versus Time for
Cu-2.0% Co Aged at Various Temperatures .... 26 Figure 2-7. The Band Diagram of Copper ................. 32

Figure 2-8. Reflectance Spectra for Copper and
Various Brasses ............................ 33

Figure 2-9. Composition Dependence of Copper Threshold
Transition ................................. 37

Figure 2-10. Reflectance Spectra for Copper and Two
Copper-Nickel Alloys ....................... 39

Figure 2-11. Reflectivity Spectrum for Cobalt as
Calculated from Measurements of n and k
by Johnson and Christy ..................... 42

Figure 3-1. Schematic of Differential Reflectometer .... 48 Figure 4-1. Hardness vs Time for Alloys Aged at 6000C..55 Figure 4-2. Hardness vs Time for Alloys Aged at 5000C..57 Figure 4-3. Hardness vs Time for Alloys Aged at 4000C..59 Figure 4-4. Hardness vs Time for Cu-2.7% Co Aged at
6000C, 5000C, and 4000C .................... 61



vi















LIST OF FIGURES (continued)



Page

Figure 4-5. Hardness vs Time for Cu-2.0% Co Aged
at 6000C, 5000C, and 4000C...................62

Figure 4-6. Hardness vs Time for Cu-l.0% Co Aged
at 6000C, 5000C, and 4000C...................63

Figure 4-7. Differential Reflectograms of Cu-l.5% Ni
and Cu-1.5% Co ..............................69

Figure 4-8. Differential Reflectograms of Various
Copper-Cobalt Alloys ........................71

Figure 4-9. Differential Reflectograms of Cu-2.7% Co
versus Cu-U.5% Co, Cu-l.0% Co, Cu-l.5% Co,
Cu-2.0% Co, and Cu-2.5% Co. ..................75

Figure 4-10. Differential Reflectograms of Cu-2.0% Co
versus Pure Copper, Cu-0.5% Co, Cu-l.0% Co,
and Cu-l.5% Co ..............................77

Figure 4-11. Differential Reflectograms of Cu-1% Co
versus Pure Copper and Cu-0.5% Co ...........78

Figure 4-12. Signal Strength (AR/R) versus Difference
in Cobalt Concentration ..................... 61

Figure 4-13. Differential Reflectogram of a Cu-2.0% Co
Alloy .......................................84

Figure 4-14. Differential Reflectograms of the Aging
Sequence of a Cu-2.0% Co Alloy Aged at
6000C ......o................................85

Figure 4-15. Peak Height vs Time for Various CopperCobalt Alloys Aged at 6000C .................87

Figure 4-16. Peak Height vs Time for Various CopperCobalt Alloys Aged at 5000C .................89

Figure 4-17. Peak Height vs Time for Various CopperCobalt Alloys Aged at 4000C .................91

vii















LIST OF FIGURES (continued)


Page

Figure 4-18. Peak Height vs Time for Cu-2.7% Co at
Various Aging Temperatures................... 92

Figure 4-19. Peak Height vs Time for Cu-2.O% Co at
Various Aging Temperatures................... 94

Figure 4-20. Peak Height vs Time for Cu-1.0% Co at
Various Aging Temperatures................... 95

Figure 4-21. Signal Strength vs Difference in Cobalt
Concentration for Solution Heat Treated
Samples and Aged Samples..................... 96

Figure 4-22. Comparison of Spectra from Aging Experiments and Compositional Modulation
Experiments................................. 106

Figure 4-23. Fraction Transformed vs Time at 6000C ......117 Figure 4-24. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 6000C.................... 119

Figure 4-25. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 5000C.................... 122

Figure 4-26. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 4000C.................... 123


















viii















Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy




OPTICAL STUDIES OF PRECIPITATION
IN DILUTE COPPER-COBALT ALLOYS
USING DIFFERENTIAL REFLECTOMETRY By

WILLIAM MICHAEL GOHO

May 1986




Chairman: Rolf E. Hummel
Major Department: Materials and Engineering


Differential ref lectometry has been successfully applied to the study of precipitation in dilute copper-cobalt alloys. Experiments were designed to exploit the capability of the differential reflectometer to measure the difference in solute content between two alloys based on an altered electronic structure.

Composition modulation was performed in order to determine the effects that solid solutions of cobalt in copper have on the optical properties of the dilute alloys. It has been observed that the energy of the threshold electronic transition in copper at 2.2 eV has no dependence on the cobalt solid solution content. This lack of dependency has ix









been compared to similar results for nickel in copper, a phenomenon which has been treated by others with the theory of virtual-bound-states. it has also been determined that the strength of the differential reflectometric signal has a linear dependence at 2.2 eV on the difference in solid solution cobalt content between the two samples measured by this method.

Differential ref lectometry was then applied to the study of aged copper-cobalt alloys. Three alloy compositions were used in these experiments: Cu-2.7 a/o Co, Cu-2.Q a/o Co, and Cu-l.Q a/o Co. The precipitation reaction was observed for all compositions at three aging temperatures: 600'C, 500'C, and 4000C. Additionally, Cu-2.7 a/o Co was aged at 5500C and 4500C. The precipitation reaction was followed by means of the increase in the strength of the optical signal which resulted from a decrease in the matrix solute content as the reaction progressed. A site saturated, diffusion controlled growth rate was observed for all compositions. The precipitates have been found to decrease the strength of the optical signal in a way which is linearly dependent on the volume fraction of the precipitates, thus allowing a measure of the microstructural state of an alloy to be obtained from measurements of the optical properties.

Microhardness measurements were performed on these aged alloys to provide an independent verification of the optical results. These microhardness measurements were in good temporal agreement with the optical measurements of this work


x









and with the results of previous measurements of mechanical properties of aged copper-cobalt alloys.





















































xi














CHAPTER 1
INTRODUCTION



The color of alloys of metals has from ancient times been recognized as being influenced by the composition of the alloys. Artisans of many cultures surely experimented with combinations of metals in order to achieve the color they desired in the pieces they created. It was not until this century, however, that the link between the composition of an alloy and its color was understood. 1 With the development of solid state physics came the realization that the optical properties of metals and alloys are a reflection of their electronic structure, specifically the valence band. 2

one instrument which has been successful in measuring the optical properties of alloys in order that electronic structure could be better understood is the differential reflectometer. 3,4 With this instrument, the electronic structures of copper alloys containing multivalent solutes, 5,6,7 copper-nickel, 7 copper-gold, 5 noble metal alloys, 5,8 and nickel-based alloys 9,10 have been investigated for composition dependence. In addition the effect on the electronic structure of the arrangement of constituents within alloys has been explored in studies of long range order 11 and short range order. 12 Finally, the removal of

1







2

an element from an alloy has been observed in experiments dealing with dezincification in brasses.13

Precipitation from a solid solution is a decomposition from a metastable one phase system to a two phase system. This reaction is characterized by the rejection of solute atoms by the matrix in order that a second phase be formed. This rearrangement of solute within the alloy would be expected to change the physical properties of the alloy. This is indeed the case. The measurement of electric,14'15 magnetic,16"17'18 thermal,19 and dimensional properties20'21 have often been used to follow the course of a precipitation reaction. The use of these methods exploits a particular sensitivity to some aspect of the physical changes occurring during a precipitation reaction. None of these methods can provide a complete description of the phenomenon. However, differential reflectometry has the capability, because of its extreme sensitivity to composition, of following a precipitation reaction from start to finish. This work will be devoted to the study by differential ref lectometry of precipitation in dilute copper-cobalt alloys.

in the next chapter, a review of the literature is

presented in three sections. The first section deals with the phenomenon of precipitation in a general way. In this manner, some understanding of this solid state reaction can be reached before the specific system of dilute coppercobalt alloys is presented in the second section. A short analysis of the methods used for studying precipitation in







3

this system will also be presented here. The last section of this chapter focusses on the optical properties of copper and copper alloys. more specifically, the relationship between the composition of copper alloys and its electron band structure is explored.

Three types of experiments were performed in order to accomplish the goal of this work. Firstly, microhardness tests were performed on precipitation hardened alloys. Secondly, optical measurements were carried out on samples which were known to differ in composition only. Lastly, optical measurements were performed on samples which had experienced a precipitation reaction. The details of these experiments and the justification for performing them in this manner are given in the third chapter.

Presented in the fourth chapter are the results of

these experiments as well as a discussion of the findings. Each set of results will be evaluated in terms of what other researchers have found in their studies of precipitation hardening in copper-cobalt as well as in terms of how the results compare against each other. In addition, a section on the effect of cobalt on the electronic structure of copper is presented.

The final chapter summarizes the findings of these experiments.















CHAPTER 2
OBSERVATIONS CONCERNING PRECIPITATION
AND OPTICAL PROPERTIES OF ALLOYS


2.1 Precipitation: General

Since the end of the first decade of this century, when Alfred Wilm 22first demonstrated the means by which certain aluminum alloys could be strengthened, precipitation hardening has been used by metallurgists and materials scientists to improve the mechanical properties of the alloys of many base metals. Although aluminum-based alloys, particularly with additions of copper and magnesium, have probably been the most studied of all precipitation hardenable alloys, precipitation heat treatments are commonly used in many commercial alloys. Two notable examples are the addition of copper to malleable cast iron and the addition of titanium and aluminum to both semi-austenitic stainless steels and nickel-based superalloys.

Precipitation hardening is a process by which the mechanical and physical properties of an alloy can be dramatically altered. Performed under controlled conditions the strength and hardness of an alloy can be considerably increased. For instance, in a commonly used copper-beryllium alloy -- Cu-l.7 wt/o Be, 0.3 wt/o Co -- precipitation hardening can produce an increase in tensile strength from



4







5

410 MPa to 1030 MPa while at the same time increasing the hardness from 125 to 310 on the Vickers hardness scale. Changes in physical properties are also manifested by alloys during precipitation. In general, a significant increase in electrical and thermal conductivity along with changes in volume, magnetic properties, Hall coefficient and optical properties can be observed during precipitation. What follows is a simple description of phenomena which pertain to precipitation and the methods by which they are studied. Greater detail on particular subjects can be found elsewhere. 23-27

The objective in producing a precipitation reaction is to induce the nucleation and growth of a second phase from a metastable solid solution. The reaction is expressed in the following manner, a ->. a + where a is a solid solution and 6 is the precipitated phase. Although the formation of the second phase can be accomplished by changes in pressure or additions of another element, precipitation is most commonly carried out by the application of specific heat treatments, the details of which are given below.

The requirements to produce precipitation hardening (or age hardening) are that the alloying element is capable of achieving a solid solution, usually up to at least a few percent, with the base metal and that the solubility for the alloying element decreases with temperature. (in fact, there is another definitive requirement in oraer for precipitation hardening to be present, which is that the





6

alloy actually hardens as a result of the precipitation reaction.) In Figure 2-1, a phase diagram for a hypothetical age hardenable alloy has been drawn. It can be seen that the two requirements mentioned above have been met. To achieve precipitation, an alloy, which contains a few percent (C') of element B is held at Ts, the solution heat treatment temperature. This solution heat treatment allows all of element B to exist in a solid solution of the a phase. If the alloy is then quenched quickly enough to Tq, usually room temperature, the alloying element B can be made to remain in a metastable solid solution. In order to induce precipitation, the alloy is given an isothermal aging heat treatment at Ta. At this temperature, the metastable phase decomposes into two phases, a and a, approaching the composition defined by the phase diagram. During this decomposition, the matrix phase a rejects B atoms which go to form the phase having a concentration C6, which consequently lowers the matrix concentration of element B to the saturated state Ca. The amount of the second phase produced is determined by the tie line established by the aging temperature. At the completion of the reaction, the percent of a phase is

%a = CO Ca X 100%. (1)
C"F Ca

The precipitation reaction is generally considered to

proceed in three stages: nucleation, growth, and coarsening. A brief, qualitative overview of these processes is given






7


















I2 TT

LU I









U
z AG~z
II



J AG



C" CO CONC. B Cp








Figure 2-1. Phase Diagram of Hypothetical Precipitation
Hardenable Alloy and Corresponding Free Energy
Diagram.






8

here in order to provide a basis from which the specifics of the copper-cobalt precipitation reaction will be discussed.

When an alloy is held at a temperature at which its

solute composition extends beyond the solves, the lattice will reject solute atoms. As the solute atoms are rejected, they will begin to form clusters. This is the first stage of precipitation and is called nucleation. Thermodynamically, nucleation is driven by the difference in the volume free energy of the solid solution and the volume free energy of the decomposed system consisting of the precipitate phase and the matrix phase which is still a solid solution, though possessing a reduced solute content. Schematically, this is shown in Figure 2-1. The a phase at c' can be seen to possess a higher free energy, Ga, than the free energy of the decomposed system, Ga+a. If, as is the case of precipitation hardenable alloys, the solubility decreases with temperature, then the difference in the free energies, AG, will increase the farther the alloy is held below the solvus (the greater the undercooling). This increases the nucleation rate and decreases the size to which a cluster must grow before it becomes stable and capable of increasing its size through growth. In general it is held that there are two "energies" which oppose the formation of stable clusters: surface energy and strain energy. When a cluster forms, it must eventually form an interface with the surrounding matrix. Because surface energy is added







9

to the system with the creation of this interface, the volume free energy difference, AG, driving the reaction must be large enough to compensate for this additional energy. Also, because the precipitates are composed of atoms of a different size than the matrix and have a different lattice parameter than the matrix, they create strain in the lattice. This strain energy must also be offset by the volume free energy reduction.

Nucleation is also influenced by the number of sites

available for the formation of second phase particles. Because of the difference in size of the atoms of the precipitates and the matrix, formation of the second phase is favored at locations where strain can be readily accommodated, such as grain boundaries or dislocations. For this reason, nucleation will normally occur more rapidly in a fine grained or a heavily cold worked material where there are many sites at which precipitates can begin to form.

The same forces which operate in the nucleation of

stable particles continue to operate during their growth. That is to say, the driving force continues to be a reduction in the volume free energy of the system with the product being a decomposed solid solution with precipitate particles interspersed throughout the alloy. The creation of new surface and the strain added to the system by growing particles also continue to influence precipitate growth. The balance between these forces will determine the shape of the precipitates, such that they try to achieve the





10

lowest energy configuration. For instance, in the early stages of growth small precipitates may form on planes which have low strain but a high surface energy. As the planes grow the surface energy becomes very large and the precipitates may change their shape to spheres which possess lower surface energy, but which also produce more strain in the lattice. The stages intermediate to achieving a final shape are called transition lattices.

In terms of composition, the growth of precipitates is accomplished by a depletion from the matrix of solute atoms from the concentration CO, the supersaturated concentration, to Ca, the concentration of solute atoms at the solubility limit. The classic, phenomenological approach to this process finds that the time dependence of the matrix composition is expressed as


Z (t) = Ca + (CO-Ca)e (-t/T )n (2)

where C(t) is the solute concentration at time t, T is a time constant, and n is dependent upon the particulars of the growth process.

Although the kinetics of the precipitation reaction

can be very complicated, there are some rules that apply in general to the reaction rate. Growth of the precipitate is often controlled by the diffusion of solute atoms through the matrix to the precipitate. For this reason, the precipitation rate is faster at higher aging heat treatment temperatures. In addition, because diffusion is controlled






11

by the number of vacancies, dislocations, and other lattice defects, growth will normally occur more rapidly in an alloy which has experienced a rapid quench, heavy cold work, or radiation damage than in an alloy in which these conditions are not present.

Coarsening refers to the increase in interparticle

spacing which has been found to occur during the final steps of precipitation reactions. It is most easily described by the familiar axiom of materials science, "Large particles grow at the expense of smaller ones." In contrast to nucleation and growth, which were driven by the lowering of the volume free energy in going from a supersaturated solution to a decomposed two phase system, coarsening is driven by a reduction in surface energy. It is generally considered to occur after all chemically-driven growth has stopped, with no change in the volume fraction of second phase. Given these considerations, it can be seen that coarsening is also characterized by a decrease in the number of precipitates and an increase in the average particle size with time.

Precipitation is also characterized by the distribution of the second phase throughout the matrix. In what is known as general precipitation, the precipitate is distributed randomly throughout the matrix. The reaction occurs simultaneously in all parts of the matrix. The result of this is a uniform precipitate structure.

In contrast to this, localized precipitation is characterized by growth of precipitates at lattice defects or






12

grain boundaries. Similar to general precipitation, it occurs simultaneously throughout the alloy; however, because the precipitates form at defects, the precipitates are distributed non-uniformly.

Finally, discontinuous precipitation is characterized 25 by the formation of second phase in random parts of the alloy at random times. Discontinuous precipitation is associated with the movement of an interface, such as a grain boundary during recrystallization and grain growth.

The effect of precipitation on mechanical properties depends on several microstructural aspects, such as the extent of the solid solution, the coherency of the precipitate, the dispersion of the second phase, and recrystallization. 24All mechanical properties are affected by these microstructural factors; however, for the reason that microhardness tests were performed for this work, the changes in hardness experienced by an alloy undergoing a precipitation reaction will now be considered. In Figure 2-2, a composite hardness curve is depicted with the contributions from each microstructural factor also shown. The details of this graph are discussed below.

Solid solution hardening takes place because the difference in size between the atoms of the host metal and the solute atoms necessitates the accommodation of solute atoms at places where strain is introduced the least. As mentioned earlier, this means that solute atoms collect at defects in the lattice such as dislocations and grain boundaries.





13












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14

By collecting at dislocations, solute atoms pin them and prevent them from moving during an applied stress. In addition, solute atoms can either replace solvent atoms on regular lattice sites (substitution) or they can occupy sites between lattice positions (interstitial). In either case, the solute atom will create strain in the lattice, which impedes the movement of dislocations. These mechanisms account for the increase in hardness upon the addition of solute atoms to an alloy. During a precipitation reaction, solute atoms are removed from the matrix in order to form the precipitates. Thus as shown in Figure 2-2, as the aging of the alloy progresses solid solution hardening decreases.

The most important contribution to the hardening of an alloy during precipitation comes from coherent precipitates. In the case of general precipitation the first precipitates to form are coherent with the lattice, that is, the lattice of the precipitate matches point for point the lattice of the matrix. Such clusters of a relatively large number of atoms of different size than the matrix exert strain which extends well beyond the immediate vicinity of the precipitates. As long as coherency is maintained, the larger the precipitate becomes, the more strain is exerted on the lattice. The interaction of a moving dislocation with this strain field requires more energy for movement than if there were no precipitate. Thus a dramatic increase in hardness is seen in Figure 2-2 upon the formation of coherent precipitates. As the decomposition proceeds, the





15

precipitates become so large as to require dislocations to maintain a limited amount of coherency with the lattice. This is called a "quasi-coherent" state 27 and marks the beginning of the formation of an interface. As the precipitation continues, the particles become large enough to require a definite interface between the growing precipitate and the matrix. At this stage, the precipitate is completely incoherent with the matrix, and dislocations at the interface between the particle and the matrix accommodate the strain produced by the precipitate. Thus, the effect of the precipitate on the movement of dislocations is diminished, and there is consequently a dramatic loss in hardness.

Dispersion hardening arises from the fact that at the beginning of the process there are many particles spaced fairly close together. As precipitation continues, coarsening can occur with larger particles growing at the expense of smaller ones, causing the precipitate structure to evolve to one in which there are fewer particles spaced farther apart. This process accounts for the slight rise in hardness followed by the slight softening seen in Figure 2-2.

The final factor that affects the composite hardness

curve is recrystallization of the alloy. This is a complicated phenomenon, which itself is influenced by many factors. These include aging temperature, aging time, amount of deformation, composition, and grain size. It is necessary,







16

but hardly sufficient, to state that if recrystallization occurs during aging, the result will always be a loss of hardness brought about by the replacement of deformed, and therefore hard, grains by unreformed, softer grains.

Changes in the physical properties of alloys undergoing precipitation have long been observed and used as tools to measure the kinetics of the reaction and to help to determine the mechanisms by which the reaction takes place. Although these measurements are indirect, at the very least, the measurement of physical properties yields the initial state of the alloy, the changes that occur during the reaction, and the point at which the reaction is complete.

Measurements of resistivity, saturation magnetization, Curie temperature and density or volume are common techniques in studying precipitation. These methods fall into two categories. Firstly, there are those which follow the growth of the second phase, as in the case of a magnetic second phase precipitating from a non-magnetic matrix. Here, measurements of magnetic saturation or coercive force are used in determining the details of the reaction. Secondly, there are studies which follow the depletion of solute from the matrix phase. This type of experiment might be used in the case of a magnetic matrix phase and a non-magnetic second phase, where the rise in the Curie temperature could be measured to determine the rate at which solute was being removed from the matrix by precipitation.







17

Another example, where the removal of solute is measured, is electrical resistivity measurements. Figure 2-3 shows a resistivity curve for a hypothetical alloy. As is shown, the resistivity of the precipitation hardenable alloy is dependent on two variables, the depletion of the solid solution and the coherency strains produced by the precipitate. Here, unlike the case of hardness where the extent of coherency was the dominant factor, the solid solution depletion is more important. As solute atoms are rejected by the matrix in order to form second phase particles, the number of electronic scattering centers is reduced, thus lowering the resistivity. The extended strain field of coherent particles acts to increase the resistivity of the alloy. However, as the precipitates grow and become incoherent, the lattice returns to a more relaxed state and the resistivity consequently decreases.




2.2 Precipitation in Dilute Copper-Cobalt Alloys


Interest in the copper-cobalt system as an example of

a precipitation hardenable alloy, although never as intense as in the more commercially important aluminum age hardenable alloys, has nonetheless been steady.16,28-48 one of the reasons for this lies in the simplicity of the coppercobalt system, the phase diagram of which can be seen in Figure 2-4.49 The copper-cobalt phase diagram shows a miscibility gap with a peritectic transformation on the








18











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Co-Cu 1400


1200



.U1000 cx3

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ATOMIC % COPPER




Figure 2-4. Phase Diagram of Copper-Cobalt System.
(Ref. 49)






20


copper-rich side. The peritectic temperature is 11100C, at which is also found the maximum solubility for cobalt in copper. It is this region of solid solubility on the copperrich side of the phase diagram to which attention is focussed when precipitation hardening is being considered. It is evident that this region possesses the primary condition necessary to achieve age hardening, that is, a decreasing solubility for cobalt with decreasing temperature. Solubility drops from about 5.5 wt/o at 11100C to below 0.1 wt/o at 500'0C. Experiments conducted on dilute coppercobalt alloys have generally employed alloy compositions ranging from slightly below 1.0 wt/o to about 3.0 wt/o. The range of aging temperatures investigated extends from 4000C to 7000C, concentrating attention around 6000C. The fact that these alloys age at such moderately high temperatures is advantageous for the experimenter because the alloys will not age at room temperature.37

The precipitate that forms in these alloys upon aging can be seen by the phase diagram to be a cobalt solid solution containing approximately 10 wt/o copper. This precipitate, containing such a large amount of cobalt, is ferromagnetic.162729,5051 The precipitate has been found to possess an FCC structure and to form as a spherical particle.17,51-52 No intermediate lattices or shapes have been noted.34 The dominant precipitation mode is a general precipitation, although some localized and discontinuous precipitation have been observed.27'33'47 only in the





21


extremely overaged condition has a shape change in the precipitate been observed,17 that being from spheres to plates.

As stated above, the cobalt-rich precipitate which forms during aging contains enough cobalt for the precipitate to possess ferromagnetism. Prior to coalescence, cobalt atoms do not have a ferromagnetic character due to the absence of a sufficient exchange interaction with neighboring cobalt atoms.53'54 Thus as precipitation occurs the magnetic state of the alloy changes from diamagnetic to ferromagnetic. Becker!6 used the term "superparamagnetic" for the latter condition. As the precipitates grow, the magnetic coupling of the cobalt atoms becomes stronger and the saturation magnetization of the alloy becomes larger. From this, Becker16 and others29-31,33,36,41,44 were able to deduce the volume of precipitate formed, the radius of the average precipitate, and the volume fraction of precipitate.

From magnetic measurements on a Cu-2% Co alloy aged at 600'C, Livingston and Becker29 concluded that all of the cobalt was precipitated during the first few minutes of aging and that subsequent growth of the precipitates took place by coarsening, a process in which the total volume and the volume fraction of precipitate remained constant after the first few minutes of aging. They also concluded that the radius of the precipitate increased linearly with the logarithm of aging time. This same conclusion was reached by Witt and Gerald37 for copper alloys containing






22


1.4%, 2.0%, and 3.0% cobalt when aged at 6000C. However, in the same experiment, analysis of their data reveals that for Cu-Q.6% Co the volume fraction increased linearly with time up to 32 hours of aging at 6000C.

it was also through the use of magnetic measurements that experimenters concluded that the precipitates were spherical.17'52 This conclusion was reached on the basis of only very slight magnetic anisotropy observed in the aged single crystal alloys. Finally, the lattice of the cobalt-rich precipitate has been found to be 2% smaller than the lattice of the matrix.55

In another study of precipitation in copper-cobalt,

Servi and Turnbull38 aged the various alloys at temperatures such that the solute composition did not deviate much from equilibrium. This was performed in order to determine the effect of undercooling upon the nucleation rate. By following the change in resistivity, they obtained a measure of the volume fraction transformed through the use of Equation

3 and the relation

X CO C(t) (3)


where X is the volume fraction transformed. Although the transformation was observed to begin very shortly after aging was started, analysis of the data indicates that full transformation was never achieved, in contrast to what was observed in the magnetic studies cited above. The data did, however, confirm the growth of spherical precipitates.







23

A more direct method of observing precipitation in

copper-cobalt alloys has been carried out by a number of researchers.31-35 This is the observation of coherency strains in the lattice caused by the precipitates and detected by means of transmission electron microscopy (TEM). The TEM theory of diffraction contrast was used to obtain particle diameters from the "double D" diffracted image, which is the signature of spherical, coherent particles. Here, as in the case of magnetic measurements, the radii of growing particles increased linearly with the logarithm of aging time.33 Observations that the number of precipitates seen in the micrographs decreased with time were attributed to coarsening,33'34 although the data were never quantitatively compared to coarsening theory. Likewise, no quantitative comparison was made between this work and previous magnetic measurements, which had also indicated growth by coarsening.

TEM observations have indicated in quenched alloys

that a complete solid solution with no formation of precipitates is possible to achieve. Phillips and Livingston31 have shown that no precipitates were observable in solution heat treated and quenched alloys. They also noted that precipitates were seen shortly after the aging heat treatment was begun.

As was discussed in Section 2.1, mechanical properties, such as hardness, yield strength, and tensile strength, tend to rise from the onset of precipitation, go through a peak,







24

which is influenced to the greatest extent by coherency of the precipitate, and then decline as the alloy softens when the precipitates grow too large to maintain their coherency. Softening is also the result of the coarsening of the precipitate structure when the interparticle spacing becomes too large to prevent easy motion by dislocations.

Copper-cobalt is not an exception to these mechanisms. In Figures 2-5 and 2-6, data from Livingston and Becker29 and Livingston30 are presented. In these curves are displayed characteristics which are typical of a precipitation reaction. In Figure 2-5,29 data for a Cu-2% Co alloy aged at 6000C are presented. An increase in hardness is observed as the alloy is aged up to approximately fifteen hours, at which point a peak hardness is obtained. Past this peak, the loss of coherency of the precipitate with the lattice causes softening to occur. In Figure 2-6,30 yield strength and hardness data for a Cu-2% Co alloy aged at 6000C, 6500C and 700'C are presented. Here, several observations can be made which reveal the characteristics of the precipitation process in copper-cobalt. Not only are peaks seen to occur at each aging temperature in both yield strength and hardness, but it is also evident that as the aging temperature is increased, the time for each mechanical property to reach its peak is reduced. This is a consequence of the increased diffusion rate as temperature is increased. The faster diffusion occurs, the faster the precipitates can form. Finally, as the aging temperature is reduced, the higher






25









60

1A
LUJ
z
a
<40 AGING TEMR= 600C





020 /
/

.110000
I I
As 10 100 1000 10000
Quenched MINUTES



Figure 2-5. Hardness versus Time for Cu-2.0% Co Alloy Aged
at 6000C. (Ref. 29)





26




6000C
30


'"' 650*C
IdI L-a
7000C
,- ,20 .- //
I- I
20 /
L,

o ;!


J 600*C
100/-'







1I I-!
z
-8 0 kA^n

//7000C a

60




A.Q. 1 100 10000
MINUTES


Figure 2-6. Yield Strength and Hardness versus Time for
Cu-2.0% Co Aged at Various Temperatures.
(Ref. 30)







27

the peak value of the yield stress and the hardness becomes. This was reported by Livingston30 to be due to the reduced solubility at the lower temperature, which leads to a greater volume fraction of precipitate.

In Table 2-1 data are compiled from studies of the mechanical properties of copper-cobalt alloys. The table shows the aging temperature and length of time required to reach a peak in the particular property investigated. Most studies indicated that the higher the temperature at which the alloys were aged, the faster the growth of the precipitate. Perovic and Purdy,47 in their investigation of precipitation in these alloys aged from 4000C to 8000C, found that the precipitate had a growth rate maximum between 5500C and 6000C.

There is some controversy concerning the length of time necessary to bring the precipitation reaction in this system to completion. This may be due to the fact that each of the methods used have sensitivities that are particular to certain aspects of the reaction. For example, whereas TEM does allow a direct observation of precipitate formation, compositional changes can not be determined quantitatively. No statistical methods have been applied which reveal whether the growth of precipitates is due to depletion of matrix solute or due to coarsening of the precipitate structure.

Because the precipitate in this system is ferromagnetic, magnetic measurements provide a method of following the growth of the precipitate. The model of Becker16 has generally been used to quantitatively determine the average radius







28







Table 2-1. Time to Peak Property
for Copper-Cobalt Precipitation


Aging Time to
Temp. % Co Measurement Peak (hr) Ref.

2500C 3.2% Hardness > 1000 28

3750C 3.2% Hardness > 1000 28

5500C 2.0% Yield Strength 160 30
3.2% Hardness 175 28

6000C 2.0% Yield Strength 16 30
2.0% --12 45
2.0% --11 46
3.1% TEM (Coherency strains) 12 33

6500C 2.0% Yield Strength 1.5 30
2.0% CRSS 4.0 44
3.1% TEM (Coherency strains) 1.5 33
3.1% Yield Strength 1.5 34

7000C 2.0% Yield Strength 0.5 30
2.0% CRSS 1.0 44
3.1% TEM (Coherency strains) 0.7 33
3.2% Hardness 3.0 28







29

of the precipitate and the volume fraction transformed. However, this model assumes that no precipitate is larger than 10 nm and that there is an equal number of particles of each size in the distribution. The validity of these assumptions has not been independently established. Furthermore, the saturation magnetization continues to increase as the precipitates coarsen,16 and therefore, it is difficult to determine with precision when equilibrium has been reached.

Measurements of the electrical resistivity of alloys are useful for following the depletion of solute from the matrix, and have been used38 in following the nucleation and growth of the second phase in this system. In following the depletion of solute from the matrix, however, this method offers little information about the precipitate and its effects on the physical properties of the alloy.

Measurements of the mechanical properties during precipitation are valuable in determining the microstructural state of the alloy, particularly whether or not the precipitate is coherent with the matrix. However, these methods provide only qualitative information about the extent of the transformation or the fraction transformed.

In contrast, differential reflectometry offers a method that can be sensitive to both the changing solute concentration of the matrix and the formation of the second phase. This sensitivity is not limited fundamentally as is the case in the other experimental techniques.

To conclude, the investigations of precipitation in the







30

copper-cobalt system have revealed a fairly typical reaction. Although there is some discrepancy in the length of time measured for the reaction to achieve a fully transformed state

-- that is, the point at which microstructural changes are due only to coarsening -- it has been observed that the precipitate produced is a sphere and has no intermediate shapes. Furthermore, the precipitates form throughout the matrix with some localized precipitation at the grain boundaries. The changes in mechanical properties during aging likewise have been seen to be representative of an age hardenable alloy. The ascent-peak-descent curves seen in the graphs of hardness vs. aging time for these alloys are the unmistakable fingerprint of precipitation. The generally good agreement between the data of these various research efforts reveals a well characterized system. These data also provide a backdrop against which the hardness tests described in this work can be compared.




2.3 Optical Properties of Copper and Copper Alloys


The effects of solute additions on the mechanical properties of metals have already been discussed. Some change in the yield strength, tensile strength, ductility, hardness, and impact strength is the inevitable consequence of altering the composition of a metal. Some changes may be beneficial as in the case of adding zinc to copper, thus producing an alloy that is both stronger and more ductile than pure







31

copper;56 or the effect of alloying may be detrimental such as the brittleness that is produced when a small addition of iron is made to copper.57

Physical properties are also very much a function of composition. Upon addition of another element to a pure metal, its melting point, density, electrical and thermal conductivity, magnetic and optical properties are affected. These property changes upon alloying are the direct result of an altered electronic band structure. This is particularly true of optical properties. In this section, the relationship of the optical properties of copper to its band structure will be considered. In addition, attention will be directed to the response of the band structure, and hence optical properties to composition changes and to methods by which these changes have been measured.

In Figure 2-7, the band diagram of pure copper is presented.58 Because the electronic configuration of copper is 3dl04sl, it is expected that the d-bands of copper would lie entirely below the Fermi energy. This is indeed the case, with the top of the d-bands lying slightly more than 2 eV below the Fermi energy. The partially filled s-bands and p-bands are labelled in the figure. When photons of sufficient energy are incident upon a metal, electrons from filled states are raised into unoccupied states above the Fermi energy. The result of these direct interband transitions can be seen in Figure 2-8,1 where curve A depicts the optical reflectivity for pure copper as a function of







32


















f4 be






00~


L~%







0




~44










C-4)




Ga -uB~u3

44.






33










-We!!enlange 10 70 6 0.5 04 0.) 02

o 0A Kupfer
8 2.5 /.Zink v 5 Z.ink 80 10% Zink
iC 15 linkc
1. 3 0 I.nk

~60
C
CU







20 6 Ff A



Energie








Figure 2-8. Reflectance Spectra for Copper and Various
Brasses (Ref. 1).






34

energy. It is evident that at energies below 2.2 eV the reflectivity is close to 100%. However, at 2.2 eV light is absorbed initiating the first interband transition. These transitions, which occur from the upper d-bands to s-bands and p-bands at the Fermi energy, are believed to occur near the L symmetry point.5 These transitions also give rise to the characteristic salmon pink color of pure copper, since they produce a much lower reflectivity in the green and blue regions of the spectrum than in the yellow and red regions. Other transitions which influence the reflectivity of copper occur between the Fermi energy and the s-states (1,21 to L 1) around 4.2 eV and between the lower d-bands and the Fermi energy at approximately 5.5 eV.59

The influence of solute additions upon the reflectivity of copper can also be seen in Figure 2-8, which presents reflectivity spectra for various brasses. There is a drop in reflectivity in the energy range of 1.8 2.2 eV, as a result of the dependence of reflectivity upon resistivity expressed by the Hagen-Rubens relation:1 R = 1 2(upo) (4)


where R is the reflectivity, u is the frequency of the incident radiation and P0 is the dc resistivity. Since the addition of solute atoms increases the metal's resistivity by increasing the number of scattering centers, the reflectivity is consequently reduced. Although this empirical relation was discovered before there was any knowledge of band







35

diagrams and interband transitions, it still holds f or those regions where no interband transitions occur.

In addition to this decreased reflectivity, the transition which occurs at 2.2 eV is shifted to higher energies as the zinc concentration in the brass is increased. This increase in the threshold energy causes the change in color in brasses from red at low zinc concentrations to yellow at high zinc concentrations. It has been found that upon alloying with elements having a valence of greater than one, that the subsequent energy increase of the threshold transition above

2.2 eV is caused by a rise in the Fermi energy due to the addition of extra electrons from these elements and to a narrowing and raising of the d-bands.5'60 The earliest attempt to explain the transition energy increase upon adding elements of higher valence than the host metal was proposed by Mott6l,62 in 1935 in the rigid band model. Although the model did correctly predict the rise in the Fermi energy, it did not predict the shift that occurs in the d-band upon alloying. This led to a prediction of a larger shift in the transition energy at 2.2 eV than was seen experimentally. Calculations made by Bansil et al.60 accounted for the shift upward in the d-bands as well as the Fermi energy and therefore the smaller shift in the threshold energy.

Hummiel's laboratory5'6'7 has experimentally verified

that the shift in the transition energy at 2.2 eV is smaller than that predicted by the rigid band model. Using a differential ref lectometer, the energies of electronic







36

transitions were measured for copper solid solutions containing various multivalent alloy additions. It was found that the transition energy was a function of composition (see Figure 2-9).5 Up to 1% solute there is no change in the threshold energy. Past 1% solute, the transition energy is a linear function of composition. It is evident that Figure 2-9 can also be used as a calibration curve, so that if the transition energy of an unknown alloy is measured, then the quantity of solute in that alloy can be determined. Thus, it is possible to use optical measurements as a means of determining the solute concentration of a binary copper alloy. In the case of multivalent solutes in copper, of course, this method would only be useful for solute concentrations above one percent.

So far, the discussion has been directed only at alloys of copper which contained solutes having two or more valence electrons, where the increase in the Fermi energy could be understood on an intuitive basis. The situation becomes more complex when transition elements are added to copper. As an example of a copper-transition metal alloy, coppernickel has been studied in great detail,7,63-66 because they display complete solid solubility. Since nickel has an unfilled d-band -- its electronic configuration is 3d84s2 -the intuitive expectation is that when nickel is added to copper, the copper 4s electron might supply the extra electrons necessary to fill the d-band of nickel. It would then be expected that the Fermi energy of copper would be lowered,







37








Ln






m M
< 0
o x H
4J 0 (A -i
ul

4
Ln C-4
10
1-4
0


vZ 4
co
4




LW
0

u












04
E
0








Ln C*4
cq C-4
LLJ 44







38

and accordingly the threshold energy for direct interband transitions would be decreased. These are the predictions of the rigid band model.62 Experimentally, however, it has been determined by means of optical measurements7,63 and photoelectron spectroscopy63 that the transition energy at 2.2 eV in copper is unchanged by solute additions of nickel. Instead, evidence indicates that the nickel d-bands remain independent of the copper d-bands and that they retain their character within the matrix. These nickel d-bands are found to exist within one electron volt of the copper Fermi energy and become the source of low energy transitions. In Figure 2-10, the reflectance spectra from Seib and Spicer63 for pure copper, Cu-13% Ni, and Cu-23% Ni are presented. In contrast to the reflectance spectra for copper-zinc alloys, there is no change in the transition energy at 2.2 eV as nickel is added to copper. There is a drop in reflectivity below 2.2 eV which is caused by transitions from the nickel d-bands to the Fermi energy, thus decreasing the magnitude of the 2.2 eV transition. These results verified the proposals of Friede167 and Anderson68 who had predicted this type of behavior -known as virtual-bound-states -- for transition elements in copper. It is clear that there is no composition dependence of the 2.2 eV transition, such as was the case in copper with multivalent solutes. Using photoemission Seib and Spicer63 did find that the band width of the virtual-bound-states of nickel did increase as the amount of nickel increased.

Using differential reflectometry, Hummel et al.7 also





39





0.8 -0.90.8 NN
0.6


1*. 0.7-'

U 0.4-J6




N...




0~~ ~ 23 0 1
kvy IVI Figur 2-10 -Reflctane SCtruo ope n






Copper-Nickel Alloys. (Ref. 63)







40

found no shift in energy of the threshold transition at 2.2 eV in copper-nickel alloys. The alloys studied in this work ranged from copper containing less than one percent nickel to greater than twelve percent nickel. This result, which confirmed the existence of virtual-bound-states in copper-nickel alloys, provided no strict method of determining the solute concentration of an unknown alloy. It was noted that the "sharpness" of the peak in the differential ref lectogram associated with the 2.2 eV transition did possess a composition dependence. However, no definitive composition dependence was observed at 2.2 eV as in the case of copper containing multivalent solutes. 5,6 ,7

Beaglehole and Kunz69 did find a composition dependence on the difference in reflectivity of various dilute coppernickel alloys. Their data showed a linear relationship between the difference in reflectivity at 628 nm and the difference in the composition of the alloys measured, which agreed with that of other investigators.66'70'71 This linear relationship was found to be valid up to approximately 20% solute, demonstrating that optical measurement might be used to determine the composition of an alloy containing a transition element.

For the reason that this work centers on optical investigations of precipitation in copper-cobalt alloys and that the precipitates in this system are a cobalt solid solution

-- approximately 9OCo-lOCu -- it is necessary to consider the optical properties and the electronic structure of cobalt.







41

Cobalt is a transition metal and resides next to nickel in the periodic table. Its electronic configuration is 3d74s2. Again, as in the case of nickel which has an unfilled d-band, the electronic band structure of cobalt is found to possess d-bands which contain both filled and unfilled states and which lie within a few electron volts of the Fermi energy.72

-76 A high density of states, therefore, exists just above and just below the Fermi energy. Although quantum mechanical considerations can not be put aside, for all practical purposes, this large density of states around the Fermi energy can be considered to be a continuum. This implies firstly that electronic transitions can be stimulated by incident light at low energies, and secondly that an incremental increase in the energy of the incident light will be matched by an increase in the number of transitions stimulated. This can be seen in the reflectivity curve for cobalt (Figure 2-11), which was calculated from optical contants determined by Johnson and Christy.77 The reflectivity is already below 80% at 1 eV, due to low energy optical absorbtion which stimulates d-band transitions. Also seen is a monotonic decrease in reflectivity caused by the stimulation of a greater number of transitions as the energy of the incident light is increased. In addition there is no sharp change in the reflectivity in the range of 1 eV to 6 eV indicative of interband transitions or plasma resonances.






42















0 0)
4
4-4

41

4
u










>0


44 LU z :3 f:
w '4




C4 0

-W 41
-i :
>

S4
V2
44 rZ Q) a)







0 0
%0 4n C)
IV 4
El AIIAII331133

rT4















CHAPTER 3
EXPERIMENTAL PROCEDURE




3.1 Experimental Approach


The experiments comprising this work on Cu-Co alloys

fall into three categories. Firstly, differential reflectometry was performed on samples to establish spectra solely on composition differences, hereafter known as compositional modulation. Secondly, differential ref lectometry was performed on samples which had been given various aging heat treatments. Finally, microhardness testing was performed upon samples to study the change in that mechanical property upon precipitation.

The purpose of performing the compositional modulation experiments was twofold. First, it was necessary to obtain spectra which were produced due specifically to composition differences between two samples. In the aging experiments carried out on the differential reflectometer, spectra were to be produced by the difference between an aged and a solution heat treated sample. For reasons that have already been described, the aged sample would have less cobalt in the alloy matrix. Thus at least some of this spectrum would be due to composition differences between the


43





44


aged and the unaged samples. By having composition modulation spectra, it becomes possible to identify which part(s) of the differential ref lectometry spectra in the aging experiments were due to composition differences and which part(s) were due to some other aspect of aging which would produce a change in the optical properties of the alloys.

Second, by performing compositional modulation experiments, it is possible to obtain information about the effects of additions of Co upon the electronic structure of Cu. Although somewhat limited by the small solubility of Cu for Co, the predictions of the virtual-bound-state theory vs. the rigid band model could be investigated.

As was discussed in the last chapter, the changes in

hardness that occur in an alloy during a precipitation reaction are well documented and well understood. As has already been discussed, hardness tests provide a clear, if indirect, method by which the kinetics of the precipitation reaction and the microstructural changes involved in that reaction can be interpreted. For this reason, microhardness tests were chosen as a method against which the results of the optical data could be compared and contrasted.



3.2 Alloy Preparation

All alloys used in these experiments were produced by combining appropriate amounts of Cu-2.7 a/o Co powder and pure Cu powder. The powders were blended and placed into






45

a graphite crucible for melting. A sodium borate flux was used to protect the melt from oxygen contamination. Because of the very narrow alpha plus liquid phase field (See Figure 2-4) segregation upon solidification was deemed not to be a problem and the ingots were allowed to solidify in the furnace. Upon removal from the crucible, each ingot was cleaned of any remaining flux and dipped for a few seconds into an etchant (5:1 nitric acid:water) to remove any surface contaminants. Each ingot was then rolled by 50%, recrystallized under vacuum at 3500C for one hour, and rolled again by approximately 33%. Each ingot was then placed in a graphite crucible and covered with sodium borate flux and given a solution heat treatment at 10000C for approximately 70 hours. The ingots were then quenched in iced brine to complete the solution heat treatment. The ingots were then cleaned by etching and cut on a diamond wheel to a size of approximately 0.25 cm 2 for differential ref lectometry and microhardness testing. A few pieces were selected at random and tested on the differential ref lectometer for compositional inhomogeneities. This was done by illuminating only one sample in the differential ref lectometer. Any inhomogeneities in the sample would produce a non-zero signal in the differential ref lectometer output. None could be detected. In Tables 3-1 and 3-2, those alloys used in the compositional modulation and aging experiments are listed, respectively.







46







Table 3-1. Alloys Used in Composition Modulation Experiments Cu 2.7 a/o Co Cu 2.5 a/o Co Cu 2.0 a/o Co Cu 1.5 a/o Co Cu i.0 a/o Co Cu 0.5 a/o Co Pure Cu









Table 3-2. Alloys Used in Aging Experiments

Cu 2.7 a/o Co Cu 2.0 a/o Co Cu 1.0 a/o Co







47

3.3 Differential Reflectometer


The differential reflectometer is a kind of optical spectrometer, the output of which is a normalized difference in reflectivity of two samples as a function of wave3,4
length, AR/R vs X. Originally conceived to experimentally determine the shift in energy of interband transitions that occur upon alloying,5'6'7 the differential reflectometer has proven successful in studying long11 and short12 range ordering, dezincification of alpha
13
brasses, thickness and formation kinetics of corrosion
78
products, and in situ studies of the corrosion of Cu and Cu-Ni alloys.79

The differential reflectometer has been demonstrated

to be very sensitive in detecting small differences in composition. Compositional differences as small as 0.05 a/o 80
have been detected in selected applications. It was the aim of this work to exploit this capability in order to detect changes in composition of an alloy matrix as precipitation occurred.

A detailed description of the differential reflectometer has been given elsewhere.3,4 Only a brief description of its functions will be given here, in conjunction with Figure 3-1.

The usable output of the xenon light source lies in

the range of 200-800 nm. This light enters a double scanning monochromator, which for all experiments in this work,








48


















.54.

-L 0E


x. o

414







'A 0
0 .








4 -44






0




00 o 9')
VI4

rC)






49


was operated at a scan rate of 200 nm/mmn. After exiting the monochromator, the beam is reflected from a flat mirror to an oscillating mirror which focusses the beam at near normal incidence alternately on each sample. The spot size of the beam on each sample is approximately 2 X 2 mm2 Once reflected from the samples, the beam is focussed by a fixed mirror onto a ground plane of fused quartz causing the light to diffuse upon the face of the photomultiplier tube (PMT) to quash any effects caused by the oscillating light beam. The amplified signal of the PMT is divided into two channels, one of which is a low pass filter which yields the average reflectivity, R = (R 1+R 2)/2. The other channel containes a lock-in amplifier where the difference in reflectivity, AR = R 2-R 1 is produced. A ratio of these two signals is made and is used as input for the y-axis of an x-y recorder. The x-axis input is connected through a variable resistor to the drive of the monochromator, the result being a spectrum of AR/R vs. -X.

In order to maximize the signal, the two samples analyzed in the differential ref lectometer must be mounted as close to each other as possible. This is achieved by grinding a flat surface on each sample and holding them together in a thermosetting metallurgical mount. After polishing, the mount is clamped onto a stage in the differential ref lectometer. The stage is capable of being moved vertically, by which the beam can be centered, or







50

horizontally, by which different areas along the juncture of the samples can be studied. In most cases, three such areas were measured.




3.4 Polishing Procedure


Each sample studied in the differential ref lectometer was prepared in the following manner.

1. The two specimens -- either of differing composition or differing heat treatment -- were
mounted adjacent to each other in a quick setting
polymeric material. 81

2. In order to bring the surfaces of both specimens
into the same plane, the sample was ground on a
grinding wheel using 180 grit paper with filtered kerosene as a lubricant.

3. The sample was then ground by hand using successively finer grits -- 240, 320, 400, 600 -- with
filtered kerosene as a lubricant.

4. Final polishing was performed with 1 micron diamond paste on a felt cloth using an oil base
lubricant.

5. The sample was then rinsed in methanol, dried
in a stream of desiccated air, and taxen immediately to the differential reflectometer for
measurement.

With the exception that only one specimen needed to be mounted, samples used in the microhardness tests were ground and polished by the same method as above through the diamond polish. in order to reveal the grain structure the samples were swabbed with an etchant composed of 2:1:1 ammonium hydroxide:hydrogen peroxide (3%):water. These







51

samples were then rinsed in methanol and blown dry and taken immediately to the microhardness tester.




3.5 Aging


Aging temperatures were chosen to reflect a range of precipitation rates from slow to moderately rapid growth. To that end, all three alloy compositions -- Cu-l a/o Co, Cu-2 a/o Co, and Cu-2.7 a/o Co -- were given aging heat treatments at 4000C, 5000C, and 6000C. in addition, Cu2.7 a/o Co was aged at 4500C and 5500C.

All samples to be aged were placed in a fused quartz

tube which was evacuated with a mechanical pump to a pressure of approximately 0.1 Torr. The pump remained connected to the tube and operated continuously during the aging heat treatment. At the end of the aging heat treatment helium was used to break the vacuum, and the samples were immediately quenched in tap water.

For a specific isothermal aging heat treatment, the

aging times were recorded accumulatively. For example, if a given alloy had been aged for fifteen minutes and examined, and the next test required a thirty minute aging heat treatment, the same sample was demounted, aged for f ifteen minutes and remounted. in this way any possible error involved in using different samples was avoided.

Upon removal from the furnace, samples aged for six

hours or less appeared to be clean and free of contamination.







52

Samples aged longer than six hours were observed to have a flaky black surface scale. The origin of the scale was probably a combination of oxide and residue from the mechanical pump oil. However, because all samples were of necessity ground and polished subsequent to each aging heat treatment, any contamination resulting from that treatment was removed.



3.6 Microhardness Tests


Diamond pyramid hardness tests (Vickers scale) were

conducted upon Cu alloys containing 2.7 a/o, 2.0 a/o, and 1.0 a/o Co. Each of the alloys was given a series of isothermal aging heat treatments at 4000C, 5000C, and 6000C. All samples were subjected to a 500g load applied by the indenter. By maintaining the load at this specified value, no load dependent variations were introduced into the measurements. Although the sample depth probed in a microhardness test is much larger than the sample depth probed by a light beam (approximately 40 pm vs. 0.01 =), microhardness tests were considered to be a more appropriate alternative than standard hardness tests where the desparity in probe depth would have been far greater.

For each time in the aging sequence of a sample, a set of twenty-five microhardness measurements was made. From these measurements a diamond pyramid hardness number (DPN) was calculated along with the 95% confidence






53

interval. As was the case with the optical data, a sequence of measurements comprising a set of isothermal heat treatments was carried out on individual samples. Care was taken to remove the damage of the previous measurements caused by the indenter. This was done by grinding well below the level of the indentations made during the previous run.















CHAPTER 4
EXPERIMENTAL RESULTS AND DISCUSSION




4.1 Microhardness Tests: Results and Discussion


Previous experiments on dilute copper-cobalt alloys

have established that the changes in hardness which occur during aging heat treatments are caused by the formation of spherical cobalt-rich precipitates. The purpose of performing microhardness measurements for this work was to provide a link from these previous experiments to the optical measurements designed for this work. In this section, results of the microhardness tests will be presented. The results will be seen to be consistent with that which is known to occur during a precipitation reaction. Furthermore, it will be shown that the results of these measurements verify the findings of other researchers who have performed similar measurements.

Microhardness measurements were carried out on alloys containing 2.7 a/o Co, 2.0 a/o Co, and 1.0 a/o Co. These alloys were aged at three different temperatures -- 6000C, 5000C, and 4000C. The results of these measurements can be seen in Figures 4-1 to.4-6.

In Figure 4-1, the diamond pyramid number is plotted versus aging time for alloys containing the three amounts 54





55







120


*m
2.7%Co
r 100
z

LU
I.

80-/ ," 2.0%. zoCo
zi


I.
80 I1 1.0% Co


> 60 .





40 -0o

I I I
As 1 10 100 1000
quenched TIME Chr3



Figure 4-1. Hardness vs Time for Alloys Aged at 6000C.






56

of cobalt mentioned above and aged at 6000C. For the as quenched alloys the hardness increases with solute content. This proved to be the case in all samples analyzed, and is consistent with the theory of the effect of solute elements on the hardness of solid solutions. Solute atoms have been shown to impede the movement of dislocations by collecting at them and pinning them. 57,82 As the concentration of solute atoms increases, more dislocations can be pinned, leading to increased hardness.

Figure 4-1 shows that for all alloys which had been

aged at 6000C, the hardness increased considerably between the as quenched state and fifteen minutes of aging. After this, the hardness increased steadily, but more moderately, up to its peak value at about nine hours. Past nine hours, the hardness decreased steadily. At all times, the alloy with the greater solute concentration exhibited higher hardness.

Aging each alloy at 500'C produced results indicative of the slower diffusion rate which exists at this lower heat treating temperature. As is seen in Figure 4-2, the increase in hardness from the as quenched state to the first aging time of 15 minutes is much more moderate than in the case of aging at 600'C. The increase was less than half the increase seen at 6000C. In addition, increases tended to be moderate and no peak was reached even after aging for 220 hours, although the values of hardness at 220 hours are higher than the peak values for the alloys





57



120





100
I,,
100- 2.7% Co



z
CL 2.0% Co




0..
a
U 80LU
a
91.0% CO

60


4O
LU



40[


5000C


20 I I I
As 1 10 100
quenched TIME hr


Figure 4-2. hardness vs Time for Alloys Aged at 500C.

Figure 4-2. Hardness vs Time for Alloys Aged at 5000C.






58


aged at 6000C. The fact that these values are higher can be accounted for by the lower solubility at 5000C for Co in Cu. At 6000C, the solubility for cobalt is about 0.4% whereas at 5000C, it is less than 0.1%. This decreased solubility leads to a greater volume fraction of precipitate as determined by the phase diagram tie line, which in turn leads to a higher hardness. Again, it can be seen that at each aging time the alloy containing a greater amount of solute possesses a higher hardness.

The results of aging each alloy at 4000C can be seen in Figure 4-3. At 4000C there is only a very slight increase in the hardness for each composition in aging up to 26 hours, indicating that the precipitation reaction has barely begun even after this length of time. The diffusion rate is evidently so slow at this temperature that in terms of aging time several more orders of magnitude of time would be necessary to bring these alloys into a condition of peak hardness. These results did show, however, that room temperature aging would not occur and that therefore it was not necessary to give the sample a solution heat treatment before each aging experiment was performed. This allowed the use of individual samples for a series of aging times thus avoiding the error associated with using different samples. This observation was also made by Witt and Gerold. 37

In Figures 4-4 to 4-6 are plotted the diamond pyramid number versus aging time for each composition where aging




59




100



ril
Z 80
o 2.7%Co
L.I



S60 -4 1.0%Co





> 40



4000C 20 I I
40100 As 1 10 100
quenched TIME Chr3



Figure 4-3. Hardness vs Time for Alloys Aged at 4000C.







60

temperature is the variable parameter. In these figures, the role of aging temperature in influencing the precipitation rate is clearly seen. In Figure 4-4, for example, which shows microhardness data for a Cu-2.7% Co alloy aged at 6000C, 5000C, and 4000C; the increased precipitation rate with increasing temperature is quite evident. Starting from essentially the same hardness in the as quenched state, the alloy aged at 6000C proceeds to reach a peak in microhardness much faster than those alloys aged at 5000C or 400'C. This same pattern is repeated for the Cu-2.O% Co alloys and the Cu-l% Co alloys, seen in Figures 4-5 and 4-6 respectively.

The microhardness data presented here can be seen to

represent the type of data that would be found in a typical precipitation reaction. The increase in hardness, although influenced by a number of factors, is principally influenced by the fraction of coherent precipitate. The peak value in the microhardness is indicative of that point where the precipitates have grown to a size that warrants the formation of an interface. This is achieved by the creation of dislocations to accommodate the strain introduced to the lattice by the mismatch between the precipitate and the matrix. The subsequent decrease in hardness past the peak is a manifestation of more and more particles achieving the critical size at which they change from a coherent to incoherent state.





61





120 6000



I-1
z
0100
a
U
o5000
Lu
z I
<. 80'- a
a


60





60


40
Cu-2.7% Co I I I
I I
As I 10 100 1000
quenched
TIME rchr


Figure 4-4. Hardness vs Time for Cu-2.7% Co Aged at 6000C,
5000C, and 4000C.






62








1001

Il 000
z
CL
a
LI

1^80,0*
4A



00*

~60 ;,/






40 Cu-2.O% Co



As 1 10 100 1000
quenched
TIME Chr3





Figure 4-5. Hardness vs Time for Cu-2.O% Co Aged at 6000C
5000C, and 4000C.





63










r80- 600
z


1" 500

z
S60- / 4000

LA
Cu-1.0% Co 4O0

I I I
As 1 10 100 1000
quenchedT
TIME Chr'




Figure 4-6. Hardness vs Time for Cu-1.0% Co Aged at 6000C
5000C, and 4000C.






64


There are various values reported for this critically sized particle in the Cu-Co system, i.e., the size at which the precipitate changes from the coherent to incoherent state. Generally, these values, seen in Table 4-1, fall in the range of 40-100 A. The only values to fall outside of this range is 175 A which was reported by Phillips and Livingston 31 and 120 A which was reported by Humphreys. 35 Both of these values for radii were found using samples which had experienced no deformation after the aging heat treatment. Phillips 33 has also reported the maintainence of coherency up to precipitate radii of 250 A in the absence of any deformation. However, the application of any deformation to the sample assists in the nucleation of dislocations which provides for the establishment of an interface in changing from a coherent to incoherent state. In the present work, both the use of the indenter in the microhardness tests and the use of the polishing wheel in order to obtain a specular surface for taking optical measurements could provide the deformation necessary to cause an interface to be formed between the precipitate and the matrix. Therefore, the results presented here most likely coincide with a radius of 40-100 A at peak hardness.

Based upon the data obtained from the microhardness tests and the coincidence of this data with the work of others who have studied precipitation in the copper-cobalt system, the conclusion can be reached that the alloys were







65




Table 4-1. Radius of Precipitate at Peak Property for Copper-Cobalt System



Particle Radius at Peak Measurement Ref.
0
Livingston & Becker 70 A Hardness 29
0
Livingston 70 A Yield Stress 30
0
Phillips 46-75 A Hardness 33
0
Phillips & Livingston 175 A* TEM 31
0
Phillips 50 A Yield Stress 34
0
Humphreys 120 A TEM 35
0
Threadgill & Wilshire 40-75 A Creep 43
0
Amin, Gerold & Kralik 100 A Hardness 44
0
Wilhelm 70 A Not Specified 46
0
Tautzenburger & Gerold 40 A Creep 48





* Sample Undeformed






66

heat treated properly to produce a precipitation reaction. Furthermore, the results indicate that the goal of observing precipitation in regions of relatively rapid, moderate, and slow growth has been achieved.

Among the researchers who have studied this system,

there is little disagreement as to the nature of the precipitation reaction. It is generally conceded that the precipitate is spherical, face-centered cubic, and remains coherent with the lattice until it achieves a size of approximately 40-100 A. There has been nothing found so far in this work to contradict these findings.




4.2 Compositional Modulation: Results and Discussion


As has been discussed in Chapter 2, the optical properties of copper alloys have been found to be strongly dependent on composition. in the case of copper with multivalent solutes, a linear shift of the threshold electronic transition at 2.2 eV to higher energies was found as the average solute concentration was increased above one percent. 5 in the case of copper-nickel alloys, however, there was no composition dependence seen in the energy of the threshold transition. 7 Additions of up to 24% nickel produced no change in this transition energy. The demonstration of this phenomenon by both differential reflectometry 7 and photoelectron spectroscopy 63 was offered as confirmation of the virtual-bound-state model of Friedel 67 and






67


Anderson, 68 who had predicted this type of behavior for copper-nickel alloys.

The purpose of performing compositional modulation experiments for this work was twofold. Firstly, it was necessary to determine the manner in which cobalt would affect the optical properties of copper. To do this, "traditional" compositional modulation experiments were performed, in which the optical properties of the average compositions of the two samples were investigated. The design and results of these experiments are discussed below. Because cobalt and nickel lie next to each other in the periodic table and because they both derive their ferromagnetism from spin imbalance of their unfilled d-bands, 83 the results of these experiments on Cu-Co alloys are compared to previous research on the optical properties of Cu-Ni alloys. Particular attention is made to the virtualbound-state model.

Secondly, another type of compositional modulation

experiment on Cu-Co alloys was performed. in this investigation, the difference in solute concentration between the two samples studied is the variable parameter. The design and the results of these compositional modulation experiments will be discussed in the second half of this section. in particular, the relationship between these experiments and the optical properties of aged alloys will be considered.






68

In Figure 4-7, differential reflectograms for average sample compositions of Cu-l.5% Ni and Cu-l.5% Co are presented. In this figure, an almost identical pattern in optical response is evident. The features of the coppernickel differential reflectogram have already been described by Hummel.84 The structure from "a" to "b" is caused by interband transitions at the threshold energy of 2.2 eV. The maximum designated "d" is a manifestation of transitions from the lower d-bands of copper to the Fermi energy. Finally, the broad structure at "c" has been ascribed to electronic transitions involving the d-bands of nickel. The similarity between these two reflectograms represents a new type of pattern seen in differential reflectograms. Previous work on copper with multivalent salutes revealed that all differential reflectograms of this alloy group had a common pattern. The evidence here suggests that there will be one pattern for all differential reflectograms of copper-transition metal alloys.

The study of the effect of cobalt composition on the electronic structure of copper was then broadened. These compositional modulation experiments were conducted by changing the average composition of the two samples studied by differential reflectometry. (It has been shown that the transition energies measured by differential reflectometry are the equivalent of the transition energies for an alloy whose composition is the average of the composition of the two alloys measured, provided that the difference in







69




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70

composition is small.) Although somewhat hampered by the limited solubility for cobalt in copper, this research did provide a measure of compositional dependence up to about

2.4% Co. In Figure 4-8, differential ref lectograms are shown for average compositions of Cu-0.5% Co, Cu-1.5% Co, and Cu-2.4% Co. To obtain these average compositions the following pairs of samples were examined: pure Cu and Cu1% Co, Cu-l% Co and Cu-2% Co, and Cu-2% Co and Cu-2.7% Co.

As in the case of nickel, there was no shift seen in the transition energy as the composition was changed. As has been discussed, the reason for this composition independence of the threshold transition energy has been accounted for by the virtual-bound-state model of Friedel 67 and Anesn 8Their contention that the nickel electrons

maintain highly localized levels around nickel atoms when alloyed with copper, seems to extend to cobalt impurity atoms as well.

Peak 1'd", which is caused by transitions from the lower d-bands of copper to the Fermi energy, does show a very small composition dependence. It can be seen that this peak shifts to slightly higher energies as the amount of cobalt is increased. This same shift toward higher energies with increasing solute content has also been observed in copper-nickel alloys. 7The minimum designated "c" in these differential ref lectograms, although seen in Figure 4-8 to shift toward higher energies as cobalt content was increased showed no strict composition dependence in other






71





ENERGY CeV3
1.6 2 2.5 3 4 5.5

d
I "I I I I d

2.4 % Co 1.5% Co


0.5% Co





2
II.

Lu






N
09





Z

b

I I I I !
800 700 600 500 400 300 200
WAVELENGTH rnm





Figure 4-8. Differential Reflectograms of Various CopperCobalt Alloys. (Compositions indicate average
cobalt content of the two samples used.)






72

differential reflectograms. In copper-nickel alloys, this minimum is thought to be caused by nickel electronic transitions, but cobalt has been found to have no strong optical transitions in this energy range. 75,77,85

As has been established, a precipitation reaction is defined to be the decomposition of a metastable solid solution in which a second phase nucleates, grows, and coarsens, and in which the matrix is necessarily depleted of solute in order that the second phase be produced. So far, this work has established the conditions under which a precipitation reaction can be produced, and has verified the presence of a second phase by means of microhardness measurements. However, measurements of mechanical properties, such as the microhardness of an alloy, only yield information about the state of the precipitate, for example, whether or not coherency has been maintained. While this is, of course, useful, no information has been obtained about the extent to which the decomposition has progressed. There is no metallurgical law which establishes a link between the hardness of an alloy and the volume fraction of precipitate, or conversely, the composition of the matrix.

It has been seen that the optical properties of an

alloy are very strongly dependent upon its composition (See Section 2.3), and therefore, their measurement should be a candidate for a method of determining the changes in composition which occur in the matrix during a precipitation reaction. Finnegan13 has already shown the utility of







73

making optical measurements, specifically differential reflectometry, in determining the extent of dezincification in alpha brasses when they are subjected to various corrosive environments. Although in the case of dezincification, the alloy experiences an actual loss of solute, a precipitation reaction can be viewed in a similar manner, for the reason that the solute is removed from the matrix by the formation of the second phase.

It has been demonstrated that the optical properties of copper-cobalt alloys parallel those of copper-nickel alloys, and that these findings indicate that copper-cobalt alloys behave according to the virtual-bound-state model. Using Figure 4-8, it has been shown that Co additions do not affect the energy of the copper threshold transition at 2.2 eV, as in the case of multivalent solute additions. Because the differential ref lectometer yields information about the alloy composition which is the average of the two samples investigated and because no shift in transition energy occurs as the average alloy composition was changed, an alternative method for determining the effect of cobalt additions on the optical properties of copper was chosen. The average of the composition of the two samples was replaced by the difference in the composition of the two samples.

In this second type of compositional modulation, experiments were conducted in a manner so as to simulate the aging experiments which are described in the next section.






74


Specifically, in these experiments, the solute composition of one sample was held constant while the solute composition of the samples measured against it was successively decreased. in this way, the difference in solute content between the two samples was made the independent variable. All of the samples used in these experiments were given solution heat treatments in order that there was no precipitate present, therefore, the results would be indicative of composition effects only. The results of these experiments can be seen in Figures 4-9 to 4-11.

In Figure 4-9, a Cu-2.7% Co alloy was measured against copper alloys containing 2.5% Co, 2.0% Co, 1.5% Co, 1.0% Co, and 0.5% Co. The shape of these curves can be seen to be similar to those curves described in the first part of this section, where the effect of cobalt upon the electron band structure of copper was discussed. Qualitatively, it is immediately apparent that as the Qifference in solute composition of the two samples is increased that the signal strength of the spectra is also increased. in order to attempt to quantify this increase in the signal strength, two features of the spectra, which are present in all spectra and which lend themselves to measurement (the minimum formed between approximately 600-550 nm and the maximum at 270 nm), were examined. These two features are the results of changes in strength of the two most prominent valence transitions in copper, specifically the threshold transitions at 2.2 eV and the L 2 -L, transition at 4.5 eV (See




75

ENERGY C*V3
1.6 2 2.5 3 4 5.5



I IIz

w2

z

LU




0









800 600 400 200
WAVELENGTH Enm3
Figure 4-9. Differential Reflectograms of Cu-2.7% Co
versus Cu-O.5% Go, Cu-1.O% Co, Cu-1.5% Co,
Cu-2.O% Co, and Cu-2.5% Co.






76

Section 2.3). Because of the absence of a reference point from which the peak at 270 nm could be measured, the change in the differential reflectivity between 600-550 nm. was chosen as the basis upon which the signal strength was measured. of note is the fact that even when the difference in the solute content is only 0.2% (bottom curve of Figure 4-9), the change in the differential reflectivity at the threshold transition is slightly more than 0.5%. This demonstrates the utility of performing optical measurements in determining small differences in composition. It is apparent that differences in composition at least as small as 0.1% can easily be detected.

In Figures 4-10 and 4-11 are seen the spectra showing Cu-2.0% Co and Cu-1.0% Co compared against samples of lesser cobalt content. It is again apparent in these figures that as the difference in solute content in the two samples is increased that the signal strength of the spectra is increased. Furthermore, the relationship between the difference in solute content and the signal strength in all three sets of experiments depicted in these figures was found to be the same. By using this observation and by plotting the signal strength at the threshold transition as a function of the difference in solute content, the calibration curve shown in Figure 4-12 was produce ?d. As is evident, a linear relationship was found to exist between the percent change in differential reflectivity (signal





77



ENERGY EeV3
1.6 2 2.5 3 4 5.5
I I II I


0/2.0






LU J




U 0.5/2.0
LU




LU 1.0/2.0
N



0 z
1.5/2.0




I I
800 600 400 200
WAVELENGTH Enm3


Figure 4-10. Differential Reflectograms of Cu-2.0% Co
versus Pure Copper, Cu-0.5% Co, Cu-1.0% Co,
and Cu-1.5% Co.





78







ENERGY eV3
1.6 2 2.5 3 4 5.5
I I I I I

0/1.0





21 0.5/1.0



0
z2
w




I I
800 600 400 200
WAVELENGTH [nm]



Figure 4-11. Differential Reflectograms of Cu-i% Co versus
Pure Copper and Cu-0.5% Co.







79

strength) and the difference in solute content. The slope of the line is approximately 3%/%AC.

This relationship between signal strength and the difference in composition between the two samples measured is an observation which has been previously unexploited in differential reflectometry. The reason for this lies in the nature of the solute element, which in this case is a transition metal. As has previously been discussed (see Section 2.3), when copper is alloyed with multivalent solutes, such as zinc, the energy of the electronic transitions shifts as a function of solute content. By measuring the change in the energy of these transitions by differential reflectometry, it has been possible to determine the solute content of unknown alloys. This was the method which was used by Finnegan et al.13 to determine the extent of dezincification in alpha brasses. For the reason that cobalt is a virtual-bound-state element in copper, and hence no shift in energy of the electronic transition occurs, the composition dependence of the signal strength must be used to determine the composition of an unknown alloy.

This relationship between the differential reflectivity and the solute composition of a transition metal in copper has been experimentally observed by other researchers.63,69 It can qualitatively be seen in Figure 2-10, which shows reflectivity data for pure copper, Cu-13% Ni, and Cu-23% Ni.63 The reduction of the reflectivity for the alloyed samples in the energy region preceding the drop in







80

reflectivity at the threshold can be seen to be approximately linear. This combined with the fact that the reflectivity of all samples crosses at approximately the same value would yield a differential reflectivity change that was linear with the difference in solute content.

More quantitatively, Beaglehole and Kunz 69 in measuring differential reflectivity of dilute copper-nickel alloys found that this quantity changed directly as a function of the difference is solute composition at 628 nm. Although no measurements of the optical properties of copper-cobalt alloys have been performed by other researchers, it has been shown that cobalt 85,86 and nickel 63-66,70 are both virtualbound-state elements in copper. This fact, combined with their similar electronic structure and position in the periodic table, makes the determination that they display a similar influence upon the optical properties of copper alloys seem quite reasonable.

The utility of the calibration curve in Figure 4-i2

as it applies to a precipitation reaction can be demonstrated in the following example. if two samples of known solute content, one of which has been solution heat treated and the other of which has been solution heat treated and aged, are measured by differential reflectometry, the difference in the matrix solute content between the two samples can be obtained by determining the signal strength of the resulting spectrum. This yields a measure of the extent to which the precipitation reaction has progressed. The





81





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utility of differential reflectometry in determining the depletion of solute from the matrix during precipitation will be discussed in the following section.




4.3 Aging Experiments


in the preceding section, experimental data describing the relationship between the composition of Cu-Co alloys and the optical properties of these alloys was presented. It was also demonstrated that differential ref lectometry provides a method by which the cobalt concentration of an unknown Cu-Co alloy can be determined provided that a reference sample of known solute concentration is available. in this section, the utility of differential ref lectometry in following a precipitation reaction by tracking the associated matrix depletion of solute will be explored. In addition, any additional optical effects that occur during the precipitation reaction that are not based solely upon composition differences will be acknowledged.

In these experiments three alloys of varying cobalt

content were studied -- Cu-2.7% Co, Cu-2.O% Co, and Cu-l.O% Co. Each alloy was aged at 6000C, 5000C, and 4000C. In addition, the Cu-2.7% Co alloy was aged at 5500C and 4500C.

in order to determine the kinetics of the solute depletion during precipitation, differential ref lectometry was performed on samples that were identical in initial solute composition, but differed in subsequent heat treatment. In






83

these experiments, both samples were given solution heat treatments. One of the samples was then additionally aged at a specific temperature for a series of times. Differential ref lectometry spectra were obtained to record the difference in optical properties between the two samples as a result of the aging regime.

Figure 4-13 shows a typical differential reflectogram from these experiments. The two samples used to obtain this spectrum were both Cu-2.O% Co. One sample was solution heat treated while the other was solution heat treated and aged at 6000C for one hour. The two most prominent features of this spectrum are a minimum formed between 600 nm and 550 nm and a maximum occuring at 280 nm. These features appear at the same wavelengths as those described in the previous section during the compositional modulation experiments. On the basis of the signal strengths of the minima centered at 550 nm, the difference in composition between the two samples is approximately 0.5% Co. lt was also determined that the aged sample was the sample which contained the lesser amount of matrix solute. This finding is interpreted to be the fundamental result of a precipitation reaction, in which cobalt is removed from the matrix in order that cobalt-rich precipitates can be formed.

In Figure 4-14 a series of differential reflectograms for a Cu-2.0% Co alloy are displayed. Again, one sample was solution heat treated while the other was solution heat treated and then aged. Figure 4-14 shows the spectra for





84






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86

0.5 hr, 3.0 hr, and 26.0 hr of aging. The 0 hr spectrum depicts two samples that were identically solution heat treated. The lack of any clearly defined structure in this spectrum shows that the samples started in an identical condition. In response to the aging heat treatments given to the one sample, however, the spectra indicate that the composition difference between the two samples increased with aging time due to the decreased solute concentration in the aged sample. in the spectra in Figure 4-14, the signal strength indicates that after 26 hours of aging the matrix solute content has been reduced by approximately one percent.

In order to determine the effects of aging time, aging temperature, and solute concentration on the optical properties of these alloys during a precipitation reaction, the signal strength at the threshold transition was plotted as a function of aging time. The results are shown in Figures 4-15 to 4-20. In all cases the first differential reflectogram taken was of two solution heat treated samples, to verify that the samples were identical in the initial condition. A featureless differential reflectogram was expected and was obtained in all cases.

Figure 4-15 shows the change in threshold transition magnitude for the various solute compositions of samples aged at 600'C. As seen in Figure 4-15, the signal strength caused by the samples' composition difference immediately increases after the first aging heat treatment of fifteen





87







AGING TEMP. 600'C
80
2.7% Co

I,8









/ I 2.0% Co
460
Aa
0









As 1 100 100 0 0 &M

x 40












Quenche TIME Chr3

Figure 4-15. Peak Height vs Time for Various Copper-Cobalt
Alloys Aged at 6000C.






88

minutes. in addition, the size of the initial rise in signal strength increases with solute content. After this initial rise, the signal strength increases monotonically for all compositions. For all other compositions and aging times, the signal strength is largest for the alloy containing the most solute. Because signal strength is directly related to difference in solute content, these data indicate that the alloy containing the greatest amount of solute is losing the greatest amount of solute during aging. This is consistent with the gradient-driven mechanism of precipitation.

At the conclusion of the reaction, the matrix solute content will be the limit of solubility for cobalt in copper (about 0.4% Co at,600'C). This value is the same for all initial solute compositions. Therefore, alloys with higher initial solute concentrations must reject more solute than alloys having lower initial solute concentrations in order to reach the solubility limit. Consequently, the disparity in matrix solute content between a solution heat treated and aged sample and one which has been solution heat treated only will be larger in an alloy that has higher solute concentration.

This pattern of finding larger signal strength for larger solute concentration is also seen in Figure 4-16, where the signal strength as a function of time is plotted for each of the three compositions aged at 5000C. Again, the signal strength increases monotonically for all compositions,




89

I III
AGING TEMP.= 500*C
40 30
2.7% Co


,20
1


10
a




20 ----
S2.0%Co 10


0


10 1.O Co


0
As 1 10 100
Quenched
TIME Ehr3

Figure 4-16. Peak Height vs Time for Various Copper-Cobalt
Alloys Aged at 5000C.




Full Text
25
Quenched MINUTES
Figure 2-5- Hardness versus Time for Cu-2.0% Co Alloy Aged
at 600C. (Ref. 29)


19
Figure 2-4.
Phase Diagram of Copper-Cobalt System.
(Ref. 49)


38
and accordingly the threshold energy for direct interband
transitions would be decreased. These are the predictions
of the rigid band model.62 Experimentally, however, it has
been determined by means of optical measurements7'63 and pho
toelectron spectroscopy63 that the transition energy at 2.2
eV in copper is unchanged by solute additions of nickel. In
stead, evidence indicates that the nickel d-bands remain in
dependent of the copper d-bands and that they retain their
character within the matrix. These nickel d-bands are found
to exist within one electron volt of the copper Fermi energy
and become the source of low energy transitions. In Figure
2-10, the reflectance spectra from Seib and Spicer63 for pure
copper, Cu-13% Ni, and Cu-23% Ni are presented. In contrast
to the reflectance spectra for copper-zinc alloys, there is
no change in the transition energy at 2.2 eV as nickel is
added to copper. There is a drop in reflectivity below 2.2
eV which is caused by transitions from the nickel d-bands to
the Fermi energy, thus decreasing the magnitude of the 2.2 eV
transition. These results verified the proposals of Friedel67
and Anderson66 who had predicted this type of behavior
known as virtual-bound-states -- for transition elements in
copper. It is clear that there is no composition dependence
of the 2.2 eV transition, such as was the case in copper with
multivalent solutes. Using photoemission Seib and Spicer63
did find that the band width of the virtual-bound-states of
nickel did increase as the amount of nickel increased.
Using differential reflectometry, Hummel et al.7 also


51
samples were then rinsed in methanol and blown dry and
taken immediately to the microhardness tester.
3.5 Aging
Aging temperatures were chosen to reflect a range of
precipitation rates from slow to moderately rapid growth.
To that end, all three alloy compositions Cu-1 a/o Co,
Cu-2 a/o Co, and Cu-2.7 a/o Co -- were given aging heat
treatments at 400C, 500C, and 600C. In addition, Cu-
2.7 a/o Co was aged at 450C and 550C.
All samples to be aged were placed in a fused quartz
tube which was evacuated with a mechanical pump to a pres
sure of approximately 0.1 Torr. The pump remained connected
to the tube and operated continuously during the aging
heat treatment. At the end of the aging heat treatment
helium was used to break the vacuum, and the samples were
immediately quenched in tap water.
For a specific isothermal aging heat treatment, the
aging times were recorded accumulatively. For example, if
a given alloy had been aged for fifteen minutes and exa
mined, and the next test required a thirty minute aging
heat treatment, the same sample was demounted, aged for fif
teen minutes and remounted. In this way any possible
error involved in using different samples was avoided.
Upon removal from the furnace, samples aged for six
hours or less appeared to be clean and free of contamination.


LIST OF FIGURES (continued)
Page
Figure 4-18. Peak Height vs Time for Cu-2.7% Co at
Various Aging Temperatures 92
Figure 4-19. Peak Height vs Time for Cu-2.0% Co at
Various Aging Temperatures 94
Figure 4-20. Peak Height vs Time for Cu-1.0% Co at
Various Aging Temperatures 95
Figure 4-21. Signal Strength vs Difference in Cobalt
Concentration for Solution Heat Treated
Samples and Aged Samples 96
Figure 4-22. Comparison of Spectra from Aging Experi
ments and Compositional Modulation
Experiments 106
Figure 4-23. Fraction Transformed vs Time at 600C 117
Figure 4-24. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at b00C 119
Figure 4-25. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 500C 122
Figure 4-26. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 400C 123
viii


94
Figure 4-19.
Peak Height vs Time for Cu-2.0% Co at
Various Aging Temperatures.


56
of cobalt mentioned above and aged at 600C. For the as
quenched alloys the hardness increases with solute content.
This proved to be the case in all samples analyzed, and is
consistent with the theory of the effect of solute elements
on the hardness of solid solutions. Solute atoms have been
shown to impede the movement of dislocations by collecting
57 8 2
at them and pinning them. As the concentration of
solute atoms increases, more dislocations can be pinned,
leading to increased hardness.
Figure 4-1 shows that for all alloys which had been
aged at 600C, the hardness increased considerably between
the as quenched state and fifteen minutes of aging. After
this, the hardness increased steadily, but more moderately,
up to its peak value at about nine hours. Past nine hours,
the hardness decreased steadily. At all times, the alloy
with the greater solute concentration exhibited higher
hardness.
Aging each alloy at 500C produced results indicative
of the slower diffusion rate which exists at this lower
heat treating temperature. As is seen in Figure 4-2, the
increase in hardness from the as quenched state to the
first aging time of 15 minutes is much more moderate than
in the case of aging at 600C. The increase was less than
half the increase seen at 600C. In addition, increases
tended to be moderate and no peak was reached even after
aging for 220 hours, although the values of hardness at
220 hours are higher than the peak values for the alloys


4 5.5
ENERGY CeVH
1.6 2 2.5 3
800 600 400 200
WAVELENGTH Enm]
Differential Reflectograms of Cu-1.5% Ni (Ref. 84) and Cu-i.5% Co.
(Compositions indicate average solute content of the two samples used.)
Figure 4-7.


100
independent research efforts support the conclusion that the
reaction at 600C brings the system into equilibrium in a
range of times from several minutes to several hours.16 30>
37,38 The observation that the signal strengths shown in
Figure 4-15 can be interpreted as showing no further increase
after 26 hours of aging is consistent with the viewpoint that
the system has been brought into equilibrium by the precipi
tation reaction.
As can be seen in Table 4-1, the precipitates that form
in this system are quite fine. This requires that some con
sideration be given to a possible shift toward higher solute
concentrations of the equilibrium solute concentration due
to capillarity. The magnitude of the capillarity shift is
inversely proportional to the radius of the precipitate, so
that in a finely divided system, the shift can be signifi
cant. However, there are two considerations which argue
against any strong effects due to capillarity in this system.
Firstly, Witt and Gerold^7 have performed aging experiments
at 600C on a Cu-0.6% Co alloy and have reported that pre
cipitates are formed. This would not be possible if there
were a significant capillarity shift. Secondly, and perhaps
more significantly, assuming that the experimental value
given by Servi and Turnbull38 for the surface energy of 190
ergs/cm^ for the precipitate-matrix interface is valid, the
capillarity shift for precipitates having a radius of 10 nm
can be calculated to be only 3% of the equilibrium solute
concentration. That is, for precipitates of this size, the


PERCENT DIFFERENCE IN REFLECTIVITY
0.5 1.0 1.5 2.0 2.5
PERCENT DIFFERENCE IN COMPOSITION
Figure 4-12. Signal Strength (AR/R) versus Difference in Cobalt Concentrat


20
10
0
20
10
0
10
0
A
uer
2 4-
89
, 1"
AGING TEMP.s 500C
ched
16. Peak Height vs Time for Various Copper-Cobalt
Alloys Aged at 500C.


105
alloys. Attempts were made to quantify this relationship,
but none proved successful. Qualitatively, however, this
observation should be noted.
In Figure 4-22 are seen two differential reflectograms.
The lower spectrum is a compositional modulation spectrum
in which one alloy is Cu-2.7% Co and the other is Cu-1.0%
Co. Both alloys were solution heat treated. The upper
spectrum is taken from the aging experiments in which both
alloys are Cu-2.7% Co, of which one has been solution heat
treated and the other has been solution heat treated and
fully aged. As has been noted, a fully aged alloy has a
matrix solute concentration of 0.4% Co. It is apparent in
Figure 4-22 that the depth of the "well" at approximately
3.2 eV is much more shallow in the spectrum from the aging
experiments than in the spectrum from the compositional
modulation experiments. Qualitatively, this would indicate
only a small difference in cobalt content between the aged
alloy and the alloy against which it is being compared, per
haps on the order of a few tenths of a percent. Because the
difference in solid solution cobalt concentration is known
to be 2.3% Co (2.7% Co 0.4% Co -- the equilibrium solute
concentration), it is possible to conclude that the signal
contributing to this "well" comes not only from the solute
in solid solution, but also from the cobalt in the precipi
tates. Although this conclusion is somewhat speculative,
taken in context with the rest of the data it seems


130
59. R. Rosei, S. Modesti, V. Prantera, and I. Davoli, J.
Phys. F: Metal Phys. 9_ (1979 ) 2275.
60. A. Bansil, H. Ehrenreich, L. Schwartz, and R. E. Watson,
Phys. Rev. B 9^ (1974) 445.
61. N. F. Mott, Proc. Phys. Soc. 4J7 ( 1935) 571.
62. N. F. Mott, Phil. Mag. 2_2 (1936 ) 266.
63. D. H. Seib and V. E. Spicer, Phys. Rev. B 2 (1970 ) 1676 .
64. D. H. Drew and R. E. Doezema, Phys. Rev. Lett. 2J3 (1972 )
1581.
65. S. Hlfner, G. K. Wertheim, R. L. Cohen, and J. H. Wer-
nick, PHYS. Rev. Lett. 28 (1972) 488.
66. W. Scouler, J. Feinleib, and J. Hanus, J. Appl. Phys.
40 (1969) 1400.
67. J. Friedel, Can. J. Phys. 3_4 (1956) 1190.
68. P. W. Anderson, Phys. Rev. 124 (1961) 41.
69. D. Beaglehole and C. Kunz, J. Phys. F: Metal Phys. 1_
(1977) 1923.
70. K. SchrOder and D. nenglt, Phys. Rev. 162 (1967 ) 628 .
71. D. H. Seib and W. E. Spicer, Phys. Rev. Lett. 2_0 (1968 )
1441.
72. K. C. Wong, E. D. P. Wohlfarth, and D. M. Hum, Phys.
Lett. 29A (1969) 452.
73. S. Wakoh and J. Yamashita, J. Phys. Soc. Japan 2_8 (1970)
1151.
74. S. Ishida, J. Phys. Soc. Japan 3J. (1972) 369.
75. R. A. Ballinger and C. A. W. Marshall, J. Phys. F:
Metal Phys. 3 (1973) 735.
76. F. Batallan, I. Rosenman, and C. B. Sommers, Phys. Rev.
B 11 (1975) 545.
77. P. B. Johnson and R. W. Christy, Phys. Rev. B £ (1974)
5056.
78. C. W. Shanley, R. E. Hummel, and E. D. Verink, Jr.,
Corr. Sci. 20 (1980) 467.


NORM. DIFF. IN REFLEC.
78
ENERGY CeV3
WAVELENGTH CnmJ
Figure 4-li. Differential Reflectograms of Cu-1% Co versus
Pure Copper and Cu-0.5% Co.


R,b:
Figure 2-9. Composition Dependence of Copper Threshold Transition.
(Ref. 5)


TEMP.
/
Figure 2-1.
Phase Diagram of Hypothetical Precipitation
Hardenable Alloy and Corresponding Free Energy
Diagram.


44
aged and the unaged samples. By having composition modula
tion spectra, it becomes possible to identify which part(s)
of the differential reflectometry spectra in the aging ex
periments were due to composition differences and which
part(s) were due to some other aspect of aging which would
produce a change in the optical properties of the alloys.
Second, by performing compositional modulation exper
iments, it is possible to obtain information about the
effects of additions of Co upon the electronic structure
of Cu. Although somewhat limited by the small solubility
of Cu for Co, the predictions of the virtual-bound-state
theory vs. the rigid band model could be investigated.
As was discussed in the last chapter, the changes in
hardness that occur in an alloy during a precipitation reac
tion are well documented and well understood. As has al
ready been discussed, hardness tests provide a clear, if
indirect, method by which the kinetics of the precipitation
reaction and the microstructural changes involved in that
reaction can be interpreted. For this reason, microhard
ness tests were chosen as a method against which the results
of the optical data could be compared and contrasted.
3.2 Alloy Preparation
All alloys used in these experiments were produced by
combining appropriate amounts of Cu-2.7 a/o Co powder and
pure Cu powder. The powders were blended and placed into


67
6 8
Anderson, who had predicted this type of behavior for
copper-nickel alloys.
The purpose of performing compositional modulation
experiments for this work was twofold. Firstly, it was
necessary to determine the manner in which cobalt would
affect the optical properties of copper. To do this,
"traditional" compositional modulation experiments were
performed, in which the optical properties of the average
compositions of the two samples were investigated. The
design and results of these experiments are discussed below.
Because cobalt and nickel lie next to each other in the
periodic table and because they both derive their ferro-
8 3
magnetism from spin imbalance of their unfilled d-bands,
the results of these experiments on Cu-Co alloys are com
pared to previous research on the optical properties of
Cu-Ni alloys. Particular attention is made to the virtual-
bound-state model.
Secondly, another type of compositional modulation
experiment on Cu-Co alloys was performed. In this inves
tigation, the difference in solute concentration between
the two samples studied is the variable parameter. The
design and the results of these compositional modulation
experiments will be discussed in the second half of this
section. In particular, the relationship between these
experiments and the optical properties of aged alloys will
be considered.


70
composition is small.) Although somewhat hampered by the
limited solubility for cobalt in copper, this research did
provide a measure of compositional dependence up to about
2.4% Co. In Figure 4-8, differential reflectograms are
shown for average compositions of Cu-0.5% Co, Cu-1.5% Co,
and Cu-2.4% Co. To obtain these average compositions the
following pairs of samples were examined: pure Cu and Cu-
1% Co, Cu-1% Co and Cu-2% Co, and Cu-2% Co and Cu-2.7% Co.
As in the case of nickel, there was no shift seen in
the transition energy as the composition was changed. As
has been discussed, the reason for this composition inde
pendence of the threshold transition energy has been ac
counted for by the virtual-bound-state model of Friedel^7
6 8
and Anderson. Their contention that the nickel electrons
maintain highly localized levels around nickel atoms when
alloyed with copper, seems to extend to cobalt impurity
atoms as well.
Peak "d", which is caused by transitions from the lower
d-bands of copper to the Fermi energy, does show a very
small composition dependence. It can be seen that this
peak shifts to slightly higher energies as the amount of
cobalt is increased. This same shift toward higher ener
gies with increasing solute content has also been observed
in copper-nickel alloys.7 The minimum designated "c" in
these differential reflectograms, although seen in Figure
4-8 to shift toward higher energies as cobalt content was
increased showed no strict composition dependence in other


86
0.5 hr, 3.0 hr, and 26.0 hr of aging. The 0 hr spectrum
depicts two samples that were identically solution heat
treated. The lack of any clearly defined structure in this
spectrum shows than the samples started in an identical
condition. In response to the aging heat treatments given
to the one sample, however, the spectra indicate that the
composition difference between the two samples increased
with aging time due to the decreased solute concentration
in the aged sample. In the spectra in Figure 4-14, the
signal strength indicates that after 26 hours of aging the
matrix solute content has been reduced by approximately
one percent.
In order to determine the effects of aging time, aging
temperature, and solute concentration on the optical proper
ties of these alloys during a precipitation reaction, the
signal strength at the threshold transition was plotted as
a function of aging time. The results are shown in Figures
4-15 to 4-20. In all cases the first differential reflec-
togram taken was of two solution heat treated samples, to
verify that the samples were identical in the initial con
dition. A featureless differential reflectogram was ex
pected and was obtained in all cases.
Figure 4-15 shows the change in threshold transition
magnitude for the various solute compositions of samples
aged at 600C. As seen in Figure 4-15, the signal strength
caused by the samples' composition difference immediately
increases after tne first aging heat treatment of fifteen


73
making optical measurements, specifically differential re-
flectometry, in determining the extent of dezincification
in alpha brasses when they are subjected to various cor
rosive environments. Although in the case of dezincifica
tion, the alloy experiences an actual loss of solute, a
precipitation reaction can be viewed in a similar manner,
for the reason that the solute is removed from the matrix
by the formation of the second phase.
It has been demonstrated that the optical properties
of copper-cobalt alloys parallel those of copper-nickel
alloys, and that these findings indicate that copper-cobalt
alloys behave according to the virtual-bound-state model.
Using Figure 4-8, it has been shown that Co additions do
not affect the energy of the copper threshold transition at
2.2 eV, as in the case of multivalent solute additions. Be
cause the differential reflectometer yields information
about the alloy composition which is the average of the two
samples investigated and because no shift in transition
energy occurs as the average alloy composition was changed,
an alternative method for determining the effect of cobalt
additions on the optical properties of copper was chosen.
The average of the composition of the two samples was re
placed by the difference in the composition of the two
samples.
In this second type of compositional modulation, exper
iments were conducted in a manner so as to simulate the
aging experiments which are described in the next section.


6
alloy actually hardens as a result of the precipitation
reaction.) In Figure 2-1, a phase diagram for a hypothe
tical age hardenable alloy has been drawn. It can be seen
that the two requirements mentioned above have been met. To
achieve precipitation, an alloy, which contains a few per
cent (C) of element B is held at Ts, the solution heat
treatment temperature. This solution heat treatment allows
all of element B to exist in a solid solution of the a phase.
If the alloy is then quenched quickly enough to Tg, usually
room temperature, the alloying element B can be made to re
main in a metastable solid solution. In order to induce
precipitation, the alloy is given an isothermal aging heat
treatment at Ta. At this temperature, the metastable phase
decomposes into two phases, a and 8, approaching the com
position defined by the phase diagram. During this decom
position, the matrix phase a rejects B atoms which go to
form the 8 phase having a concentration C which conse
quently lowers the matrix concentration of element B to the
saturated state Ca. The amount of the second phase produced
is determined by the tie line established by the aging tem
perature. At the completion of the reaction, the percent
of 8 phase is
p pot
%8 = ^ x 100%- (D
The precipitation reaction is generally considered to
proceed in three stages: nucleation, growth, and coarsening.
A brief, qualitative overview of these processes is given


72
differential reflectograms. In copper-nickel alloys, this
minimum is thought to be caused by nickel electronic tran
sitions, but cobalt has been found to have no strong opti-
75 77 85
cal transitions in this energy range. '
As has been established, a precipitation reaction is
defined to be the decomposition of a metastable solid
solution in which a second phase nucleates, grows, and
coarsens, and in which the matrix is necessarily depleted
of solute in order that the second phase be produced. So
far, this work has established the conditions under which a
precipitation reaction can be produced, and has verified
the presence of a second phase by means of microhardness
measurements. However, measurements of mechanical proper
ties, such as the microhardness of an alloy, only yield
information about the state of the precipitate, for example,
whether or not coherency has been maintained. While this
is, of course, useful, no information has been obtained
about the extent to which the decomposition has progressed.
There is no metallurgical law which establishes a link be
tween the hardness of an alloy and the volume fraction of
precipitate, or conversely, the composition of the matrix.
It has been seen that the optical properties of an
alloy are very strongly dependent upon its composition (See
Section 2.3), and therefore, their measurement should be
a candidate for a method of determining the changes in com
position which occur in the matrix during a precipitation
reaction. Finnegan^^has already shown the utility of


60
temperature is the variable parameter. In these figures,
the role of aging temperature in influencing the precipi
tation rate is clearly seen. In Figure 4-4, for example,
which shows microhardness data for a Cu-2.7% Co alloy aged
at 600C, 500C, and 400C; the increased precipitation
rate with increasing temperature is quite evident. Start
ing from essentially the same hardness in the as quenched
state, the alloy aged at 600C proceeds to reach a peak in
microhardness much faster than those alloys aged at 500C
or 400C. This same pattern is repeated for the Cu-2.0%
Co alloys and the Cu-1% Co alloys, seen in Figures 4-5
and 4-6 respectively.
The microhardness data presented here can be seen to
represent the type of data that would be found in a typical
precipitation reaction. The increase in hardness, although
influenced by a number of factors, is principally influ
enced by the fraction of coherent precipitate. The peak
value in the microhardness is indicative of that point
where the precipitates have grown to a size that warrants
the formation of an interface. This is achieved by the
creation of dislocations to accommodate the strain intro
duced to the lattice by the mismatch between the precipi
tate and the matrix. The subsequent decrease in hardness
past the peak is a manifestation of more and more particles
achieving the critical size at which they change from a
coherent to incoherent state.


95
Q ill 1
As 1 10 100
Quenched
TIME Chr3
Figure 4-20. Peak Height vs Time for Cu-1.0% Co at Various
Aging Temperatures.


27
the peak value of the yield stress and the hardness becomes.
This was reported by Livingston^O to be due to the reduced
solubility at the lower temperature, which leads to a great
er volume fraction of precipitate.
In Table 2-1 data are compiled from studies of the me
chanical properties of copper-cobalt alloys. The table shows
the aging temperature and length of time required to reach a
peak in the particular property investigated. Most studies
indicated that the higher the temperature at which the alloys
were aged, the faster the growth of the precipitate. Perovic
and Purdy,47 in their investigation of precipitation in these
alloys aged from 400C to 800C, found that the precipitate
had a growth rate maximum between 550C and 600C.
There is some controversy concerning the length of time
necessary to bring the precipitation reaction in this system
to completion. This may be due to the fact that each of the
methods used have sensitivities that are particular to cer
tain aspects of the reaction. For example, whereas TEM does
allow a direct observation of precipitate formation, compo
sitional changes can not be determined quantitatively. No
statistical methods have been applied which reveal whether
the growth of precipitates is due to depletion of matrix
solute or due to coarsening of the precipitate structure.
Because the precipitate in this system is ferromagnetic,
magnetic measurements provide a method of following the
growth of the precipitate. The model of Becker-^ has gener
ally been used to quantitatively determine the average radius


Light Source
Monochromator
Photomultiplier
Output
4^
CD
Figure 3-1. Schematic of Differential Reflectometer. (Ref. 3)


i i i i I r
1.6 2.0 25 3.0 4j0 5.5
A(nm)
E(eV)
Figure 4-22. Comparison of Spectra from Aging Experiments (Top)
and Compositional Modulation Experiments (Bottom).
106


CHAPTER 5
SUMMARY
In this work, differential reflectoraetry has been used
to investigate the effect of cobalt additions on the elec
tronic band structure of copper and to determine the kine
tics of the precipitation of the cobalt-rich phase from dilute
copper-cobalt solid solutions. The latter research is the
first instance that differential reflectometry has been used
to identify the kinetics of a phase transformation.
It has been demonstrated that additions of up to 2.7%
cobalt in copper do not change the energy of the copper
threshold transition. Investigations of other copper elec
tronic transitions also revealed no solute dependence, ex
cept for the peak revealing electronic transitions from the
lower d-bands of copper to the Fermi energy, which showed a
very slight increase in energy with increased cobalt content.
This behavior replicates that observed by other researchers,
who studied the effects of nickel additions on the band
structure of copper. This common pattern of optical pro
perty behavior for the class of copper-transition metal al
loys can be accounted for by the phenomenon of virtual-bound
states for both cobalt and nickel. For this first time,
optical measurements have been used to demonstrate this
shared behavior.
124


115
slightly less than one. A value of n = 1 can be interpre
ted, in the case of site saturation, diffusion controlled
growth, as the growth of precipitates in the shape of
platelets.
The result that the precipitates grow in the shape of
platelets contradicts a general result of other studies of
this system. That is, most researchers have reported that
the precipitates in this system grow as spheres.
There are two possibilities that may explain this dis
crepancy. Firstly, the method by which the alloys in this
work were handled might have produced platelets. It must
be recalled that the ingots were rolled by approximately
75% after they were made. After this step, they were re
crystallized. It is possible that some texture remained as
a result of the rolling step. This could have had the effect
of producing preferred planes on which the precipitates nu
cleated to form platelets. Performing TEM on sections of
the alloys would determine the shape of the precipitates.
Secondly, although the model used to interpret these
results produced a consistent value of n, the model is based
on the assumption that the lower calibration curve in Figure
4-21 is correct in that the suppression of the signal strength
is linearly dependent on the fraction transformed. Because
the effect of the precipitates on the optical signal is not
precisely known at this time, it is possible that the inter
action of the optical signal between the precipitates and the
matrix is more complicated than this simple relationship.


CHAPTER 3
EXPERIMENTAL PROCEDURE
3.1 Experimental Approach
The experiments comprising this work on Cu-Co alloys
fall into three categories. Firstly, differential reflec-
tometry was performed on samples to establish spectra
solely on composition differences, hereafter known as com
positional modulation. Secondly, differential reflecto-
metry was performed on samples which had been given various
aging heat treatments. Finally, microhardness testing was
performed upon samples to study the change in that mechan
ical property upon precipitation.
The purpose of performing the compositional modulation
experiments was twofold. First, it was necessary to obtain
spectra which were produced due specifically to composition
differences between two samples. In the aging experiments
carried out on the differential reflectometer, spectra
were to be produced by the difference between an aged and
a solution heat treated sample. For reasons that have al
ready been described, the aged sample would have less co
balt in the alloy matrix. Thus at least some of this spec
trum would be due to composition differences between the
43


LIST OF FIGURES (continued)
Page
Figure 4-5. Hardness vs Time for Cu-2.0% Co Aged
at 600 C, 500C, and 400C 62
Figure 4-6. Hardness vs Time for Cu-1.0% Co Aged
at 600 C, 500C, and 400C 63
Figure 4-7. Differential Reflectograms of Cu-1.5% Ni
and Cu-1.5% Co 69
Figure 4-6. Differential Reflectograms of Various
Copper-Cobalt Alloys 71
Figure 4-9. Differential Reflectograms of Cu-2.7% Co
versus Cu-0.5% Co, Cu-1.0% Co, Cu-1.5% Co,
Cu-2.0% Co, and Cu-2.5% Co 75
Figure 4-10. Differential Reflectograms of Cu-2.0% Co
versus Pure Copper, Cu-0.5% Co, Cu-1.0% Co,
and Cu-1.5% Co 77
Figure 4-11. Differential Reflectograms of Cu-1% Co
versus Pure Copper and Cu-0.5% Co 78
Figure 4-12. Signal Strength (AR/R) versus Difference
in Cobalt Concentration 81
Figure 4-13. Differential Reflectogram of a Cu-2.0% Co
Alloy 84
Figure 4-14. Differential Reflectograms of the Aging
Sequence of a Cu-2.0% Co Alloy Aged at
600 C 85
Figure 4-15. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 600C 87
Figure 4-16. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 500C 89
Figure 4-17. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 400C 91
vii


66
heat treated properly to produce a precipitation reaction.
Furthermore, the results indicate that the goal of obser
ving precipitation in regions of relatively rapid, moderate,
and slow growth has been achieved.
Among the researchers who have studied this system,
there is little disagreement as to the nature of the pre
cipitation reaction. It is generally conceded that the
precipitate is spherical, face-centered cubic, and remains
coherent with the lattice until it achieves a size of ap
proximately 40-100 A. There has been nothing found so far
in this work to contradict these findings.
4.2 Compositional Modulation: Results and Discussion
As has been discussed in Chapter 2, the optical proper
ties of copper alloys have been found to be strongly depen
dent on composition. In the case of copper with multiva
lent solutes, a linear shift of the threshold electronic
transition at 2.2 eV to higher energies was found as the
average solute concentration was increased above one per
cent.5 In the case of copper-nickel alloys, however, there
was no composition dependence seen in the energy of the
threshold transition.^ Additions of up to 24% nickel pro
duced no change in this transition energy. The demonstra
tion of this phenomenon by both differential reflectometry7
6 3
and photoelectron spectroscopy was offered as confirma-
6 7
tion of the virtual-bound-state model of Friedel and


22
1.4%, 2.0%, and 3.0% cobalt when aged at 600C. However,
in the same experiment, analysis of their data reveals that
for Cu-0.6% Co the volume fraction increased linearly with
time up to 32 hours of aging at 600C.
It was also through the use of magnetic measurements
that experimenters concluded that the precipitates were
spherical.17>55 This conclusion was reached on the basis
of only very slight magnetic anisotropy observed in the
aged single crystal alloys. Finally, the lattice of the
cobalt-rich precipitate has been found to be 2% smaller
than the lattice of the matrix.55
In another study of precipitation in copper-cobalt,
Servi and Turnbull58 aged the various alloys at temperatures
such that the solute composition did not deviate much from
equilibrium. This was performed in order to determine the
effect of undercooling upon the nucleation rate. By follow
ing the change in resistivity, they obtained a measure of
the volume fraction transformed through the use of Equation
3 and the relation
X
C C(t)
c ca
(3)
where X is the volume fraction transformed. Although the
transformation was observed to begin very shortly after
aging was started, analysis of the data indicates that full
transformation was never achieved, in contrast to what was
observed in the magnetic studies cited above. The data
did, however, confirm the growth of spherical precipitates.


123
80
70
60
50
TIME C hr J
Figure 4-26. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 400C.
HARDNESS DPN


FRAC. TRANS.
1
.8
Q- 1.0%Co (Serv and Turnbull Ref. 38)
- 1.4%Co (Witt and Gerold Ref. 37)
f 0.6%Co (Witt and Gerold Ref. 37)
Q- 2.3%Co (Gerold Ref. 92)
2.7%Co (This work)
2.0%Co (This work) q
1.0*Co (This work)
Aging Temp. 600C
As
Quenched
.01
1

x
0
0


.1
10
100
TIME (hr)
Figure 4-23. Fraction Transformed vs Time at 600C.
117


82
utility of differential reflectometry in determining the
depletion of solute from the matrix during precipitation
will be discussed in the following section.
4.3 Aging Experiments
In the preceding section, experimental data describing
the relationship between the composition of Cu-Co alloys
and the optical properties of these alloys was presented.
It was also demonstrated that differential reflectometry
provides a method by which the cobalt concentration of an
unknown Cu-Co alloy can be determined provided that a re
ference sample of known solute concentration is available.
In this section, the utility of differential reflectometry
in following a precipitation reaction by tracking the as
sociated matrix depletion of solute will be explored. In
addition, any additional optical effects that occur during
the precipitation reaction that are not based solely upon
composition differences will be acknowledged.
In these experiments three alloys of varying cobalt
content were studied Cu-2.7% Co, Cu-2.0% Co, and Cu-1.0%
Co. Each alloy was aged at 600C, 500C, and 400C. In
addition, the Cu-2.7% Co alloy was aged at 550C and 450C.
In order to determine the kinetics of the solute deple
tion during precipitation, differential reflectometry was
performed on samples that were identical in initial solute
composition, but differed in subsequent heat treatment. In


NORMALIZED DIFFERENCE IN REFLECTIVITY
77
ENERGY CeVU
1.6 2 2.5 3 4 5.5
WAVELENGTH Cnm3
Figure 4-10. Differential Reflectograms of Cu-2.0% Co
versus Pure Copper, Cu-0.5% Co, Cu-i.0% Co,
and Cu-i.5% Co.


20
copper-rich side. The peritectic temperature is 1110C,
at which is also found the maximum solubility for cobalt in
copper. It is this region of solid solubility on the copper-
rich side of the phase diagram to which attention is focus
sed when precipitation hardening is being considered. It
is evident that this region possesses the primary condition
necessary to achieve age hardening, that is, a decreasing
solubility for cobalt with decreasing temperature. Solu
bility drops from about 5.5 wt/o at 1110C to below 0.1
wt/o at 500C. Experiments conducted on dilute copper-
cobalt alloys have generally employed alloy compositions
ranging from slightly below 1.0 wt/o to about 3.0 wt/o.
The range of aging temperatures investigated extends from
400C to 700C, concentrating attention around 600C. The
fact that these alloys age at such moderately high tempera
tures is advantageous for the experimenter because the al
loys will not age at room temperature.57
The precipitate that forms in these alloys upon aging
can be seen by the phase diagram to be a cobalt solid sol
ution containing approximately 10 wt/o copper. This pre
cipitate, containing such a large amount of cobalt, is
ferromagnetic.'27-29,50-51 The precipitate has been found
to possess an FCC structure and to form as a spherical par
ticle.17'51-52 No intermediate lattices or shapes have
been noted.54 The dominant precipitation mode is a general
precipitation, although some localized and discontinuous
precipitation have been observed.27'55'47 Only in the


20
10
0
20
10
0
20
10
91
_ AGING TEMP. = 400C
2.7%Co
2.0%Co
1.0%Co
TIME ChrU
-17. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 400C.


99
and the alloys investigated in this work are fully aged, the
conclusion would have to be reached that there is a differ
ent equilibrium solute concentration for each composition.
This conclusion can not be supported by any principle of
materials science.
One last possibility exists when considering this matter.
It may be that the Cu-1.0% Co alloy has reached equilibrium,
but the other two compositions have not. Analysis of Figure
4-15 shows that there is little or no change in the signal
strength at 2.2 eV between 26 hours and 590 hours of aging
for both of the remaining compositions. Furthermore, as
stated above, analysis of the matrix solute concentration of
these alloys would indicate values of approximately 1% Co
after 590 hours. Clearly, a concentration gradient should
exist to drive the reaction toward completion. In the case
of Cu-1.0% Co, this gradient could be seen to have driven
the reaction to completion in 15-25 hours. It is inconsis
tent to state that the reaction for Cu-1.0% Co proceeds
fairly rapidly, but when the Cu-2.0% Co and Cu-2.7% Co alloys
reach a solute concentration of 1.0% cobalt that the reac
tion proceeds very slowly, if at all.
This last observation begins to address the question of
whether or not the data can be interpreted as indicating
that the reaction is not entirely complete after aging for
590 hours at 600C. There are numerous observations re
ported in the literature that this system can be brought
into equilibrium.16 30,37,38,88,89 Furthermore, in general,


28
Table 2-1. Time to Peak Property
for Copper-Cobalt Precipitation
Aging
Temp.
% Co
Measurement
Time to
Peak (hr)
Ref
250 C
3.2%
Hardness
> 1000
28
37 5 C
3.2%
Hardness
> 1000
28
550 C
2.0%
Yield Strength
160
30
3.2%
Hardness
175
28
600C
2.0%
Yield Strength
16
30
2.0%
--
12
45
2.0%
--
11
46
3.1%
TEM (Coherency strains)
12
33
650 C
2.0%
Yield Strength
1.5
30
2.0%
CRSS
4.0
44
3.1%
TEM (Coherency strains)
1.5
33
3.1%
Yield Strength
1.5
34
700C
2.0%
Yield Strength
0.5
30
2.0%
CRSS
1.0
44
3.1%
TEM (Coherency strains)
0.7
33
3.2%
Hardness
3.0
28


122
Figure 4-25.
Peak Height and Hardness vs Time for Cu-2.7%
Co Aged at 500C.
HARDNESS


17
Another example, where the removal of solute is meas
ured, is electrical resistivity measurements. Figure 2-3
shows a resistivity curve for a hypothetical alloy. As is
shown, the resistivity of the precipitation hardenable
alloy is dependent on two variables, the depletion of the
solid solution and the coherency strains produced by the
precipitate. Here, unlike the case of hardness where the
extent of coherency was the dominant factor, the solid
solution depletion is more important. As solute atoms are
rejected by the matrix in order to form second phase par
ticles, the number of electronic scattering centers is re
duced, thus lowering the resistivity. The extended strain
field of coherent particles acts to increase the resistiv
ity of the alloy. However, as the precipitates grow and
become incoherent, the lattice returns to a more relaxed
state and the resistivity consequently decreases.
2.2 Precipitation in Dilute Copper-Cobalt Alloys
Interest in the copper-cobalt system as an example of
a precipitation hardenable alloy, although never as intense
as in the more commercially important aluminum age harden
able alloys, has nonetheless been steady.16,28-48 one of
the reasons for this lies in the simplicity of the copper-
cobalt system, the phase diagram of which can be seen in
Figure 2-4.49 The copper-cobalt phase diagram shows a
miscibility gap with a peritectic transformation on the


b~SSH
ENERGY CeV3
WAVELENGTH Cnm^
Figure 4-13. Differential Reflectogram of a Cu-2.0% Co Alloy. (One Sample was
Solution Heat Treated and Aged for One Hour at 600C, the Other-
Sample was Solution Heat Treated.)


NORMALIZED DIFFERENCE IN REFLECTIVITY
71
ENERGY CeV]
1.6 2 2.5 3 4 5.5
WAVELENGTH CnmJ
Figure 4-8. Differential Reflectograms of Various Copper-
Cobalt Alloys. (Compositions indicate average
cobalt content of the two samples used.)


55
Figure 4-1.
Hardness vs Time for Alloys Aged at 600C.


23
A more direct method of observing precipitation in
copper-cobalt alloys has been carried out by a number of
researchers.31-35 This is the observation of coherency
strains in the lattice caused by the precipitates and detec
ted by means of transmission electron microscopy (TEM).
The TEM theory of diffraction contrast was used to obtain
particle diameters from the "double D" diffracted image,
which is the signature of spherical, coherent particles.
Here, as in the case of magnetic measurements, the radii of
growing particles increased linearly with the logarithm of
aging time.33 Observations that the number of precipitates
seen in the micrographs decreased with time were attributed
to coarsening,33,34 although the data were never quantita
tively compared to coarsening theory. Likewise, no quan
titative comparison was made between this work and previous
magnetic measurements, which had also indicated growth by
coarsening.
TEM observations have indicated in quenched alloys
that a complete solid solution with no formation of precipi
tates is possible to achieve. Phillips and Livingston31
have shown that no precipitates were observable in solution
heat treated and quenched alloys. They also noted that
precipitates were seen shortly after the aging heat treat
ment was begun.
As was discussed in Section 2.1, mechanical properties,
such as hardness, yield strength, and tensile strength, tend
to rise from the onset of precipitation, go through a peak,


59
Figure 4-3
Hardness vs Time for Alloys Aged at 400C.


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
% c
Rolf E. Hummel, Chairman
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
j1 H. Holloway U
Paul H. Holloway
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
Associate Professor of Chemical
Engineering


98
concentration alone (upper line in Figure 4-21) analysis
revealed that the matrix solute concentration for the alloys
aged for 590 hours at 600C was as follows: the Cu-2.7% Co
alloy had a matrix solute concentration of 1.1% Co; the Cu-
2.0% Co alloy had a matrix solute concentration of 0.9% Co;
and the Cu-1.0% Co alloy had a matrix solute concentration
of 0.6% Co. The equilibrium solute concentration at 600C
for cobalt in copper has been given as 0.4% Co. It is ap
parent from this analysis that none of these alloys has
reached the equilibrium solute concentration after being
aged at 600C for 590 hours. This might be due to one or
more of the following reasons: the value of the equilibrium
concentration is not 0.4% Co, but some other value; the
precipitation is not complete; there is a capillarity shift
of the equilibrium concentration due to a finely divided
precipitate structure in this system; the observed solute
depletion of the matrix is due to selective oxidation of co
balt during the aging heat treatment; the electronic proper
ties of the matrix and the precipitates are not completely
without interaction and the precipitates may play a role in
the signal strength at 2.2 eV.
The proposal that the equilibrium solute concentration
is not 0.4% Co is probably not valid. Four independent in
vestigations^ 38,88,89 using two different techniques have
established 0.4% Co as the equilibrium solute concentration
for cobalt in copper. Furthermore, if one makes the assump
tion that 0.4% Co is not the equilibrium solute concentration


113
only the volume traction transformed can be obtained as the
ratio of the measured signal strength to the maximum signal
strength:
meas
x comp
max
Z,
(ID
-comp
It has been seen, however, that the signal strength is di
minished by the presence of precipitates. Furthermore, it
has been demonstrated that the greater the amount of preci
pitates present, the greater is the suppression of the sig
nal strength. If this suppression of the signal strength is
proportional to the volume fraction, then
meas
XZ
max
comp
XZ
max
precip
(12)
rri6 3. s
where Z is the measured value of the signal strength,
and Zmax is the maximum amount of suppression, which is
precip ^
caused by a sample that is fully aged. It can be concluded,
therefore, that the volume fraction transformed can be ob
tained by the following equation:
meas
X =
^max vmax
comp ^precip
(13)
The data from the optical measurements of the aged cop
per-cobalt alloys were treated in this way in order to de
termine the constant, n, in the Avrami equation. The re
sults of these calculations can be seen in Table 4-2, which
lists n for various compositions and aging temperatures. As
can be seen all values for n fall in a narrow range of


76
Section 2.3). Because of the absence of a reference point
from which the peak at 270 nm could be measured, the change
in the differential reflectivity between 600-550 nm was
chosen as the basis upon which the signal strength was
measured. Of note is the fact that even when the differ
ence in the solute content is only 0.2% (bottom curve of
Figure 4-9), the change in the differential reflectivity
at the threshold transition is slightly more than 0.5%.
This demonstrates the utility of performing optical measure
ments in determining small differences in composition. It
is apparent that differences in composition at least as
small as 0.1% can easily be detected.
In Figures 4-10 and 4-11 are seen the spectra showing
Cu-2.0% Co and Cu-i.0% Co compared against samples of les
ser cobalt content. It is again apparent in these figures
that as the difference in solute content in the two samples
is increased that the signal strength of the spectra is
increased. Furthermore, the relationship between the dif
ference in solute content and the signal strength in all
three sets of experiments depicted in these figures was
found to be the same. By using this observation and by
plotting the signal strength at the threshold transition
as a function of the difference in solute content, the cal
ibration curve shown in Figure 4-12 was produced. As is
evident, a linear relationship was found to exist between
the percent change in differential reflectivity (signal


97
For Cu-2.0% Co the difference is 1.6% Co (point "b") and for
Cu-1.0% Co the difference is 0.6% Co (point "c"). This sup
pression of the signal strength is attributed to the influ
ence of the precipitates on the optical properties of those
alloys.
The question arises whether or not the second calibration
curve (lower line in Figure 4-21) is a reasonable interpre
tation of the data obtained from the optical measurements
of the aged alloys.
It is necessary to recall that the upper line in Figure
4-21 was obtained by measuring the signal strength at 2.2
eV caused by the difference in solid solution solute concen
tration between the two alloys. In performing the optical
measurements on precipitation heat treated alloys, two al
loys of identical solute concentration were measured by dif
ferential reflectometry. One alloy was solution heat treat
ed and the other alloy was solution heat treated and aged.
As discussed above, when alloys of three different solute
concentrations Cu-2.7% Co, Cu-2.0% Co, and Cu-1.0% Co --
were aged and measured by differential reflectometry in the
manner mentioned above, an increase in the signal strength
at the 2.2 eV electronic transition was noted. This was
ascribed to a depletion in the matrix solute concentration
in the aged alloys which accompanied the formation of a
second phase. When the signal strength of the differential
reflectograms was compared to the calibration curve obtained
from samples that differed in solid solution solute


120
alloys used in this work, recrystallization at 600C occurs
very rapidly and would not contribute to the hardness curve
in a time dependent manner. Although there is some solid
solution hardening (see Figure 4-1), its contribution to
the hardness is small and therefore the depletion of solute
from the matrix would not cause a great loss of hardness.
Because the precipitation reaction is not completed (preci
pitates are still being added to the system) before the
alloy begins to lose hardness, it is unlikely that the par
ticle spacing is becoming larger. Therefore, the loss of
hardness must correspond to the loss of coherency of the
precipitates with the matrix.
One point of contrast between the findings of this work
and that of several other reports in the literature is the
time necessary for the precipitation reaction to be complete.
Although there is agreement between the data of this work and
data in the literature concerning the time to achieve a max
imum in mechanical properties (see Table 2-1), there are a
number of studies in the literature that state that at 600C
the precipitation reaction is complete within fifteen minutes
of aging. Therefore, increases in the mechanical properties
of Cu-Co after this time must be accomplished by the growth
of precipitates by coarsening.
However, all of the data presented in the literature is
by no means consistent. There are other reports which sup
port a more gradual depletion of solute from the matrix.
Tauzenberger and Gerold^S show both types of precipitation


16
but hardly sufficient, to state that if recrystallization
occurs during aging, the result will always be a loss of
hardness brought about by the replacement of deformed, and
therefore hard, grains by undeformed, softer grains.
Changes in the physical properties of alloys undergoing
precipitation have long been observed and used as tools to
measure the kinetics of the reaction and to help to deter
mine the mechanisms by which the reaction takes place. Al
though these measurements are indirect, at the very least,
the measurement of physical properties yields the initial
state of the alloy, the changes that occur during the reac
tion, and the point at which the reaction is complete.
Measurements of resistivity, saturation magnetization,
Curie temperature and density or volume are common techni
ques in studying precipitation. These methods fall into
two categories. Firstly, there are those which follow the
growth of the second phase, as in the case of a magnetic
second phase precipitating from a non-magnetic matrix.
Here, measurements of magnetic saturation or coercive force
are used in determining the details of the reaction. Sec
ondly, there are studies which follow the depletion of
solute from the matrix phase. This type of experiment
might be used in the case of a magnetic matrix phase and a
non-magnetic second phase, where the rise in the Curie
temperature could be measured to determine the rate at
which solute was being removed from the matrix by precipi
tation .


52
Samples aged longer than six hours were observed to have
a flaky black surface scale. The origin of the scale was
probably a combination of oxide and residue from the
mechanical pump oil. However, because all samples were of
necessity ground and polished subsequent to each aging heat
treatment, any contamination resulting from that treatment
was removed.
3.6 Microhardness Tests
Diamond pyramid hardness tests (Vickers scale) were
conducted upon Cu alloys containing 2.7 a/o, 2.0 a/o, and
1.0 a/o Co. Each of the alloys was given a series of iso
thermal aging heat treatments at 400C, 500C, and 600C.
All samples were subjected to a 500g load applied by the
indenter. By maintaining the load at this specified value,
no load dependent variations were introduced into the mea
surements. Although the sample depth probed in a micro
hardness test is much larger than the sample depth probed
by a light beam (approximately 40 pm vs. 0.01 pm), micro
hardness tests were considered to be a more appropriate
alternative than standard hardness tests where the des-
parity in probe depth would have been far greater.
For each time in the aging sequence of a sample, a
set of twenty-five microhardness measurements was made.
From these measurements a diamond pyramid hardness num
ber (DPN) was calculated along with the 95% confidence


30
copper-cobalt system have revealed a fairly typical reaction.
Although there is some discrepancy in the length of time mea
sured for the reaction to achieve a fully transformed state
-- that is, the point at which microstructural changes are
due only to coarsening -- it has been observed that the pre
cipitate produced is a sphere and has no intermediate shapes.
Furthermore, the precipitates form throughout the matrix
with some localized precipitation at the grain boundaries.
The changes in mechanical properties during aging likewise
have been seen to be representative of an age hardenable
alloy. The ascent-peak-descent curves seen in the graphs
of hardness vs. aging time for these alloys are the unmis
takable fingerprint of precipitation. The generally good
agreement between the data of these various research efforts
reveals a well characterized system. These data also pro
vide a backdrop against which the hardness tests described
in this work can be compared.
2.3 Optical Properties of Copper and Copper Alloys
The effects of solute additions on the mechanical prop
erties of metals have already been discussed. Some change
in the yield strength, tensile strength, ductility, hardness,
and impact strength is the inevitable consequence of altering
the composition of a metal. Some changes may be beneficial
as in the case of adding zinc to copper, thus producing an
alloy that is both stronger and more ductile than pure


47
3.3 Differential Reflectometer
The differential reflectometer is a kind of optical
spectrometer, the output of which is a normalized differ
ence in reflectivity of two samples as a function of wave-
length, AR/R vs A. Originally conceived to experi
mentally determine the shift in energy of interband tran-
5 6 7
sitions that occur upon alloying, ' the differential
ref lectometer has proven successful in studying long1"*-
12
and short range ordering, dezincification of alpha
13
brasses, thickness and formation kinetics of corrosion
7 8
products, and in situ studies of the corrosion of Cu and
Cu-Ni alloys.7^
The differential reflectometer has been demonstrated
to be very sensitive in detecting small differences in com
position. Compositional differences as small as 0.05 a/o
8 0
have been detected in selected applications. It was the
aim of this work to exploit this capability in order to
detect changes in composition of an alloy matrix as preci
pitation occurred.
A detailed description of the differential reflecto-
3 4
meter has been given elsewhere. Only a brief descrip
tion of its functions will be given here, in conjunction
3
with Figure 3-1.
The usable output of the xenon light source lies in
the range of 200-800 nm. This light enters a double scan
ning monochromator, which for all experiments in this work


46
Table 3-1.
Table 3
Alloys Used in Composition Modulation
Experiments
Cu
- 2.
7
a/o
Co
Cu
- 2.
5
a/o
Co
Cu
- 2.
0
a/o
Co
Cu
- 1.
5
a/o
Co
Cu
- 1.
0
a/o
Co
Cu
- 0.
5
a/o
Co
Pure
Cu
-2. Alloys Used in Aging Experiments
Cu 2.7 a/o Co
Cu 2.0 a/o Co
Cu 1.0 a/o Co


Ill
of n. From this determination of a value for the constant,
n, the shape of the precipitate can be obtained. Servi and
Turnbull^S used this method when studying precipitation in
dilute copper-cobalt alloys by means of electrical resistiv
ity measurements. The value of n determined by these re
searchers varied from 1 to 2 depending on the aging temper
ature. For diffusion controlled growth, the growth radius
depends on t2. On this basis (an average of 1.5 for n),
Servi and Turnbull concluded that the shape of the precipi
tate was spherical.
It is then necessary to extract information from the
differential reflectograms which will relate the measured
quantity, the signal strength, to the volume fraction trans
formed. It has been seen that the signal strength, £, at
the 2.2 eV minimum is dependent on two factors. One is the
difference in matrix solid solution composition between an
aged and an unaged sample; the other is the effect of the
precipitates. These two effects will now be discussed
separately.
As the difference in matrix solid solution composition
increases, so does the strength of the optical signal, £.
On the basis of the difference in composition alone, it can
be seen in Figure 4-12 that
^rneas
comp
kAC
(6)
where £ is the measured signal strength due to composition
effects; AC is the difference in matrix composition between


101
equilibrium solute concentration is shifted from 0.4% Co to
slightly above 0.41% Co. This small shift of the equilib
rium solute concentration would not significantly affect the
results of this work.
The question now arises whether or not the aging heat
treatments may have influenced the cobalt concentration in
these alloys by a selective oxidation mechanism in which co
balt was removed from the alloy during the heat treatments
thereby producing alloys depleted of cobalt. This mechanism
could account for the observed increase in signal strength
at 2.2 eV in the differential reflectograms by leaving a
zone near the surface of the alloys which was depleted of
cobalt. Because light penetrates approximately the first
10 nm of the surface of a metallic alloy, this effect could
be important. It must be recalled, however, that these al
loys were polished after the aging heat treatments. This
polishing removed at least 100 microns from the surface of
the alloys. In this case, the question becomes whether or
not a depleted zone from the selective oxidation of cobalt
could extend to a depth of 100 microns or more. Using an
activation energy for the diffusion of cobalt in copper of
54,100 cal/mole,90 a diffusion coefficient of 1.93 cm^/sec,
90 and a growth factor of 1,38 a diffusion distance on the
order of one micron was calculated for an aging temperature
of 600C for 100 hours. This distance can be seen to be
much smaller than the depth to which these alloys were


79
strength) and the difference in solute content. The slope
of the line is approximately 3%/%AC.
This relationship between signal strength and the dif
ference in composition between the two samples measured is
an observation which has been previously unexploited in
differential reflectometry. The reason for this lies in
the nature of the solute element, which in this case is
a transition metal. As has previously been discussed (see
Section 2.3), when copper is alloyed with multivalent sol
utes, such as zinc, the energy of the electronic transitions
shifts as a function of solute content. By measuring the
change in the energy of these transitions by differential
reflectometry, it has been possible to determine the solute
content of unknown alloys. This was the method which was
used by Finnegan et al.^3 to determine the extent of de-
zincification in alpha brasses. For the reason that cobalt
is a virtual-bound-state element in copper, and hence no
shift in energy of the electronic transition occurs, the
composition dependence of the signal strength must be used
to determine the composition of an unknown alloy.
This relationship between the differential reflectivity
and the solute composition of a transition metal in copper
has been experimentally observed by other researchers.^'^
It can qualitatively be seen in Figure 2-10, which shows
reflectivity data for pure copper, Cu-13% Ni, and Cu-23%
Ni.63 The reduction of the reflectivity for the alloyed
samples in the energy region preceding the drop in


64
There are various values reported for this critically
sized particle in the Cu-Co system, i.e., the size at which
the precipitate changes from the coherent to incoherent
state. Generally, these values, seen in Table 4-1, fall
in the range of 40-100 A. The only values to fall outside
O
of this range is 175 A which was reported by Phillips and
31 0 35
Livingston and 120 A which was reported by Humphreys.
Both of these values for radii were found using samples
which had experienced no deformation after the aging heat
33 .
treatment. Phillips has also reported the maintainence

of coherency up to precipitate radii of 250 A in the ab
sence of any deformation. However, the application of any
deformation to the sample assists in the nucleation of
dislocations which provides for the establishment of an
interface in changing from a coherent to incoherent state.
In the present work, both the use of the indenter in the
microhardness tests and the use of the polishing wheel in
order to obtain a specular surface for taking optical mea
surements could provide the deformation necessary to cause
an interface to be formed between the precipitate and the
matrix. Therefore, the results presented here most likely
O
coincide with a radius of 40-100 A at peak hardness.
Based upon the data obtained from the microhardness
tests and the coincidence of this data with the work of
others who have studied precipitation in the copper-cobalt
system, the conclusion can be reached that the alloys were


41
Cobalt is a transition metal and resides next to nickel in
the periodic table. Its electronic configuration is 3d74s2.
Again, as in the case of nickel which has an unfilled d-band,
the electronic band structure of cobalt is found to possess
d-bands which contain both filled and unfilled states and
which lie within a few electron volts of the Fermi energy.72
"76 a high density of states, therefore, exists just above
and just below the Fermi energy. Although quantum mechan
ical considerations can not be put aside, for all practical
purposes, this large density of states around the Fermi en
ergy can be considered to be a continuum. This implies
firstly that electronic transitions can be stimulated by in
cident light at low energies, and secondly that an incre
mental increase in the energy of the incident light will be
matched by an increase in the number of transitions stimu
lated. This can be seen in the reflectivity curve for co
balt (Figure 2-11), which was calculated from optical con-
tants determined by Johnson and Christy.77 The reflectivity
is already below 80% at 1 eV, due to low energy optical ab-
sorbtion which stimulates d-band transitions. Also seen is
a monotonic decrease in reflectivity caused by the stimula
tion of a greater number of transitions as the energy of the
incident light is increased. In addition there is no sharp
change in the reflectivity in the range of 1 eV to 6 eV in
dicative of interband transitions or plasma resonances.


11
by the number of vacancies, dislocations, and other lattice
defects, growth will normally occur more rapidly in an alloy
which has experienced a rapid quench, heavy cold work, or
radiation damage than in an alloy in which these conditions
are not present.
Coarsening refers to the increase in interparticle
spacing which has been found to occur during the final steps
of precipitation reactions. It is most easily described by
the familiar axiom of materials science, "Large particles
grow at the expense of smaller ones." In contrast to nucle-
ation and growth, which were driven by the lowering of the
volume free energy in going from a supersaturated solution
to a decomposed two phase system, coarsening is driven by a
reduction in surface energy. It is generally considered to
occur after all chemically-driven growth has stopped, with
no change in the volume fraction of second phase. Given
these considerations, it can be seen that coarsening is
also characterized by a decrease in the number of precipi
tates and an increase in the average particle size with time.
Precipitation is also characterized by the distribution
of the second phase throughout the matrix. In what is
known as general precipitation, the precipitate is distri
buted randomly throughout the matrix. The reaction occurs
simultaneously in all parts of the matrix. The result of
this is a uniform precipitate structure.
In contrast to this, localized precipitation is charac
terized by growth of precipitates at lattice defects or


5
410 MPa to 1030 MPa while at the same time increasing the
hardness from 125 to 310 on the Vickers hardness scale.
Changes in physical properties are also manifested by alloys
during precipitation. In general, a significant increase
in electrical and thermal conductivity along with changes in
volume, magnetic properties, Hall coefficient and optical
properties can be observed during precipitation. What fol
lows is a simple description of phenomena which pertain to
precipitation and the methods by which they are studied.
Greater detail on particular subjects can be found else-
, 23-27
where.
The objective in producing a precipitation reaction is
to induce the nucleation and growth of a second phase from
a metastable solid solution. The reaction is expressed
in the following manner, a -* a + 6 where a is a solid solu
tion and 6 is the precipitated phase. Although the forma
tion of the second phase can be accomplished by changes in
pressure or additions of another element, precipitation is
most commonly carried out by the application of specific
heat treatments, the details of which are given below.
The requirements to produce precipitation hardening
(or age hardening) are that the alloying element is cap
able of achieving a solid solution, usually up to at least
a few percent, with the base metal and that the solubility
for the alloying element decreases with temperature. (In
fact, there is another definitive requirement in order for
precipitation hardening to be present, which is that the


40
found no shift in energy of the threshold transition at 2.2
eV in copper-nickel alloys. The alloys studied in this work
ranged from copper containing less than one percent nickel to
greater than twelve percent nickel. This result, which con
firmed the existence of virtual-bound-states in copper-nickel
alloys, provided no strict method of determining the solute
concentration of an unknown alloy. It was noted that the
"sharpness" of the peak in the differential reflectogram as
sociated with the 2.2 eV transition did possess a composition
dependence. However, no definitive composition dependence
was observed at 2.2 eV as in the case of copper containing
multivalent solutes.5'^/7
Beaglehole and Kunz^9 did find a composition dependence
on the difference in reflectivity of various dilute copper-
nickel alloys. Their data showed a linear relationship be
tween the difference in reflectivity at 628 nm and the dif
ference in the composition of the alloys measured, which
agreed with that of other investigators.66,VO,71 This lin
ear relationship was found to be valid up to approximately
20% solute, demonstrating that optical measurement might be
used to determine the composition of an alloy containing a
transition element.
For the reason that this work centers on optical inves
tigations of precipitation in copper-cobalt alloys and that
the precipitates in this system are a cobalt solid solution
approximately 90Co-10Cu it is necessary to consider
the optical properties and the electronic structure of cobalt.


VICKERS HARDNESS CDPND
61
Figure 4-4.
Hardness vs Time for Cu-2.7% Co Aged at 600C,
500C, and 400C.


VICKERS HARDNESS CDPNU
63
Figure 4-6.
Hardness vs Time for Cu-1.0% Co Aged at 600C
500C, and 400C.


109
treatments given to these alloys at 600C brought the system
to a fully aged condition and that the equilibrium solute
concentration of 0.4% cobalt was achieved. This permitted
analysis of the data on the basis that the difference in
solid solution cobalt concentration was known and the points
on the lower calibration curve in Figure 4-21 to be accu
rately placed. It has also been concluded that the sup
pression of the signal strength at 2.2 eV obtained from
optical measurements on aged alloys is caused by the influ
ence of the precipitates on the optical properties of these
alloys. The suppression of this signal strength may be due
to strain or an interaction of the electronic properties of
the precipitates and the matrix. Experiments have been pro
posed which might reveal the precise influence of the preci
pitates on the optical properties of these alloys. This
additional sensitivity of the differential reflectometer to
reveal a difference in microstructural state has not been
shown until this study.
4.4 The Kinetics of the Precipitation Reaction
There is disagreement in the literature concerning the
time dependency of the precipitation reaction in the copper-
cobalt system. There are reports of those researchers 29-31,
33,34,44 wj10 ciaj_m that the precipitation reaction occurs
so rapidly that it can not be observed as having any time
dependency and that all changes in mechanical properties


TABLE OF CONTENTS (continued)
Page
4.5 Comparison of Microhardness and
Optical Results 116
CHAPTER 5. SUMMARY 12 4
REFERENCES 127
BIOGRAPHICAL SKETCH 132
IV


80
70
40
J I I 1 1
1 2 3 4 5 6
ENERGY C*V1
Figure 2-11. Reflectivity Spectrum for Cobalt as Calculated from
Measurements of n ana k by Johnson and Christy (Ref. 77).


121
rates at 600C, depending on the amount of cobalt in copper.
The findings of this work can only be interpreted that for
aging at 600C, the precipitation reaction takes between 15-
25 hours to complete.
In Figure 4-25 the comparative data of microhardness
and optical measurements for Cu-2.7% Co aged at 500C are
presented. It can be seen that the more moderate rate of
depletion of solute is accompanied by a more moderate in
crease in microhardness. It is also evident that neither has
the microhardness reached a peak nor has the depletion of
matrix solute been completed even after 100 hours of aging.
Because the diffusion rate is much slower at 500C, these
data conform well to precipitation theory. In addition,
they are self-consistent.
In Figure 4-26, data are presented for Cu-2.7% Co aged
at 400C. At this temperature, the diffusion rate is so
low that there is only a slight depletion of solute. The
microhardness data confirm this by exhibiting a minute
increase.


VICKERS HARDNESS CDPND
57
Figure 4-2.
Hardness vs Time for Alloys Aged at 500C.


110
take place by coarsening of the precipitate structure. Re
ports-^ / 28,38,43,47 also exist that are based on a time de
pendent rate of growth which follows a time independent
nucleation event (site saturation). In one case, both types
of behavior have been observed for the precipitation reac
tion. 37 xn this investigation, the average solute concen
tration of the matrix was seen to change with aging time.
Because coarsening would involve no change in the solute
concentration of the matrix, the results of this investiga
tion indicate a growth process for the precipitation reac
tion. It remains that the data obtained by these optical
measurements yield consistent results when analyzed by a
standard model for the precipitates.
In this section, the kinetic data, which were obtained
by taking optical measurements of the aged copper-cobalt
alloys, will be evaluated quantitatively.
One method employed to follow the transformation kine
tics of a solid state reaction is the application of the
Avrami equation:
X = 1 exp(-t/r)n. (5)
In this equation, X is the volume fraction transformed; t is
the aging time; t is a time constant, and n is a constant
which depends on the shape of the precipitate and other par
ticulars of the reaction. Generally, the volume fraction
transformed, X, is obtained and log(ln(l X) ^) is plotted
versus log t. This yields a straight line which has a slope


49
was operated at a scan rate of 200 nm/min. After exiting
the monochromator, the beam is reflected from a flat mirror
to an oscillating mirror which focusses the beam at near
normal incidence alternately on each sample. The spot
2
size of the beam on each sample is approximately 2 X 2 mm .
Once reflected from the samples, the beam is focussed by
a fixed mirror onto a ground plane of fused quartz causing
the light to diffuse upon the face of the photomultiplier
tube (PMT) to quash any effects caused by the oscillating
light beam. The amplified signal of the PMT is divided
into two channels, one of which is a low pass filter which
yields the average reflectivity, R = (R^+R^)/^. The other
channel containes a lock-in amplifier where the difference
in reflectivity, AR = R^-R-^ s produced. A ratio of these
two signals is made and is used as input for the y-axis of
an x-y recorder. The x-axis input is connected through a
variable resistor to the drive of the monochromator, the
result being a spectrum of AR/Rvs. A.
In order to maximize the signal, the two samples anal
yzed in the differential reflectometer must be mounted as
close to each other as possible. This is achieved by
grinding a flat surface on each sample and holding them
together in a thermosetting metallurgical mount. After
polishing, the mount is clamped onto a stage in the diff
erential reflectometer. The stage is capable of being
moved vertically, by which the beam can be centered, or


31
copper;or the effect of alloying may be detrimental such
as the brittleness that is produced when a small addition
of iron is made to copper.57
Physical properties are also very much a function of com
position. Upon addition of another element to a pure metal,
its melting point, density, electrical and thermal conduc
tivity, magnetic and optical properties are affected. These
property changes upon alloying are the direct result of an
altered electronic band structure. This is particularly
true of optical properties. In this section, the relation
ship of the optical properties of copper to its band struc
ture will be considered. In addition, attention will be
directed to the response of the band structure, and hence
optical properties to composition changes and to methods by
which these changes have been measured.
In Figure 2-7, the band diagram of pure copper is pre
sented. 58 Because the electronic configuration of copper is
3dl4sl, it is expected that the d-bands of copper would lie
entirely below the Fermi energy. This is indeed the case,
with the top of the d-bands lying slightly more than 2 eV
below the Fermi energy. The partially filled s-bands and
p-bands are labelled in the figure. When photons of suffi
cient energy are incident upon a metal, electrons from
filled states are raised into unoccupied states above the
Fermi energy. The result of these direct interband transi
tions can be seen in Figure 2-8,1 where curve A depicts the
optical reflectivity for pure copper as a function of


112
the two samples; and k is equal to the slope of the line.
In the case of one sample having been aged and the
other sample having been solution heat treated, it is appar
ent that
AC = C C(t)
(7)
where C is the matrix composition for the solution heat
treated sample, and C(t) is the average matrix composition
of the sample after being aged for time, t. Also, using
the extremes of the line,
max
, ^comp (8)
k 'cs-ca
where is equal to the maximum signal strength measured,
which occurs when AC = C Ca, where Ca is equal to the
maximum solid solubility for cobalt in copper at a particu
lar aging temperature.
Substituting the expression for AC and k into Equation
5 yields
meas max rC-C(t)
comp 1 comp1 C-Ca ^ *
Further,
meas
^comp C-C(t)
max C-Ca
E
comp
C(t)-Ca
C-Ca
(10)
The right side of the equation is equal to X, the volume
fraction transformed. Therefore, for composition effects


29
of the precipitate and the volume fraction transformed. How
ever, this model assumes that no precipitate is larger than
10 nm and that there is an equal number of particles of each
size in the distribution. The validity of these assumptions
has not been independently established. Furthermore, the
saturation magnetization continues to increase as the preci
pitates coarsen,16 and therefore, it is difficult to deter
mine with precision when equilibrium has been reached.
Measurements of the electrical resistivity of alloys are
useful for following the depletion of solute from the matrix,
and have been used16 in following the nucleation and growth
of the second phase in this system. In following the deple
tion of solute from the matrix, however, this method offers
little information about the precipitate and its effects on
the physical properties of the alloy.
Measurements of the mechanical properties during preci
pitation are valuable in determining the microstructural
state of the alloy, particularly whether or not the precipi
tate is coherent with the matrix. However, these methods
provide only qualitative information about the extent of the
transformation or the fraction transformed.
In contrast, differential reflectometry offers a method
that can be sensitive to both the changing solute concentra
tion of the matrix and the formation of the second phase.
This sensitivity is not limited fundamentally as is the case
in the other experimental techniques.
To conclude, the investigations of precipitation in the


103
therefore, concluded that the suppression of the signal
strength at 2.2 eV is due to the presence of precipitates in
the aged alloys.
However, there is no direct evidence that this suppres
sion of the signal strength is due to the precipitates. The
remainder of this section will be devoted to an evaluation
of the data that indicates that the precipitates influence
the optical properties of these alloys. Although the evi
dence is indirect, it will provide a basis for future exper
iments. These experiments will be discussed at the end of
the section.
It is evident from Figure 4-21 that the amount of the
suppression of the signal strength at 2.2 eV is dependent
on the volume fraction of precipitate present. Specifically,
the precent volume of precipitate phase for a fully aged Cu-
2.7% Co alloy is 2.6%, for a fully aged Cu-2.0% Co alloy
is 1.8%, and for a fully aged Cu-1.0% Co alloy is 0.7%.
This is consistent with precipitation theory. If the preci
pitates influence the optical properties of these alloys,
then the alloy containing the greatest volume fraction of
precipitates should show the greatest effect on its optical
properties.
However, it can be argued that the magnitude of the sup
pression of the signal strength at 2.2 eV is too large to be
due to the precipitates alone. For a Cu-2.7% Co alloy the
volume fraction of precipitates is approximately 3%, but the
signal strength is suppressed approximately 30%. Hummel^l


116
The experiments outlined in the previous section should
facilitate a more precise interpretation of this relation
ship .
Finally, the kinetics of the reaction for this work were
compared with data analyzed from other research efforts.27f
38,89 jn Figure 4-23, the fraction transformed is plotted
as a function of time for alloys of varying cobalt content
aged at 600C. When compared with themselves, the data from
this work show a slight increase in the fraction transformed
as the cobalt concentration increases. This is explainable
by the larger driving force for precipitation that exists
the farther an alloy concentration is from equilibrium.
When compared with the other data obtained for this system,
it can be seen that the kinetics of the reaction in this
work are slightly slower than the rates reported by Witt and
Gerold27 for Cu-1.4% Co and Gerold ^2, but overall the values
fit into a middle range of all the values reported.
4.5 Comparison of Microhardness and Optical Results
In this section, a comparison of the results of the
microhardness and the differential reflectometer measure
ments will be presented. The data from these two tech
niques provide overlapping and straightforward evidence of
the method by which the precipitation reaction in the Cu-Co
system proceeds. For the reason that the discussion of this


PERCENT DIFFERENCE IN REFLECTIVITY
Figure 4-21. Signal Strength vs Difference in Cobalt Concentration
for Solution Heat Treated Samples (Top Curve) and Aged
Samples (Bottom Curve).


126
between 15-25 hours of aging for all solute concentrations.
This finding is consistent with microhardness measurements
performed on precipitation hardened alloys. It has further
been determined, by the monotonic depletion of solute from
the matrix as aging continued, that the hardening observed
in these alloys takes place due to growth of the precipitate,
as opposed to coarsening of the precipitate structure.
Because the cobalt-rich precipitate in this system has
no strong electronic transitions in the spectral range of
the differential reflectometer, the precipitates were found
not to produce any new feature on the differential reflecto-
grams by which their growth could be followed. However,
it has been determined that the magnitude of the signal
strength was suppressed as a result of the influence of the
precipitates on the optical signal.
To conclude, this work has contributed in the following
ways to the understanding of metals:
1) This work has verified the common behavior in the
electronic structure of copper-cobalt and copper-
nickel alloys.
2) This work has provided a method by which optical
and mechanical properties can be coupled to reveal
the nature of a precipitation reaction.
This work has provided a demonstration that differ
ential reflectivity is sensitive not only to dif
ferences in composition, but also to the physical
state of the material under investigation.
3)


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been compared to similar results for nickel in copper, a
phenomenon which has been treated by others with the theory
of virtual-bound-states. It has also been determined that
the strength of the differential reflectometric signal has
a linear dependence at 2.2 eV on the difference in solid sol
ution cobalt content between une two samples measured by this
method.
Differential reflectometry was then applied to the study
of aged copper-cobalt alloys. Three alloy compositions were
used in these experiments: Cu-2.7 a/o Co, Cu-2.0 a/o Co, and
Cu-1.0 a/o Co. The precipitation reaction was observed for
all compositions at three aging temperatures: 600C, 500C,
and 400C. Additionally, Cu-2.7 a/o Co was aged at 550C and
450C. The precipitation reaction was followed by means of
the increase in the strength of the optical signal which re
sulted from a decrease in the matrix solute content as the
reaction progressed. A site saturated, diffusion controlled
growth rate was observed for all compositions. The precipi
tates have been found to decrease the strength of the optical
signal in a way which is linearly dependent on the volume
fraction of the precipitates, thus allowing a measure of the
microstructural state of an alloy to be obtained from mea
surements of the optical properties.
Microhardness measurements were performed on these aged
alloys to provide an independent verification of the optical
results. These microhardness measurements were in good tem
poral agreement with the optical measurements of this work
x


93
aged and unaged samples increases as aging temperature
increases.
This same pattern manifests itself for Cu-2.0% Co and
Cu-1.0% Co alloys, the data for which can be seen in Fi
gures 4-19 and 4-20, respectively. Here, again, the signal
strength is at all times larger as the aging temperature
is increased. It is evident, however, that the magnitude
of the signal strength decreases as the solute concentra
tion of the alloys decreases.
Finally, the differential reflectograms were examined
for effects, other than those related to straightforward
compositional differences, which could be caused by the co
balt-rich precipitates. Two such effects were apparent and
are discussed in detail below. Firstly, there was a change
in shape of the spectra involving the feature designated "c"
in Figure 4-7. Secondly, based on the assumption that the
alloys were fully aged at 600C and that therefore the dif
ferences in matrix solute content could be determined from
the equilibrium solute concentration for each alloy concen
tration, the signal strength was found to be suppressed when
compared with data obtained from compositional modulation.
The results of this suppression can be seen in Figure 4-21,
where the lower curve was constructed in the following way.
Because the equilibrium solute concentration for cobalt in
copper is 0.4% Co, the difference in matrix solute concen
tration between a fully aged 2.7% Co alloy and a solution
heat treated alloy is 2.3% Co (point "a" on the graph).


3
this system will also be presented here. The last section
of this chapter focusses on the optical properties of copper
and copper alloys. More specifically, the relationship
between the composition of copper alloys and its electron
band structure is explored.
Three types of experiments were performed in order to
accomplish the goal of this work. Firstly, microhardness
tests were performed on precipitation hardened alloys. Sec
ondly, optical measurements were carried out on samples
which were known to differ in composition only. Lastly,
optical measurements were performed on samples which had
experienced a precipitation reaction. The details of these
experiments and the justification for performing them in
this manner are given in the third chapter.
Presented in the fourth chapter are the results of
these experiments as well as a discussion of the findings.
Each set of results will be evaluated in terms of what
other researchers have found in their studies of precipita
tion hardening in copper-cobalt as well as in terms of how
the results compare against each other. In addition, a
section on the effect of cobalt on the electronic structure
of copper is presented.
The final chapter summarizes the findings of these
experiments.


45
a graphite crucible for melting. A sodium borate flux was
used to protect the melt from oxygen contamination. Because
of the very narrow alpha plus liquid phase field (See Fi
gure 2-4) segregation upon solidification was deemed not
to be a problem and the ingots were allowed to solidify in
the furnace. Upon removal from the crucible, each ingot
was cleaned of any remaining flux and dipped for a few se
conds into an etchant (5:1 nitric acid:water) to remove
any surface contaminants. Each ingot was then rolled by
50%, recrystallized under vacuum at 350C for one hour,
and rolled again by approximately 33%. Each ingot was then
placed in a graphite crucible and covered with sodium bor
ate flux and given a solution heat treatment at 100UC for
approximately 70 hours. The ingots were then quenched in
iced brine to complete the solution heat treatment. The
ingots were then cleaned by etching and cut on a diamond
2
wheel to a size of approximately 0.25 cm for differential
reflectometry and microhardness testing. A few pieces
were selected at random and tested on the differential
reflectometer for compositional inhomogeneities. This was
done by illuminating only one sample in the differential
reflectometer. Any inhomogeneities in the sample would
produce a non-zero signal in the differential reflectometer
output. None could be detected. In Tables 3-1 and 3-2,
those alloys used in the compositional modulation and aging
experiments are listed, respectively.


RESISTIVITY
Quenched
TIME Carb. units]
Figure 2-3.
Composite Curve showing the Effect of Precipitation on
Electrical Resistivity. (Ref. 24)


118
data can be extended to the other two alloy compositions
that were investigated in this work, Cu-2.7% Co will be ex
amined in detail.
In Figures 4-24 to 4-26, microhardness data and optical
data are shown as a function of aging time, for the three
aging temperatures -- 600C, 500C, and 400C -- respec
tively. In Figure 4-24 a characteristic hardness curve is
seen. The immediate sharp rise in the microhardness of the
alloy aged at 600C is accompanied by a large increase in
the signal strength in differential reflectivity. This sig
nal strength has been determined to be caused by a depletion
of solute from the matrix in the alloy. Further aging leads
to more depletion of the alloy matrix as evidenced by the
growing signal strength of the optical measurements. A con
tinued increase in hardness corresponds to this depletion.
The optical signal strength ceases its growth after approx
imately 25 hours of aging, signalling an end to the precipi
tation reaction. Although the hardness of the alloy contin
ues to rise for a time as the solute depletion occurs, the
peak hardness of the alloy is achieved before the reaction
is complete, as determined optically. This peak is expected
and occurs after approximately nine hours of aging.
Figure 2-2 shows that there are four factors which con
tribute to the decrease of hardness prior to "complete"
solute depletion: recrystallization, depletion of the solid
solution, coalescence or coarsening of the precipitate struc
ture, and loss of particle coherency. For the dilute Cu-Co


34
energy. It is evident that at energies below 2.2 eV the re
flectivity is close to 100%. However, at 2.2 eV light is
absorbed initiating the first interband transition. These
transitions, which occur from the upper d-bands to s-bands
and p-bands at the Fermi energy, are believed to occur near
the L symmetry point.^ These transitions also give rise to
the characteristic salmon pink color of pure copper, since
they produce a much lower reflectivity in the green and blue
regions of the spectrum than in the yellow and red regions.
Other transitions which influence the reflectivity of copper
occur between the Fermi energy and the s-states (L21 to )
around 4.2 eV and between the lower d-bands and the Fermi
energy at approximately 5.5 eV.^9
The influence of solute additions upon the reflectivity
of copper can also be seen in Figure 2-8, which presents re
flectivity spectra for various brasses. There is a drop in
reflectivity in the energy range of 1.8 2.2 eV, as a result
of the dependence of reflectivity upon resistivity expressed
by the Hagen-Rubens relation
R = 1 2(up )h (4)
o
where R is the reflectivity, u is the frequency of the inci
dent radiation and pQ is the dc resistivity. Since the addi
tion of solute atoms increases the metal's resistivity by
increasing the number of scattering centers, the reflectiv
ity is consequently reduced. Although this empirical rela
tion was discovered before there was any knowledge of band


NORMALIZED DIFFERENCE IN REFLECTIVITY
ENERGY CV3
1.6 2 2.5 3 4 5.5
WAVELENGTH CnnO
Figure 4-l4. Differential Reflectograms of the Aging Sequence of a Cu-2.0
Co Alloy Aged at 600C.


83
these experiments, both samples were given solution heat
treatments. One of the samples was then additionally aged
at a specific temperature for a series of times. Differen
tial reflectometry spectra were obtained to record the
difference in optical properties between the two samples
as a result of the aging regime.
Figure 4-13 shows a typical differential reflectogram
from these experiments. The two samples used to obtain
this spectrum were both Cu-2.0% Co. One sample was solu
tion heat treated while the other was solution heat treated
and aged at 600C for one hour. The two most prominent
features of this spectrum are a minimum formed between 600
nm and 550 nm and a maximum occuring at 280 nm. These fea
tures appear at the same wavelengths as those described in
the previous section during the compositional modulation
experiments. On the basis of the signal strengths of the
minima centered at 550 nm, the difference in composition
between the two samples is approximately 0.5% Co. It was
also determined that the aged sample was the sample which
contained the lesser amount of matrix solute. This finding
is interpreted to be the fundamental result of a precipita
tion reaction, in which cobalt is removed from the matrix
in order that cobalt-rich precipitates can be formed.
In Figure 4-14 a series of differential reflectograms
for a Cu-2.0% Co alloy are displayed. Again, one sample
was solution heat treated while the other was solution heat
treated and then aged. Figure 4-14 shows the spectra for


131
79. R. J. Smith, Doctoral Dissertation, University of
Florida (1984 ) .
80. W. M. Goho, unpublished.
81. Met-a-Test, trademark GCA/Precision Scientific.
82. W. Hume-Rothery, W. E. Smallman, and C. W. Haworth,
The Structure of Metals and Alloys, Pergamon Press
(London, 1969 ) .
83. B. D. Cullity, Introduction to Magnetic Materials, Ad-
dison-Wesley (Reading, Massachusetts, 1972).
84. R. E. Hummel, Phys. Stat. Sol. A 7J> (1983) 11.
85. P. Heimann, E. Marschall, H. Neddermeyer, M. Pessa, and
H. F. Roloff, Phys. Rev. B lj) (1977) 2575.
86. H. Hflchst, P. Steiner, and S. Hlfner, Z. Physik B 3_8
(1980) 201.
87. S. Heeger, Solid State Physics, vol. 23, Academic
Press (New York, 1970).
88. G. Tammann and W. Oelsen, Z. an. all. Chem. 186 (1930)
257.
89. A. Knappwost, Z. Phys. Chem. 12^ (1957 ) 30.
90. C. A. Machiet, Phys. Rev. 109 (1958) 1964.
91. R. E. Hummel, Optics Comm. 3j) (1981) 55.
92. V. Gerold, private communication.


REFERENCES
1. R. E. Humme1, Optische Eigenschaften von Metallen und
Legierungen, Springer-Verlag (Berlin, 1971).
2. H. Ehrenreich, IEEE Spectrum 2 (1965) 162.
3. R. E. Hummel, D. B. Dove, and J. A. Holbrook, Phys. Rev.
Lett. 25 (1970) 290.
4. J. A. Holbrook and R. E. Hummel, Rev. Sci. Instr. 4_4
(1973) 463.
5. R. J. Nastasi-Andrews and R. E. Hummel, Phys. Rev. B
16 (1977) 4314.
6. R. E. Hummel and J. B. Andrews, Phys. Rev. B £ (1973)
2449.
7. R. E. Hummel, J. A. Holbrook, and J. B. Andrews, Surf.
Sci. 37 (1973) 717.
8. D. Beaglehole and E. Erlbach, Phys. Rev. B 6^ (1972)
1209 .
9. M. Tokumoto, Phys. Rev. B 2_2 (1980 ) 638 .
10. M. Tokumoto, H. D. Drew, and A. Bagchi, Phys. Rev. B 8^
(1977) 3497.
11. R. E. Hummel, J. B. Andrews, and J. A. Holbrook, Z.
Metallkunde 64 (1973) 573.
12. J. B. Andrews, R. J. Nastasi-Andrews, and R. E. Hummel,
Phys. Rev. B 22 (1980) 1837.
13. J. E. Finnegan, R. E. Hummel, and E. D. Verink, Jr.,
Corrosion 3_7 (1981) 256.
14. W. Desurbo, H. N. Treaftis, and D. Turnbull, Acta Met.
6 (1958) 401.
15 D. Turnbull, H. S. Rosenbaum, and H. N. Treaftis, Acta
Met. 8 (1960) 277.
16. J. J. Becker, Trans. AIME 209 (1957) 59.
127


114
Table 4-2. Functional Dependency, n, of the Exponent
in the Avrami Equation
Composition
Temperature
n
2.7% Co
600 C
.91
2.7% Co
500 C
.84
2.0% Co
600 C
.87
2.0% Co
5 0 0 0 C
.84
1.0% Co
600 C
.89
1.0% Co
500 C
.85


125
Differential reflectometry has clearly revealed that
as the difference in solute content between two samples is
increased the signal strength of the differential reflecto-
grams is increased. The signal strength of the copper thres
hold transition, seen as a minumum at 2.2 eV in the differ
ential reflectograms of dilute copper-cobalt alloys, was
chosen as the basis for measuring the magnitude of the sig
nal strength. A straightforward linear dependence of the
magnitude of the signal strength on the difference in solid
solution solute content was found. Quantitatively, the
change in the magnitude of the signal strength is 3%/A%C.
Differential reflectometry has also been used to closely
monitor the depletion of solute from the matrix during a
precipitation reaction. Such a study offers additional in
formation about the electronic structure of alloys, since
not only do the compositions of the samples differ -- as in
the above-mentioned comparison of solid solution alloys --
but so do the physical states of the alloying constituents.
The magnitude of the signal strength of the 2.2 eV minimum
has been demonstrated to be a measure of the progress of
the precipitation of a cobalt-rich second phase in these
dilute copper-cobalt alloys. While observing the precipi
tation reaction for three different temperatures (600C,
500C, and 400C) and for three different cobalt concentra
tions (Cu-2.7% Co, Cu-2.0% Co, and Cu-1.0% Co), it has been
determined that the higher the aging temperature the faster
the reaction occurs. At 600C, the reaction is complete


128
17. C. P. Bean, J. D. Livingston, and D. S. Rodbell, Acta
Met. 5 (1957) 682.
18. J. W. Cahn, Trans. AIME 209 (1957) 1309.
19. F. W. Jones and P. Leech, J. Inst. Metals 6J7 (1941) 9.
20. A. H. Geisler, Trans. AIME 180 (1949) 230.
21. D. A. Petrov, J. Inst. Metals 6_2 (1938) 81.
22. A. Wilm, Metallurgie 1 (1911) 225.
23. Z. Jeffries, ed., Age Hardening in Metals, ASM (Cleve
land, 1940).
24. A. H. Geisler, Phase Transformations in Solids, John
Wiley and Sons (New York, 1951).
25. J. W. Martin, Precipitation Hardening, Pergamon Press
(Oxford, 1968) .
26. H. K. Hardy and T. J. Heal, Progress in Metal Physics,
vol. 5, Pergamon Press (Oxford, 1954).
27. A. Kerry and R. B. Nickolson, Progress in Metal Physics,
vol. 10, Pergamon Press (Oxford, 1963).
28. R. B. Gordon and M. N. Cohen, Age Hardening of Metals,
ASM (Cleveland, 19.40).
29. J. D. Livingston and J. J. Becker, Trans. AIME 212
(1958) 316.
30. J. D. Livingston, Trans. AIME 215 (1959) 566.
31. V. A. Phillips and J. D. Livingston, Phil. Mag. 1_ (1962 )
969 .
32. M. F. Ashby and L. M. Brown, Phil. Mag. 8 (1963) 1083.
33. V. A. Phillips, Trans. AIME 230 (1964) 967.
34. V. A. Phillips, Phil. Mag. 11 (1965) 775.
35. F. J. Humphreys, Acta Met. 16^ (1968) 1069 .
36. M. Witt and V. Gerold, Scripta Met. 3 (1969) 371.
37. M. Witt and V. Gerold, Z. Metallkunde 60_ (1969) 482.
38. I. W. Servi and D. Turnbull, Acta Met. 14 (1966) 161.


Specifically, in these experiments, the solute composition
of one sample was held constant while the solute composition
of the samples measured against it was successively de
creased. In this way, the difference in solute content
between the two samples was made the independent variable.
All of the samples used in these experiments were given
solution heat treatments in order that there was no preci
pitate present, therefore, the results would be indicative
of composition effects only. The results of these experi
ments can be seen in Figures 4-9 to 4-11.
In Figure 4-9, a Cu-2.7% Co alloy was measured against
copper alloys containing 2.5% Co, 2.0% Co, 1.5% Co, 1.0%
Co, and 0.5% Co. The shape of these curves can be seen to
be similar to those curves described in the first part of
this section, where the effect of cobalt upon the electron
band structure of copper was discussed. Qualitatively, it
is immediately apparent that as the difference in solute
composition of the two samples is increased that the signal
strength of the spectra is also increased. In order to
attempt to quantify this increase in the signal strength,
two features of the spectra, which are present in all spec
tra and which lend themselves to measurement (the minimum
formed between approximately 600-550 nm and the maximum at
270 nm), were examined. These two features are the results
of changes in strength of the two most prominent valence
transitions in copper, specifically tne tnreshold transi
tions at 2.2 eV and the ,-L^ transicin at 4.5 eV (See


CHAPTER 2
OBSERVATIONS CONCERNING PRECIPITATION
AND OPTICAL PROPERTIES OF ALLOYS
2.1 Precipitation; General
Since the end of the first decade of this century, when
22
Alfred Wilm first demonstrated the means by which certain
aluminum alloys could be strengthened, precipitation harden
ing has been used by metallurgists and materials scientists
to improve the mechanical properties of the alloys of many
base metals. Although aluminum-based alloys, particularly
with additions of copper and magnesium, have probably been
the most studied of all precipitation hardenable alloys,
precipitation heat treatments are commonly used in many
commercial alloys. Two notable examples are the addition
of copper to malleable cast iron and the addition of titan
ium and aluminum to both semi-austenitic stainless steels
and nickel-based superalloys.
Precipitation hardening is a process by which the mech
anical and physical properties of an alloy can be drama
tically altered. Performed under controlled conditions the
strength and hardness of an alloy can be considerably in
creased. For instance, in a commonly used copper-beryllium
alloy -- Cu-1.7 wt/o Be, 0.3 wt/o Co -- precipitation har
dening can produce an increase in tensile strength from
4


PEAK HEIGHT Corb. unif*3
87
Figure 4-15.
Peak Height vs Time for Various Copper-Cobalt
Alloys Aged at 600C.


LIST OF TABLES
Page
Table 2-1. Time to Peak Property for Copper-Cobalt
Precipitation 2 8
Table 3-1. Alloys Used in Composition Modulation
Experiments 4 6
Table 3-2. Alloys Used in Aging Experiments 46
Table 4-1. Radius of Precipitate at Peak Property for
Copper-Cobalt System 65
Table 4-2. Functional Dependency, n, of the Exponent
in the Avrami Equation 114
v


90
although more moderately than those samples aged at 60C.
These monotonic increases in the signal strength are an
indication that as the aging heat treatment continues, the
matrix solute content of the aged samples is continuously
diminisning as solute atoms are used to form precipitates.
Figure 4-17 shows the data for the alloys when aged at
400C. It should be noted that even after 70 hours of aging
there is only a slight increase in the signal strengtn.
This, of course, means that precipitation is slow and that
the matrix solute concentration in the aged alloys does
not change significantly during these heat treatments due
to precipitation at this temperature.
In Figures 4-18 to 4-20 signal strength is plotted as
a function of time in graphs which show more clearly the
effect of temperature. Figure 4-18 shows data for Cu-2.7%
Co aged at 600C, 550C, 500C, 450C, and 400C. To be
noted is the very large initial increase in signal strength
for the alloy at 600C, indicating that at this temperature
the precipitation is well under way after 15 minutes aging.
In temperature regimes where precipitation is controlled by
diffusion, it is expected that the precipitation reaction
will proceed at a faster rate when a higher aging temper
ature is employed. As has been previously stated, the
signal strength is proportional to the difference in the
matrix solute concentration between the aged and the solu
tion heat treated samples. For this reason it can be seen
that the disparity in matrix solute content between the


14
By collecting at dislocations, solute atoms pin them and
prevent them from moving during an applied stress. In addi
tion, solute atoms can either replace solvent atoms on regu
lar lattice sites (substitution) or they can occupy sites
between lattice positions (interstitial). In either case,
the solute atom will create strain in the lattice, which
impedes the movement of dislocations. These mechanisms
account for the increase in hardness upon the addition of
solute atoms to an alloy. During a precipitation reaction,
solute atoms are removed from the matrix in order to form
the precipitates. Thus as shown in Figure 2-2, as the aging
of the alloy progresses solid solution hardening decreases.
The most important contribution to the hardening of an
alloy during precipitation comes from coherent precipitates.
In the case of general precipitation the first precipitates
to form are coherent with the lattice, that is, the lattice
of the precipitate matches point for point the lattice of
the matrix. Such clusters of a relatively large number of
atoms of different size than the matrix exert strain which
extends well beyond the immediate vicinity of the precipi
tates. As long as coherency is maintained, the larger the
precipitate becomes, the more strain is exerted on the
lattice. The interaction of a moving dislocation with this
strain field requires more energy for movement than if
there were no precipitate. Thus a dramatic increase in
hardness is seen in Figure 2-2 upon the formation of coher
ent precipitates. As the decomposition proceeds, the


OPTICAL STUDIES OF PRECIPITATION
IN DILUTE COPPER-COBALT ALLOYS
USING DIFFERENTIAL REFLECTOMETRY
By
WILLIAM MICHAEL GOHO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

ACKNOWLEDGEMENTS
The author wishes to recognize the contributions of the
following people, without whose efforts this work could not
have been completed.
The typing of this dissertation was done by Susan Matts
Goho. This enormous task represents a tiny fraction of the
support which she has provided. She has provided me with
the technical, academic, and emotional means with which to
bring this long process to an end. This accomplishment must
be shared equally with her.
The author is grateful to Dr. R. E. Hummel for his
unique attitude in helping his students in all aspects of
their concerns as well as for his technical advice. I have
benefitted greatly from his tutelage and aspire to be as
good a teacher as he.
Dr. P. H. Holloway has provided many hours of helpful
discussions on matters of concern to this dissertation. He
has also provided much needed encouragement at crucial times
during the writing of this work.
The author wishes to thank all the members of the dis
sertation committee for their efforts.
11

TABLE OF CONTENTS
Page
ACKNOWLEGDEMENTS
LIST OF TABLES v
LIST OF FIGURES vi
ABSTRACT ix
CHAPTER 1. INTRODUCTION 1
CHAPTER 2. OBSERVATIONS CONCERNING PRECIPITATION
AND OPTICAL PROPERTIES OF ALLOYS 4
2.1 Precipitation: General 4
2.2 Precipitation in Dilute Copper-
Cobalt Alloys 17
2.3 Optical Properties of Copper and
Copper Alloys 30
CHAPTER 3. EXPERIMENTAL PROCEDURE 4 3
3.1 Experimental Approach 43
3.2 Alloy Preparation 44
3.3 Differential Reflectometer 47
3.4 Polishing Procedure 50
3.5 Aging 51
3.6 Microhardness Tests 52
CHAPTER 4. EXPERIMENTAL RESULTS AND DISCUSSION 5 4
4.1 Microhardness Tests: Results and
Discussion 54
4.2 Compositional Modulation: Results
and Discussion 66
4.3 Aging Experiments 82
4.4 The Kinetics of the Precipitation
Reaction 109
iii

TABLE OF CONTENTS (continued)
Page
4.5 Comparison of Microhardness and
Optical Results 116
CHAPTER 5. SUMMARY 12 4
REFERENCES 127
BIOGRAPHICAL SKETCH 132
IV

LIST OF TABLES
Page
Table 2-1. Time to Peak Property for Copper-Cobalt
Precipitation 2 8
Table 3-1. Alloys Used in Composition Modulation
Experiments 4 6
Table 3-2. Alloys Used in Aging Experiments 46
Table 4-1. Radius of Precipitate at Peak Property for
Copper-Cobalt System 65
Table 4-2. Functional Dependency, n, of the Exponent
in the Avrami Equation 114
v

LIST OF FIGURES
Pa^e
Figure 2-1. Phase Diagram of Hypothetiacl Precipitation
Hardenable Alloy and Corresponding Free
Energy Diagram 7
Figure 2-2. Composite Hardness Curve 13
Figure 2-3. Composite Curve showing the Effect of
Precipitation on Electrical Resistivity.... 18
Figure 2-4. Phase Diagram of Copper-Cobalt System 19
Figure 2-5. Hardness versus Time for Cu-2.0% Co
Aged at 600C 25
Figure 2-6. Yield Strength and Hardness versus Time for
Cu-2.0% Co Aged at Various Temperatures.... 26
Figure 2-7. The Band Diagram of Copper 32
Figure 2-8. Reflectance Spectra for Copper and
Various Brasses 33
Figure 2-9. Composition Dependence of Copper Threshold
Transition 37
Figure 2-10. Reflectance Spectra for Copper and Two
Copper-Nickel Alloys 39
Figure 2-11. Reflectivity Spectrum for Cobalt as
Calculated from Measurements of n and k
by Johnson and Christy 42
Figure 3-1. Schematic of Differential Reflectometer....48
Figure 4-1. Hardness vs Time for Alloys Aged at 600C..55
Figure 4-2. Hardness vs Time for Alloys Aged at 500C..57
Figure 4-3. Hardness vs Time for Alloys Aged at 400C..59
Figure 4-4. Hardness vs Time for Cu-2.7% Co Aged at
600 C, 500 C, and 400C 61
vi

LIST OF FIGURES (continued)
Page
Figure 4-5. Hardness vs Time for Cu-2.0% Co Aged
at 600 C, 500C, and 400C 62
Figure 4-6. Hardness vs Time for Cu-1.0% Co Aged
at 600 C, 500C, and 400C 63
Figure 4-7. Differential Reflectograms of Cu-1.5% Ni
and Cu-1.5% Co 69
Figure 4-6. Differential Reflectograms of Various
Copper-Cobalt Alloys 71
Figure 4-9. Differential Reflectograms of Cu-2.7% Co
versus Cu-0.5% Co, Cu-1.0% Co, Cu-1.5% Co,
Cu-2.0% Co, and Cu-2.5% Co 75
Figure 4-10. Differential Reflectograms of Cu-2.0% Co
versus Pure Copper, Cu-0.5% Co, Cu-1.0% Co,
and Cu-1.5% Co 77
Figure 4-11. Differential Reflectograms of Cu-1% Co
versus Pure Copper and Cu-0.5% Co 78
Figure 4-12. Signal Strength (AR/R) versus Difference
in Cobalt Concentration 81
Figure 4-13. Differential Reflectogram of a Cu-2.0% Co
Alloy 84
Figure 4-14. Differential Reflectograms of the Aging
Sequence of a Cu-2.0% Co Alloy Aged at
600 C 85
Figure 4-15. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 600C 87
Figure 4-16. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 500C 89
Figure 4-17. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 400C 91
vii

LIST OF FIGURES (continued)
Page
Figure 4-18. Peak Height vs Time for Cu-2.7% Co at
Various Aging Temperatures 92
Figure 4-19. Peak Height vs Time for Cu-2.0% Co at
Various Aging Temperatures 94
Figure 4-20. Peak Height vs Time for Cu-1.0% Co at
Various Aging Temperatures 95
Figure 4-21. Signal Strength vs Difference in Cobalt
Concentration for Solution Heat Treated
Samples and Aged Samples 96
Figure 4-22. Comparison of Spectra from Aging Experi
ments and Compositional Modulation
Experiments 106
Figure 4-23. Fraction Transformed vs Time at 600C 117
Figure 4-24. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at b00C 119
Figure 4-25. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 500C 122
Figure 4-26. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 400C 123
viii

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
OPTICAL STUDIES OF PRECIPITATION
IN DILUTE COPPER-COBALT ALLOYS
USING DIFFERENTIAL REFLECTOMETRY
By
WILLIAM MICHAEL GOHO
May 1986
Chairman: Rolf E. Hummel
Major Department: Materials and Engineering
Differential reflectometry has been successfully applied
to the study of precipitation in dilute copper-cobalt alloys.
Experiments were designed to exploit the capability of the
differential reflectometer to measure the difference in
solute content between two alloys based on an altered elec
tronic structure.
Composition modulation was performed in order to deter
mine the effects that solid solutions of cobalt in copper
have on the optical properties of the dilute alloys. It has
been observed that the energy of the threshold electronic
transition in copper at 2.2 eV has no dependence on the
cobalt solid solution content. This lack of dependency has
IX

been compared to similar results for nickel in copper, a
phenomenon which has been treated by others with the theory
of virtual-bound-states. It has also been determined that
the strength of the differential reflectometric signal has
a linear dependence at 2.2 eV on the difference in solid sol
ution cobalt content between une two samples measured by this
method.
Differential reflectometry was then applied to the study
of aged copper-cobalt alloys. Three alloy compositions were
used in these experiments: Cu-2.7 a/o Co, Cu-2.0 a/o Co, and
Cu-1.0 a/o Co. The precipitation reaction was observed for
all compositions at three aging temperatures: 600C, 500C,
and 400C. Additionally, Cu-2.7 a/o Co was aged at 550C and
450C. The precipitation reaction was followed by means of
the increase in the strength of the optical signal which re
sulted from a decrease in the matrix solute content as the
reaction progressed. A site saturated, diffusion controlled
growth rate was observed for all compositions. The precipi
tates have been found to decrease the strength of the optical
signal in a way which is linearly dependent on the volume
fraction of the precipitates, thus allowing a measure of the
microstructural state of an alloy to be obtained from mea
surements of the optical properties.
Microhardness measurements were performed on these aged
alloys to provide an independent verification of the optical
results. These microhardness measurements were in good tem
poral agreement with the optical measurements of this work
x

and with the results of previous measurements of mechanical
properties of aged copper-cobalt alloys.
xi

CHAPTER 1
INTRODUCTION
The color of alloys of metals has from ancient times
been recognized as being influenced by the composition of
the alloys. Artisans of many cultures surely experimented
with combinations of metals in order to achieve the color
they desired in the pieces they created. It was not until
this century, however, that the link between the composition
of an alloy and its color was understood. ^ With the develop
ment of solid state physics came the realization that the
optical properties of metals and alloys are a reflection of
2
their electronic structure, specifically the valence band.
One instrument which has been successful in measuring
the optical properties of alloys in order that electronic
structure could be better understood is the differential
3 4
reflectometer. With this instrument, the electronic
structures of copper alloys containing multivalent sol
utes, 5''7 copper-nickel,7 copper-gold,5 noble metal al
loys,5' and nickel-based alloys^have been investigated
for composition dependence. In addition the effect on the
electronic structure of the arrangement of constituents
within alloys has been explored in studies of long range
11 12
order and short range order. Finally, the removal of
1

2
an element from an alloy has been observed in experiments
dealing with dezincification in brasses.1^
Precipitation from a solid solution is a decomposition
from a metastable one phase system to a two phase system.
This reaction is characterized by the rejection of solute
atoms by the matrix in order that a second phase be formed.
This rearrangement of solute within the alloy would be ex
pected to change the physical properties of the alloy. This
is indeed the case. The measurement of electric,14,15 mag
netic, ,17,18 thermal,19 and dimensional properties^> 21
have often been used to follow the course of a precipitation
reaction. The use of these methods exploits a particular
sensitivity to some aspect of the physical changes occurring
during a precipitation reaction. None of these methods can
provide a complete description of the phenomenon. However,
differential reflectometry has the capability, because of its
extreme sensitivity to composition, of following a precipi
tation reaction from start to finish. This work will be
devoted to the study by differential reflectometry of preci
pitation in dilute copper-cobalt alloys.
In the next chapter, a review of the literature is
presented in three sections. The first section deals with
the phenomenon of precipitation in a general way. In this
manner, some understanding of this solid state reaction
can be reached before the specific system of dilute copper-
cobalt alloys is presented in the second section. A short
analysis of the methods used for studying precipitation in

3
this system will also be presented here. The last section
of this chapter focusses on the optical properties of copper
and copper alloys. More specifically, the relationship
between the composition of copper alloys and its electron
band structure is explored.
Three types of experiments were performed in order to
accomplish the goal of this work. Firstly, microhardness
tests were performed on precipitation hardened alloys. Sec
ondly, optical measurements were carried out on samples
which were known to differ in composition only. Lastly,
optical measurements were performed on samples which had
experienced a precipitation reaction. The details of these
experiments and the justification for performing them in
this manner are given in the third chapter.
Presented in the fourth chapter are the results of
these experiments as well as a discussion of the findings.
Each set of results will be evaluated in terms of what
other researchers have found in their studies of precipita
tion hardening in copper-cobalt as well as in terms of how
the results compare against each other. In addition, a
section on the effect of cobalt on the electronic structure
of copper is presented.
The final chapter summarizes the findings of these
experiments.

CHAPTER 2
OBSERVATIONS CONCERNING PRECIPITATION
AND OPTICAL PROPERTIES OF ALLOYS
2.1 Precipitation; General
Since the end of the first decade of this century, when
22
Alfred Wilm first demonstrated the means by which certain
aluminum alloys could be strengthened, precipitation harden
ing has been used by metallurgists and materials scientists
to improve the mechanical properties of the alloys of many
base metals. Although aluminum-based alloys, particularly
with additions of copper and magnesium, have probably been
the most studied of all precipitation hardenable alloys,
precipitation heat treatments are commonly used in many
commercial alloys. Two notable examples are the addition
of copper to malleable cast iron and the addition of titan
ium and aluminum to both semi-austenitic stainless steels
and nickel-based superalloys.
Precipitation hardening is a process by which the mech
anical and physical properties of an alloy can be drama
tically altered. Performed under controlled conditions the
strength and hardness of an alloy can be considerably in
creased. For instance, in a commonly used copper-beryllium
alloy -- Cu-1.7 wt/o Be, 0.3 wt/o Co -- precipitation har
dening can produce an increase in tensile strength from
4

5
410 MPa to 1030 MPa while at the same time increasing the
hardness from 125 to 310 on the Vickers hardness scale.
Changes in physical properties are also manifested by alloys
during precipitation. In general, a significant increase
in electrical and thermal conductivity along with changes in
volume, magnetic properties, Hall coefficient and optical
properties can be observed during precipitation. What fol
lows is a simple description of phenomena which pertain to
precipitation and the methods by which they are studied.
Greater detail on particular subjects can be found else-
, 23-27
where.
The objective in producing a precipitation reaction is
to induce the nucleation and growth of a second phase from
a metastable solid solution. The reaction is expressed
in the following manner, a -* a + 6 where a is a solid solu
tion and 6 is the precipitated phase. Although the forma
tion of the second phase can be accomplished by changes in
pressure or additions of another element, precipitation is
most commonly carried out by the application of specific
heat treatments, the details of which are given below.
The requirements to produce precipitation hardening
(or age hardening) are that the alloying element is cap
able of achieving a solid solution, usually up to at least
a few percent, with the base metal and that the solubility
for the alloying element decreases with temperature. (In
fact, there is another definitive requirement in order for
precipitation hardening to be present, which is that the

6
alloy actually hardens as a result of the precipitation
reaction.) In Figure 2-1, a phase diagram for a hypothe
tical age hardenable alloy has been drawn. It can be seen
that the two requirements mentioned above have been met. To
achieve precipitation, an alloy, which contains a few per
cent (C) of element B is held at Ts, the solution heat
treatment temperature. This solution heat treatment allows
all of element B to exist in a solid solution of the a phase.
If the alloy is then quenched quickly enough to Tg, usually
room temperature, the alloying element B can be made to re
main in a metastable solid solution. In order to induce
precipitation, the alloy is given an isothermal aging heat
treatment at Ta. At this temperature, the metastable phase
decomposes into two phases, a and 8, approaching the com
position defined by the phase diagram. During this decom
position, the matrix phase a rejects B atoms which go to
form the 8 phase having a concentration C which conse
quently lowers the matrix concentration of element B to the
saturated state Ca. The amount of the second phase produced
is determined by the tie line established by the aging tem
perature. At the completion of the reaction, the percent
of 8 phase is
p pot
%8 = ^ x 100%- (D
The precipitation reaction is generally considered to
proceed in three stages: nucleation, growth, and coarsening.
A brief, qualitative overview of these processes is given

TEMP.
/
Figure 2-1.
Phase Diagram of Hypothetical Precipitation
Hardenable Alloy and Corresponding Free Energy
Diagram.

8
here in order to provide a basis from which the specifics
of the copper-cobalt precipitation reaction will be dis
cussed
When an alloy is held at a temperature at which its
solute composition extends beyond the solvus, the lattice
will reject solute atoms. As the solute atoms are rejected,
they will begin to form clusters. This is the first stage
of precipitation and is called nucleation. Thermodynami
cally, nucleation is driven by the difference in the volume
free energy of the solid solution and the volume free energy
of the decomposed system consisting of the precipitate
phase and the matrix phase which is still a solid solution,
though possessing a reduced solute content. Schematically,
this is shown in Figure 2-1. The a phase at c can be seen
to possess a higher free energy, Ga, than the free energy
of the decomposed system, Ga+B. If, as is the case of preci
pitation hardenable alloys, the solubility decreases with
temperature, then the difference in the free energies, AG,
will increase the farther the alloy is held below the sol
vus (the greater the undercooling). This increases the
nucleation rate and decreases the size to which a cluster
must grow before it becomes stable and capable of increas
ing its size through growth. In general it is held that
there are two "energies" which oppose the formation of
stable clusters: surface energy and strain energy. When a
cluster forms, it must eventually form an interface with
the surrounding matrix. Because surface energy is added

9
to the system with the creation of this interface, the
volume free energy difference, AG, driving the reaction
must be large enough to compensate for this additional
energy. Also, because the precipitates are composed of
atoms of a different size than the matrix and have a differ
ent lattice parameter than the matrix, they create strain
in the lattice. This strain energy must also be offset by
the volume free energy reduction.
Nucleation is also influenced by the number of sites
available for the formation of second phase particles. Be
cause of the difference in size of the atoms of the preci
pitates and the matrix, formation of the second phase is
favored at locations where strain can be readily accommo
dated, such as grain boundaries or dislocations. For this
reason, nucleation will normally occur more rapidly in a
fine grained or a heavily cold worked material where there
are many sites at which precipitates can begin to form.
The same forces which operate in the nucleation of
stable particles continue to operate during their growth.
That is to say, the driving force continues to be a reduc
tion in the volume free energy of the system with the prod
uct being a decomposed solid solution with precipitate
particles interspersed throughout the alloy. The creation
of new surface and the strain added to the system by growing
particles also continue to influence precipitate growth.
The balance between these forces will determine the shape
of the precipitates, such that they try to achieve the

10
lowest energy configuration. For instance, in the early
stages of growth small precipitates may form on planes
which have low strain but a high surface energy. As the
planes grow the surface energy becomes very large and the
precipitates may change their shape to spheres which pos
sess lower surface energy, but which also produce more
strain in the lattice. The stages intermediate to achiev
ing a final shape are called transition lattices.
In terms of composition, the growth of precipitates is
accomplished by a depletion from the matrix of solute atoms
from the concentration C, the supersaturated concentration,
to Ca, the concentration of solute atoms at the solubility
limit. The classic, phenomenological approach to this pro
cess finds that the time dependence of the matrix composi
tion is expressed as
C(t) = Ca + (C0-Ca)e(~t'/T } (2)
where C(t) is the solute concentration at time t, x is a
time constant, and n is dependent upon the particulars of
the growth process.
Although the kinetics of the precipitation reaction
can be very complicated, there are some rules that apply in
general to the reaction rate. Growth of the precipitate is
often controlled by the diffusion of solute atoms through
the matrix to the precipitate. For this reason, the preci
pitation rate is faster at higher aging heat treatment tem
peratures. In addition, because diffusion is controlled

11
by the number of vacancies, dislocations, and other lattice
defects, growth will normally occur more rapidly in an alloy
which has experienced a rapid quench, heavy cold work, or
radiation damage than in an alloy in which these conditions
are not present.
Coarsening refers to the increase in interparticle
spacing which has been found to occur during the final steps
of precipitation reactions. It is most easily described by
the familiar axiom of materials science, "Large particles
grow at the expense of smaller ones." In contrast to nucle-
ation and growth, which were driven by the lowering of the
volume free energy in going from a supersaturated solution
to a decomposed two phase system, coarsening is driven by a
reduction in surface energy. It is generally considered to
occur after all chemically-driven growth has stopped, with
no change in the volume fraction of second phase. Given
these considerations, it can be seen that coarsening is
also characterized by a decrease in the number of precipi
tates and an increase in the average particle size with time.
Precipitation is also characterized by the distribution
of the second phase throughout the matrix. In what is
known as general precipitation, the precipitate is distri
buted randomly throughout the matrix. The reaction occurs
simultaneously in all parts of the matrix. The result of
this is a uniform precipitate structure.
In contrast to this, localized precipitation is charac
terized by growth of precipitates at lattice defects or

12
grain boundaries. Similar to general precipitation, it
occurs simultaneously throughout the alloy; however, be
cause the precipitates form at defects, the precipitates
are distributed non-uniformly.
25
Finally, discontinuous precipitation is characterized
by the formation of second phase in random parts of the
alloy at random times. Discontinuous precipitation is as
sociated with the movement of an interface, such as a grain
boundary during recrystallization and grain growth.
The effect of precipitation on mechanical properties
depends on several microstructural aspects, such as the
extent of the solid solution, the coherency of the precipi
tate, the dispersion of the second phase, and recrystalliza-
24
tion. All mechanical properties are affected by these
microstructural factors; however, for the reason that micro
hardness tests were performed for this work, the changes
in hardness experienced by an alloy undergoing a precipita
tion reaction will now be considered. In Figure 2-2, a
composite hardness curve is depicted with the contributions
from each microstructural factor also shown. The details
of this graph are discussed below.
Solid solution hardening takes place because the differ
ence in size between the atoms of the host metal and the
solute atoms necessitates the accommodation of solute atoms
at places where strain is introduced the least. As mention
ed earlier, this means that solute atoms collect at defects
in the lattice such as dislocations and grain boundaries.

HARDNESS
Quenched
TIME Carb. units]
gure 2-2. Composite Hardness Curve. (Ref. 24)

14
By collecting at dislocations, solute atoms pin them and
prevent them from moving during an applied stress. In addi
tion, solute atoms can either replace solvent atoms on regu
lar lattice sites (substitution) or they can occupy sites
between lattice positions (interstitial). In either case,
the solute atom will create strain in the lattice, which
impedes the movement of dislocations. These mechanisms
account for the increase in hardness upon the addition of
solute atoms to an alloy. During a precipitation reaction,
solute atoms are removed from the matrix in order to form
the precipitates. Thus as shown in Figure 2-2, as the aging
of the alloy progresses solid solution hardening decreases.
The most important contribution to the hardening of an
alloy during precipitation comes from coherent precipitates.
In the case of general precipitation the first precipitates
to form are coherent with the lattice, that is, the lattice
of the precipitate matches point for point the lattice of
the matrix. Such clusters of a relatively large number of
atoms of different size than the matrix exert strain which
extends well beyond the immediate vicinity of the precipi
tates. As long as coherency is maintained, the larger the
precipitate becomes, the more strain is exerted on the
lattice. The interaction of a moving dislocation with this
strain field requires more energy for movement than if
there were no precipitate. Thus a dramatic increase in
hardness is seen in Figure 2-2 upon the formation of coher
ent precipitates. As the decomposition proceeds, the

15
precipitates become so large as to require dislocations to
maintain a limited amount of coherency with the lattice.
27
This is called a "quasi-coherent" state and marks the
beginning of the formation of an interface. As the preci
pitation continues, the particles become large enough to
require a definite interface between the growing precipitate
and the matrix. At this stage, the precipitate is com
pletely incoherent with the matrix, and dislocations at
the interface between the particle and the matrix accommo
date the strain produced by the precipitate. Thus, the
effect of the precipitate on the movement of dislocations
is diminished, and there is consequently a dramatic loss
in hardness.
Dispersion hardening arises from the fact that at the
beginning of the process there are many particles spaced
fairly close together. As precipitation continues, coar
sening can occur with larger particles growing at the ex
pense of smaller ones, causing the precipitate structure to
evolve to one in which there are fewer particles spaced
farther apart. This process accounts for the slight rise
in hardness followed by the slight softening seen in Fi
gure 2-2.
The final factor that affects the composite hardness
curve is recrystallization of the alloy. This is a compli
cated phenomenon, which itself is influenced by many factors.
These include aging temperature, aging time, amount of
deformation, composition, and grain size. It is necessary,

16
but hardly sufficient, to state that if recrystallization
occurs during aging, the result will always be a loss of
hardness brought about by the replacement of deformed, and
therefore hard, grains by undeformed, softer grains.
Changes in the physical properties of alloys undergoing
precipitation have long been observed and used as tools to
measure the kinetics of the reaction and to help to deter
mine the mechanisms by which the reaction takes place. Al
though these measurements are indirect, at the very least,
the measurement of physical properties yields the initial
state of the alloy, the changes that occur during the reac
tion, and the point at which the reaction is complete.
Measurements of resistivity, saturation magnetization,
Curie temperature and density or volume are common techni
ques in studying precipitation. These methods fall into
two categories. Firstly, there are those which follow the
growth of the second phase, as in the case of a magnetic
second phase precipitating from a non-magnetic matrix.
Here, measurements of magnetic saturation or coercive force
are used in determining the details of the reaction. Sec
ondly, there are studies which follow the depletion of
solute from the matrix phase. This type of experiment
might be used in the case of a magnetic matrix phase and a
non-magnetic second phase, where the rise in the Curie
temperature could be measured to determine the rate at
which solute was being removed from the matrix by precipi
tation .

17
Another example, where the removal of solute is meas
ured, is electrical resistivity measurements. Figure 2-3
shows a resistivity curve for a hypothetical alloy. As is
shown, the resistivity of the precipitation hardenable
alloy is dependent on two variables, the depletion of the
solid solution and the coherency strains produced by the
precipitate. Here, unlike the case of hardness where the
extent of coherency was the dominant factor, the solid
solution depletion is more important. As solute atoms are
rejected by the matrix in order to form second phase par
ticles, the number of electronic scattering centers is re
duced, thus lowering the resistivity. The extended strain
field of coherent particles acts to increase the resistiv
ity of the alloy. However, as the precipitates grow and
become incoherent, the lattice returns to a more relaxed
state and the resistivity consequently decreases.
2.2 Precipitation in Dilute Copper-Cobalt Alloys
Interest in the copper-cobalt system as an example of
a precipitation hardenable alloy, although never as intense
as in the more commercially important aluminum age harden
able alloys, has nonetheless been steady.16,28-48 one of
the reasons for this lies in the simplicity of the copper-
cobalt system, the phase diagram of which can be seen in
Figure 2-4.49 The copper-cobalt phase diagram shows a
miscibility gap with a peritectic transformation on the

RESISTIVITY
Quenched
TIME Carb. units]
Figure 2-3.
Composite Curve showing the Effect of Precipitation on
Electrical Resistivity. (Ref. 24)

19
Figure 2-4.
Phase Diagram of Copper-Cobalt System.
(Ref. 49)

20
copper-rich side. The peritectic temperature is 1110C,
at which is also found the maximum solubility for cobalt in
copper. It is this region of solid solubility on the copper-
rich side of the phase diagram to which attention is focus
sed when precipitation hardening is being considered. It
is evident that this region possesses the primary condition
necessary to achieve age hardening, that is, a decreasing
solubility for cobalt with decreasing temperature. Solu
bility drops from about 5.5 wt/o at 1110C to below 0.1
wt/o at 500C. Experiments conducted on dilute copper-
cobalt alloys have generally employed alloy compositions
ranging from slightly below 1.0 wt/o to about 3.0 wt/o.
The range of aging temperatures investigated extends from
400C to 700C, concentrating attention around 600C. The
fact that these alloys age at such moderately high tempera
tures is advantageous for the experimenter because the al
loys will not age at room temperature.57
The precipitate that forms in these alloys upon aging
can be seen by the phase diagram to be a cobalt solid sol
ution containing approximately 10 wt/o copper. This pre
cipitate, containing such a large amount of cobalt, is
ferromagnetic.'27-29,50-51 The precipitate has been found
to possess an FCC structure and to form as a spherical par
ticle.17'51-52 No intermediate lattices or shapes have
been noted.54 The dominant precipitation mode is a general
precipitation, although some localized and discontinuous
precipitation have been observed.27'55'47 Only in the

21
extremely overaged condition has a shape change in the
precipitate been observed,17 that being from spheres to
plates.
As stated above, the cobalt-rich precipitate which forms
during aging contains enough cobalt for the precipitate to
possess ferromagnetism. Prior to coalescence, cobalt
atoms do not have a ferromagnetic character due to the ab
sence of a sufficient exchange interaction with neighboring
cobalt atoms.^'^ Thus as precipitation occurs the magne
tic state of the alloy changes from diamagnetic to ferro
magnetic. Becker1^ used the term "superparamagnetic" for
the latter condition. As the precipitates grow, the magne
tic coupling of the cobalt atoms becomes stronger and the
saturation magnetization of the alloy becomes larger. From
this, Becker1^ and others29-31,33,36,41,44 were able to
deduce the volume of precipitate formed, the radius of the
average precipitate, and the volume fraction of precipitate.
From magnetic measurements on a Cu-2% Co alloy aged at
600C, Livingston and Becker^9 concluded that all of the
cobalt was precipitated during the first few minutes of
aging and that subsequent growth of the precipitates took
place by coarsening, a process in which the total volume
and the volume fraction of precipitate remained constant
after the first few minutes of aging. They also concluded
that the radius of the precipitate increased linearly with
the logarithm of aging time. This same conclusion was
reached by Witt and Gerold^7 for copper alloys containing

22
1.4%, 2.0%, and 3.0% cobalt when aged at 600C. However,
in the same experiment, analysis of their data reveals that
for Cu-0.6% Co the volume fraction increased linearly with
time up to 32 hours of aging at 600C.
It was also through the use of magnetic measurements
that experimenters concluded that the precipitates were
spherical.17>55 This conclusion was reached on the basis
of only very slight magnetic anisotropy observed in the
aged single crystal alloys. Finally, the lattice of the
cobalt-rich precipitate has been found to be 2% smaller
than the lattice of the matrix.55
In another study of precipitation in copper-cobalt,
Servi and Turnbull58 aged the various alloys at temperatures
such that the solute composition did not deviate much from
equilibrium. This was performed in order to determine the
effect of undercooling upon the nucleation rate. By follow
ing the change in resistivity, they obtained a measure of
the volume fraction transformed through the use of Equation
3 and the relation
X
C C(t)
c ca
(3)
where X is the volume fraction transformed. Although the
transformation was observed to begin very shortly after
aging was started, analysis of the data indicates that full
transformation was never achieved, in contrast to what was
observed in the magnetic studies cited above. The data
did, however, confirm the growth of spherical precipitates.

23
A more direct method of observing precipitation in
copper-cobalt alloys has been carried out by a number of
researchers.31-35 This is the observation of coherency
strains in the lattice caused by the precipitates and detec
ted by means of transmission electron microscopy (TEM).
The TEM theory of diffraction contrast was used to obtain
particle diameters from the "double D" diffracted image,
which is the signature of spherical, coherent particles.
Here, as in the case of magnetic measurements, the radii of
growing particles increased linearly with the logarithm of
aging time.33 Observations that the number of precipitates
seen in the micrographs decreased with time were attributed
to coarsening,33,34 although the data were never quantita
tively compared to coarsening theory. Likewise, no quan
titative comparison was made between this work and previous
magnetic measurements, which had also indicated growth by
coarsening.
TEM observations have indicated in quenched alloys
that a complete solid solution with no formation of precipi
tates is possible to achieve. Phillips and Livingston31
have shown that no precipitates were observable in solution
heat treated and quenched alloys. They also noted that
precipitates were seen shortly after the aging heat treat
ment was begun.
As was discussed in Section 2.1, mechanical properties,
such as hardness, yield strength, and tensile strength, tend
to rise from the onset of precipitation, go through a peak,

24
which is influenced to the greatest extent by coherency of
the precipitate, and then decline as the alloy softens when
the precipitates grow too large to maintain their coherency.
Softening is also the result of the coarsening of the pre
cipitate structure when the interparticle spacing becomes
too large to prevent easy motion by dislocations.
Copper-cobalt is not an exception to these mechanisms.
In Figures 2-5 and 2-6, data from Livingston and Becker^^
and Livingston^O are presented. In these curves are dis
played characteristics which are typical of a precipitation
reaction. In Figure 2-5,29 data for a Cu-2% Co alloy aged
at 600C are presented. An increase in hardness is observed
as the alloy is aged up to approximately fifteen hours, at
which point a peak hardness is obtained. Past this peak,
the loss of coherency of the precipitate with the lattice
causes softening to occur. In Figure 2-6,30 yield strength
and hardness data for a Cu-2% Co alloy aged at 600C, 650C
and 700C are presented. Here, several observations can be
made which reveal the characteristics of the precipitation
process in copper-cobalt. Not only are peaks seen to occur
at each aging temperature in both yield strength and hard
ness, but it is also evident that as the aging temperature
is increased, the time for each mechanical property to reach
its peak is reduced. This is a consequence of the increased
diffusion rate as temperature is increased. The faster
diffusion occurs, the faster the precipitates can form.
Finally, as the aging temperature is reduced, the higher

25
Quenched MINUTES
Figure 2-5- Hardness versus Time for Cu-2.0% Co Alloy Aged
at 600C. (Ref. 29)

0.5% YIELD STR. CKSn
26
100
A.Q. 1
100
MINUTES
10000
Figure 2-6. Yield Strength and Hardness versus Tine for
Cu-2.0% Co Aged at Various Temperatures.
(Ref. 30)
HARDNESS EDPN3

27
the peak value of the yield stress and the hardness becomes.
This was reported by Livingston^O to be due to the reduced
solubility at the lower temperature, which leads to a great
er volume fraction of precipitate.
In Table 2-1 data are compiled from studies of the me
chanical properties of copper-cobalt alloys. The table shows
the aging temperature and length of time required to reach a
peak in the particular property investigated. Most studies
indicated that the higher the temperature at which the alloys
were aged, the faster the growth of the precipitate. Perovic
and Purdy,47 in their investigation of precipitation in these
alloys aged from 400C to 800C, found that the precipitate
had a growth rate maximum between 550C and 600C.
There is some controversy concerning the length of time
necessary to bring the precipitation reaction in this system
to completion. This may be due to the fact that each of the
methods used have sensitivities that are particular to cer
tain aspects of the reaction. For example, whereas TEM does
allow a direct observation of precipitate formation, compo
sitional changes can not be determined quantitatively. No
statistical methods have been applied which reveal whether
the growth of precipitates is due to depletion of matrix
solute or due to coarsening of the precipitate structure.
Because the precipitate in this system is ferromagnetic,
magnetic measurements provide a method of following the
growth of the precipitate. The model of Becker-^ has gener
ally been used to quantitatively determine the average radius

28
Table 2-1. Time to Peak Property
for Copper-Cobalt Precipitation
Aging
Temp.
% Co
Measurement
Time to
Peak (hr)
Ref
250 C
3.2%
Hardness
> 1000
28
37 5 C
3.2%
Hardness
> 1000
28
550 C
2.0%
Yield Strength
160
30
3.2%
Hardness
175
28
600C
2.0%
Yield Strength
16
30
2.0%
--
12
45
2.0%
--
11
46
3.1%
TEM (Coherency strains)
12
33
650 C
2.0%
Yield Strength
1.5
30
2.0%
CRSS
4.0
44
3.1%
TEM (Coherency strains)
1.5
33
3.1%
Yield Strength
1.5
34
700C
2.0%
Yield Strength
0.5
30
2.0%
CRSS
1.0
44
3.1%
TEM (Coherency strains)
0.7
33
3.2%
Hardness
3.0
28

29
of the precipitate and the volume fraction transformed. How
ever, this model assumes that no precipitate is larger than
10 nm and that there is an equal number of particles of each
size in the distribution. The validity of these assumptions
has not been independently established. Furthermore, the
saturation magnetization continues to increase as the preci
pitates coarsen,16 and therefore, it is difficult to deter
mine with precision when equilibrium has been reached.
Measurements of the electrical resistivity of alloys are
useful for following the depletion of solute from the matrix,
and have been used16 in following the nucleation and growth
of the second phase in this system. In following the deple
tion of solute from the matrix, however, this method offers
little information about the precipitate and its effects on
the physical properties of the alloy.
Measurements of the mechanical properties during preci
pitation are valuable in determining the microstructural
state of the alloy, particularly whether or not the precipi
tate is coherent with the matrix. However, these methods
provide only qualitative information about the extent of the
transformation or the fraction transformed.
In contrast, differential reflectometry offers a method
that can be sensitive to both the changing solute concentra
tion of the matrix and the formation of the second phase.
This sensitivity is not limited fundamentally as is the case
in the other experimental techniques.
To conclude, the investigations of precipitation in the

30
copper-cobalt system have revealed a fairly typical reaction.
Although there is some discrepancy in the length of time mea
sured for the reaction to achieve a fully transformed state
-- that is, the point at which microstructural changes are
due only to coarsening -- it has been observed that the pre
cipitate produced is a sphere and has no intermediate shapes.
Furthermore, the precipitates form throughout the matrix
with some localized precipitation at the grain boundaries.
The changes in mechanical properties during aging likewise
have been seen to be representative of an age hardenable
alloy. The ascent-peak-descent curves seen in the graphs
of hardness vs. aging time for these alloys are the unmis
takable fingerprint of precipitation. The generally good
agreement between the data of these various research efforts
reveals a well characterized system. These data also pro
vide a backdrop against which the hardness tests described
in this work can be compared.
2.3 Optical Properties of Copper and Copper Alloys
The effects of solute additions on the mechanical prop
erties of metals have already been discussed. Some change
in the yield strength, tensile strength, ductility, hardness,
and impact strength is the inevitable consequence of altering
the composition of a metal. Some changes may be beneficial
as in the case of adding zinc to copper, thus producing an
alloy that is both stronger and more ductile than pure

31
copper;or the effect of alloying may be detrimental such
as the brittleness that is produced when a small addition
of iron is made to copper.57
Physical properties are also very much a function of com
position. Upon addition of another element to a pure metal,
its melting point, density, electrical and thermal conduc
tivity, magnetic and optical properties are affected. These
property changes upon alloying are the direct result of an
altered electronic band structure. This is particularly
true of optical properties. In this section, the relation
ship of the optical properties of copper to its band struc
ture will be considered. In addition, attention will be
directed to the response of the band structure, and hence
optical properties to composition changes and to methods by
which these changes have been measured.
In Figure 2-7, the band diagram of pure copper is pre
sented. 58 Because the electronic configuration of copper is
3dl4sl, it is expected that the d-bands of copper would lie
entirely below the Fermi energy. This is indeed the case,
with the top of the d-bands lying slightly more than 2 eV
below the Fermi energy. The partially filled s-bands and
p-bands are labelled in the figure. When photons of suffi
cient energy are incident upon a metal, electrons from
filled states are raised into unoccupied states above the
Fermi energy. The result of these direct interband transi
tions can be seen in Figure 2-8,1 where curve A depicts the
optical reflectivity for pure copper as a function of

Energy
U>
ro
Figure 2-7.
The Band Diagram of Copper (Ref. 58).

33
Weenlange
Figure 2-8.
Reflectance Spectra for Copper and Various
Brasses (Ref. 1) .

34
energy. It is evident that at energies below 2.2 eV the re
flectivity is close to 100%. However, at 2.2 eV light is
absorbed initiating the first interband transition. These
transitions, which occur from the upper d-bands to s-bands
and p-bands at the Fermi energy, are believed to occur near
the L symmetry point.^ These transitions also give rise to
the characteristic salmon pink color of pure copper, since
they produce a much lower reflectivity in the green and blue
regions of the spectrum than in the yellow and red regions.
Other transitions which influence the reflectivity of copper
occur between the Fermi energy and the s-states (L21 to )
around 4.2 eV and between the lower d-bands and the Fermi
energy at approximately 5.5 eV.^9
The influence of solute additions upon the reflectivity
of copper can also be seen in Figure 2-8, which presents re
flectivity spectra for various brasses. There is a drop in
reflectivity in the energy range of 1.8 2.2 eV, as a result
of the dependence of reflectivity upon resistivity expressed
by the Hagen-Rubens relation
R = 1 2(up )h (4)
o
where R is the reflectivity, u is the frequency of the inci
dent radiation and pQ is the dc resistivity. Since the addi
tion of solute atoms increases the metal's resistivity by
increasing the number of scattering centers, the reflectiv
ity is consequently reduced. Although this empirical rela
tion was discovered before there was any knowledge of band

35
diagrams and interband transitions, it still holds for those
regions where no interband transitions occur.
In addition to this decreased reflectivity, the transi
tion which occurs at 2.2 eV is shifted to higher energies as
the zinc concentration in the brass is increased. This in
crease in the threshold energy causes the change in color in
brasses from red at low zinc concentrations to yellow at high
zinc concentrations. It has been found that upon alloying
with elements having a valence of greater than one, that the
subsequent energy increase of the threshold transition above
2.2 eV is caused by a rise in the Fermi energy due to the
addition of extra electrons from these elements and to a nar
rowing and raising of the d-bands.5>60 The earliest attempt
to explain the transition energy increase upon adding ele
ments of higher valence than the host metal was proposed by
Mott61'62 j_n 1935 in the rigid band model. Although the
model did correctly predict the rise in the Fermi energy, it
did not predict the shift that occurs in the d-band upon al
loying. This led to a prediction of a larger shift in the
transition energy at 2.2 eV than was seen experimentally.
Calculations made by Bansil et al.60 accounted for the shift
upward in the d-bands as well as the Fermi energy and there
fore the smaller shift in the threshold energy.
Hummel's laboratory5>6,7 has experimentally verified
that the shift in the transition energy at 2.2 eV is smaller
than that predicted by the rigid band model. Using a dif
ferential reflectometer, the energies of electronic

36
transitions were measured for copper solid solutions contain
ing various multivalent alloy additions. It was found that
the transition energy was a function of composition (see
Figure 2-9).5 Up to 1% solute there is no change in the
threshold energy. Past 1% solute, the transition energy is
a linear function of composition. It is evident that Figure
2-9 can also be used as a calibration curve, so that if the
transition energy of an unknown alloy is measured, then the
quantity of solute in that alloy can be determined. Thus, it
is possible to use optical measurements as a means of deter
mining the solute concentration of a binary copper alloy.
In the case of multivalent solutes in copper, of course, this
method would only be useful for solute concentrations above
one percent.
So far, the discussion has been directed only at alloys
of copper which contained solutes having two or more valence
electrons, where the increase in the Fermi energy could be
understood on an intuitive basis. The situation becomes
more complex when transition elements are added to copper.
As an example of a copper-transition metal alloy, copper-
nickel has been studied in great detail,7< 63-66 because they
display complete solid solubility. Since nickel has an un
filled d-band -- its electronic configuration is 3d^4s^ --
the intuitive expectation is that when nickel is added to
copper, the copper 4s electron might supply the extra elec
trons necessary to fill the d-band of nickel. It would then
be expected that the Fermi energy of copper would be lowered,

R,b:
Figure 2-9. Composition Dependence of Copper Threshold Transition.
(Ref. 5)

38
and accordingly the threshold energy for direct interband
transitions would be decreased. These are the predictions
of the rigid band model.62 Experimentally, however, it has
been determined by means of optical measurements7'63 and pho
toelectron spectroscopy63 that the transition energy at 2.2
eV in copper is unchanged by solute additions of nickel. In
stead, evidence indicates that the nickel d-bands remain in
dependent of the copper d-bands and that they retain their
character within the matrix. These nickel d-bands are found
to exist within one electron volt of the copper Fermi energy
and become the source of low energy transitions. In Figure
2-10, the reflectance spectra from Seib and Spicer63 for pure
copper, Cu-13% Ni, and Cu-23% Ni are presented. In contrast
to the reflectance spectra for copper-zinc alloys, there is
no change in the transition energy at 2.2 eV as nickel is
added to copper. There is a drop in reflectivity below 2.2
eV which is caused by transitions from the nickel d-bands to
the Fermi energy, thus decreasing the magnitude of the 2.2 eV
transition. These results verified the proposals of Friedel67
and Anderson66 who had predicted this type of behavior
known as virtual-bound-states -- for transition elements in
copper. It is clear that there is no composition dependence
of the 2.2 eV transition, such as was the case in copper with
multivalent solutes. Using photoemission Seib and Spicer63
did find that the band width of the virtual-bound-states of
nickel did increase as the amount of nickel increased.
Using differential reflectometry, Hummel et al.7 also

REFLECTANCE
39
Figure 2-10. Reflectance Spectra for Copper and Two
Copper-Nickel Alloys. (Ref. 63)

40
found no shift in energy of the threshold transition at 2.2
eV in copper-nickel alloys. The alloys studied in this work
ranged from copper containing less than one percent nickel to
greater than twelve percent nickel. This result, which con
firmed the existence of virtual-bound-states in copper-nickel
alloys, provided no strict method of determining the solute
concentration of an unknown alloy. It was noted that the
"sharpness" of the peak in the differential reflectogram as
sociated with the 2.2 eV transition did possess a composition
dependence. However, no definitive composition dependence
was observed at 2.2 eV as in the case of copper containing
multivalent solutes.5'^/7
Beaglehole and Kunz^9 did find a composition dependence
on the difference in reflectivity of various dilute copper-
nickel alloys. Their data showed a linear relationship be
tween the difference in reflectivity at 628 nm and the dif
ference in the composition of the alloys measured, which
agreed with that of other investigators.66,VO,71 This lin
ear relationship was found to be valid up to approximately
20% solute, demonstrating that optical measurement might be
used to determine the composition of an alloy containing a
transition element.
For the reason that this work centers on optical inves
tigations of precipitation in copper-cobalt alloys and that
the precipitates in this system are a cobalt solid solution
approximately 90Co-10Cu it is necessary to consider
the optical properties and the electronic structure of cobalt.

41
Cobalt is a transition metal and resides next to nickel in
the periodic table. Its electronic configuration is 3d74s2.
Again, as in the case of nickel which has an unfilled d-band,
the electronic band structure of cobalt is found to possess
d-bands which contain both filled and unfilled states and
which lie within a few electron volts of the Fermi energy.72
"76 a high density of states, therefore, exists just above
and just below the Fermi energy. Although quantum mechan
ical considerations can not be put aside, for all practical
purposes, this large density of states around the Fermi en
ergy can be considered to be a continuum. This implies
firstly that electronic transitions can be stimulated by in
cident light at low energies, and secondly that an incre
mental increase in the energy of the incident light will be
matched by an increase in the number of transitions stimu
lated. This can be seen in the reflectivity curve for co
balt (Figure 2-11), which was calculated from optical con-
tants determined by Johnson and Christy.77 The reflectivity
is already below 80% at 1 eV, due to low energy optical ab-
sorbtion which stimulates d-band transitions. Also seen is
a monotonic decrease in reflectivity caused by the stimula
tion of a greater number of transitions as the energy of the
incident light is increased. In addition there is no sharp
change in the reflectivity in the range of 1 eV to 6 eV in
dicative of interband transitions or plasma resonances.

80
70
40
J I I 1 1
1 2 3 4 5 6
ENERGY C*V1
Figure 2-11. Reflectivity Spectrum for Cobalt as Calculated from
Measurements of n ana k by Johnson and Christy (Ref. 77).

CHAPTER 3
EXPERIMENTAL PROCEDURE
3.1 Experimental Approach
The experiments comprising this work on Cu-Co alloys
fall into three categories. Firstly, differential reflec-
tometry was performed on samples to establish spectra
solely on composition differences, hereafter known as com
positional modulation. Secondly, differential reflecto-
metry was performed on samples which had been given various
aging heat treatments. Finally, microhardness testing was
performed upon samples to study the change in that mechan
ical property upon precipitation.
The purpose of performing the compositional modulation
experiments was twofold. First, it was necessary to obtain
spectra which were produced due specifically to composition
differences between two samples. In the aging experiments
carried out on the differential reflectometer, spectra
were to be produced by the difference between an aged and
a solution heat treated sample. For reasons that have al
ready been described, the aged sample would have less co
balt in the alloy matrix. Thus at least some of this spec
trum would be due to composition differences between the
43

44
aged and the unaged samples. By having composition modula
tion spectra, it becomes possible to identify which part(s)
of the differential reflectometry spectra in the aging ex
periments were due to composition differences and which
part(s) were due to some other aspect of aging which would
produce a change in the optical properties of the alloys.
Second, by performing compositional modulation exper
iments, it is possible to obtain information about the
effects of additions of Co upon the electronic structure
of Cu. Although somewhat limited by the small solubility
of Cu for Co, the predictions of the virtual-bound-state
theory vs. the rigid band model could be investigated.
As was discussed in the last chapter, the changes in
hardness that occur in an alloy during a precipitation reac
tion are well documented and well understood. As has al
ready been discussed, hardness tests provide a clear, if
indirect, method by which the kinetics of the precipitation
reaction and the microstructural changes involved in that
reaction can be interpreted. For this reason, microhard
ness tests were chosen as a method against which the results
of the optical data could be compared and contrasted.
3.2 Alloy Preparation
All alloys used in these experiments were produced by
combining appropriate amounts of Cu-2.7 a/o Co powder and
pure Cu powder. The powders were blended and placed into

45
a graphite crucible for melting. A sodium borate flux was
used to protect the melt from oxygen contamination. Because
of the very narrow alpha plus liquid phase field (See Fi
gure 2-4) segregation upon solidification was deemed not
to be a problem and the ingots were allowed to solidify in
the furnace. Upon removal from the crucible, each ingot
was cleaned of any remaining flux and dipped for a few se
conds into an etchant (5:1 nitric acid:water) to remove
any surface contaminants. Each ingot was then rolled by
50%, recrystallized under vacuum at 350C for one hour,
and rolled again by approximately 33%. Each ingot was then
placed in a graphite crucible and covered with sodium bor
ate flux and given a solution heat treatment at 100UC for
approximately 70 hours. The ingots were then quenched in
iced brine to complete the solution heat treatment. The
ingots were then cleaned by etching and cut on a diamond
2
wheel to a size of approximately 0.25 cm for differential
reflectometry and microhardness testing. A few pieces
were selected at random and tested on the differential
reflectometer for compositional inhomogeneities. This was
done by illuminating only one sample in the differential
reflectometer. Any inhomogeneities in the sample would
produce a non-zero signal in the differential reflectometer
output. None could be detected. In Tables 3-1 and 3-2,
those alloys used in the compositional modulation and aging
experiments are listed, respectively.

46
Table 3-1.
Table 3
Alloys Used in Composition Modulation
Experiments
Cu
- 2.
7
a/o
Co
Cu
- 2.
5
a/o
Co
Cu
- 2.
0
a/o
Co
Cu
- 1.
5
a/o
Co
Cu
- 1.
0
a/o
Co
Cu
- 0.
5
a/o
Co
Pure
Cu
-2. Alloys Used in Aging Experiments
Cu 2.7 a/o Co
Cu 2.0 a/o Co
Cu 1.0 a/o Co

47
3.3 Differential Reflectometer
The differential reflectometer is a kind of optical
spectrometer, the output of which is a normalized differ
ence in reflectivity of two samples as a function of wave-
length, AR/R vs A. Originally conceived to experi
mentally determine the shift in energy of interband tran-
5 6 7
sitions that occur upon alloying, ' the differential
ref lectometer has proven successful in studying long1"*-
12
and short range ordering, dezincification of alpha
13
brasses, thickness and formation kinetics of corrosion
7 8
products, and in situ studies of the corrosion of Cu and
Cu-Ni alloys.7^
The differential reflectometer has been demonstrated
to be very sensitive in detecting small differences in com
position. Compositional differences as small as 0.05 a/o
8 0
have been detected in selected applications. It was the
aim of this work to exploit this capability in order to
detect changes in composition of an alloy matrix as preci
pitation occurred.
A detailed description of the differential reflecto-
3 4
meter has been given elsewhere. Only a brief descrip
tion of its functions will be given here, in conjunction
3
with Figure 3-1.
The usable output of the xenon light source lies in
the range of 200-800 nm. This light enters a double scan
ning monochromator, which for all experiments in this work

Light Source
Monochromator
Photomultiplier
Output
4^
CD
Figure 3-1. Schematic of Differential Reflectometer. (Ref. 3)

49
was operated at a scan rate of 200 nm/min. After exiting
the monochromator, the beam is reflected from a flat mirror
to an oscillating mirror which focusses the beam at near
normal incidence alternately on each sample. The spot
2
size of the beam on each sample is approximately 2 X 2 mm .
Once reflected from the samples, the beam is focussed by
a fixed mirror onto a ground plane of fused quartz causing
the light to diffuse upon the face of the photomultiplier
tube (PMT) to quash any effects caused by the oscillating
light beam. The amplified signal of the PMT is divided
into two channels, one of which is a low pass filter which
yields the average reflectivity, R = (R^+R^)/^. The other
channel containes a lock-in amplifier where the difference
in reflectivity, AR = R^-R-^ s produced. A ratio of these
two signals is made and is used as input for the y-axis of
an x-y recorder. The x-axis input is connected through a
variable resistor to the drive of the monochromator, the
result being a spectrum of AR/Rvs. A.
In order to maximize the signal, the two samples anal
yzed in the differential reflectometer must be mounted as
close to each other as possible. This is achieved by
grinding a flat surface on each sample and holding them
together in a thermosetting metallurgical mount. After
polishing, the mount is clamped onto a stage in the diff
erential reflectometer. The stage is capable of being
moved vertically, by which the beam can be centered, or

50
horizontally, by which different areas along the juncture
of the samples can be studied. In most cases, three such
areas were measured.
3.4 Polishing Procedure
Each sample studied in the differential reflectometer
was prepared in tne following manner.
1. The two specimens -- either of differing compo
sition or differing heat treatment -- were
mounted adjacent to each other in a quick setting
polymeric material.
2. In order to bring the surfaces of both specimens
into the same plane, the sample was ground on a
grinding wheel using 180 grit paper with fil
tered kerosene as a lubricant.
3. The sample was then ground by hand using succes
sively finer grits 240, 320, 400, 600 -- with
filtered kerosene as a lubricant.
4. Final polishing was performed with 1 micron dia
mond paste on a felt cloth using an oil base
lubricant.
5. The sample was then rinsed in methanol, dried
in a stream of desiccated air, and taKen imme
diately to the differential reflectometer for
measurement.
With the exception that only one specimen needed to
be mounted, samples used in the microhardness tests were
ground and polished by the same method as above through
the diamond polish. In order to reveal the grain structure
the samples were swabbed with an etchant composed of 2:1:1
ammonium hydroxide:hydrogen peroxide (3%):water. These

51
samples were then rinsed in methanol and blown dry and
taken immediately to the microhardness tester.
3.5 Aging
Aging temperatures were chosen to reflect a range of
precipitation rates from slow to moderately rapid growth.
To that end, all three alloy compositions Cu-1 a/o Co,
Cu-2 a/o Co, and Cu-2.7 a/o Co -- were given aging heat
treatments at 400C, 500C, and 600C. In addition, Cu-
2.7 a/o Co was aged at 450C and 550C.
All samples to be aged were placed in a fused quartz
tube which was evacuated with a mechanical pump to a pres
sure of approximately 0.1 Torr. The pump remained connected
to the tube and operated continuously during the aging
heat treatment. At the end of the aging heat treatment
helium was used to break the vacuum, and the samples were
immediately quenched in tap water.
For a specific isothermal aging heat treatment, the
aging times were recorded accumulatively. For example, if
a given alloy had been aged for fifteen minutes and exa
mined, and the next test required a thirty minute aging
heat treatment, the same sample was demounted, aged for fif
teen minutes and remounted. In this way any possible
error involved in using different samples was avoided.
Upon removal from the furnace, samples aged for six
hours or less appeared to be clean and free of contamination.

52
Samples aged longer than six hours were observed to have
a flaky black surface scale. The origin of the scale was
probably a combination of oxide and residue from the
mechanical pump oil. However, because all samples were of
necessity ground and polished subsequent to each aging heat
treatment, any contamination resulting from that treatment
was removed.
3.6 Microhardness Tests
Diamond pyramid hardness tests (Vickers scale) were
conducted upon Cu alloys containing 2.7 a/o, 2.0 a/o, and
1.0 a/o Co. Each of the alloys was given a series of iso
thermal aging heat treatments at 400C, 500C, and 600C.
All samples were subjected to a 500g load applied by the
indenter. By maintaining the load at this specified value,
no load dependent variations were introduced into the mea
surements. Although the sample depth probed in a micro
hardness test is much larger than the sample depth probed
by a light beam (approximately 40 pm vs. 0.01 pm), micro
hardness tests were considered to be a more appropriate
alternative than standard hardness tests where the des-
parity in probe depth would have been far greater.
For each time in the aging sequence of a sample, a
set of twenty-five microhardness measurements was made.
From these measurements a diamond pyramid hardness num
ber (DPN) was calculated along with the 95% confidence

53
interval. As was the case with the optical data, a se
quence of measurements comprising a set of isothermal heat
treatments was carried out on individual samples. Care was
taken to remove the damage of the previous measurements
caused by the indenter. This was done by grinding well
below the level of the indentations made during the pre
vious run.

CHAPTER 4
EXPERIMENTAL RESULTS AND DISCUSSION
4.1 Microhardness Tests: Results and Discussion
Previous experiments on dilute copper-cobalt alloys
have established that the changes in hardness which occur
during aging heat treatments are caused by the formation
of spherical cobalt-rich precipitates. The purpose of
performing microhardness measurements for this work was to
provide a link from these previous experiments to the
optical measurements designed for this work. In this sec
tion, results of the microhardness tests will be presented.
The results will be seen to be consistent with that which
is known to occur during a precipitation reaction. Fur
thermore, it will be shown that the results of these mea
surements verify the findings of other researchers who
have performed similar measurements.
Microhardness measurements were carried out on alloys
containing 2.7 a/o Co, 2.0 a/o Co, and 1.0 a/o Co. These
alloys were aged at three different temperatures -- 600C,
500C, and 400C. The results of these measurements can be
seen in Figures 4-1 to.4-6.
In Figure 4-1, the diamond pyramid number is plotted
versus aging time for alloys containing the three amounts
54

55
Figure 4-1.
Hardness vs Time for Alloys Aged at 600C.

56
of cobalt mentioned above and aged at 600C. For the as
quenched alloys the hardness increases with solute content.
This proved to be the case in all samples analyzed, and is
consistent with the theory of the effect of solute elements
on the hardness of solid solutions. Solute atoms have been
shown to impede the movement of dislocations by collecting
57 8 2
at them and pinning them. As the concentration of
solute atoms increases, more dislocations can be pinned,
leading to increased hardness.
Figure 4-1 shows that for all alloys which had been
aged at 600C, the hardness increased considerably between
the as quenched state and fifteen minutes of aging. After
this, the hardness increased steadily, but more moderately,
up to its peak value at about nine hours. Past nine hours,
the hardness decreased steadily. At all times, the alloy
with the greater solute concentration exhibited higher
hardness.
Aging each alloy at 500C produced results indicative
of the slower diffusion rate which exists at this lower
heat treating temperature. As is seen in Figure 4-2, the
increase in hardness from the as quenched state to the
first aging time of 15 minutes is much more moderate than
in the case of aging at 600C. The increase was less than
half the increase seen at 600C. In addition, increases
tended to be moderate and no peak was reached even after
aging for 220 hours, although the values of hardness at
220 hours are higher than the peak values for the alloys

VICKERS HARDNESS CDPND
57
Figure 4-2.
Hardness vs Time for Alloys Aged at 500C.

58
aged at 600C. The fact that these values are higher can
be accounted for by the lower solubility at 500C for Co
in Cu. At 600C, the solubility for cobalt is about 0.4%
whereas at 500C, it is less than 0.1%. This decreased
solubility leads to a greater volume fraction of precipitate
as determined by the phase diagram tie line, which in turn
leads to a higher hardness. Again, it can be seen that
at each aging time the alloy containing a greater amount
of solute possesses a higher hardness.
The results of aging each alloy at 400C can be seen
in Figure 4-3. At 400C there is only a very slight in
crease in the hardness for each composition in aging up
to 26 hours, indicating that the precipitation reaction
has barely begun even after this length of time. The dif
fusion rate is evidently so slow at this temperature that
in terms of aging time several more orders of magnitude
of time would be necessary to bring these alloys into a
condition of peak hardness. These results did show, how
ever, that room temperature aging would not occur and that
therefore it was not necessary to give the sample a solu
tion heat treatment before each aging experiment was per
formed. This allowed the use of individual samples for
a series of aging times thus avoiding the error associated
with using different samples. This observation was also
37
made by Witt and Gerold.
In Figures 4-4 to 4-6 are plotted the diamond pyramid
number versus aging time for each composition where aging

59
Figure 4-3
Hardness vs Time for Alloys Aged at 400C.

60
temperature is the variable parameter. In these figures,
the role of aging temperature in influencing the precipi
tation rate is clearly seen. In Figure 4-4, for example,
which shows microhardness data for a Cu-2.7% Co alloy aged
at 600C, 500C, and 400C; the increased precipitation
rate with increasing temperature is quite evident. Start
ing from essentially the same hardness in the as quenched
state, the alloy aged at 600C proceeds to reach a peak in
microhardness much faster than those alloys aged at 500C
or 400C. This same pattern is repeated for the Cu-2.0%
Co alloys and the Cu-1% Co alloys, seen in Figures 4-5
and 4-6 respectively.
The microhardness data presented here can be seen to
represent the type of data that would be found in a typical
precipitation reaction. The increase in hardness, although
influenced by a number of factors, is principally influ
enced by the fraction of coherent precipitate. The peak
value in the microhardness is indicative of that point
where the precipitates have grown to a size that warrants
the formation of an interface. This is achieved by the
creation of dislocations to accommodate the strain intro
duced to the lattice by the mismatch between the precipi
tate and the matrix. The subsequent decrease in hardness
past the peak is a manifestation of more and more particles
achieving the critical size at which they change from a
coherent to incoherent state.

VICKERS HARDNESS CDPND
61
Figure 4-4.
Hardness vs Time for Cu-2.7% Co Aged at 600C,
500C, and 400C.

VICKERS HARDNESS C DPN D
62
As 1 10 100 1000
quenched
TIME C hr 3
Figure 4-5. Hardness vs Time for Cu-2.0% Co Aged at 600C
500C, and 400C.

VICKERS HARDNESS CDPNU
63
Figure 4-6.
Hardness vs Time for Cu-1.0% Co Aged at 600C
500C, and 400C.

64
There are various values reported for this critically
sized particle in the Cu-Co system, i.e., the size at which
the precipitate changes from the coherent to incoherent
state. Generally, these values, seen in Table 4-1, fall
in the range of 40-100 A. The only values to fall outside
O
of this range is 175 A which was reported by Phillips and
31 0 35
Livingston and 120 A which was reported by Humphreys.
Both of these values for radii were found using samples
which had experienced no deformation after the aging heat
33 .
treatment. Phillips has also reported the maintainence

of coherency up to precipitate radii of 250 A in the ab
sence of any deformation. However, the application of any
deformation to the sample assists in the nucleation of
dislocations which provides for the establishment of an
interface in changing from a coherent to incoherent state.
In the present work, both the use of the indenter in the
microhardness tests and the use of the polishing wheel in
order to obtain a specular surface for taking optical mea
surements could provide the deformation necessary to cause
an interface to be formed between the precipitate and the
matrix. Therefore, the results presented here most likely
O
coincide with a radius of 40-100 A at peak hardness.
Based upon the data obtained from the microhardness
tests and the coincidence of this data with the work of
others who have studied precipitation in the copper-cobalt
system, the conclusion can be reached that the alloys were

65
Table 4-1. Radius of Precipitate at Peak Property
for Copper-Cobalt System
Particle Radius
at Peak
Measurement
Ref
Livingston
& Becker
O
70 A
Hardness
29
Livingston
70 A
Yield Stress
30
Phillips
46-75 A
Hardness
33
Phillips &
Livingston
175 A*
TEM
31
Phillips
50 A
Yield Stress
34
Humphreys
120 A
TEM
35
Threadgill
& Wilshire
40-75 A
Creep
43
Amin, Gerold & Kralik
100 A
Hardness
44
Wilnelm
70 A
Not Specified
46
Tautzenburger & Gerold
O
40 A
Creep
48
*
Sample Undeformed

66
heat treated properly to produce a precipitation reaction.
Furthermore, the results indicate that the goal of obser
ving precipitation in regions of relatively rapid, moderate,
and slow growth has been achieved.
Among the researchers who have studied this system,
there is little disagreement as to the nature of the pre
cipitation reaction. It is generally conceded that the
precipitate is spherical, face-centered cubic, and remains
coherent with the lattice until it achieves a size of ap
proximately 40-100 A. There has been nothing found so far
in this work to contradict these findings.
4.2 Compositional Modulation: Results and Discussion
As has been discussed in Chapter 2, the optical proper
ties of copper alloys have been found to be strongly depen
dent on composition. In the case of copper with multiva
lent solutes, a linear shift of the threshold electronic
transition at 2.2 eV to higher energies was found as the
average solute concentration was increased above one per
cent.5 In the case of copper-nickel alloys, however, there
was no composition dependence seen in the energy of the
threshold transition.^ Additions of up to 24% nickel pro
duced no change in this transition energy. The demonstra
tion of this phenomenon by both differential reflectometry7
6 3
and photoelectron spectroscopy was offered as confirma-
6 7
tion of the virtual-bound-state model of Friedel and

67
6 8
Anderson, who had predicted this type of behavior for
copper-nickel alloys.
The purpose of performing compositional modulation
experiments for this work was twofold. Firstly, it was
necessary to determine the manner in which cobalt would
affect the optical properties of copper. To do this,
"traditional" compositional modulation experiments were
performed, in which the optical properties of the average
compositions of the two samples were investigated. The
design and results of these experiments are discussed below.
Because cobalt and nickel lie next to each other in the
periodic table and because they both derive their ferro-
8 3
magnetism from spin imbalance of their unfilled d-bands,
the results of these experiments on Cu-Co alloys are com
pared to previous research on the optical properties of
Cu-Ni alloys. Particular attention is made to the virtual-
bound-state model.
Secondly, another type of compositional modulation
experiment on Cu-Co alloys was performed. In this inves
tigation, the difference in solute concentration between
the two samples studied is the variable parameter. The
design and the results of these compositional modulation
experiments will be discussed in the second half of this
section. In particular, the relationship between these
experiments and the optical properties of aged alloys will
be considered.

68
In Figure 4-7, differential reflectograms for average
sample compositions of Cu-1.5% Ni and Cu-1.5% Co are pre
sented. In this figure, an almost identical pattern in
optical response is evident. The features of the copper-
nickel differential reflectogram have already been described
8 4
oy Hummel. The structure from "a" to "b" is caused by
interband transitions at the threshold energy of 2.2 eV.
The maximum designated "d" is a manifestation of transitions
from the lower d-bands of copper to the Fermi energy. Fi
nally, the broad structure at "c" has been ascribed to
electronic transitions involving the d-bands of nickel. The
similarity between these two reflectograms represents a
new type of pattern seen in differential reflectograms.
Previous work on copper with multivalent solutes revealed
that all differential reflectograms of this alloy group had
a common pattern. The evidence here suggests that there
will be one pattern for all differential reflectograms of
copper-transition metal alloys.
The study of the effect of cobalt composition on the
electronic structure of copper was then broadened. These
compositional modulation experiments were conducted by
changing the average composition of the two samples studied
by differential reflectometry. (It has been shown11 that
the transition energies measured by differential reflecto-
metry are the equivalent of the transition energies for an
alloy whose composition is the average of the composition
of the two alloys measured, provided that the difference in

4 5.5
ENERGY CeVH
1.6 2 2.5 3
800 600 400 200
WAVELENGTH Enm]
Differential Reflectograms of Cu-1.5% Ni (Ref. 84) and Cu-i.5% Co.
(Compositions indicate average solute content of the two samples used.)
Figure 4-7.

70
composition is small.) Although somewhat hampered by the
limited solubility for cobalt in copper, this research did
provide a measure of compositional dependence up to about
2.4% Co. In Figure 4-8, differential reflectograms are
shown for average compositions of Cu-0.5% Co, Cu-1.5% Co,
and Cu-2.4% Co. To obtain these average compositions the
following pairs of samples were examined: pure Cu and Cu-
1% Co, Cu-1% Co and Cu-2% Co, and Cu-2% Co and Cu-2.7% Co.
As in the case of nickel, there was no shift seen in
the transition energy as the composition was changed. As
has been discussed, the reason for this composition inde
pendence of the threshold transition energy has been ac
counted for by the virtual-bound-state model of Friedel^7
6 8
and Anderson. Their contention that the nickel electrons
maintain highly localized levels around nickel atoms when
alloyed with copper, seems to extend to cobalt impurity
atoms as well.
Peak "d", which is caused by transitions from the lower
d-bands of copper to the Fermi energy, does show a very
small composition dependence. It can be seen that this
peak shifts to slightly higher energies as the amount of
cobalt is increased. This same shift toward higher ener
gies with increasing solute content has also been observed
in copper-nickel alloys.7 The minimum designated "c" in
these differential reflectograms, although seen in Figure
4-8 to shift toward higher energies as cobalt content was
increased showed no strict composition dependence in other

NORMALIZED DIFFERENCE IN REFLECTIVITY
71
ENERGY CeV]
1.6 2 2.5 3 4 5.5
WAVELENGTH CnmJ
Figure 4-8. Differential Reflectograms of Various Copper-
Cobalt Alloys. (Compositions indicate average
cobalt content of the two samples used.)

72
differential reflectograms. In copper-nickel alloys, this
minimum is thought to be caused by nickel electronic tran
sitions, but cobalt has been found to have no strong opti-
75 77 85
cal transitions in this energy range. '
As has been established, a precipitation reaction is
defined to be the decomposition of a metastable solid
solution in which a second phase nucleates, grows, and
coarsens, and in which the matrix is necessarily depleted
of solute in order that the second phase be produced. So
far, this work has established the conditions under which a
precipitation reaction can be produced, and has verified
the presence of a second phase by means of microhardness
measurements. However, measurements of mechanical proper
ties, such as the microhardness of an alloy, only yield
information about the state of the precipitate, for example,
whether or not coherency has been maintained. While this
is, of course, useful, no information has been obtained
about the extent to which the decomposition has progressed.
There is no metallurgical law which establishes a link be
tween the hardness of an alloy and the volume fraction of
precipitate, or conversely, the composition of the matrix.
It has been seen that the optical properties of an
alloy are very strongly dependent upon its composition (See
Section 2.3), and therefore, their measurement should be
a candidate for a method of determining the changes in com
position which occur in the matrix during a precipitation
reaction. Finnegan^^has already shown the utility of

73
making optical measurements, specifically differential re-
flectometry, in determining the extent of dezincification
in alpha brasses when they are subjected to various cor
rosive environments. Although in the case of dezincifica
tion, the alloy experiences an actual loss of solute, a
precipitation reaction can be viewed in a similar manner,
for the reason that the solute is removed from the matrix
by the formation of the second phase.
It has been demonstrated that the optical properties
of copper-cobalt alloys parallel those of copper-nickel
alloys, and that these findings indicate that copper-cobalt
alloys behave according to the virtual-bound-state model.
Using Figure 4-8, it has been shown that Co additions do
not affect the energy of the copper threshold transition at
2.2 eV, as in the case of multivalent solute additions. Be
cause the differential reflectometer yields information
about the alloy composition which is the average of the two
samples investigated and because no shift in transition
energy occurs as the average alloy composition was changed,
an alternative method for determining the effect of cobalt
additions on the optical properties of copper was chosen.
The average of the composition of the two samples was re
placed by the difference in the composition of the two
samples.
In this second type of compositional modulation, exper
iments were conducted in a manner so as to simulate the
aging experiments which are described in the next section.

Specifically, in these experiments, the solute composition
of one sample was held constant while the solute composition
of the samples measured against it was successively de
creased. In this way, the difference in solute content
between the two samples was made the independent variable.
All of the samples used in these experiments were given
solution heat treatments in order that there was no preci
pitate present, therefore, the results would be indicative
of composition effects only. The results of these experi
ments can be seen in Figures 4-9 to 4-11.
In Figure 4-9, a Cu-2.7% Co alloy was measured against
copper alloys containing 2.5% Co, 2.0% Co, 1.5% Co, 1.0%
Co, and 0.5% Co. The shape of these curves can be seen to
be similar to those curves described in the first part of
this section, where the effect of cobalt upon the electron
band structure of copper was discussed. Qualitatively, it
is immediately apparent that as the difference in solute
composition of the two samples is increased that the signal
strength of the spectra is also increased. In order to
attempt to quantify this increase in the signal strength,
two features of the spectra, which are present in all spec
tra and which lend themselves to measurement (the minimum
formed between approximately 600-550 nm and the maximum at
270 nm), were examined. These two features are the results
of changes in strength of the two most prominent valence
transitions in copper, specifically tne tnreshold transi
tions at 2.2 eV and the ,-L^ transicin at 4.5 eV (See

NORMALIZED DIFFERENCE IN REFLECTIVITY
75
ENERGY CtVD
1.6 2 2.5 3 4 5.5
Figure 4-9. Differential Reflectograms of Cu-2.7% Co
versus Cu-0.5% Co, Cu-i.0% Co, Cu-I.5% Co,
Cu-2.0% Co, and Cu-2.5% Co.

76
Section 2.3). Because of the absence of a reference point
from which the peak at 270 nm could be measured, the change
in the differential reflectivity between 600-550 nm was
chosen as the basis upon which the signal strength was
measured. Of note is the fact that even when the differ
ence in the solute content is only 0.2% (bottom curve of
Figure 4-9), the change in the differential reflectivity
at the threshold transition is slightly more than 0.5%.
This demonstrates the utility of performing optical measure
ments in determining small differences in composition. It
is apparent that differences in composition at least as
small as 0.1% can easily be detected.
In Figures 4-10 and 4-11 are seen the spectra showing
Cu-2.0% Co and Cu-i.0% Co compared against samples of les
ser cobalt content. It is again apparent in these figures
that as the difference in solute content in the two samples
is increased that the signal strength of the spectra is
increased. Furthermore, the relationship between the dif
ference in solute content and the signal strength in all
three sets of experiments depicted in these figures was
found to be the same. By using this observation and by
plotting the signal strength at the threshold transition
as a function of the difference in solute content, the cal
ibration curve shown in Figure 4-12 was produced. As is
evident, a linear relationship was found to exist between
the percent change in differential reflectivity (signal

NORMALIZED DIFFERENCE IN REFLECTIVITY
77
ENERGY CeVU
1.6 2 2.5 3 4 5.5
WAVELENGTH Cnm3
Figure 4-10. Differential Reflectograms of Cu-2.0% Co
versus Pure Copper, Cu-0.5% Co, Cu-i.0% Co,
and Cu-i.5% Co.

NORM. DIFF. IN REFLEC.
78
ENERGY CeV3
WAVELENGTH CnmJ
Figure 4-li. Differential Reflectograms of Cu-1% Co versus
Pure Copper and Cu-0.5% Co.

79
strength) and the difference in solute content. The slope
of the line is approximately 3%/%AC.
This relationship between signal strength and the dif
ference in composition between the two samples measured is
an observation which has been previously unexploited in
differential reflectometry. The reason for this lies in
the nature of the solute element, which in this case is
a transition metal. As has previously been discussed (see
Section 2.3), when copper is alloyed with multivalent sol
utes, such as zinc, the energy of the electronic transitions
shifts as a function of solute content. By measuring the
change in the energy of these transitions by differential
reflectometry, it has been possible to determine the solute
content of unknown alloys. This was the method which was
used by Finnegan et al.^3 to determine the extent of de-
zincification in alpha brasses. For the reason that cobalt
is a virtual-bound-state element in copper, and hence no
shift in energy of the electronic transition occurs, the
composition dependence of the signal strength must be used
to determine the composition of an unknown alloy.
This relationship between the differential reflectivity
and the solute composition of a transition metal in copper
has been experimentally observed by other researchers.^'^
It can qualitatively be seen in Figure 2-10, which shows
reflectivity data for pure copper, Cu-13% Ni, and Cu-23%
Ni.63 The reduction of the reflectivity for the alloyed
samples in the energy region preceding the drop in

8
reflectivity at the threshold can be seen to be approxi
mately linear. This combined with the fact that the reflec
tivity of all samples crosses at approximately the same
value would yield a differential reflectivity change that
was linear with the difference in solute content.
More quantitatively, Beaglehole and Kunz^9 in measuring
differential reflectivity of dilute copper-nickel alloys
found that this quantity changed directly as a function of
the difference is solute composition at 628 nm. Although
no measurements of the optical properties of copper-cobalt
alloys have been performed by other researchers, it has been
shown that cobalt ana nickel are both virtual-
bound-state elements in copper. This fact, combined with
their similar electronic structure and position in the per
iodic table, makes the determination that they display a
similar influence upon the optical properties of copper
alloys seem quite reasonable.
The utility of the calibration curve in Figure 4-12
as it applies to a precipitation reaction can be demonstra-
tea in the following example. If two samples of known
solute content, one of which has been solution heat treated
and the other of which has been solution heat treated and
aged, are measured by differential reflectometry, the dif
ference in the matrix solute content between the two samples
can be obtained by determining the signal strength of the
resulting spectrum. This yields a measure of the extent to
which the precipitation reaction has progressed. The

PERCENT DIFFERENCE IN REFLECTIVITY
0.5 1.0 1.5 2.0 2.5
PERCENT DIFFERENCE IN COMPOSITION
Figure 4-12. Signal Strength (AR/R) versus Difference in Cobalt Concentrat

82
utility of differential reflectometry in determining the
depletion of solute from the matrix during precipitation
will be discussed in the following section.
4.3 Aging Experiments
In the preceding section, experimental data describing
the relationship between the composition of Cu-Co alloys
and the optical properties of these alloys was presented.
It was also demonstrated that differential reflectometry
provides a method by which the cobalt concentration of an
unknown Cu-Co alloy can be determined provided that a re
ference sample of known solute concentration is available.
In this section, the utility of differential reflectometry
in following a precipitation reaction by tracking the as
sociated matrix depletion of solute will be explored. In
addition, any additional optical effects that occur during
the precipitation reaction that are not based solely upon
composition differences will be acknowledged.
In these experiments three alloys of varying cobalt
content were studied Cu-2.7% Co, Cu-2.0% Co, and Cu-1.0%
Co. Each alloy was aged at 600C, 500C, and 400C. In
addition, the Cu-2.7% Co alloy was aged at 550C and 450C.
In order to determine the kinetics of the solute deple
tion during precipitation, differential reflectometry was
performed on samples that were identical in initial solute
composition, but differed in subsequent heat treatment. In

83
these experiments, both samples were given solution heat
treatments. One of the samples was then additionally aged
at a specific temperature for a series of times. Differen
tial reflectometry spectra were obtained to record the
difference in optical properties between the two samples
as a result of the aging regime.
Figure 4-13 shows a typical differential reflectogram
from these experiments. The two samples used to obtain
this spectrum were both Cu-2.0% Co. One sample was solu
tion heat treated while the other was solution heat treated
and aged at 600C for one hour. The two most prominent
features of this spectrum are a minimum formed between 600
nm and 550 nm and a maximum occuring at 280 nm. These fea
tures appear at the same wavelengths as those described in
the previous section during the compositional modulation
experiments. On the basis of the signal strengths of the
minima centered at 550 nm, the difference in composition
between the two samples is approximately 0.5% Co. It was
also determined that the aged sample was the sample which
contained the lesser amount of matrix solute. This finding
is interpreted to be the fundamental result of a precipita
tion reaction, in which cobalt is removed from the matrix
in order that cobalt-rich precipitates can be formed.
In Figure 4-14 a series of differential reflectograms
for a Cu-2.0% Co alloy are displayed. Again, one sample
was solution heat treated while the other was solution heat
treated and then aged. Figure 4-14 shows the spectra for

b~SSH
ENERGY CeV3
WAVELENGTH Cnm^
Figure 4-13. Differential Reflectogram of a Cu-2.0% Co Alloy. (One Sample was
Solution Heat Treated and Aged for One Hour at 600C, the Other-
Sample was Solution Heat Treated.)

NORMALIZED DIFFERENCE IN REFLECTIVITY
ENERGY CV3
1.6 2 2.5 3 4 5.5
WAVELENGTH CnnO
Figure 4-l4. Differential Reflectograms of the Aging Sequence of a Cu-2.0
Co Alloy Aged at 600C.

86
0.5 hr, 3.0 hr, and 26.0 hr of aging. The 0 hr spectrum
depicts two samples that were identically solution heat
treated. The lack of any clearly defined structure in this
spectrum shows than the samples started in an identical
condition. In response to the aging heat treatments given
to the one sample, however, the spectra indicate that the
composition difference between the two samples increased
with aging time due to the decreased solute concentration
in the aged sample. In the spectra in Figure 4-14, the
signal strength indicates that after 26 hours of aging the
matrix solute content has been reduced by approximately
one percent.
In order to determine the effects of aging time, aging
temperature, and solute concentration on the optical proper
ties of these alloys during a precipitation reaction, the
signal strength at the threshold transition was plotted as
a function of aging time. The results are shown in Figures
4-15 to 4-20. In all cases the first differential reflec-
togram taken was of two solution heat treated samples, to
verify that the samples were identical in the initial con
dition. A featureless differential reflectogram was ex
pected and was obtained in all cases.
Figure 4-15 shows the change in threshold transition
magnitude for the various solute compositions of samples
aged at 600C. As seen in Figure 4-15, the signal strength
caused by the samples' composition difference immediately
increases after tne first aging heat treatment of fifteen

PEAK HEIGHT Corb. unif*3
87
Figure 4-15.
Peak Height vs Time for Various Copper-Cobalt
Alloys Aged at 600C.

88
minutes. In addition, the size of the initial rise in
signal strength increases with solute content. After this
initial rise, the signal strength increases monotonically
for all compositions. For all other compositions and aging
times, the signal strength is largest for the alloy con
taining the most solute. Because signal strength is di
rectly related to difference in solute content, these data
indicate that the alloy containing the greatest amount of
solute is losing the greatest amount of solute during aging.
This is consistent with the gradient-driven mechanism of
precipitation.
At the conclusion of the reaction, the matrix solute
content will be the limit of solubility for cobalt in cop
per (about 0.4% Co at 600C). This value is the same for
all initial solute compositions. Therefore, alloys with
higher initial solute concentrations must reject more solute
than alloys having lower initial solute concentrations in
order to reach the solubility limit. Consequently, the dis
parity in matrix solute content between a solution heat
treated and aged sample and one which has been solution heat
treated only will be larger in an alloy that has higher
solute concentration.
This pattern of finding larger signal strength for lar
ger solute concentration is also seen in Figure 4-16, where
the signal strength as a function of time is plotted for
each of the three compositions aged at 500C. Again, the
signal strength increases monotonically for all compositions,

20
10
0
20
10
0
10
0
A
uer
2 4-
89
, 1"
AGING TEMP.s 500C
ched
16. Peak Height vs Time for Various Copper-Cobalt
Alloys Aged at 500C.

90
although more moderately than those samples aged at 60C.
These monotonic increases in the signal strength are an
indication that as the aging heat treatment continues, the
matrix solute content of the aged samples is continuously
diminisning as solute atoms are used to form precipitates.
Figure 4-17 shows the data for the alloys when aged at
400C. It should be noted that even after 70 hours of aging
there is only a slight increase in the signal strengtn.
This, of course, means that precipitation is slow and that
the matrix solute concentration in the aged alloys does
not change significantly during these heat treatments due
to precipitation at this temperature.
In Figures 4-18 to 4-20 signal strength is plotted as
a function of time in graphs which show more clearly the
effect of temperature. Figure 4-18 shows data for Cu-2.7%
Co aged at 600C, 550C, 500C, 450C, and 400C. To be
noted is the very large initial increase in signal strength
for the alloy at 600C, indicating that at this temperature
the precipitation is well under way after 15 minutes aging.
In temperature regimes where precipitation is controlled by
diffusion, it is expected that the precipitation reaction
will proceed at a faster rate when a higher aging temper
ature is employed. As has been previously stated, the
signal strength is proportional to the difference in the
matrix solute concentration between the aged and the solu
tion heat treated samples. For this reason it can be seen
that the disparity in matrix solute content between the

20
10
0
20
10
0
20
10
91
_ AGING TEMP. = 400C
2.7%Co
2.0%Co
1.0%Co
TIME ChrU
-17. Peak Height vs Time for Various Copper-
Cobalt Alloys Aged at 400C.

.92
Figure 4-18. Peak Height vs Time for Cu-2.7% Co at Various
Aging Temperatures.

93
aged and unaged samples increases as aging temperature
increases.
This same pattern manifests itself for Cu-2.0% Co and
Cu-1.0% Co alloys, the data for which can be seen in Fi
gures 4-19 and 4-20, respectively. Here, again, the signal
strength is at all times larger as the aging temperature
is increased. It is evident, however, that the magnitude
of the signal strength decreases as the solute concentra
tion of the alloys decreases.
Finally, the differential reflectograms were examined
for effects, other than those related to straightforward
compositional differences, which could be caused by the co
balt-rich precipitates. Two such effects were apparent and
are discussed in detail below. Firstly, there was a change
in shape of the spectra involving the feature designated "c"
in Figure 4-7. Secondly, based on the assumption that the
alloys were fully aged at 600C and that therefore the dif
ferences in matrix solute content could be determined from
the equilibrium solute concentration for each alloy concen
tration, the signal strength was found to be suppressed when
compared with data obtained from compositional modulation.
The results of this suppression can be seen in Figure 4-21,
where the lower curve was constructed in the following way.
Because the equilibrium solute concentration for cobalt in
copper is 0.4% Co, the difference in matrix solute concen
tration between a fully aged 2.7% Co alloy and a solution
heat treated alloy is 2.3% Co (point "a" on the graph).

94
Figure 4-19.
Peak Height vs Time for Cu-2.0% Co at
Various Aging Temperatures.

95
Q ill 1
As 1 10 100
Quenched
TIME Chr3
Figure 4-20. Peak Height vs Time for Cu-1.0% Co at Various
Aging Temperatures.

PERCENT DIFFERENCE IN REFLECTIVITY
Figure 4-21. Signal Strength vs Difference in Cobalt Concentration
for Solution Heat Treated Samples (Top Curve) and Aged
Samples (Bottom Curve).

97
For Cu-2.0% Co the difference is 1.6% Co (point "b") and for
Cu-1.0% Co the difference is 0.6% Co (point "c"). This sup
pression of the signal strength is attributed to the influ
ence of the precipitates on the optical properties of those
alloys.
The question arises whether or not the second calibration
curve (lower line in Figure 4-21) is a reasonable interpre
tation of the data obtained from the optical measurements
of the aged alloys.
It is necessary to recall that the upper line in Figure
4-21 was obtained by measuring the signal strength at 2.2
eV caused by the difference in solid solution solute concen
tration between the two alloys. In performing the optical
measurements on precipitation heat treated alloys, two al
loys of identical solute concentration were measured by dif
ferential reflectometry. One alloy was solution heat treat
ed and the other alloy was solution heat treated and aged.
As discussed above, when alloys of three different solute
concentrations Cu-2.7% Co, Cu-2.0% Co, and Cu-1.0% Co --
were aged and measured by differential reflectometry in the
manner mentioned above, an increase in the signal strength
at the 2.2 eV electronic transition was noted. This was
ascribed to a depletion in the matrix solute concentration
in the aged alloys which accompanied the formation of a
second phase. When the signal strength of the differential
reflectograms was compared to the calibration curve obtained
from samples that differed in solid solution solute

98
concentration alone (upper line in Figure 4-21) analysis
revealed that the matrix solute concentration for the alloys
aged for 590 hours at 600C was as follows: the Cu-2.7% Co
alloy had a matrix solute concentration of 1.1% Co; the Cu-
2.0% Co alloy had a matrix solute concentration of 0.9% Co;
and the Cu-1.0% Co alloy had a matrix solute concentration
of 0.6% Co. The equilibrium solute concentration at 600C
for cobalt in copper has been given as 0.4% Co. It is ap
parent from this analysis that none of these alloys has
reached the equilibrium solute concentration after being
aged at 600C for 590 hours. This might be due to one or
more of the following reasons: the value of the equilibrium
concentration is not 0.4% Co, but some other value; the
precipitation is not complete; there is a capillarity shift
of the equilibrium concentration due to a finely divided
precipitate structure in this system; the observed solute
depletion of the matrix is due to selective oxidation of co
balt during the aging heat treatment; the electronic proper
ties of the matrix and the precipitates are not completely
without interaction and the precipitates may play a role in
the signal strength at 2.2 eV.
The proposal that the equilibrium solute concentration
is not 0.4% Co is probably not valid. Four independent in
vestigations^ 38,88,89 using two different techniques have
established 0.4% Co as the equilibrium solute concentration
for cobalt in copper. Furthermore, if one makes the assump
tion that 0.4% Co is not the equilibrium solute concentration

99
and the alloys investigated in this work are fully aged, the
conclusion would have to be reached that there is a differ
ent equilibrium solute concentration for each composition.
This conclusion can not be supported by any principle of
materials science.
One last possibility exists when considering this matter.
It may be that the Cu-1.0% Co alloy has reached equilibrium,
but the other two compositions have not. Analysis of Figure
4-15 shows that there is little or no change in the signal
strength at 2.2 eV between 26 hours and 590 hours of aging
for both of the remaining compositions. Furthermore, as
stated above, analysis of the matrix solute concentration of
these alloys would indicate values of approximately 1% Co
after 590 hours. Clearly, a concentration gradient should
exist to drive the reaction toward completion. In the case
of Cu-1.0% Co, this gradient could be seen to have driven
the reaction to completion in 15-25 hours. It is inconsis
tent to state that the reaction for Cu-1.0% Co proceeds
fairly rapidly, but when the Cu-2.0% Co and Cu-2.7% Co alloys
reach a solute concentration of 1.0% cobalt that the reac
tion proceeds very slowly, if at all.
This last observation begins to address the question of
whether or not the data can be interpreted as indicating
that the reaction is not entirely complete after aging for
590 hours at 600C. There are numerous observations re
ported in the literature that this system can be brought
into equilibrium.16 30,37,38,88,89 Furthermore, in general,

100
independent research efforts support the conclusion that the
reaction at 600C brings the system into equilibrium in a
range of times from several minutes to several hours.16 30>
37,38 The observation that the signal strengths shown in
Figure 4-15 can be interpreted as showing no further increase
after 26 hours of aging is consistent with the viewpoint that
the system has been brought into equilibrium by the precipi
tation reaction.
As can be seen in Table 4-1, the precipitates that form
in this system are quite fine. This requires that some con
sideration be given to a possible shift toward higher solute
concentrations of the equilibrium solute concentration due
to capillarity. The magnitude of the capillarity shift is
inversely proportional to the radius of the precipitate, so
that in a finely divided system, the shift can be signifi
cant. However, there are two considerations which argue
against any strong effects due to capillarity in this system.
Firstly, Witt and Gerold^7 have performed aging experiments
at 600C on a Cu-0.6% Co alloy and have reported that pre
cipitates are formed. This would not be possible if there
were a significant capillarity shift. Secondly, and perhaps
more significantly, assuming that the experimental value
given by Servi and Turnbull38 for the surface energy of 190
ergs/cm^ for the precipitate-matrix interface is valid, the
capillarity shift for precipitates having a radius of 10 nm
can be calculated to be only 3% of the equilibrium solute
concentration. That is, for precipitates of this size, the

101
equilibrium solute concentration is shifted from 0.4% Co to
slightly above 0.41% Co. This small shift of the equilib
rium solute concentration would not significantly affect the
results of this work.
The question now arises whether or not the aging heat
treatments may have influenced the cobalt concentration in
these alloys by a selective oxidation mechanism in which co
balt was removed from the alloy during the heat treatments
thereby producing alloys depleted of cobalt. This mechanism
could account for the observed increase in signal strength
at 2.2 eV in the differential reflectograms by leaving a
zone near the surface of the alloys which was depleted of
cobalt. Because light penetrates approximately the first
10 nm of the surface of a metallic alloy, this effect could
be important. It must be recalled, however, that these al
loys were polished after the aging heat treatments. This
polishing removed at least 100 microns from the surface of
the alloys. In this case, the question becomes whether or
not a depleted zone from the selective oxidation of cobalt
could extend to a depth of 100 microns or more. Using an
activation energy for the diffusion of cobalt in copper of
54,100 cal/mole,90 a diffusion coefficient of 1.93 cm^/sec,
90 and a growth factor of 1,38 a diffusion distance on the
order of one micron was calculated for an aging temperature
of 600C for 100 hours. This distance can be seen to be
much smaller than the depth to which these alloys were

102
polished. It is therefore unlikely that the signal strength
of the optical measurements was influenced by a selective
oxidation mechanism.
On the basis of these arguments, the conclusion can be
reached that the observed signal strength at 2.2 eV for al
loys aged at 600C is the product of a precipitation reac
tion, which after 590 hours of aging has been completed.
Furthermore, it is evident that the equilibrium solute con
centration has been reached. Therefore, for alloys of all
compositions aged at 600C, the matrix solute concentration
after 590 hours of aging should be 0.4% Co. It must be re
called how the optical measurements on the aged samples
were carried out. An alloy, which was aged, was measured by
differential reflectometry against an alloy which contained
the identical solute concentration, but in solid solution.
Therefore, the difference in solid solution solute concen
tration between these two alloys can be assumed to be known.
Because this difference is the independent variable on the
calibration curve of Figure 4-21, the lower curve of this
figure was constructed.
It must also be recalled that the difference between the
two curves shown in Figure 4-21 is that the upper curve was
produced from data taken from alloys which differed by a
known solid solution solute concentration only, whereas the
lower curve was produced from data taken from alloys which
differed by a known solid solution solute concentration and
in which one of the alloys contained precipitates. It is,

103
therefore, concluded that the suppression of the signal
strength at 2.2 eV is due to the presence of precipitates in
the aged alloys.
However, there is no direct evidence that this suppres
sion of the signal strength is due to the precipitates. The
remainder of this section will be devoted to an evaluation
of the data that indicates that the precipitates influence
the optical properties of these alloys. Although the evi
dence is indirect, it will provide a basis for future exper
iments. These experiments will be discussed at the end of
the section.
It is evident from Figure 4-21 that the amount of the
suppression of the signal strength at 2.2 eV is dependent
on the volume fraction of precipitate present. Specifically,
the precent volume of precipitate phase for a fully aged Cu-
2.7% Co alloy is 2.6%, for a fully aged Cu-2.0% Co alloy
is 1.8%, and for a fully aged Cu-1.0% Co alloy is 0.7%.
This is consistent with precipitation theory. If the preci
pitates influence the optical properties of these alloys,
then the alloy containing the greatest volume fraction of
precipitates should show the greatest effect on its optical
properties.
However, it can be argued that the magnitude of the sup
pression of the signal strength at 2.2 eV is too large to be
due to the precipitates alone. For a Cu-2.7% Co alloy the
volume fraction of precipitates is approximately 3%, but the
signal strength is suppressed approximately 30%. Hummel^l

104
has investigated a binary two phase system, silver-aluminum,
and found that in the two phase field that there was a non
linear optical response to the relative amounts of each
phase. Perhaps this type of behavior is seen in the copper-
cobalt system as well.
Another possibility is that the precipitates might be
influencing a much larger volume than is equal to the volume
fraction because they exert strain in the lattice. As long
as the precipitates remained coherent, the strain exerted by
them would extend into an appreciable volume of the alloy.
This strain would have the effect of changing the lattice
parameter of the alloy which, in turn, would influence the
optical properties. This could account for the large sup
pression of the signal strength that was observed in the
optical properties of the aged alloys.
Finally, the behavior of the feature in the differential
reflectograms labelled "c" in Figure 4-8 was examined to
determine whether or not the precipitates influenced the
optical properties of the alloys. This feature of the
differential reflectograms is seen to be formed in the shape
of a "well". It is believed to be the result of electronic
transitions from cobalt d-bands to the Fermi energy and thus
might provide a measure of the amount of cobalt in an alloy.
Analysis of the data from the compositional modulation ex
periments revealed that the depth of this "well" was depen
dent on the difference in cobalt concentration between two

105
alloys. Attempts were made to quantify this relationship,
but none proved successful. Qualitatively, however, this
observation should be noted.
In Figure 4-22 are seen two differential reflectograms.
The lower spectrum is a compositional modulation spectrum
in which one alloy is Cu-2.7% Co and the other is Cu-1.0%
Co. Both alloys were solution heat treated. The upper
spectrum is taken from the aging experiments in which both
alloys are Cu-2.7% Co, of which one has been solution heat
treated and the other has been solution heat treated and
fully aged. As has been noted, a fully aged alloy has a
matrix solute concentration of 0.4% Co. It is apparent in
Figure 4-22 that the depth of the "well" at approximately
3.2 eV is much more shallow in the spectrum from the aging
experiments than in the spectrum from the compositional
modulation experiments. Qualitatively, this would indicate
only a small difference in cobalt content between the aged
alloy and the alloy against which it is being compared, per
haps on the order of a few tenths of a percent. Because the
difference in solid solution cobalt concentration is known
to be 2.3% Co (2.7% Co 0.4% Co -- the equilibrium solute
concentration), it is possible to conclude that the signal
contributing to this "well" comes not only from the solute
in solid solution, but also from the cobalt in the precipi
tates. Although this conclusion is somewhat speculative,
taken in context with the rest of the data it seems

i i i i I r
1.6 2.0 25 3.0 4j0 5.5
A(nm)
E(eV)
Figure 4-22. Comparison of Spectra from Aging Experiments (Top)
and Compositional Modulation Experiments (Bottom).
106

107
reasonable. This observation of a shallow "well" was con
sistent in all of the reflectograms in the aging experiments.
There are several experiments which can be performed to
determine more precisely the manner in which the precipitates
influence the optical signal in the aged alloys. If the pre
cipitates are exerting strain on the lattice thereby altering
the electronic structure of the alloys, it would be valuable
to age the alloys for very long times producing a very coarse
precipitate structure in which the effects of strain would be
minimized. Any changes in the differential reflectometric
spectra could be ascribed to a decrease in strain due to
coarsening. It must be noted, however, that the microhard
ness measurements have revealed that the aged alloys are
well past peak hardness after being aged for 590 hours at
600C. No changes in the spectra have been observed past
26 hours of aging, as softening occurred. This may indicate
that lattice strain is not a "first order" phenomenon, but
spectra taken after very long aging times would still be
useful in this regard.
A second experiment would be necessary to determine
whether or not the optical signal from the precipitates is
independent of the optical signal of the matrix. As was
discussed above, the suppression of the signal strength is
not in direct relation to the volume fraction of precipitates.
It has been noted that a 3% volume fraction of precipitates
suppresses the signal strength approximately 30%. If the
optical signal of the precipitates were independent of that

108
of the matrix, one would expect that the magnitude of the
suppression would be the same as the volume fraction of pre
cipitates, in this case 3%. It is suggested that the re
flectivity of the precipitates -- Co-10% Cu -- be obtained
and add an appropriate percentage of this reflectivity to
the reflectivity of a solution heat treated Cu-0.4% Co al
loy (the equilibrium solute concentration of the alloys).
This would provide a situation in which the two reflectiv
ities were completely independent. It would then be pos
sible to determine quantitatively if this reflectivity dif
fered from the reflectivity of an alloy in which the precipi
tates are actually embedded in the lattice on an aged alloy.
This type of analysis would provide a method for determining
the precise interaction between the optical properties of
the precipitates and the matrix.
Lastly, experiments could be performed which explore the
two phase field in the copper-cobalt system. These exper
iments would be similar in scope to the types of experiments
Hummel^i performed on the silver-aluminum system. They could
be designed to explore the optical properties of alloys which
contain different amounts of the second phase. With this as
the independent variable, the optical properties of the sec
ond phase and its interaction with the primary phase might
be revealed more precisely.
In conclusion, the validity of the calibration curve
obtained from the optical measurements of the aged alloys
has been analyzed. It has been reasoned that the aging heat

109
treatments given to these alloys at 600C brought the system
to a fully aged condition and that the equilibrium solute
concentration of 0.4% cobalt was achieved. This permitted
analysis of the data on the basis that the difference in
solid solution cobalt concentration was known and the points
on the lower calibration curve in Figure 4-21 to be accu
rately placed. It has also been concluded that the sup
pression of the signal strength at 2.2 eV obtained from
optical measurements on aged alloys is caused by the influ
ence of the precipitates on the optical properties of these
alloys. The suppression of this signal strength may be due
to strain or an interaction of the electronic properties of
the precipitates and the matrix. Experiments have been pro
posed which might reveal the precise influence of the preci
pitates on the optical properties of these alloys. This
additional sensitivity of the differential reflectometer to
reveal a difference in microstructural state has not been
shown until this study.
4.4 The Kinetics of the Precipitation Reaction
There is disagreement in the literature concerning the
time dependency of the precipitation reaction in the copper-
cobalt system. There are reports of those researchers 29-31,
33,34,44 wj10 ciaj_m that the precipitation reaction occurs
so rapidly that it can not be observed as having any time
dependency and that all changes in mechanical properties

110
take place by coarsening of the precipitate structure. Re
ports-^ / 28,38,43,47 also exist that are based on a time de
pendent rate of growth which follows a time independent
nucleation event (site saturation). In one case, both types
of behavior have been observed for the precipitation reac
tion. 37 xn this investigation, the average solute concen
tration of the matrix was seen to change with aging time.
Because coarsening would involve no change in the solute
concentration of the matrix, the results of this investiga
tion indicate a growth process for the precipitation reac
tion. It remains that the data obtained by these optical
measurements yield consistent results when analyzed by a
standard model for the precipitates.
In this section, the kinetic data, which were obtained
by taking optical measurements of the aged copper-cobalt
alloys, will be evaluated quantitatively.
One method employed to follow the transformation kine
tics of a solid state reaction is the application of the
Avrami equation:
X = 1 exp(-t/r)n. (5)
In this equation, X is the volume fraction transformed; t is
the aging time; t is a time constant, and n is a constant
which depends on the shape of the precipitate and other par
ticulars of the reaction. Generally, the volume fraction
transformed, X, is obtained and log(ln(l X) ^) is plotted
versus log t. This yields a straight line which has a slope

Ill
of n. From this determination of a value for the constant,
n, the shape of the precipitate can be obtained. Servi and
Turnbull^S used this method when studying precipitation in
dilute copper-cobalt alloys by means of electrical resistiv
ity measurements. The value of n determined by these re
searchers varied from 1 to 2 depending on the aging temper
ature. For diffusion controlled growth, the growth radius
depends on t2. On this basis (an average of 1.5 for n),
Servi and Turnbull concluded that the shape of the precipi
tate was spherical.
It is then necessary to extract information from the
differential reflectograms which will relate the measured
quantity, the signal strength, to the volume fraction trans
formed. It has been seen that the signal strength, £, at
the 2.2 eV minimum is dependent on two factors. One is the
difference in matrix solid solution composition between an
aged and an unaged sample; the other is the effect of the
precipitates. These two effects will now be discussed
separately.
As the difference in matrix solid solution composition
increases, so does the strength of the optical signal, £.
On the basis of the difference in composition alone, it can
be seen in Figure 4-12 that
^rneas
comp
kAC
(6)
where £ is the measured signal strength due to composition
effects; AC is the difference in matrix composition between

112
the two samples; and k is equal to the slope of the line.
In the case of one sample having been aged and the
other sample having been solution heat treated, it is appar
ent that
AC = C C(t)
(7)
where C is the matrix composition for the solution heat
treated sample, and C(t) is the average matrix composition
of the sample after being aged for time, t. Also, using
the extremes of the line,
max
, ^comp (8)
k 'cs-ca
where is equal to the maximum signal strength measured,
which occurs when AC = C Ca, where Ca is equal to the
maximum solid solubility for cobalt in copper at a particu
lar aging temperature.
Substituting the expression for AC and k into Equation
5 yields
meas max rC-C(t)
comp 1 comp1 C-Ca ^ *
Further,
meas
^comp C-C(t)
max C-Ca
E
comp
C(t)-Ca
C-Ca
(10)
The right side of the equation is equal to X, the volume
fraction transformed. Therefore, for composition effects

113
only the volume traction transformed can be obtained as the
ratio of the measured signal strength to the maximum signal
strength:
meas
x comp
max
Z,
(ID
-comp
It has been seen, however, that the signal strength is di
minished by the presence of precipitates. Furthermore, it
has been demonstrated that the greater the amount of preci
pitates present, the greater is the suppression of the sig
nal strength. If this suppression of the signal strength is
proportional to the volume fraction, then
meas
XZ
max
comp
XZ
max
precip
(12)
rri6 3. s
where Z is the measured value of the signal strength,
and Zmax is the maximum amount of suppression, which is
precip ^
caused by a sample that is fully aged. It can be concluded,
therefore, that the volume fraction transformed can be ob
tained by the following equation:
meas
X =
^max vmax
comp ^precip
(13)
The data from the optical measurements of the aged cop
per-cobalt alloys were treated in this way in order to de
termine the constant, n, in the Avrami equation. The re
sults of these calculations can be seen in Table 4-2, which
lists n for various compositions and aging temperatures. As
can be seen all values for n fall in a narrow range of

114
Table 4-2. Functional Dependency, n, of the Exponent
in the Avrami Equation
Composition
Temperature
n
2.7% Co
600 C
.91
2.7% Co
500 C
.84
2.0% Co
600 C
.87
2.0% Co
5 0 0 0 C
.84
1.0% Co
600 C
.89
1.0% Co
500 C
.85

115
slightly less than one. A value of n = 1 can be interpre
ted, in the case of site saturation, diffusion controlled
growth, as the growth of precipitates in the shape of
platelets.
The result that the precipitates grow in the shape of
platelets contradicts a general result of other studies of
this system. That is, most researchers have reported that
the precipitates in this system grow as spheres.
There are two possibilities that may explain this dis
crepancy. Firstly, the method by which the alloys in this
work were handled might have produced platelets. It must
be recalled that the ingots were rolled by approximately
75% after they were made. After this step, they were re
crystallized. It is possible that some texture remained as
a result of the rolling step. This could have had the effect
of producing preferred planes on which the precipitates nu
cleated to form platelets. Performing TEM on sections of
the alloys would determine the shape of the precipitates.
Secondly, although the model used to interpret these
results produced a consistent value of n, the model is based
on the assumption that the lower calibration curve in Figure
4-21 is correct in that the suppression of the signal strength
is linearly dependent on the fraction transformed. Because
the effect of the precipitates on the optical signal is not
precisely known at this time, it is possible that the inter
action of the optical signal between the precipitates and the
matrix is more complicated than this simple relationship.

116
The experiments outlined in the previous section should
facilitate a more precise interpretation of this relation
ship .
Finally, the kinetics of the reaction for this work were
compared with data analyzed from other research efforts.27f
38,89 jn Figure 4-23, the fraction transformed is plotted
as a function of time for alloys of varying cobalt content
aged at 600C. When compared with themselves, the data from
this work show a slight increase in the fraction transformed
as the cobalt concentration increases. This is explainable
by the larger driving force for precipitation that exists
the farther an alloy concentration is from equilibrium.
When compared with the other data obtained for this system,
it can be seen that the kinetics of the reaction in this
work are slightly slower than the rates reported by Witt and
Gerold27 for Cu-1.4% Co and Gerold ^2, but overall the values
fit into a middle range of all the values reported.
4.5 Comparison of Microhardness and Optical Results
In this section, a comparison of the results of the
microhardness and the differential reflectometer measure
ments will be presented. The data from these two tech
niques provide overlapping and straightforward evidence of
the method by which the precipitation reaction in the Cu-Co
system proceeds. For the reason that the discussion of this

FRAC. TRANS.
1
.8
Q- 1.0%Co (Serv and Turnbull Ref. 38)
- 1.4%Co (Witt and Gerold Ref. 37)
f 0.6%Co (Witt and Gerold Ref. 37)
Q- 2.3%Co (Gerold Ref. 92)
2.7%Co (This work)
2.0%Co (This work) q
1.0*Co (This work)
Aging Temp. 600C
As
Quenched
.01
1

x
0
0


.1
10
100
TIME (hr)
Figure 4-23. Fraction Transformed vs Time at 600C.
117

118
data can be extended to the other two alloy compositions
that were investigated in this work, Cu-2.7% Co will be ex
amined in detail.
In Figures 4-24 to 4-26, microhardness data and optical
data are shown as a function of aging time, for the three
aging temperatures -- 600C, 500C, and 400C -- respec
tively. In Figure 4-24 a characteristic hardness curve is
seen. The immediate sharp rise in the microhardness of the
alloy aged at 600C is accompanied by a large increase in
the signal strength in differential reflectivity. This sig
nal strength has been determined to be caused by a depletion
of solute from the matrix in the alloy. Further aging leads
to more depletion of the alloy matrix as evidenced by the
growing signal strength of the optical measurements. A con
tinued increase in hardness corresponds to this depletion.
The optical signal strength ceases its growth after approx
imately 25 hours of aging, signalling an end to the precipi
tation reaction. Although the hardness of the alloy contin
ues to rise for a time as the solute depletion occurs, the
peak hardness of the alloy is achieved before the reaction
is complete, as determined optically. This peak is expected
and occurs after approximately nine hours of aging.
Figure 2-2 shows that there are four factors which con
tribute to the decrease of hardness prior to "complete"
solute depletion: recrystallization, depletion of the solid
solution, coalescence or coarsening of the precipitate struc
ture, and loss of particle coherency. For the dilute Cu-Co

PEAK HEIGHT Corb. units]
119
Figure 4-24.
Peaje Height and Hardness vs Time for Cu-2.7%
Co Aged at 600C.
VICKERS HARDNESS CDPN3

120
alloys used in this work, recrystallization at 600C occurs
very rapidly and would not contribute to the hardness curve
in a time dependent manner. Although there is some solid
solution hardening (see Figure 4-1), its contribution to
the hardness is small and therefore the depletion of solute
from the matrix would not cause a great loss of hardness.
Because the precipitation reaction is not completed (preci
pitates are still being added to the system) before the
alloy begins to lose hardness, it is unlikely that the par
ticle spacing is becoming larger. Therefore, the loss of
hardness must correspond to the loss of coherency of the
precipitates with the matrix.
One point of contrast between the findings of this work
and that of several other reports in the literature is the
time necessary for the precipitation reaction to be complete.
Although there is agreement between the data of this work and
data in the literature concerning the time to achieve a max
imum in mechanical properties (see Table 2-1), there are a
number of studies in the literature that state that at 600C
the precipitation reaction is complete within fifteen minutes
of aging. Therefore, increases in the mechanical properties
of Cu-Co after this time must be accomplished by the growth
of precipitates by coarsening.
However, all of the data presented in the literature is
by no means consistent. There are other reports which sup
port a more gradual depletion of solute from the matrix.
Tauzenberger and Gerold^S show both types of precipitation

121
rates at 600C, depending on the amount of cobalt in copper.
The findings of this work can only be interpreted that for
aging at 600C, the precipitation reaction takes between 15-
25 hours to complete.
In Figure 4-25 the comparative data of microhardness
and optical measurements for Cu-2.7% Co aged at 500C are
presented. It can be seen that the more moderate rate of
depletion of solute is accompanied by a more moderate in
crease in microhardness. It is also evident that neither has
the microhardness reached a peak nor has the depletion of
matrix solute been completed even after 100 hours of aging.
Because the diffusion rate is much slower at 500C, these
data conform well to precipitation theory. In addition,
they are self-consistent.
In Figure 4-26, data are presented for Cu-2.7% Co aged
at 400C. At this temperature, the diffusion rate is so
low that there is only a slight depletion of solute. The
microhardness data confirm this by exhibiting a minute
increase.

122
Figure 4-25.
Peak Height and Hardness vs Time for Cu-2.7%
Co Aged at 500C.
HARDNESS

123
80
70
60
50
TIME C hr J
Figure 4-26. Peak Height and Hardness vs Time for
Cu-2.7% Co Aged at 400C.
HARDNESS DPN

CHAPTER 5
SUMMARY
In this work, differential reflectoraetry has been used
to investigate the effect of cobalt additions on the elec
tronic band structure of copper and to determine the kine
tics of the precipitation of the cobalt-rich phase from dilute
copper-cobalt solid solutions. The latter research is the
first instance that differential reflectometry has been used
to identify the kinetics of a phase transformation.
It has been demonstrated that additions of up to 2.7%
cobalt in copper do not change the energy of the copper
threshold transition. Investigations of other copper elec
tronic transitions also revealed no solute dependence, ex
cept for the peak revealing electronic transitions from the
lower d-bands of copper to the Fermi energy, which showed a
very slight increase in energy with increased cobalt content.
This behavior replicates that observed by other researchers,
who studied the effects of nickel additions on the band
structure of copper. This common pattern of optical pro
perty behavior for the class of copper-transition metal al
loys can be accounted for by the phenomenon of virtual-bound
states for both cobalt and nickel. For this first time,
optical measurements have been used to demonstrate this
shared behavior.
124

125
Differential reflectometry has clearly revealed that
as the difference in solute content between two samples is
increased the signal strength of the differential reflecto-
grams is increased. The signal strength of the copper thres
hold transition, seen as a minumum at 2.2 eV in the differ
ential reflectograms of dilute copper-cobalt alloys, was
chosen as the basis for measuring the magnitude of the sig
nal strength. A straightforward linear dependence of the
magnitude of the signal strength on the difference in solid
solution solute content was found. Quantitatively, the
change in the magnitude of the signal strength is 3%/A%C.
Differential reflectometry has also been used to closely
monitor the depletion of solute from the matrix during a
precipitation reaction. Such a study offers additional in
formation about the electronic structure of alloys, since
not only do the compositions of the samples differ -- as in
the above-mentioned comparison of solid solution alloys --
but so do the physical states of the alloying constituents.
The magnitude of the signal strength of the 2.2 eV minimum
has been demonstrated to be a measure of the progress of
the precipitation of a cobalt-rich second phase in these
dilute copper-cobalt alloys. While observing the precipi
tation reaction for three different temperatures (600C,
500C, and 400C) and for three different cobalt concentra
tions (Cu-2.7% Co, Cu-2.0% Co, and Cu-1.0% Co), it has been
determined that the higher the aging temperature the faster
the reaction occurs. At 600C, the reaction is complete

126
between 15-25 hours of aging for all solute concentrations.
This finding is consistent with microhardness measurements
performed on precipitation hardened alloys. It has further
been determined, by the monotonic depletion of solute from
the matrix as aging continued, that the hardening observed
in these alloys takes place due to growth of the precipitate,
as opposed to coarsening of the precipitate structure.
Because the cobalt-rich precipitate in this system has
no strong electronic transitions in the spectral range of
the differential reflectometer, the precipitates were found
not to produce any new feature on the differential reflecto-
grams by which their growth could be followed. However,
it has been determined that the magnitude of the signal
strength was suppressed as a result of the influence of the
precipitates on the optical signal.
To conclude, this work has contributed in the following
ways to the understanding of metals:
1) This work has verified the common behavior in the
electronic structure of copper-cobalt and copper-
nickel alloys.
2) This work has provided a method by which optical
and mechanical properties can be coupled to reveal
the nature of a precipitation reaction.
This work has provided a demonstration that differ
ential reflectivity is sensitive not only to dif
ferences in composition, but also to the physical
state of the material under investigation.
3)

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tion, vol. 2, ASM (Metals Park, Ohio, 1979).
57. R. M. Brick, A. W. Pense, and R. B. Gordon, Structure
and Properties of Engineering Materials, McGraw-Hill
(New York, 1977 ) .
58. B. Segall, Phys. Rev. 125 (1962) 109.

130
59. R. Rosei, S. Modesti, V. Prantera, and I. Davoli, J.
Phys. F: Metal Phys. 9_ (1979 ) 2275.
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Phys. Rev. B 9^ (1974) 445.
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40 (1969) 1400.
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(1977) 1923.
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131
79. R. J. Smith, Doctoral Dissertation, University of
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80. W. M. Goho, unpublished.
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The Structure of Metals and Alloys, Pergamon Press
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(1980) 201.
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257.
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92. V. Gerold, private communication.

BIOGRAPHICAL SKETCH
William Michael Goho was born on July 4, 1954, in Har
risburg, Pennsylvania. He attended Central Dauphin East
High School located in that same city and graduated in 1972.
In 1976, he graduated from Gettysburg College in Gettysburg,
Pennsylvania, with a Bachelor of Arts degree in physics and
mathematics. He began his graduate work in materials science
and engineering at the University of Florida in 1978. For
the past two years, he has been teaching college physics in
the Rochester, New York, area. In September 1985, he joined
the faculty of Monroe Community College, Rochester, New York,
in the Department of Physics and Engineering Science.
The author is a member of The American Physical Society,
The American Vacuum Society, and The American Association of
Physics Teachers.
132

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
% c
Rolf E. Hummel, Chairman
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
j1 H. Holloway U
Paul H. Holloway
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality
as a dissertation for the degree of Doctor of Philosophy.
Associate Professor of Chemical
Engineering

This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
May, 1986
Dean, College of Engineering
Dean, Graduate School



21
extremely overaged condition has a shape change in the
precipitate been observed,17 that being from spheres to
plates.
As stated above, the cobalt-rich precipitate which forms
during aging contains enough cobalt for the precipitate to
possess ferromagnetism. Prior to coalescence, cobalt
atoms do not have a ferromagnetic character due to the ab
sence of a sufficient exchange interaction with neighboring
cobalt atoms.^'^ Thus as precipitation occurs the magne
tic state of the alloy changes from diamagnetic to ferro
magnetic. Becker1^ used the term "superparamagnetic" for
the latter condition. As the precipitates grow, the magne
tic coupling of the cobalt atoms becomes stronger and the
saturation magnetization of the alloy becomes larger. From
this, Becker1^ and others29-31,33,36,41,44 were able to
deduce the volume of precipitate formed, the radius of the
average precipitate, and the volume fraction of precipitate.
From magnetic measurements on a Cu-2% Co alloy aged at
600C, Livingston and Becker^9 concluded that all of the
cobalt was precipitated during the first few minutes of
aging and that subsequent growth of the precipitates took
place by coarsening, a process in which the total volume
and the volume fraction of precipitate remained constant
after the first few minutes of aging. They also concluded
that the radius of the precipitate increased linearly with
the logarithm of aging time. This same conclusion was
reached by Witt and Gerold^7 for copper alloys containing


PEAK HEIGHT Corb. units]
119
Figure 4-24.
Peaje Height and Hardness vs Time for Cu-2.7%
Co Aged at 600C.
VICKERS HARDNESS CDPN3


107
reasonable. This observation of a shallow "well" was con
sistent in all of the reflectograms in the aging experiments.
There are several experiments which can be performed to
determine more precisely the manner in which the precipitates
influence the optical signal in the aged alloys. If the pre
cipitates are exerting strain on the lattice thereby altering
the electronic structure of the alloys, it would be valuable
to age the alloys for very long times producing a very coarse
precipitate structure in which the effects of strain would be
minimized. Any changes in the differential reflectometric
spectra could be ascribed to a decrease in strain due to
coarsening. It must be noted, however, that the microhard
ness measurements have revealed that the aged alloys are
well past peak hardness after being aged for 590 hours at
600C. No changes in the spectra have been observed past
26 hours of aging, as softening occurred. This may indicate
that lattice strain is not a "first order" phenomenon, but
spectra taken after very long aging times would still be
useful in this regard.
A second experiment would be necessary to determine
whether or not the optical signal from the precipitates is
independent of the optical signal of the matrix. As was
discussed above, the suppression of the signal strength is
not in direct relation to the volume fraction of precipitates.
It has been noted that a 3% volume fraction of precipitates
suppresses the signal strength approximately 30%. If the
optical signal of the precipitates were independent of that


OPTICAL STUDIES OF PRECIPITATION
IN DILUTE COPPER-COBALT ALLOYS
USING DIFFERENTIAL REFLECTOMETRY
By
WILLIAM MICHAEL GOHO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA


LIST OF FIGURES
Pa^e
Figure 2-1. Phase Diagram of Hypothetiacl Precipitation
Hardenable Alloy and Corresponding Free
Energy Diagram 7
Figure 2-2. Composite Hardness Curve 13
Figure 2-3. Composite Curve showing the Effect of
Precipitation on Electrical Resistivity.... 18
Figure 2-4. Phase Diagram of Copper-Cobalt System 19
Figure 2-5. Hardness versus Time for Cu-2.0% Co
Aged at 600C 25
Figure 2-6. Yield Strength and Hardness versus Time for
Cu-2.0% Co Aged at Various Temperatures.... 26
Figure 2-7. The Band Diagram of Copper 32
Figure 2-8. Reflectance Spectra for Copper and
Various Brasses 33
Figure 2-9. Composition Dependence of Copper Threshold
Transition 37
Figure 2-10. Reflectance Spectra for Copper and Two
Copper-Nickel Alloys 39
Figure 2-11. Reflectivity Spectrum for Cobalt as
Calculated from Measurements of n and k
by Johnson and Christy 42
Figure 3-1. Schematic of Differential Reflectometer....48
Figure 4-1. Hardness vs Time for Alloys Aged at 600C..55
Figure 4-2. Hardness vs Time for Alloys Aged at 500C..57
Figure 4-3. Hardness vs Time for Alloys Aged at 400C..59
Figure 4-4. Hardness vs Time for Cu-2.7% Co Aged at
600 C, 500 C, and 400C 61
vi


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
OPTICAL STUDIES OF PRECIPITATION
IN DILUTE COPPER-COBALT ALLOYS
USING DIFFERENTIAL REFLECTOMETRY
By
WILLIAM MICHAEL GOHO
May 1986
Chairman: Rolf E. Hummel
Major Department: Materials and Engineering
Differential reflectometry has been successfully applied
to the study of precipitation in dilute copper-cobalt alloys.
Experiments were designed to exploit the capability of the
differential reflectometer to measure the difference in
solute content between two alloys based on an altered elec
tronic structure.
Composition modulation was performed in order to deter
mine the effects that solid solutions of cobalt in copper
have on the optical properties of the dilute alloys. It has
been observed that the energy of the threshold electronic
transition in copper at 2.2 eV has no dependence on the
cobalt solid solution content. This lack of dependency has
IX


53
interval. As was the case with the optical data, a se
quence of measurements comprising a set of isothermal heat
treatments was carried out on individual samples. Care was
taken to remove the damage of the previous measurements
caused by the indenter. This was done by grinding well
below the level of the indentations made during the pre
vious run.


10
lowest energy configuration. For instance, in the early
stages of growth small precipitates may form on planes
which have low strain but a high surface energy. As the
planes grow the surface energy becomes very large and the
precipitates may change their shape to spheres which pos
sess lower surface energy, but which also produce more
strain in the lattice. The stages intermediate to achiev
ing a final shape are called transition lattices.
In terms of composition, the growth of precipitates is
accomplished by a depletion from the matrix of solute atoms
from the concentration C, the supersaturated concentration,
to Ca, the concentration of solute atoms at the solubility
limit. The classic, phenomenological approach to this pro
cess finds that the time dependence of the matrix composi
tion is expressed as
C(t) = Ca + (C0-Ca)e(~t'/T } (2)
where C(t) is the solute concentration at time t, x is a
time constant, and n is dependent upon the particulars of
the growth process.
Although the kinetics of the precipitation reaction
can be very complicated, there are some rules that apply in
general to the reaction rate. Growth of the precipitate is
often controlled by the diffusion of solute atoms through
the matrix to the precipitate. For this reason, the preci
pitation rate is faster at higher aging heat treatment tem
peratures. In addition, because diffusion is controlled


HARDNESS
Quenched
TIME Carb. units]
gure 2-2. Composite Hardness Curve. (Ref. 24)


129
39. H. Kreye and E. Hornbogen, J. Mat. Sci. ( 1970 ) 89 .
40. B. G. Koepke and T. E. Scott, Scripta Met. _4 (1970 ) 81.
41. K. Hartmann, Z. Metallkunde 62^ ( 1971 ) 7 36 .
42. K. Hartmann, Z. Metallkunde 62^ (1971 ) 877 .
43. P. L. Threadgill and B. Wilshire, Metal Sci. (3 (1974 )
117 .
44. K. E. Amin, V. Gerold, and G. Kralik, J. Mat. Sci. 1^
(1975) 1519.
45. R. Meyer, V. Gerold, and M. Wilhelm, Acta Met. 2_5 (1977)
1187.
46. M. Wilhelm, Mat. Sci. and Eng. 4_8 (1981) 91.
47. A. Perovic and G. R. Purdy, Acta Met. 2j) (1981) 53.
48. P. Tauzenberger and V. Gerold, Z. Metallkunde 7_2 (1981)
329.
49. M. Hansen, Constitution of Binary Zvlloys, McGraw-Hill
(New York, 1955 ) .
50. L. G. Bonar and A. Kelly, Proc. Inti. Cong. Electron
Microscopy, vol. 1, Academic Press (New York, 1962).
51. D. S. Rodbell, J. Appl. Phys. 2_9 (1958) 311.
52. C. P. Bean, J. D. Livingston, and D. S. Rodbell, Jour,
de Physique et la Radium _20 (1959) 298 .
53. R. Tournier and A. Blandin, Phys. Rev. Lett. 2_4 (1970 )
397 .
54. J. B. Sokoloff, Phys. Rev. 161 (1961) 540.
55. J. B. Peterson, Handbook of Lattice Spacings, Pergamon
Press (New York, 1958).
56. American Society of Metals, Metals Handbook, 9th edi
tion, vol. 2, ASM (Metals Park, Ohio, 1979).
57. R. M. Brick, A. W. Pense, and R. B. Gordon, Structure
and Properties of Engineering Materials, McGraw-Hill
(New York, 1977 ) .
58. B. Segall, Phys. Rev. 125 (1962) 109.


15
precipitates become so large as to require dislocations to
maintain a limited amount of coherency with the lattice.
27
This is called a "quasi-coherent" state and marks the
beginning of the formation of an interface. As the preci
pitation continues, the particles become large enough to
require a definite interface between the growing precipitate
and the matrix. At this stage, the precipitate is com
pletely incoherent with the matrix, and dislocations at
the interface between the particle and the matrix accommo
date the strain produced by the precipitate. Thus, the
effect of the precipitate on the movement of dislocations
is diminished, and there is consequently a dramatic loss
in hardness.
Dispersion hardening arises from the fact that at the
beginning of the process there are many particles spaced
fairly close together. As precipitation continues, coar
sening can occur with larger particles growing at the ex
pense of smaller ones, causing the precipitate structure to
evolve to one in which there are fewer particles spaced
farther apart. This process accounts for the slight rise
in hardness followed by the slight softening seen in Fi
gure 2-2.
The final factor that affects the composite hardness
curve is recrystallization of the alloy. This is a compli
cated phenomenon, which itself is influenced by many factors.
These include aging temperature, aging time, amount of
deformation, composition, and grain size. It is necessary,


Energy
U>
ro
Figure 2-7.
The Band Diagram of Copper (Ref. 58).


2
an element from an alloy has been observed in experiments
dealing with dezincification in brasses.1^
Precipitation from a solid solution is a decomposition
from a metastable one phase system to a two phase system.
This reaction is characterized by the rejection of solute
atoms by the matrix in order that a second phase be formed.
This rearrangement of solute within the alloy would be ex
pected to change the physical properties of the alloy. This
is indeed the case. The measurement of electric,14,15 mag
netic, ,17,18 thermal,19 and dimensional properties^> 21
have often been used to follow the course of a precipitation
reaction. The use of these methods exploits a particular
sensitivity to some aspect of the physical changes occurring
during a precipitation reaction. None of these methods can
provide a complete description of the phenomenon. However,
differential reflectometry has the capability, because of its
extreme sensitivity to composition, of following a precipi
tation reaction from start to finish. This work will be
devoted to the study by differential reflectometry of preci
pitation in dilute copper-cobalt alloys.
In the next chapter, a review of the literature is
presented in three sections. The first section deals with
the phenomenon of precipitation in a general way. In this
manner, some understanding of this solid state reaction
can be reached before the specific system of dilute copper-
cobalt alloys is presented in the second section. A short
analysis of the methods used for studying precipitation in


9
to the system with the creation of this interface, the
volume free energy difference, AG, driving the reaction
must be large enough to compensate for this additional
energy. Also, because the precipitates are composed of
atoms of a different size than the matrix and have a differ
ent lattice parameter than the matrix, they create strain
in the lattice. This strain energy must also be offset by
the volume free energy reduction.
Nucleation is also influenced by the number of sites
available for the formation of second phase particles. Be
cause of the difference in size of the atoms of the preci
pitates and the matrix, formation of the second phase is
favored at locations where strain can be readily accommo
dated, such as grain boundaries or dislocations. For this
reason, nucleation will normally occur more rapidly in a
fine grained or a heavily cold worked material where there
are many sites at which precipitates can begin to form.
The same forces which operate in the nucleation of
stable particles continue to operate during their growth.
That is to say, the driving force continues to be a reduc
tion in the volume free energy of the system with the prod
uct being a decomposed solid solution with precipitate
particles interspersed throughout the alloy. The creation
of new surface and the strain added to the system by growing
particles also continue to influence precipitate growth.
The balance between these forces will determine the shape
of the precipitates, such that they try to achieve the


33
Weenlange
Figure 2-8.
Reflectance Spectra for Copper and Various
Brasses (Ref. 1) .


BIOGRAPHICAL SKETCH
William Michael Goho was born on July 4, 1954, in Har
risburg, Pennsylvania. He attended Central Dauphin East
High School located in that same city and graduated in 1972.
In 1976, he graduated from Gettysburg College in Gettysburg,
Pennsylvania, with a Bachelor of Arts degree in physics and
mathematics. He began his graduate work in materials science
and engineering at the University of Florida in 1978. For
the past two years, he has been teaching college physics in
the Rochester, New York, area. In September 1985, he joined
the faculty of Monroe Community College, Rochester, New York,
in the Department of Physics and Engineering Science.
The author is a member of The American Physical Society,
The American Vacuum Society, and The American Association of
Physics Teachers.
132


24
which is influenced to the greatest extent by coherency of
the precipitate, and then decline as the alloy softens when
the precipitates grow too large to maintain their coherency.
Softening is also the result of the coarsening of the pre
cipitate structure when the interparticle spacing becomes
too large to prevent easy motion by dislocations.
Copper-cobalt is not an exception to these mechanisms.
In Figures 2-5 and 2-6, data from Livingston and Becker^^
and Livingston^O are presented. In these curves are dis
played characteristics which are typical of a precipitation
reaction. In Figure 2-5,29 data for a Cu-2% Co alloy aged
at 600C are presented. An increase in hardness is observed
as the alloy is aged up to approximately fifteen hours, at
which point a peak hardness is obtained. Past this peak,
the loss of coherency of the precipitate with the lattice
causes softening to occur. In Figure 2-6,30 yield strength
and hardness data for a Cu-2% Co alloy aged at 600C, 650C
and 700C are presented. Here, several observations can be
made which reveal the characteristics of the precipitation
process in copper-cobalt. Not only are peaks seen to occur
at each aging temperature in both yield strength and hard
ness, but it is also evident that as the aging temperature
is increased, the time for each mechanical property to reach
its peak is reduced. This is a consequence of the increased
diffusion rate as temperature is increased. The faster
diffusion occurs, the faster the precipitates can form.
Finally, as the aging temperature is reduced, the higher


8
reflectivity at the threshold can be seen to be approxi
mately linear. This combined with the fact that the reflec
tivity of all samples crosses at approximately the same
value would yield a differential reflectivity change that
was linear with the difference in solute content.
More quantitatively, Beaglehole and Kunz^9 in measuring
differential reflectivity of dilute copper-nickel alloys
found that this quantity changed directly as a function of
the difference is solute composition at 628 nm. Although
no measurements of the optical properties of copper-cobalt
alloys have been performed by other researchers, it has been
shown that cobalt ana nickel are both virtual-
bound-state elements in copper. This fact, combined with
their similar electronic structure and position in the per
iodic table, makes the determination that they display a
similar influence upon the optical properties of copper
alloys seem quite reasonable.
The utility of the calibration curve in Figure 4-12
as it applies to a precipitation reaction can be demonstra-
tea in the following example. If two samples of known
solute content, one of which has been solution heat treated
and the other of which has been solution heat treated and
aged, are measured by differential reflectometry, the dif
ference in the matrix solute content between the two samples
can be obtained by determining the signal strength of the
resulting spectrum. This yields a measure of the extent to
which the precipitation reaction has progressed. The


50
horizontally, by which different areas along the juncture
of the samples can be studied. In most cases, three such
areas were measured.
3.4 Polishing Procedure
Each sample studied in the differential reflectometer
was prepared in tne following manner.
1. The two specimens -- either of differing compo
sition or differing heat treatment -- were
mounted adjacent to each other in a quick setting
polymeric material.
2. In order to bring the surfaces of both specimens
into the same plane, the sample was ground on a
grinding wheel using 180 grit paper with fil
tered kerosene as a lubricant.
3. The sample was then ground by hand using succes
sively finer grits 240, 320, 400, 600 -- with
filtered kerosene as a lubricant.
4. Final polishing was performed with 1 micron dia
mond paste on a felt cloth using an oil base
lubricant.
5. The sample was then rinsed in methanol, dried
in a stream of desiccated air, and taKen imme
diately to the differential reflectometer for
measurement.
With the exception that only one specimen needed to
be mounted, samples used in the microhardness tests were
ground and polished by the same method as above through
the diamond polish. In order to reveal the grain structure
the samples were swabbed with an etchant composed of 2:1:1
ammonium hydroxide:hydrogen peroxide (3%):water. These


36
transitions were measured for copper solid solutions contain
ing various multivalent alloy additions. It was found that
the transition energy was a function of composition (see
Figure 2-9).5 Up to 1% solute there is no change in the
threshold energy. Past 1% solute, the transition energy is
a linear function of composition. It is evident that Figure
2-9 can also be used as a calibration curve, so that if the
transition energy of an unknown alloy is measured, then the
quantity of solute in that alloy can be determined. Thus, it
is possible to use optical measurements as a means of deter
mining the solute concentration of a binary copper alloy.
In the case of multivalent solutes in copper, of course, this
method would only be useful for solute concentrations above
one percent.
So far, the discussion has been directed only at alloys
of copper which contained solutes having two or more valence
electrons, where the increase in the Fermi energy could be
understood on an intuitive basis. The situation becomes
more complex when transition elements are added to copper.
As an example of a copper-transition metal alloy, copper-
nickel has been studied in great detail,7< 63-66 because they
display complete solid solubility. Since nickel has an un
filled d-band -- its electronic configuration is 3d^4s^ --
the intuitive expectation is that when nickel is added to
copper, the copper 4s electron might supply the extra elec
trons necessary to fill the d-band of nickel. It would then
be expected that the Fermi energy of copper would be lowered,


This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
May, 1986
Dean, College of Engineering
Dean, Graduate School


65
Table 4-1. Radius of Precipitate at Peak Property
for Copper-Cobalt System
Particle Radius
at Peak
Measurement
Ref
Livingston
& Becker
O
70 A
Hardness
29
Livingston
70 A
Yield Stress
30
Phillips
46-75 A
Hardness
33
Phillips &
Livingston
175 A*
TEM
31
Phillips
50 A
Yield Stress
34
Humphreys
120 A
TEM
35
Threadgill
& Wilshire
40-75 A
Creep
43
Amin, Gerold & Kralik
100 A
Hardness
44
Wilnelm
70 A
Not Specified
46
Tautzenburger & Gerold
O
40 A
Creep
48
*
Sample Undeformed


REFLECTANCE
39
Figure 2-10. Reflectance Spectra for Copper and Two
Copper-Nickel Alloys. (Ref. 63)


8
here in order to provide a basis from which the specifics
of the copper-cobalt precipitation reaction will be dis
cussed
When an alloy is held at a temperature at which its
solute composition extends beyond the solvus, the lattice
will reject solute atoms. As the solute atoms are rejected,
they will begin to form clusters. This is the first stage
of precipitation and is called nucleation. Thermodynami
cally, nucleation is driven by the difference in the volume
free energy of the solid solution and the volume free energy
of the decomposed system consisting of the precipitate
phase and the matrix phase which is still a solid solution,
though possessing a reduced solute content. Schematically,
this is shown in Figure 2-1. The a phase at c can be seen
to possess a higher free energy, Ga, than the free energy
of the decomposed system, Ga+B. If, as is the case of preci
pitation hardenable alloys, the solubility decreases with
temperature, then the difference in the free energies, AG,
will increase the farther the alloy is held below the sol
vus (the greater the undercooling). This increases the
nucleation rate and decreases the size to which a cluster
must grow before it becomes stable and capable of increas
ing its size through growth. In general it is held that
there are two "energies" which oppose the formation of
stable clusters: surface energy and strain energy. When a
cluster forms, it must eventually form an interface with
the surrounding matrix. Because surface energy is added


VICKERS HARDNESS C DPN D
62
As 1 10 100 1000
quenched
TIME C hr 3
Figure 4-5. Hardness vs Time for Cu-2.0% Co Aged at 600C
500C, and 400C.


35
diagrams and interband transitions, it still holds for those
regions where no interband transitions occur.
In addition to this decreased reflectivity, the transi
tion which occurs at 2.2 eV is shifted to higher energies as
the zinc concentration in the brass is increased. This in
crease in the threshold energy causes the change in color in
brasses from red at low zinc concentrations to yellow at high
zinc concentrations. It has been found that upon alloying
with elements having a valence of greater than one, that the
subsequent energy increase of the threshold transition above
2.2 eV is caused by a rise in the Fermi energy due to the
addition of extra electrons from these elements and to a nar
rowing and raising of the d-bands.5>60 The earliest attempt
to explain the transition energy increase upon adding ele
ments of higher valence than the host metal was proposed by
Mott61'62 j_n 1935 in the rigid band model. Although the
model did correctly predict the rise in the Fermi energy, it
did not predict the shift that occurs in the d-band upon al
loying. This led to a prediction of a larger shift in the
transition energy at 2.2 eV than was seen experimentally.
Calculations made by Bansil et al.60 accounted for the shift
upward in the d-bands as well as the Fermi energy and there
fore the smaller shift in the threshold energy.
Hummel's laboratory5>6,7 has experimentally verified
that the shift in the transition energy at 2.2 eV is smaller
than that predicted by the rigid band model. Using a dif
ferential reflectometer, the energies of electronic


12
grain boundaries. Similar to general precipitation, it
occurs simultaneously throughout the alloy; however, be
cause the precipitates form at defects, the precipitates
are distributed non-uniformly.
25
Finally, discontinuous precipitation is characterized
by the formation of second phase in random parts of the
alloy at random times. Discontinuous precipitation is as
sociated with the movement of an interface, such as a grain
boundary during recrystallization and grain growth.
The effect of precipitation on mechanical properties
depends on several microstructural aspects, such as the
extent of the solid solution, the coherency of the precipi
tate, the dispersion of the second phase, and recrystalliza-
24
tion. All mechanical properties are affected by these
microstructural factors; however, for the reason that micro
hardness tests were performed for this work, the changes
in hardness experienced by an alloy undergoing a precipita
tion reaction will now be considered. In Figure 2-2, a
composite hardness curve is depicted with the contributions
from each microstructural factor also shown. The details
of this graph are discussed below.
Solid solution hardening takes place because the differ
ence in size between the atoms of the host metal and the
solute atoms necessitates the accommodation of solute atoms
at places where strain is introduced the least. As mention
ed earlier, this means that solute atoms collect at defects
in the lattice such as dislocations and grain boundaries.


CHAPTER 4
EXPERIMENTAL RESULTS AND DISCUSSION
4.1 Microhardness Tests: Results and Discussion
Previous experiments on dilute copper-cobalt alloys
have established that the changes in hardness which occur
during aging heat treatments are caused by the formation
of spherical cobalt-rich precipitates. The purpose of
performing microhardness measurements for this work was to
provide a link from these previous experiments to the
optical measurements designed for this work. In this sec
tion, results of the microhardness tests will be presented.
The results will be seen to be consistent with that which
is known to occur during a precipitation reaction. Fur
thermore, it will be shown that the results of these mea
surements verify the findings of other researchers who
have performed similar measurements.
Microhardness measurements were carried out on alloys
containing 2.7 a/o Co, 2.0 a/o Co, and 1.0 a/o Co. These
alloys were aged at three different temperatures -- 600C,
500C, and 400C. The results of these measurements can be
seen in Figures 4-1 to.4-6.
In Figure 4-1, the diamond pyramid number is plotted
versus aging time for alloys containing the three amounts
54


102
polished. It is therefore unlikely that the signal strength
of the optical measurements was influenced by a selective
oxidation mechanism.
On the basis of these arguments, the conclusion can be
reached that the observed signal strength at 2.2 eV for al
loys aged at 600C is the product of a precipitation reac
tion, which after 590 hours of aging has been completed.
Furthermore, it is evident that the equilibrium solute con
centration has been reached. Therefore, for alloys of all
compositions aged at 600C, the matrix solute concentration
after 590 hours of aging should be 0.4% Co. It must be re
called how the optical measurements on the aged samples
were carried out. An alloy, which was aged, was measured by
differential reflectometry against an alloy which contained
the identical solute concentration, but in solid solution.
Therefore, the difference in solid solution solute concen
tration between these two alloys can be assumed to be known.
Because this difference is the independent variable on the
calibration curve of Figure 4-21, the lower curve of this
figure was constructed.
It must also be recalled that the difference between the
two curves shown in Figure 4-21 is that the upper curve was
produced from data taken from alloys which differed by a
known solid solution solute concentration only, whereas the
lower curve was produced from data taken from alloys which
differed by a known solid solution solute concentration and
in which one of the alloys contained precipitates. It is,


.92
Figure 4-18. Peak Height vs Time for Cu-2.7% Co at Various
Aging Temperatures.


TABLE OF CONTENTS
Page
ACKNOWLEGDEMENTS
LIST OF TABLES v
LIST OF FIGURES vi
ABSTRACT ix
CHAPTER 1. INTRODUCTION 1
CHAPTER 2. OBSERVATIONS CONCERNING PRECIPITATION
AND OPTICAL PROPERTIES OF ALLOYS 4
2.1 Precipitation: General 4
2.2 Precipitation in Dilute Copper-
Cobalt Alloys 17
2.3 Optical Properties of Copper and
Copper Alloys 30
CHAPTER 3. EXPERIMENTAL PROCEDURE 4 3
3.1 Experimental Approach 43
3.2 Alloy Preparation 44
3.3 Differential Reflectometer 47
3.4 Polishing Procedure 50
3.5 Aging 51
3.6 Microhardness Tests 52
CHAPTER 4. EXPERIMENTAL RESULTS AND DISCUSSION 5 4
4.1 Microhardness Tests: Results and
Discussion 54
4.2 Compositional Modulation: Results
and Discussion 66
4.3 Aging Experiments 82
4.4 The Kinetics of the Precipitation
Reaction 109
iii


0.5% YIELD STR. CKSn
26
100
A.Q. 1
100
MINUTES
10000
Figure 2-6. Yield Strength and Hardness versus Tine for
Cu-2.0% Co Aged at Various Temperatures.
(Ref. 30)
HARDNESS EDPN3


108
of the matrix, one would expect that the magnitude of the
suppression would be the same as the volume fraction of pre
cipitates, in this case 3%. It is suggested that the re
flectivity of the precipitates -- Co-10% Cu -- be obtained
and add an appropriate percentage of this reflectivity to
the reflectivity of a solution heat treated Cu-0.4% Co al
loy (the equilibrium solute concentration of the alloys).
This would provide a situation in which the two reflectiv
ities were completely independent. It would then be pos
sible to determine quantitatively if this reflectivity dif
fered from the reflectivity of an alloy in which the precipi
tates are actually embedded in the lattice on an aged alloy.
This type of analysis would provide a method for determining
the precise interaction between the optical properties of
the precipitates and the matrix.
Lastly, experiments could be performed which explore the
two phase field in the copper-cobalt system. These exper
iments would be similar in scope to the types of experiments
Hummel^i performed on the silver-aluminum system. They could
be designed to explore the optical properties of alloys which
contain different amounts of the second phase. With this as
the independent variable, the optical properties of the sec
ond phase and its interaction with the primary phase might
be revealed more precisely.
In conclusion, the validity of the calibration curve
obtained from the optical measurements of the aged alloys
has been analyzed. It has been reasoned that the aging heat


58
aged at 600C. The fact that these values are higher can
be accounted for by the lower solubility at 500C for Co
in Cu. At 600C, the solubility for cobalt is about 0.4%
whereas at 500C, it is less than 0.1%. This decreased
solubility leads to a greater volume fraction of precipitate
as determined by the phase diagram tie line, which in turn
leads to a higher hardness. Again, it can be seen that
at each aging time the alloy containing a greater amount
of solute possesses a higher hardness.
The results of aging each alloy at 400C can be seen
in Figure 4-3. At 400C there is only a very slight in
crease in the hardness for each composition in aging up
to 26 hours, indicating that the precipitation reaction
has barely begun even after this length of time. The dif
fusion rate is evidently so slow at this temperature that
in terms of aging time several more orders of magnitude
of time would be necessary to bring these alloys into a
condition of peak hardness. These results did show, how
ever, that room temperature aging would not occur and that
therefore it was not necessary to give the sample a solu
tion heat treatment before each aging experiment was per
formed. This allowed the use of individual samples for
a series of aging times thus avoiding the error associated
with using different samples. This observation was also
37
made by Witt and Gerold.
In Figures 4-4 to 4-6 are plotted the diamond pyramid
number versus aging time for each composition where aging


NORMALIZED DIFFERENCE IN REFLECTIVITY
75
ENERGY CtVD
1.6 2 2.5 3 4 5.5
Figure 4-9. Differential Reflectograms of Cu-2.7% Co
versus Cu-0.5% Co, Cu-i.0% Co, Cu-I.5% Co,
Cu-2.0% Co, and Cu-2.5% Co.


CHAPTER 1
INTRODUCTION
The color of alloys of metals has from ancient times
been recognized as being influenced by the composition of
the alloys. Artisans of many cultures surely experimented
with combinations of metals in order to achieve the color
they desired in the pieces they created. It was not until
this century, however, that the link between the composition
of an alloy and its color was understood. ^ With the develop
ment of solid state physics came the realization that the
optical properties of metals and alloys are a reflection of
2
their electronic structure, specifically the valence band.
One instrument which has been successful in measuring
the optical properties of alloys in order that electronic
structure could be better understood is the differential
3 4
reflectometer. With this instrument, the electronic
structures of copper alloys containing multivalent sol
utes, 5''7 copper-nickel,7 copper-gold,5 noble metal al
loys,5' and nickel-based alloys^have been investigated
for composition dependence. In addition the effect on the
electronic structure of the arrangement of constituents
within alloys has been explored in studies of long range
11 12
order and short range order. Finally, the removal of
1


104
has investigated a binary two phase system, silver-aluminum,
and found that in the two phase field that there was a non
linear optical response to the relative amounts of each
phase. Perhaps this type of behavior is seen in the copper-
cobalt system as well.
Another possibility is that the precipitates might be
influencing a much larger volume than is equal to the volume
fraction because they exert strain in the lattice. As long
as the precipitates remained coherent, the strain exerted by
them would extend into an appreciable volume of the alloy.
This strain would have the effect of changing the lattice
parameter of the alloy which, in turn, would influence the
optical properties. This could account for the large sup
pression of the signal strength that was observed in the
optical properties of the aged alloys.
Finally, the behavior of the feature in the differential
reflectograms labelled "c" in Figure 4-8 was examined to
determine whether or not the precipitates influenced the
optical properties of the alloys. This feature of the
differential reflectograms is seen to be formed in the shape
of a "well". It is believed to be the result of electronic
transitions from cobalt d-bands to the Fermi energy and thus
might provide a measure of the amount of cobalt in an alloy.
Analysis of the data from the compositional modulation ex
periments revealed that the depth of this "well" was depen
dent on the difference in cobalt concentration between two


88
minutes. In addition, the size of the initial rise in
signal strength increases with solute content. After this
initial rise, the signal strength increases monotonically
for all compositions. For all other compositions and aging
times, the signal strength is largest for the alloy con
taining the most solute. Because signal strength is di
rectly related to difference in solute content, these data
indicate that the alloy containing the greatest amount of
solute is losing the greatest amount of solute during aging.
This is consistent with the gradient-driven mechanism of
precipitation.
At the conclusion of the reaction, the matrix solute
content will be the limit of solubility for cobalt in cop
per (about 0.4% Co at 600C). This value is the same for
all initial solute compositions. Therefore, alloys with
higher initial solute concentrations must reject more solute
than alloys having lower initial solute concentrations in
order to reach the solubility limit. Consequently, the dis
parity in matrix solute content between a solution heat
treated and aged sample and one which has been solution heat
treated only will be larger in an alloy that has higher
solute concentration.
This pattern of finding larger signal strength for lar
ger solute concentration is also seen in Figure 4-16, where
the signal strength as a function of time is plotted for
each of the three compositions aged at 500C. Again, the
signal strength increases monotonically for all compositions,


ACKNOWLEDGEMENTS
The author wishes to recognize the contributions of the
following people, without whose efforts this work could not
have been completed.
The typing of this dissertation was done by Susan Matts
Goho. This enormous task represents a tiny fraction of the
support which she has provided. She has provided me with
the technical, academic, and emotional means with which to
bring this long process to an end. This accomplishment must
be shared equally with her.
The author is grateful to Dr. R. E. Hummel for his
unique attitude in helping his students in all aspects of
their concerns as well as for his technical advice. I have
benefitted greatly from his tutelage and aspire to be as
good a teacher as he.
Dr. P. H. Holloway has provided many hours of helpful
discussions on matters of concern to this dissertation. He
has also provided much needed encouragement at crucial times
during the writing of this work.
The author wishes to thank all the members of the dis
sertation committee for their efforts.
11


and with the results of previous measurements of mechanical
properties of aged copper-cobalt alloys.
xi


68
In Figure 4-7, differential reflectograms for average
sample compositions of Cu-1.5% Ni and Cu-1.5% Co are pre
sented. In this figure, an almost identical pattern in
optical response is evident. The features of the copper-
nickel differential reflectogram have already been described
8 4
oy Hummel. The structure from "a" to "b" is caused by
interband transitions at the threshold energy of 2.2 eV.
The maximum designated "d" is a manifestation of transitions
from the lower d-bands of copper to the Fermi energy. Fi
nally, the broad structure at "c" has been ascribed to
electronic transitions involving the d-bands of nickel. The
similarity between these two reflectograms represents a
new type of pattern seen in differential reflectograms.
Previous work on copper with multivalent solutes revealed
that all differential reflectograms of this alloy group had
a common pattern. The evidence here suggests that there
will be one pattern for all differential reflectograms of
copper-transition metal alloys.
The study of the effect of cobalt composition on the
electronic structure of copper was then broadened. These
compositional modulation experiments were conducted by
changing the average composition of the two samples studied
by differential reflectometry. (It has been shown11 that
the transition energies measured by differential reflecto-
metry are the equivalent of the transition energies for an
alloy whose composition is the average of the composition
of the two alloys measured, provided that the difference in