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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xi, 132 leaves : ill. ; 28 cm.
Goho, William Michael, 1954-
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Copper alloys   ( lcsh )
Reflectometer   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
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theses   ( marcgt )
non-fiction   ( marcgt )


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




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

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

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

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


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


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




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

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

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

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




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




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


LIST OF FIGURES (continued)


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


LIST OF FIGURES (continued)


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


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



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


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



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



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


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.


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



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


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




z AG~z



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


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


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


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


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


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.



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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


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,


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.


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


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


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


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


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.


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,


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



<40 AGING TEMR= 600C

020 /

As 10 100 1000 10000
Quenched MINUTES

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



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

o ;!

J 600*C

1I I-!
-8 0 kA^n

//7000C a


A.Q. 1 100 10000

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


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


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


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


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


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


f4 be






Ga -uB~u3



-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


20 6 Ff A


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


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


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


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,



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

Ln C-4

vZ 4




Ln C*4
cq C-4
LLJ 44


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


0.8 -0.90.8 NN

1*. 0.7-'

U 0.4-J6


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

Copper-Nickel Alloys. (Ref. 63)


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.


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.


0 0)




44 LU z :3 f:
w '4

C4 0

-W 41
-i :

44 rZ Q) a)

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



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



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


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.


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


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
brasses, thickness and formation kinetics of corrosion
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,



-L 0E

x. o


'A 0
0 .

4 -44


00 o 9')



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


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

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

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


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.


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


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.


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



r 100


80-/ ," 2.0%. zoCo

80 I1 1.0% Co

> 60 .

40 -0o

As 1 10 100 1000
quenched TIME Chr3

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


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



100- 2.7% Co

CL 2.0% Co

U 80LU
91.0% CO





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.


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



Z 80
o 2.7%Co

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.


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.


120 6000

z I
<. 80'- a



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

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



Il 000



~60 ;,/

40 Cu-2.O% Co

As 1 10 100 1000

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


r80- 600

1" 500

S60- / 4000

Cu-1.0% Co 4O0

As 1 10 100 1000

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


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


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

Particle Radius at Peak Measurement Ref.
Livingston & Becker 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
Wilhelm 70 A Not Specified 46
Tautzenburger & Gerold 40 A Creep 48

* Sample Undeformed


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


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.


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


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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


1.6 2 2.5 3 4 5.5

I "I I I I d

2.4 % Co 1.5% Co

0.5% Co






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

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


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


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.


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


1.6 2 2.5 3 4 5.5






800 600 400 200
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.


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


1.6 2 2.5 3 4 5.5



U 0.5/2.0

LU 1.0/2.0

0 z

800 600 400 200

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.


1.6 2 2.5 3 4 5.5


21 0.5/1.0


800 600 400 200

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


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


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



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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


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


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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


2.7% Co


/ I 2.0% Co

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.


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,


40 30
2.7% Co



20 ----
S2.0%Co 10


10 1.O Co

As 1 10 100

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