• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Review of previous work
 Theory of small angle x-ray...
 Experimental equipment and...
 Experimental results
 Discussion of results
 Conclusions
 Appendix
 Bibliography
 Biographical sketch














Title: Guinier-Preston zone evolution in 7075 aluminum
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Permanent Link: http://ufdc.ufl.edu/UF00097506/00001
 Material Information
Title: Guinier-Preston zone evolution in 7075 aluminum
Physical Description: xii, 184 leaves : ill. ; 28 cm.
Language: English
Creator: Healey, John Thomas, 1950-
Publication Date: 1976
Copyright Date: 1976
 Subjects
Subject: Aluminum   ( lcsh )
Precipitation hardening   ( lcsh )
X-rays -- Scattering   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 177-183.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by John Thomas Healey.
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Bibliographic ID: UF00097506
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000175126
oclc - 03020498
notis - AAU1595

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Table of Contents
    Title Page
        Page i
        Page i-a
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
        Page ix
        Page x
    Abstract
        Page xi
        Page xii
    Introduction
        Page 1
        Page 2
        Page 3
    Review of previous work
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
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        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
    Theory of small angle x-ray scattering
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
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        Page 41
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        Page 46
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    Experimental equipment and procedures
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
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    Experimental results
        Page 64
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    Discussion of results
        Page 132
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    Conclusions
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    Appendix
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    Bibliography
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    Biographical sketch
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Full Text
















GUINIER-PRESTON ZONE EVOLUTION IN 7075 ALUMINUM

by

JOHN THOMAS HEALEY





















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



UNIVERSITY OF FLORIDA


1976






































UNIVERSITY OF FLORIDA
3 1111111111111111111111111111111111111111111262 08552 326111111111111111111
3 1262 08552 3263






























To Connie











ACKNOWLEDGMENTS


The author wishes to thank his chairman, Professor

Robert W. Gould, who devoted much of his time, and gave

both many helpful suggestions and encouragement during the

course of this study. He is also indebted to other mem-

bers of his committee, Professors John J. Hren, Robert E.

Reed-Hill and Frank Blanchard, as well as Professor Rolf

E. Hummel, whose valuable assistance and suggestions have

aided in the completion of this work.

The author is grateful to the National Science

Foundation for the financial aid of NSF grant # GH 31817.

The author also wishes to thank John M. Horn,

William Schulz, John Garrett and Vicki Turner for their

assistance provided during this endeavour.


iii















TABLE OF CONTENTS


ACKNOWLEDGMENTS...............

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

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

ABSTRACT...................

INTRODUCTION ................

CHAPTER


REVIEW OF PREVIOUS WORK................

THEORY OF SMALL ANGLE X-RAY SCATTERING.

EXPERIMENTAL EQUIPMENT AND PROCEDURES..

The Alloy...............................

Small Angle and Tensile Test Sample
Preparation.............................

Resistometry Sample Preparation.........

Solutionizing and Aging...............

Wide Angle Diffraction.................

Small Angle X-Ray Scattering...........

Resistometry Measurements..............

Tensile Testing.........................

EXPERIMENTAL RESULTS...................

Resistivity.............................


Small Angle X-Ray Scattering


. .... .. . .. .. ..... 6 7


Preliminary Studies of Initial Aging.........67


I

II

III






















IV


.............

.............

.............

.............

.............


PAGE




....vi
...vii


.... xi






.....4

....23

.... 48

....48


.... 48

....49

.... 50

....51

....53

.... 62

....63

....64

....64









PAGE

Change in Zone Size Parameter....... ........68

Relative Integrated Intensity...............110

Wide Angle Diffraction......................... 110

Metallography..................................131

V DISCUSSION OF RESULTS........................... 132

Small X-Ray Scattering.......................... 132

CONCLUSIONS ............................................152

APPENDIX ............................................ ... 155

BIOGRAPHICAL SKETCH....................................177

BIBLIOGRAPHY ...........................................178












LIST OF TABLES


Table Page

1 Equilibrium Phases.............................. 20

2 Machine Parameters .............................57

3 Summary of Aging Series........................ 67

4 Summary of Results of Wide Angle Diffraction..120

5 List of Variables Used in SAXS Program........157

6 Data Input for SAXS Program................... 160











LIST OF FIGURES


Figure Page

1 Reciprocal Space of the Aluminum Matrix
and Guinier-Preston Zones ......................26

2 Direction of Incident and Scattered Beam........32

3 Moment Distribution of a Particle About
the Origin .....................................33

4 Geometric Relation of a Particle to the
Origin .........................................36

5 Schematic Representation of Guinier De
Wolff Camera...................................52

6 Schematic of Kratky Camera from Interna-
tional Union of Crystallography Commission
on Crystallographic Apparatus.................. 54

7 Schematic of Slits System in Kratky Block......55

8a Scattering Curve for Lockheed Pyrolitic
Graphite .......................................59

8b Porod Region of Lockheed Pyrolitic Graph-
ite Scatterer...................................61

9 Resistivity Aging Behavior of 7075 Wires.......65

10 Arrhenius Plot of Resistivity Maxima............66

11 Fixed Angle Scattered Intensity for 7075
A lloy ..........................................69

12 Arrhenius Plot of Time to Reach Scattered
Intensity of 1.5 Counts Per Second.............70

13 Preliminary Study of Effect of Deforma-
tion-Fixed Angle Scattered Intensity........... 71


vii










Figure Page

14 Typical Small Angle Scattering Curve of
Directly Aged Sample ........................... 73

15 Typical Small Angle Scattering Curve from
a Preaged Sample............................... 75

16 Evolution of Guinier Radius as Determined
from SAXS for A, B, D Series................... 77

17 Evolution of Guinier Radius as Determined
from SAXS for E, F, FlH Series................. 78

18 Evolution of Guinier Radius as Determined
by SAXS for G and H Series..................... 80

19 Evolution of the Guinier Radius as Deter-
mined by SAXS for J and K Series............... 82

20 Evolution of Guinier Radius as Determined
by SAXS for L Series........................... 84

21 Evolution of Guinier Radius as Determined
by SAXS for M Series........................... 85

22 Porod Radius for A, B, D Series as Deter-
mined by SAXS ..................................88

23 Porod Radius Evolution for E, F, Flh Series
as Determined by SAXS............................90

24 Porod Radius Evolution for J and K Series
as Determined by SAXS............................91

25 Porod Radius Evolution for L Series as
Determined by SAXS...............................93

26 Porod Radius Evolution for M Series as
Determined by SAXS...............................94

27 Radius of Maximum Abundance for A, B, D
Series as Determined by SAXS...................95

28 Radius of Maximum Abundance for E, F Series
as Determined by SAXS............................96


viii










Figure Page

29 Radius of Maximum Abundance for F1H Series
as Determined by SAXS............................97

30 Radius of Maximum Abundance for J and K
Series as Determined by SAXS...................98

31 Radius of Maximum Abundance for L Series
as Determined by SAXS............................99

32 Radius of Maximum Abundance for M Series
as Determined by SAXS ......................... 100

33 Particle Size Distribution Evolution for
A Series ...................................... 101

34 Particle Size Distribution Evolution for
B Series ......................................102

35 Particle Size Distribution Evolution for
D Series ......................................10 3

36 Particle Size Distribution Evolution for
E Series ......................................104

37 Particle Size Distribution Evolution for
F1H Series ....................................105

38 Particle Size Distribution Evolution for
J Series ......................................106

39 Particle Size Distribution Evolution for
K Series ......................................107

40 Particle Size Distribution Evolution for
L Series ......................................108

41 Particle Size Distribution for M Series.......109

42 Relative Integrated Intensity for A and
B Series ......................................111

43 Relative Integrated Intensity for E, F,
F1H Series ....................................112











Figure Page

44 Relative Integrated Intensity for G and
H Series ......................................114

45 Relative Integrated Intensity for J and
K Series ......................................115

46 Relative Integrated Intensity of L Series.....117

47 Relative Integrated Intensity for M Series ....118

48 Densitometer Scans of Eseries (1250C Age)
Guinier-De Wolff Films........................ 119

49 Results of Tensile Tests for A, B, D Series...122

50 Results of Tensile Tests for E, F Series ...... 123

51 Results of Tensile Tests for G, H Series...... 124

52 Results of Tensile Tests for J Series.........126

53 Results of Tensile Tests for K Series ......... 128

54 Results of Tensile Tests for L Series.........129

55 Results of Tensile Tests for M Series.........130

56 Schematic Representation of Type B Ser-
rated Flow.....................................143

57 Interaction of a Dislocation Line With
the Coherency Strains Surrounding a Guinier-
Preston Zone...................................145

58 Representation of Area Created by Passing
of a Dislocation Through a Guinier-Preston
Zone, Along with the Applicable Geometry...... 147










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



GUINIER-PRESTON ZONE EVOLUTION IN 7075 ALUMINUM

by

John Thomas Healey

June, 1976


Chairman: Dr. Robert W. Gould
Major Department: Materials Science and Engineering


This research has been concerned with the growth of

Guinier-Preston zones, their transformations, and the re-

lation of these substructures to the mechanical properties

of 7075 aluminum. Thermomechanical treatments, as well as

thermal preage treatments, were performed on the alloy.

The principle technique of this investigation was X-ray

small angle scattering.

Mechanical treatments did not change the aging se-

quence, but did increase the aging kinetics. Preage

treatments produce a narrow stable Guinier-Preston zone

size distribution which remains stable upon final ele-

vated aging.

Wide angle scattering indicated that no large misfit

existed between the matrix and the Guinier-Preston zones,











and that the zones transformed to an intermediate precipi-

tate n', than to the equilibrium phase n.


xii











INTRODUCTION


The phenomenon of age hardening in aluminum alloys

was first observed by Wilm in 1905. The discovery was

quite accidental. Wilm had been trying to harden an alu-

minun-4% copper-0.5% silicon-0.5% manganese alloy by

quenching from 525C in a manner analogous to steels. The

experiment initially was a failure as the material proved

to be quite soft, but several days later, while measuring

the hardness, Wilm found it had hardened at room temper-

ature. Wilm could not explain this increase, as optically

he could not observe any structural differences between

the hard and soft specimens. Wilm did not publish this

work until 1911, at which time he merely presented the

results without attempting to offer an explanation.

The first explanation of this anomaly was offered by

Mercia, Waltenberg and Scott, who concluded that since the

solid solubility of copper and silicon is higher at 5250C,

the increase in strength must be due to the slow precipi-

tation of some second phase at room temperature.

Jeffries and Archer further proposed that these second

phases were really submicroscopic particles of the equi-

librium phase. The proof of the nature of the hardening













agents-had to wait until 1938, when Guinier and Preston

first demonstrated that small clusters of solute atoms

would produce diffuse x-ray scattering at small angles.

This technique provided the means to directly study these

coherent clusters, today known as Guinier-Preston zones

or merely G.P. zones.

The next major advance in the study of precipitation

was the continuing development of the transmission elec-

tron microscope and the development of sample preparation

techniques. This enables the researcher to actually see

the zones, their distribution within the matrix, and to

follow their evolution with time. Transmission electron

microscopy also offered the ability to observe the rela-

tionship of the zones to defects in the matrix, such as

dislocations and grain boundaries.

Extensive studies into many of the age hardenable

systems have been made, employing a wide variety of tech-

niques; hardness measurements, resistometry, small angle

x-ray scattering and, somewhat later, transmission elec-

tron microscopy. The basic goal of all these investi-

gations has been to obtain an insight into the complex

mechanisms of age hardening, and, thereby, be able to

predict alloy mechanical properties by a detailed knowl-

edge of the zonal state.












Polmear and Gerold have done much of the early work

on the aluminum-zinc-magnesium system. These researchers

have studied the effects of various alloy compositions,

and, in conjunction with these, many different aging se-

quences. The next logical step in the investigation of

the age hardening process is to study the complex ternary

and quaternary commercial alloys. This is the subject of

this dissertation. The present investigation is con-

cerned with characterizing the various zonal states of

the commercial 7075 alloy (5.7% Zn-2.6% Mg-1.6% Cu), and

their interrelation with mechanical properties. The main

technique of the investigation will be x-ray small angle

scattering.












CHAPTER I

REVIEW OF PREVIOUS WORK


Extensive work has been done on the decomposition of

aluminum-zinc alloy systems. Some of the earliest work on

this system was done by Guinier, who showed that the

clusters which formed homogeneously upon quenching were

spherical in shape. The rapid growth of the clusters, or

Guinier-Preston zones, has been attributed to enhanced

diffusion in a system supersaturated with quenched-in va-

cancies. Resistometry work of Panseri and Federighi2

has shown the formation energy for vacancies to be 0.70

eV, the activation diffusion energy to be 0.54 eV, and the

binding energy between zinc atoms and vacancies to be on

the order of 0.05 eV.

Using small angle x-ray scattering, Gerold3 has

shown that the spherical zones continue to grow and main-

tain a spherical shape until a Guinier Radius of approxi-

mately 35 A is reached. At this size, growth is arrested

and the zones transform to an elliptical shape before

growth recommences. This shape change is a result of in-

ternal rhombohedral straining whose anisotropy causes the

elliptical shape.












4
Gerold has further shown that the composition of

the zones can be determined from the integrated intensity.

In this manner, the limits of the metastable miscibility

gap have been calculated.

Carpenter and Garwood have shown the aging se-

quence in Al-Zn alloys to be:

Spherical G.P. zones Elliptical G.P. zones -

Rhombohedral a' Cubic a' e (hexagonal zinc)

The rhombohedral a' phase is a transition phase resulting

from a partial loss of coherency of the zones during

growth. The rhombohedral a' phase retains coherency with

the (111) plane of the matrix. Further loss of coherency

results in the formation of the cubic transition a' phase.

Both of the a' transition phases remain homogeneous

throughout the matrix as they are both nucleated from the

homogeneous Guinier-Preston zones. The final equilibrium

phase, e (hexagonal zinc), is nucleated heterogeneously on

dislocations only during high temperature aging or pro-

longed aging of the a' phases.

The commerical usefulness of the aluminum-zinc binary

alloys is practically non-existant as these alloys will

overage at temperatures below room temperature, thereby

eliminating the strengthening effect of the Guinier-

Preston zones.













The addition of magnesium to the binary aluminum-zinc

system greatly alters the aging process of the system.

The most important change in the aging character is the

ability to retain the enhanced mechanical properties at

room temperature. This feature, combined with the fact

that the aluminum-zinc-magnesium system provides the

highest strengths attainable of age hardenable aluminum

alloys, has lead to a considerable amount of research into

their aging behavior.

Polmear6-11 did much of the early work on the Al-Zn-

Mg system. Polmear used hardness measurements to follow

the aging sequence. By plotting the incubation time of

the hardness curves, that time during which no increase in

hardness is observed, versus the reciprocal of the aging

temperature, Polmear produced a series of c curves whose

intersections indicated the equal probability of the

existence of two phases. Using this technique, Polmear

constructed the surface of the upper temperature limit of

stability for Guinier-Preston zones.11 For an alloy of

5.7 / Zn-2.6 / Mg, he shows this upper temperature to

be approximately 1750C.1l Polmear explains the greater

stability of Guinier-Preston zones with increasing Mg con-

tent as the greater ability of Mg + Zn to retain coheren-

cy with the aluminum lattice.7 The explanation for the












clustering of Mg and Zn together can be explained thermo-

dynamically. A mixture of aluminum and zinc, or of alu-

minum and magnesium, show a positive heat of solution,

while a mixture of magnesium and zinc possesses a negative

heat of solution. For this reason, the magnesium and zinc

atoms will be expected to cluster together on quenching.

A minimum in the heat of solution should be obtained at

some fixed Mg:Zn ratio. Polmear1 states that the con-

tinuous nature of the Guinier-Preston zone surface indi-

cates that the composition and structure of the zones must

remain fairly constant over a wide variation in composi-
12-13
tion. Gerold, however, has shown that the composi-

tion of the zone is dependent on the Mg:Zn ratio. If the

ratio is greater than unity, the zones have a MgZn compo-

sition, and if the ratio is less than unity, the composi-

tion becomes Mg3Zn5. The continuity of Polmear surface

can be explained by the fact that there is not an abrupt

change in zinc composition at these particular ratios, but

rather a gradual transition between the two compositions,

and that the thermal response of the two are very similar.

Nicholson and Lorimerl4 used transmission electron

microscopy to determine the upper limit of Guinier-Preston

zone stability. They quenched their samples directly from













the solutionizing temperature to the aging temperature,

and observed the distribution of phases present. Since

Polmear had already shown that nucleation of Guinier-

Preston zones was homogeneous while nucleation of n from

the solid solution was not, Nicholson and Lorimer4 des-

cribed the temperature at which the nucleation switched

from homogeneous to heterogeneous as the upper temperature

limit of Guinier-Preston zones. The limit determined in

this manner was approximately 150C lower for a 5.9 / Zn-

2.9 W/ Mg alloy.14 Lorimer's procedure yields the upper

temperature limit for nucleation of zones, while Polmear's

gives the upper limit for the existence of zones nucleated

at a lower temperature.

Mondolfo, Gjosten and Levinson proposed the se-

quence of aging in the Al-Zn-Mg system to be:

spherical G.P. zones -+ -+

Embury and Nicholson,16 as well as Tomita et al.,17 have

shown that except for very low concentration (>.5 atomic %

Mg), the G.P. zones remain spherical throughout the aging
17
process. Tomita observed the diffuse scatter at the

base of the (111) peak in 6.8 atomic % Zn and .06 2.0

atomic % Mg alloys, and concluded that when this size

effect scatter disappeared, the strain in the matrix

caused by the mismatch between the zones and matrix had












become negligible. Without the rhombohedral strains pre-

sent as in binary Al-Zn alloys, the zones will not undergo

a shape change.

Graf18 has shown that the transition phase n' grows

on the (111) planes of the aluminum matrix, although some

controversy exists as to the mode of nucleation of the

phase. Asano and Hirano9-21 propose from their calo-

metric studies, that Guinier-Preston zones are an inde-

pendent aging product, and do not act as a nucleation
22 8,10-11
site for the formation of r'. Parker,22, Polmear,'

Thompson23 and Baba24 indicate that the presence of addi-

tional elements, particularly silver, chromium and copper,

aid in the heterogeneous nucleation of n'. Dinkeloh,

Kralik and Gerold,25 as well as Lorimer and Nicholson,14

support the theory that Guinier-Preston zones larger than

a certain critical size can transform directly to the

transition phase; the support for this being the homo-

geneous distribution of q'. The work of Chang and

Morral2 indicates that while the Guinier-Preston zones do

not transform directly to n', zones of sufficient size can

act as nucleation sites for the heterogeneous nucleation

of the precipitate. The homogeneous distribution of n'

often observed would be explained by this process, as the

distribution of critically sized zones which could act as












nucleation sites would be homogeneously distributed

through the matrix. Bardhan and Starke27 give the criti-

cal Guinier Radius necessary for Guinier-Preston zones to

act as nucleation sites at 35 A, which is curiously simi-

lar to the size at which zones change from spherical to

ellipsoidal in the binary Al-Zn alloys. While the n'

phase is generally accepted to be hexagonal and semico-

herent with the aluminum matrix,15,26 with lattice para-
0 0 77 28
77 Ryum28 finds n' to be mono-
meters a =4.96 A, co=8.68 A, Ryum finds q' to be mono-

clinic with lattice parameters a=b=4.97 X, c=5.54 X and
29
8=120. Thackery,2 on the other hand, finds no evidence

for the existence of the n' phase, and proposes the aging

process to be:

SOLID SOLUTION G.P. zones n

while speculating that previous x-ray investigations may

have mistaken his X phase for n'.

The equilibrium n phase (MgZn2) can be formed dir-

ectly by the change of lattice parameter and.loss of co-

herency of '.15 The MgZn2 phase can also be nucleated

heterogeneously at dislocations and grain boundaries.26'29

With Mg:Zn ratios greater than 3:7,22 the n phase will it-

self transform to the equilibrium T ((Al,Zn)49Mg32) phase

with aging treatments above 200C; although, it has been
shown by Schmalzried and Gerold12 that this transformation
shown by Schmalzried and Gerold that this transformation












remains incomplete, even with extended aging at tempera-

tures greater than 200C and is only completed with aging

above 3000C.

Ryum2830-31 shows that this aging sequence is only

one of a possible three which can occur simultaneously or

independently, depending upon the conditions. The possi-

ble aging sequences as seen by Ryum are:

SOLID SOLUTION n

SOLID SOLUTION "nuclei" n' n

SOLID SOLUTION G.P. zones n' n

The new "phase" introduced by Ryum30 ("nuclei") is defined

as a vacancy-solute atom aggregate, but with a higher

upper temperature limit. Ryum31 presents the upper tem-

perature limit of the nuclei to be 300C as opposed to

1800C for Guinier-Preston zones. The first of Ryum's se-

quences (solid solution -* ) would have a high activation
31
energy and would occur heterogeneously on dislocations

and grain boundaries, or homogeneously, with a low parti-

cle density, after long aging periods. Bardhan and
29
Starke also show the presence of quench-in MgZn2 in a

5.8 weight % Zn-.71 weight % Mg, but not in a .51 weight %

alloy. They attribute this difference to a greater degree

of quench clustering in higher magnesium alloys.











31
Ryum31 states that the second sequence (solid solu-

tion + nuclei -- nr) occurs with quenching to room

temperature, holding for five seconds, then aging at

1500C. The nuclei were not observed in the transmission

electron microscope, with n' lying on {111} matrix planes

being the first observable phase. This reaction did not

occur in the grain boundary region or adjacent to dislo-

cations in the matrix due to the low vacancy concentra-

tion. The final sequence is identical to that presented

previously.

Several authors12'16'2931 have presented the orien-

tation relationship of the MgZn2 phase andthe transition

phase q' with the matrix. Mondolfo et al.15 suggest that

the basal plane of the hexagonal q' phase lies on the

(111) plane of the aluminum with the following relation-

ship:

(0001) n',(111)Al, (1120)1 (110)A1

12
Schmalzried and Gerold 12 have proposed three possible

orientation relationships between n phase and the aluminum

matrix:

a.) (1010) nI(100)Al, (0001) 1 I(011)A

b.) (1010) n (110)A1, (0001)n (111)A1

c.) (1010)n| (121)A1, (0001) I(111)Al











Thackery29 has shown that Gerold's relationship c.) can be
written as:

(1120) n (i11(0)A, (0001)n | (Il)A

which would make this orientation identical with that dis-
covered by Mondolfo for n', thereby indicating a direct
transition between the two phases. Embury and Nicholsonl6
give the orientation relationship to be:
(0001) n|(110)Al, (1010) nl (110)A

which presents a larger mismatch between the two phases
12 29
than those presented by Gerold.2 Thackery,29 examining
an aluminum-6 weight % Zn-2 weight % Mg alloy, determined
six possible relationships of n to the aluminum matrix.

1.) (1210) II(111)A1, (0001)n (110)A

2.) (1210) n (111)A1, (3032) In(110)A

3.) (1210) 1(111)Al, (2021) 1(121)Al

4.) (1210) T (111)A1, (1014) (110)A1

5.) (0001)n I(111)Al, (1010) |(110)A1

6.) (1010) |I(110)A, (0001)n (001)A1

Type 1 orientations were observed by Thackery to be laths
lying on {111} planes of the matrix with Types 2, 3 and 4
basically similar with a rotation of the precipitate on
the (111) planes. Type 5 corresponds to Gerold's Type












b.), while Type 6, which Thackery distinguished as elon-

gated eight-sided platelets, is identical to Gerold's

Type c.). Thackery found no evidence for the existence of

Gerold's Type a.), or of the Embury-Nicholson orientation

relationship. Thackery's Type 1 precipitate is presented

as the most common, being nucleated heterogeneously on

dislocations and atgrain boundaries and forming as plate-

lets on (111) matrix planes. Type 5 Thackery represents

as forming only as coarse particles resulting from direct

high temperature quenches, while Type 6 constitutes the

majority of particles in samples first quenched to room

temperature then aged.29
28
Ryum found evidence for the existence of all three

orientations proposed by Gerold, Embury and Nicholson's
28
relationship, and those of Thackery. Ryum28 also noted

that Gerold's orientation Type a.) had an appearance simi-

lar to that of Thackery's X phase.29

Resistometry has been widely used to calculate the

formation and activation energies of vacancies and vacan-

cy complexes.2'14'23'32-39 Panseri and Federighi2'34 did

much of the early work with resistivity on the aluminum-

zinc-magnesium system. By measuring the time to reach a

maximum of resistivity as a function of aging temperature,

they were able to calculate the values for the binding en-













ergy of zinc vacancy couples to be .06 eV and that of mag-

nesium vacancy couples to be .54 .08 eV, a value also

given by Gould and Gerold.40 They also concluded that

magnesium vacancy couples can diffuse freely at room tem-

perature, and that the movement of zinc atoms occurs by

means of these couples, and not via single vacancies as in

binary aluminum-zinc alloys.
33,41
Perry, by employing the initial rate of aging

as well as the time to peak resistivity, has determined

the apparent vacancy formation energy to be .70-.71 eV.

In working with concentrated (i.e., 10 weight %) zinc

alloys, Perry41 contends that the zinc vacancy binding

energy measured is not the true binding energy, but merely

an effective value obtained due to the clustering of zinc

atoms on quenching; the value Perry obtained was .06 eV,

in agreement with Panseri. Perry, however, obtains a

vastly different binding energy (.17 eV) for the magnesium

vacancy complexes, using a .009 atomic % Mg-4.01 atomic %

Zn alloy.35 Perry also notes that this small addition of

Mg was sufficient to slow down the aging process due to

the trapping of the vacancies by magnesium atoms. Panseri

and Federighi, as well as Gould and Gerold, note that

magnesium initially slows the aging process by trapping

vacancies, but also extends the aging time by up to an













order of magnitude. This effect is due to the fact that

magnesium will act as a vacancy source when the matrix has

become depleted in vacancies.
37
Ceresara and Fiorini,37 using a similar resistometric

technique, have measured the total kinetic activation

energy in Al-5 weight % Zn-l and 3.4 weight % Mg alloys to

be .67 eV, independent of magnesium concentration.

Several authors9-21'4243 have made use of a calori-

metric method to study the thermal stability of Guinier-

Preston zones, their reversion, and transformations to
19-21
transition and equilibrium phases. Asano and Hirano

have shown that Guinier-Preston zones become stable to

higher temperatures with longer aging times at lower tem-

peratures. Their calometric scans indicate that with

short aging times, the reversion of the zones is complete

before formation of n', which would indicate heterogeneous

nucleation of the transition phase, independent of the

zones. However, with longer low temperature aging times,

the heat absorption of zone reversion overlaps the heat

evolution of n' formation, which would imply some sort of

n' nucleation on the zone sites.

Of particular importance to commercial alloys is

their quench rate sensitivity, especially due to the pre-

sence of secondary alloying elements.













Several workers22-2344-46 have studied the quench rate

sensitivity of Al-Zn-Mg alloys with the additions of chro-

mium, silver, zirconium, manganese and copper. The con-

sensus of these authors is that all these secondary alloy

elements produce quench rate sensitivity, roughly in the

order presented. The cause, however, is not the same for

all these elements. In the case of copper, which presents

the least effect, Mondolfo47 has shown that the copper

precipitate (CuMgAl) can precipitate with a lower activa-

tion energy and, being structurally similar to MgZn2, can

act as easy nucleation sites for this phase; much the same
23
is true for zirconium (Al2Zr),23 and also for silver which
42
clusters readily in aluminum alloys.42 The effects of

chromium and manganese are more complicated. Both of

these elements have a low solubility in aluminum and would
46
tend to form clusters, but more important is that both

elements act to retard recrystallization by forming sub-

grain structure.46 This structure acts as both vacancy

sinks and as additional heterogeneous nucleation sites,

the former removing vacancies from the aging sequence and

the latter, solute atoms. Both of these effects will be

detrimental LO the final mechanical properties.

The most important parameter affecting the mechanical

properties is the size and distribution of the prepre-













cipitates and the precipitates. The only two ways to mea-

sure these parameters directly are small angle scattering

and transmission electron microscopy. Many investigators

have used TEM measurements to determine the precipitates
46
present,46 their orientation relationship with the

matrix12'1427'293031 and distribution within the

matrix.26'4853 The lack of resolution during the early

stages of aging and the tediousness of measurement of G.P.

zone size using transmission electron microscopy makes x-

ray small angle scattering the most accurate and fastest

method of direct measurement of the precipitation process.

Guinier5456 and Gerold5759 developed much of the

theory as it relates to the solid solution; this will be

presented later. In addition, Gerold12-13'25'58-60 also

did much of the early work on the Al-Zn-Mg system.

Tomita,17 as well as Bardhan and Starke,27 have shown that

except for the very low concentration alloys, there is

no zone size arrest, as in the Al-Zn system. Harkness,

Gould and Hren4850 have developed the mathematics for

converting the measured experimental small angle scat-

tering parameters into actual particle size distributions;

their development will be presented elsewhere.












Most of the direct measurements of G.P. zone size

distributions as a function of aging conditions have been

done on pure research grade alloys. The next logical step

would be to measure their evolution in a commercial alloy

complicated by the presence of a large number of alloying

agents and also by the presence of impurity atoms. The

purpose of this work will be to measure quantitatively the

evolution of Guinier-Preston zones in a commerical 7075

alloy, the effects of thermomechanical treatments on the

zones, and their relationship to the mechanical proper-

ties. The main technique of this investigation will be

x-ray small angle scattering.

Equilibrium Phases

The equilibrium phases possible in the aluminum-rich

corner of the aluminum-zinc-magnesium system are given in

Table 1.

The phases possible involving the trace impurity and

alloying elements present, such as Si, Mg, Ti, Cr and Mn,

will not be considered as their concentrations are suffi-

ciently low that they will be either incorporated in solid

solution, miscible in one of the other equilibrium phases,

or so widely dispersed that they will have little effect

on the alloy as a whole.










Table 1

Equilibrium Phases

Phase Notation Crystal Lattice Parameter A
Structure

Al a FCC a =4.049 (47)

MgZn2 n HCP ao=5.16-5.22 (47)
CuMgAl c0=8.49-8.55 (47)

(Al,Zn)49Mg32 T cubic ao=14.29-14.71 (47)
CuMg4Al6

?X HCP a =2.66 (29)
0
c =4.94
o

FeAl3 X Monoclinic a=15.48
b=8.083
c=12.17
B=107043'



The a phase lattice parameter varies linearly from a

low of 4.018 A at 57 weight % zinc to a maximum of 4.1294

at 17 weight % magnesium. The n phase, MgZn2, is a proto-

type of the hexagonal Laves Phase.47 Thomas and

Nutting88 have shown that an appreciable amount of copper

can also be dissolved in the n phase. Mondolfo. Gjosten

and Levinson5 have shown that the r phase is the only

ternary phase that occurs with aging temperatures below

2000C.

The T phase, (Al,Zn)49Mg32, is a complex cubic struc-
47
ture of 162 atoms to the unit cell. The lattice













parameter varies as the Al:Zn ratio with the magnesium

content remaining essentially constant. Little,

Hume-Rothery and Raynor89 have shown that the T phase can

dissolve a significant amount of copper also, as the

CuMg4Al6 phase is completely miscible with T. Mondolfo

et al.1 have shown that the T phase is slow to nucleate

and is present only with extended aging above 2000C.

Thackery29 indicates an undetermined phase present in

Al-6 weight % Zn-2 weight % Mg, and designates it as X

phase. He determined it to be hexagonal, appearing as

triangular-shaped particles whose sides are parallel to

(110) matrix planes, and whose lattice parameters are ex-

tremely similar to those of pure zinc. The X phase may

truly be zinc precipitated from small zinc clusters with

limited quantities of alloying elements in solid solution.

The X phase is the result of iron being an impurity

in all commercial aluminum alloys. It is very slow to

homogenize and does not tie up any of the major alloying

elements, and is subsequently important to the aging pro-

cess only to the degree that it can act as a heterogeneous

nucleation site. The real importance of the X phase lies

in its detrimental effect on the fracture mechanics of the

alloy.





22






The chromium addition is present to enhance stress

corrosion resistance and the phases formed do not greatly

effect the aging process. Titanium is added as a grain

boundary refiner, and the other impurities present may

affect the kinetics of the aging process, but do not

greatly tie up the effective alloying constituents.













CHAPTER II

THEORY OF SMALL ANGLE X-RAY SCATTERING


Small angle scattering has a variety of applications;

the study of macromolecules, polymers and clays. In

1938, Guinier proposed their use for the study of

inhomogeneities in dilute alloy systems. There are sev-

eral restrictions placed on the study of dilute alloy

systems. First of all, the alloy must contain regions of

electron density inhomogeneities of a size greater than

atomic radii. Secondly, these inhomogeneities must be

smaller than 1000 X, the approximate upper limit of res-

olution at that time.

The inhomogeneity must have a fairly significant

electron density difference from the matrix and must be

reasonably concentrated (approximately 1% of scatterers

for Guinier-Preston zones) in order to produce measurable

scatter in a thin sample necessitated by x-ray absorption

in the sample. (The thickness for an aluminum alloy

using MoKa radiation is approximately 0.7 mm.)

The last of these restrictions, a measurable scat-

ter, is largely restricted by instrumental parameters.

As the electronics become quieter and more sensitive, the













minimum quantity of inhomogeneities also becomes lower.

This is a result of the statistics of the count rate.

To understand the origin of the scatter, the concept

of the reciprocal lattice must first be understood. In

reciprocal space, all lattice planes (hkt) of real space

are represented as reciprocal lattice nodes. The size,

shape and spacing of the reciprocal lattice nodes are

inversely proportional to the size and shape of the crys-

tal in real space, and the interplanar spacings, res-

pectively. Thus, large crystals in real space would be

represented as small point-like nodes in reciprocal space,

while large platelets would appear as long narrow cylin-

ders in reciprocal space.

In the case of Guinier-Preston zones, there are two

sets of reciprocal lattices; the matrix and the G.P. zones

themselves. The matrix, being large crystals, will be re-

presented by sharp reciprocal lattice points, neglecting

stress and temperature effects. The G.P. zones will have

their reciprocal lattice nodes centered at the same posi-

tion as the matrix nodes, as the G.P. zones have the same

crystal structure as the matrix. However, the small size

of the G.P. zones produces reciprocal lattice nodes which

are broad and spread.











Applying the Ewald Sphere concept, diffraction will

occur whenever the diffraction beam vector, (IS =~),

intersects a reciprocal lattice node. The diffraction

vector, S, is drawn from the center of the Ewald Sphere,
S
whose radius, |-1I, is directed to the (000) node, to any

reciprocal lattice node that intersects the Ewald Sphere.

When this happens, diffraction is said to occur. In the

case of large crystals where the nodes are sharp and

point-like, diffraction is restricted to these points,

with nothing occurring between them. This diffraction is

restricted to definite angular regions. However, with

small G.P. zones, the nodes are large; thus,-there is a

greater probability of the Ewald Sphere intersecting a

reciprocal lattice node of the G.P. zones surrounding

those of the matrix. Figure 1 shows reciprocal space of

the matrix and the G.P. zones. This accounts for the

greater angular range of diffraction for the G.P. zones.

The two diffraction peaks superimpose and the G.P. zone

peak is evidenced as a deviation from a Gaussian distri-

bution at the base of the matrix peak. This scatter is

present around all the Bragg peaks, as well as the (000)

node. Observation of this scatter is generally simplified

around the (000) node, as such effects as strain and tem-

















(1)
C-,,
L&j




NN
ccc


0


E I
U)
0



Gd
4










I
ca
:2:









0













o



0 04
r-4


0














r4
P-4













perature which cause broadening of the Bragg diffraction

peaks are not present around the (000) node. The inten-

sity is also maximized around the (000) node as the atomic

scattering factor is maximized here, and the Compton Scat-

tering, which subtracts from the intensity (as (1-cose)),

is minimized.

In order to understand the small angle scattering

that results from the Guinier-Preston zones, it is nec-

essary to start with the first principles of x-ray scat-

tering. A dilute system is one in which there is a large

volume available per particle as compared to the total

volume of all the small particles. In addition, thin

samples will only be considered such that absorption ef-

fects can be neglected. The basic development of
1,2
Guinier'2 will be mostly followed.

For the case of a small isolated crystal, such as a

G.P. zone, Guinier has shown that the scattering power

per unit cell is:

F2
Fhk 2
I(s) hk EE E (s-rhk
c hh h

where: V is the volume of the diffracting crystal

V is the volume of a unit cell
Sis the structure factor of a particular node
Fhkz is the structure factor of a particular node













E(s) is the Fourier transform of the form factor

rhk, is the structure factor of a particular node

0
S--

Around the (000) node, the vector rhk =0. Thus, around

the (000) node:

2
F(000) 2
I(s) = v0 |E(s) |
c

For very small angles, the structure factor, F(000), is

equal to the number of electrons (N) present in the unit

cell. The average electron density (p) of the unit cell

is then:

(000) N
V V
c c

The total scatter (IN(s)) from all electrons in the crys-

tal of total volume V is given by Guinier5 as:
V 2 2

c

where: V- is the total number of unit cells in the crys-
c
tal

Thus, the maximum scattered intensity occurs at s=0, where

E(0) = V.

2 2
Ima = P V
This maximum intensity peak of large crystals is masked,
This maximum intensity peak of large crystals is masked,













however, by the main unscattered beam. Since s=2sinO
20 c1
where 0 is small, s=---- Also, s= ; therefore:

d

The minimum angle where scatter can be observed is e=10-3

radians. This would correspond to a particle diameter (d)
0
of approximately 1000 A.

A Guinier-Preston zone can be considered as an iso-

lated crystal within a medium other than vacuum, as long

as it is a dilute system, as defined previously; the in-

tensity from each particle will merely add. If the med-

ium electron density is given as po and the isolated par-

ticle electron density as p, the scattering power per par-

ticle is:

I(s) = (p-po)2 |E(s)|2

54
Guinier has determined that in order to obtain the aver-

age scattering power per particle if all particles are

identical, 1(s) 2 must be averaged over the entire sphere

of radius s=|s|. Thus,

2
2 average value of 1|(s)2
I(s) = (p-po) {over the sphere }
of radius s=Is|

To obtain the average value of E(s), the form function

must be integrated over the volume, and for the case of













spheres:

E(s) = / exp(2fis-x)dV
V
54
Guinier has shown that for a spherical-shaped particle:

4 3
E(s) = I a (3(27sa)

for a sphere of radius a. Where the function p(2nsa) is

given as:

(2~s) = 3sin2as 2ias cos2aas
Q(2isa) = 3[in -- 3(2-s
(27Tas)3

Thus, the scattering power per particle is given by:

I(s) = [(p-po) a3]2 (2as)

We now wish to approximate the curvature of the in-

tensity curve at the center (s=0). The total scattering

power IN(s) for N unit cells of a particle of volume V has
54
been shown by Guinier to be:

IN(S) = (p-po)2 I(&)12

where: E(s)=V at s=0

Thus:

IN(O) = (p-po) V

For an isolated particle, the total number of scattering

electrons n=pV. For a particle in a matrix, an effective

number of scattering electrons can be defined as:













n = (p-po)V at s = 0

The total scattering power per particle, n2=(p-po)V, at
2 2
s=0 decreases with s as n (1-Ks ). K, the curvature at

the center of the intensity curve, is related to a simple

geometric parameter of the particle, and is independent of

the shape of the particle. The approximation of this cur-

vature at the center of the intensity curve is known as

the Guinier approximation.

S is the direction of the incident beam on the scat-

tering particle, as shown in Figure 2. As can be seen,

for very small scattering angles s' is in the direction D,

approximately normal to So, where s=(S-S )/X. s is in the

plane of the incident and scattered rays, and |s =- for

small angles. Take any vector, x, in real space. Then,
-* -4
s x = sxD

where xD is the projection of the vector x on D. In order

to calculate the function E(s), we must evaluate the inte-

gral:

E(s) = f o(xD) exp(27is xD)dVx
V

where o(xD) is the cross sectional area of the particle

along a plane normal to D at a distance xD from the origin

as shown in Figure 3. If the origin of the coordinate

































c-o





Cd

4-J


C/.
c
ac

rl








0
,-
C)



-c

P-
C)











0

C)
*-H


0Q














b
e--
Cl














system in real space is choose to be the center of grav-

ity of the particles, then the sum of the moments of the

particles about the origin is zero. Thus, since

ExdV = 0
x

and

dVx = a(xD)dxD

fxD o(xD)dxD = 0

Now we can expand the exponential function in the equation
2
of E(s), neglecting terms of order greater than s since

s remains very small within the scattering particle. Now:

E(s) = f o(xD) exp(27ris xD)dVx =
V

/ o(xD)dxD + 2nisfxD o(xD)dxD 2r2 s 2fx a(xD)dxD

The first term of the above equation is the volume of the

particle, while the second term is zero, due to the choice

of the origin as shown above. In order to evaluate the
2
third term, an additional term, RD, must be defined:

2 1 2
RD V xD P(xD)dxD

RD is defined as the average inertial distance along D to

the plane TD passing through the origin and perpendicular

to D.













Thus:

2 2
E(s) = V 2f s VRD

which can be rewritten in exponential form as:

2 222
E() = V exp(-22 s RD)

Then, the scattering power per particle:

I(s) = (P-Po)2 I|(s)j2

becomes

I(s) = (p-p)2V2 exp(-4f 2s2RD)

RD, as written here, assumes all particles have identical
2
orientations. For a random orientation of particles, RD
2 2
must be replaced by RD, which is the average value of RD

for all directions of D.

In order to calculate RD, we must remember that D is

merely one coordinate axis of an orthogonal coordinate

system. The other two axes, U and V, are shown in Fig-

ure 4, along with D. The origin is the center of gravity

and any point may be represented as xD, xu or xV. The

distance r of any point from the origin is given as

2 2 2 2
r = XD + x +

Similarly, R, which is the radius of gyration of a par-

ticle about its center of gravity, is given by:






36








Q









bIJ




0
41)
0~





413
w

co

co


4-4
S U
7< 1


00
r-

0






0
4i
'4




r4J
w
0
w


wr



bfl
1:.













2 2 2 2
R = R +R +R
D u V

where RD, Ru and RV are the inertial distances taken along

the three coordinate axes D, U and V, respectively. Now,

if we consider the rotation of the three coordinate planes

about the origin, as would be the case for random parti-
2 2 2 2
cle orientation, R remains constant and RD, R and R, on
D' u V, on
the average value, are equal, Therefore:

2 2
3R = R

This makes the average scattering power per particle

S2 22 2 2
2 A4iT s R 2 A nr R
I(s) = n exp(-- 7- ) = n exp(- --2 )
3 3X

The radius of gyration of a sphere is given as

R = (3 1/2a
R a

Thus:

222
2 A4TT a c
I(s) = n exp(- --4 )
5X

By taking the logarithm of both sides of the equation:

2 4 2 2 2
in I(s) = n n -41 .4343R2
3XZ

Guinier54-55 has shown that the radius of the particles

can be calculated from the slope of the line obtained by
plotting n Is) versus 2. Thus, R, assuming all parti-
plotting Zn I(s) versus E Thus, R, assuming all parti-













cles are the same size and randomly oriented in a dilute

system, is given as:

R = .416X/-a

A system does not usually contain all identical

spherical particles, but a size distribution is usually

present. To correct for this, an integration must be made

to account for each size particle:

2 6 4 2 2 2
I(s) = (p-po) Kfn(a)a (l 4s a )da
O

where n(a) is the number of particles of radius a and the

a term is the result of V2=Ka This can be written as:


I(s) = (p-po)2N KI 4-

where N is the total number of particles and
, the

average value of a, is obtained by:

= f n(a)anda
O

Rewriting the intensity equation in exponential form:

2 8

58-59
Baur and Gerold determined that by plotting n I(s)

versus the scattering angle squared (c ), one obtains a

value for the Guinier approximation which is defined as:


RG
1/2














Porod61 has also developed an approximation for the scat-

tering curve, but his deals with the tail region of the

curve, rather than the central region. Porod uses the

approximation of the form factor:

E(s) = f exp(-2ris x)dV
x

The scattering intensity may be written as

2
(p-po) a2 i 4a
I(s) = 4ra- + 4a sin4Tas
8rr s 7rrs

2
+ (-- 1-g) cos ias]
S TS

If there exists a distribution of spheres of radius aK

which varies between al and a2, and the number of spheres

of radius aK per unit mass is given by gK, then the inten-

sity may be written as:

2
(P-Po) 2 1
I(s) [EgK 4raK + '
3 s

+ Ecos4iaKs[...] + Esin2raKs[....]]

For the case where (2als-2a2s) is much larger than unity,

the two sinusoidal summations go to zero as the positive

terms cancel the negative terms. Therefore, for a large
1
s, the only remaining term is that containing For
S
large s, I(s) is written as Iasym, or the asymptotic val-

ues of the intensity.













2
(P-Po) 2 1
S [ gK 4aK
asym 8f3 -K aKs ra

The total surface of the particles per unit mass is given
2
by S = E gK 4ARK. Then, for the point collimation:

(P-Po)2 s
asym 87T3 s

Another important property of the scattering inten-

sity is the total integrated intensity, Q. Guinier and

Fournet have shown that the total integrated scattering

intensity is given by:

V
a 2 2
Q = -V(p-p dV = 44fs2 I(s)ds
O

In the case of a metal alloy, the electron densities, p

and p must be computed as the weighted average of the

elemental concentration in both the particle and the
57-59
matrix. Then, as shown by Gerold:57

S= -[B + M(ZA ZB)
a

S=V B + M2(ZA ZB)
a

where: p is the electron density of the particles

p is the electron density of the matrix

V is the atomic volume
a
M1 is the solute concentration in the particles













M2 is the solute concentration in the matrix

ZA is the atomic number of the solute

ZB is the average atomic number of the solvent

It is necessary to use ZB because in an alloy, sev-

eral solvent elements may be present; therefore, the aver-

age atomic number must be used to obtain the electron den-

sity. Then, the difference in electron density is given

by:

(P-po) -[M(ZA ZB) M2(ZA ZB)
a

-[(M1 M2) (ZA ZB)]
a
2 1 2 2
(p-po) V [(M1- M2) (ZA- ZB
a

If p represents the total volume of particles transformed

and cpV the total volume of all particles, we can get the

average solute concentration, MA, in the bulk alloy as:

cM1 + (1 C)M2 = MA

and also the integrated intensity as a function of concen-

trations:

Q = (1 C)(M1 M2) (ZA ZB)2
a
The problem remains now of evaluating the integrated in-

tensity from the measured scattered intensity. The inten-

sity measured by a radiation detector, E(s), is given by:














I nfE I(s)de -d
E(s) = --2
4r
I nf
where the constant factor, e can be written as a
4r
constant, K. Then:

E(s) = KE I(s)de- d
I nf
where: K = e
4r -
I is the Thompson factor (7.9 x 10-26 cm )
3
n is the number of atoms per cm

f is the surface area of the detector

r is the sample to detector distance

E is the incident beam intensity

I(s) is the scattering power

d is the thickness of the sample

V is the linear absorption coefficient

This equation holds true for a beam of x-rays of

point cross section. In order to evaluate the intensity

measured from a line-shaped beam, Guinier and Fournet55

have derived the following integration:

E(s) = KE de-dl (s2 + t1/2dt
o t o

where t is a reciprocal lattice parameter related to the

length of the line beam. The determination of the inte-

grated intensity is accomplished by evaluating the inte-














gral:
00 2 2 2? 1/2
Q = 4rfs I(s)ds = 4rr/I(s + t2)2dtds
O O
55
Guinier and Fournet have shown that this leads to

2y e-pd 2
Q = rErXd 2TTfsE(s)ds
0 0

where 2y is the width of the detector-receiving slit. In

order to evaluate the integral:


fsE(s)ds
O

the Porod approximation for the tail of the scattering

curve must be adjusted for a line-shaped beam to:

E(s) = ks3

Then:

S
0 2
fsE(s)ds = f sE(s) + S E(S )
O O

All of the above equations assume a dilute system,

i.e., no interparticle interference, monoshaped particles

and identical composition of all particles. If the system

is not sufficiently dilute, the diffraction maxima will

not coincide with s=0, but will be centered at some finite

s It is still possible to analyse the curvature at the

center of the scattering curve, i.e., the Guinier region,

and the tail of the curve, the Porod region.













Gerold3 has derived an expression for the Porod

radius (R ) by assuming a constant volume fraction of the

scattering zones. Combining this assumption with the

scattering curve, he concluded that the surface area of

the zones (S) computed at large angles should be given by:

2 I(~s48 s3
S = 4TNv = I(s)
(P-Po2 V
(p-poN

Combining this with the total volume of the particles:

cV =4 N
cV =

where: V is the total volume of irradiated material

c is the volume fraction of the scattering parti-

cles
3 cV
Gerold3 solved for the expression by use of the equa-
s
tion for integrated intensity given previously. He showed

that:

R 3 1 sE(s)ds
p U TTI y I(So) S3

58-59
Baur and Gerold58-59 have shown that this reduces to

R


Recently, Harkness, Gould and Hren8-50 have shown

that the particle size distribution can be obtained from

the experimentally determined values of the Guinier radius












and the Porod radius. Harkness et al.19 determined that a

log normal distribution could be used to represent the

particle size distribution. A log normal function has the

form:


F(X) exp[- ( n ) 2
FT( ~ X n a n a

where: p is the geometric mean

a is the variance

Using the general moment equation for a log normal distri-
th
bution function, the n- moment is given by:

2
n n 2
r = exp[n 9n p + -n 9n o]

Applying this relationship to the results of Baur and

Gerold,5859 Harkness et al.49 showed that


RG =]1/2 = exp[9n p + 2.59n2 o]
Re [-5-]


and


R = p

Solving these equations for p and a yields:

RG
pn y = nn R 1.71n-
G R
p

RG
a n( )
9n2 o -
3.5












Using these equations and the assumption of a log normal

distribution, it is possible to plot the zone size distri-

bution from the experimentally determined values for the

Guinier radius and the Porod radius.
49
Harkness et al. have also determined that NV, or the

number of zones per cm3, can be determined using the zone

size distribution and the volume fraction, Vf, of zones

obtained from knowledge of the miscibility gap as follows:


4rN = Vf
71 V f


In this manner, it is possible to plot the actual number

of particles within each zone size.

Changes in the volume fraction can be monitored as a

function of changes in the integrated intensity. Gerold3

has shown that the volume fraction of particles at any

time, t, can be given as:

Qo(t)
f(t) = Qo< f(t )

where: f(t) is the volume fraction at time t

f(-) is the volume fraction of the fully aged

sample as determined from the phase diagram

Qo(t) is the integrated intensity at time t

Qo(D) is the integrated intensity of the fully
aged alloy






47






Using this relationship, the volume fraction of particles

can be accurately determined throughout the aging se-

quence, and, therefore, accurate particle size distribu-

tions can be determined.














CHAPTER III

EXPERIMENTAL EQUIPMENT AND PROCEDURES


The Alloy

The 7075 commercial aluminum alloy was supplied as

3/4 inch alclad plate from the Reynolds Aluminum Company.

The alloy was analyzed spectrographically by two x-ray

methods. First, it was analyzed using an x-ray energy

dispersive system at Oak Ridge National Laboratories, and

secondly, it was analyzed using a Norelco* crystal disper-

sive x-ray spectrometer. The averaged results of these

tests showed the composition to be:

Zn-5.80 wt % Cr-.22 wt %

Mg-2.62 wt % Si-.19 wt %

Cu-1.74 wt % Ti-.04 wt %

Fe-0.27 wt % Al-balance

Small Angle Scattering and Tensile Test Sample Preparation

The plate was prepared for rolling by milling 1/16

inch off of each face in order to remove both the alclad

layer, as well as any effects of it in the 7075 substrate.

The plate was then cold-rolled on a Fennt rolling mill,



*Philips Electronic Instruments, Mount Vernon, New York

tFenn Manufacturing Company, Newington, Connecticut











with intermediate anneals of 30 minutes at 460C to thick-

nesses of .85 mm, .80 mm and .72 mm. These thicknesses

produced a constant .72 mm thickness for all samples when

the final mechanical treatments of 15%, 10% and 0% were

later applied. This large reduction with intermediate

anneals was sufficient to break up any large precipitates

present in the as-received condition.

Specimens for the tensile tests were prepared in the

same manner, with the gage section being cut on a Tensile-

Kut* high speed milling machine, according to ASTM Speci-

fication A370 (substandard size) subsequent to aging.

Resistometry Sample Preparation

Resistometry samples were prepared by first turning

1/2 inch rods from the 3/4 inch plate. This rod was

swaged on a Fenn swaging machine, with intermediate

anneals at 4600C for 30 minutes, down to .106 inches dia-

meter. This thin rod was then drawn using a wire drawer

down to .02 inches. Intermediate anneals at 4600C for 30

minutes were necessary after each draw; however, annealing

left the wire too soft to draw. Thus, it was necessary to

slightly age-harden the alloy by heating for 10 minutes at

1350C after annealing in order to develop sufficient


*Sieburg Industries, Danbury, Connecticut











strength. The wire was then made into a coil and voltage

leads were spot welded onto it.

Solution Heat Treating and Aging

The small angle scattering and tensile specimens were

solution heat treated at 4600C30C for 2 hours in a verti-

cal tube furnace equipped with a large Inconel block for

temperature stability. Quenching was accomplished by

drop-quenching the specimens and holding the rod into an

ice water bath (1/20C). The solutionized samples were

stored in liquid nitrogen prior to elevated temperature

aging.

The resistometry specimens were solutionized in a

forced air furnace for 2 hours at 4600C and were quenched

by dropping into an ice water bath. The wires were

mounted onto a phenolic board immediately after quenching

and were then promptly aged.

All elevated temperature aging was conducted in a

Lauda* constant temperature oil bath, capable of main-

taining a given temperature within .10C, containing 50 cs

Dow Corning' silicon oil. After aging, and prior to

testing, the samples were stored in a refrigerator (o4C).


*Brinkman Instruments, Westbury, New York

tDow Corning Corporation, Midland, Michigan












Retesting of specimens, even after long periods of storage

in the refrigerator, indicated that no measurable change

in the zone state had occurred, provided some elevated

temperature aging had been performed.

Wide Angle Diffraction

Small strips, approximately 1/8 inch x 5/8 inch x

.72 mm, were cut from the small angle scattering samples

to be used as samples for wide angle diffraction. The

wide angle diffraction was done using an Enraf-Nonius,*

Guinier-De Wolff camera. The essentials of this camera

are shown in Figure 5. This camera is equipped with an

incident beam, elastically curved, quartz monochromating

crystal, which focuses the primary and diffracted beams

onto the diffraction circle (i.e., the film). All expo-

sures were run at room temperature with the chamber evac-

uated to eliminate air scatter. The use of monochromatic

radiation and an evacuated path eliminates fogging of the

film and allows long time exposures to be run. The lower

limit of detection with this method is on the order of

.05 to .10% of a second phase. This technique was used to

determine any quenched-in precipitates and also to follow

the sequence of precipitation. Four samples can be run



*Enraf-Nonius, Inc., Garden City Park, New York






















L-2


tj
Q












simultaneously in a Guinier-De Wolff camera. All expo-

sures were run for 48 hours, with machine settings of

45 KV-20 ma. The films were densitometered after devel-

opment in order to determine intensities of the weak pre-

cipitate diffraction lines.

Small Angle X-Ray Scattering

The small angle scattering experiments were conducted

using a Siemen's* Kratky small angle camera. Figure 6

shows a schematic of the essentials of this type of cam-

era. Small angle scattering cannot be observed using

standard x-ray diffraction equipment due to the divergence

of the primary beam; thus, the need for such a system.

Figure 7 is a diagram of the collimation system for the

Kratky camera. The first slit, or entrance slit, re-

stricts the height of the primary beam. The next set of

slits, in the Kratky block, restrict the divergence of the

primary beam to include only parallel, or nearly so, rays

in the incident beam. These two slit systems greatly re-

duce the intensity of the primary beam by severely lim-

iting the solid angle of the x-ray beam front observed,

but, when aligned, are capable of producing a flat, parallel

beam of uniform intensity. The condition of uniform in-


*Eastern Scientific Sales Co., Marlton, New Jersey



































LLU




h/


E I


K) -





rrj

E _____.


^' \' N


4I:
.I' I3 :

-11 ~L < )


0





o
U1
0U





0 p

* r-





40

HI-- H
U C,
CO N






Q) 0




4 0 r4
Uo)

eCo







0
Sr4
COO0



Ei
0





-I4
r-o>




* O

































KRATKY BLOCK


Figure 7. Schematic of Slits System in Kratky Block












tensity and "infinite" slit width61 is necessary in order

to satisfy the conditions of the Porod equation. For the

Kratky camera, the condition of infinite width is ex-

pressed as:

Z < 2m + a

where: m is the height of observation above main beam

a is the width of the primary beam at the exit

slit

k is the length of the primary beam that is of

uniform intensity

A uniform intensity beam of 3.5 cm was obtained on align-

ment of the Kratky camera, while the rear slits were set

at 1 cm.

A graphite crystal diffracted beam monochromator was

used in order to measure only monochromatic radiation, and

pulse height selection was employed to eliminate any har-

monic diffraction which might occur.

Table 2 gives the operating machine parameters used

in this investigation. Plateau voltage curves were run on

the detector in conjunction with varying gain settings in

order to determine the peak operating voltage of the de-

tector. The pulse height selector settings were set

exactly at the base of the MoKa energy peak.












Table 2

Machine Parameters

SLIT SIZES
Front Entrance 100 p
Rear Exit 200 p x 1 cm

SPECIMEN TO DETECTOR DISTANCE 215 mm

OPERATING CONDITIONS 45 KV
20 ma
o
RADIATION MoKa X = .71 A

DETECTOR VOLTAGE 1100 V (Bicron* scintillation)

PULSE HEIGHT SELECTOR
Lower Limit 2.0 volts
Upper Limit 4.0 volts

STEP SIZE 100p



*Bicron Corporation, Newbury, Ohio



All samples were step scanned using an Ortec* Model

6713 axis controller and Ortec counting equipment. Scans

began from a height of approximately 300 p above the cen-

troid of the primary beam to about 10,000 p above the main

beam. Collection time was 1,000 seconds or at least

12,000 counts at each of the 100 p steps. All scans were

run with the Kratky block, specimen holder and tank evac-

uated in order to reduce air scatter.


WOrtec, Inc., Oak Ridge, Tennessee













62
A sample of Lockheed pyrolitic graphite was used

both as a test of proper camera alignment and as a scat-

tering standard to correct for variations in primary beam

intensity between runs. Figure 8ashows the scattering

curve of the graphite, while 8b shows the Porod region,

where a slope of -3 indicates proper camera alignment.

All intensity corrections were made with the graphite

standard. Main beam intensity variations were corrected

for by ratioing the intensity of the graphite scattered at

a fixed position before each run to that of the graphite

scatterer measured before the pure aluminum run. Varia-

tions in sample absorption were corrected for by measuring

the intensity of the graphite standard with the pure alu-

minum in the absorption position and ratioing it to that

of the graphite standard with the aluminum alloy sample in

the absorption position. The total corrected intensity

for a sample is given by:

istd Apure
1 = abs
corr meas Isam sam
g abs

where: Icorr is the corrected intensity

Imeas is the measured intensity

I s is the graphite intensity measured prior to
g
each run


























a)
rI


co








0
C)
P4



4-i
0


a)
a)





0




a)



C-3







4-3
W










co





a0





rZ4




60







I CD

co




I v
rn





I /
3 Q




i


I 0
/



(- i


0 C)






SI ,
/ I








o 0 2 o
C a LLa N LN
~5/'3 AIS 5rN






61




GRAPHITE







/00
O\ -\



13
90-
80-
hF 70 -

Z 60-

.- 50 -


40-



30 40 50 60 70 80 90

6 (RFADIAN xl -2



Figure 8b. Porod Region of Lockheed Pyrolitic Graphite
Scatterer












std
Istd is the graphite intensity measured prior to
g
the pure aluminum run

Apure is the absorption factor of the pure alu-
abs
minum

Asam is the absorption factor of the sample
abs
The sample scattering curves were corrected for back-

ground by subtracting the intensity scattered from a

99.999% pure aluminum sample with the proper correction

factors described above applied. All data was plotted

and smoothed by hand before evaluation by a computer pro-

gram written by Gould and Kirkli,6 and modified by Healey

and Hill64 for this work. This program corrects for pri-

mary beam intensity variation due to sample thickness and

tube fluctuations automatically, and calculates the

Guinier Radius, Porod Radius, integrated intensity and

the particle size distribution, based upon the method of

Harkness, Gould and Hren. 50

Resistometry Measurements

Resistometry measurements were made using a Leeds and

Northrup* Kelvin bridge-type potentiometer, standardized
65
against a .001 ohm standard resistor. Measurements were

made at liquid nitrogen temperature. It was not possible



*Leeds and Northrup Company, Philadelphia, Pennsylvania













to measure true resistivity (p) of the sample as the exact

length between the voltage leads was not known. Instead,

the resistance, or actually the voltage between the two

welded leads with an exact current of 1 amp, was measured.
R-R
This was plotted as R where Ro was the resistance
o
measured immediately after quenching.

Tensile Testing

Tensile tests were performed on the specimens cut to

ASTM Specification A370 (substandard size) on an Instron*

testing matching. All tests were run at a strain rate of

.02 inches per minute.


*Instron Corporation, Canton, Massachusetts














CHAPTER IV

EXPERIMENTAL RESULTS


All data presented here has been obtained from com-

mercial 7075 alloy, whose chemical composition is pre-

sented elsewhere. A series of isothermal aging treat-

ments, with and without deformation, were performed on the

samples. The term preaging, as used here, will include

any thermal treatment given to a series of samples prior

to the final thermal aging treatment. Table 3 presents

all treatments performed on the various series and their

designations.



Resistivity

The resistivity-aging time curves for the wire speci-

mens are given in Figure 9. This resistivity data is sum-

marized in Figure 10 as an Arrhenius plot.33 The physi-

cal significance of this plot lies in the slope of the

line having the units of energy, and corresponding to Em,

the activation energy of motion.









0

0
0
C
0

0

0

0



0
0




0


JI
0


Si


09
0,(
0
0

0p
IC~


/





I.


i I i I I l I i.


'c aCC d
000

o 0 6!--U

b


0 0 0 0 0 0-
S I* I* Ic 0


0u0






.o *e e


I')



(/


-! --








100,000 -
90,000-
80,000 -
70,000-
60,000 -
50,000 -

S40,000-

30,000-



S20,000 -


10,000
9,000
8,000
7,000
6,000
5,000


4,000 -

3,000 -


2,000)-


I I


2.60 2.55


2.40


100o/T


Figure 10. Arrhenius Plot of Resistivity Maxima


2.75


2.70


2.65


2.50


2.45


, WI .V 1


I rnni













Table 3

Summary of Aging Series

Preage Treatment Aging

NONE

NONE

NONE

NONE

NONE

1 hour 125C

NONE

NONE

100 hours 750C

25 hours 75C

100 hours 95C

25 hours 950C
5 hours 125C


Temperature

1350C

1350C

1350C

125C

1250C

1250C

750C

75C

1250C

1250C

1550C

1550C


Small Angle X-Ray Scattering


Preliminary Studies of Initial Aging

A similar study to that of resistivity was performed

using small angle scattering. A single sample was iso-

thermally aged at three temperatures (1350C, 1450C and

1650C) with homogenization at 4600C for two hours between

temperatures, and the scattered intensity was measured at


Series

A

B

D

E

F

F1H

G

H

J

K

L

M


Defm

0

5%

15%

0

15%

15%

0

15%

0

0

0

0













0.011 radians as a function of aging time. Figure 11

shows the scattering curves obtained, while Figure 12 is

an Arrhenius plot of the log of the time to reach a scat-

tering intensity of 1.5 counts per second versus 1000/Ta,

where Ta is the isothermal aging temperature.40

A preliminary study of the effects of deformation on

the initial aging rate was performed in a similar manner.

The scattering intensity at 0.011 radians is plotted ver-

sus aging time for the A, B and D series, see Figure 13.

Change in Zone Size Parameter

Entire scattering curves are necessary to determine

the two size parameters; the Guinier Radius, RG; and, the

Porod Radius, R Figures 14 and 15 show two such scat-

tering curves, one representative of a direct-aged sample

(Figure 14) and the other a sample that had been preaged

before the final aging treatment (Figure 15). Corrections

for sample variation were performed according to the pro-

cedure presented in Chapter III. The results of the evol-

ution of the Guinier Radius are given in Figures 16

through 21. Evaluation of the Guinier Radius in the

unaged or very short direct aged samples was difficult due

to the low scattering intensity. For the low temperature

aging series (G and H), this problem was encountered

throughout the aging sequence as the growth was extremely

slow.






69
















\~g Or
o0
r--I
r--4













* (Q r LU
C)2

\ x (0
,Q -o D
.CL ~- >











m
*\3 a









0 \ 0







r-4







II)
o m :l I
\IO I" \

\ <. \ v













































.50


2.40


2.30


2.20


100/A


Figure 12. Arrhenius Plot of Time to Reach Scattered
Intensity of 1.5 Counts Per Second


20,000-


/0,000
9,000
8,000
7,000
6,COO
5,000

4,000

3,000


2,000


1,0001
2


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The results for the Porod radius are presented in

Figures 22 through 26. It was not possible to obtain a

meaningful Porod radius for the very short aging time

samples as the Porod region was either at too high an

angle, or buried within the background. Also, it was not

possible to obtain a Porod radius with physical signifi-

cance for the G and H series as the Porod region was be-

yond the workable angular range of the Kratky camera.

The radius of maximum abundance values are plotted

in Figures 27 through 32. These determinations assume a

log normal distribution.

It was not possible to obtain a radius of maximum

abundance for samples for which no Porod radius could be

calculated. The Porod radius is necessary for this deter-

mination as described in Chapter II.

Frequency distribution plots of the particle radii as

a function of aging time are presented in Figures 33

through 41. These distributions were generated assuming

a log normal distribution, and spherical particles, and

again were generated only for samples for which it was

possible to obtain both a Guinier and Porod radius.

All of the above parameters were calculated using the

modified computer program of Gould and Kirklin63-64 which

is described in the Appendix.




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