l
I
1

H

‘l\
‘
l
|‘
l
x
l
I

l
i

|

\
1

)

W

125
456

 

.THS_

 

Haste: _, ml emu—
I/j' :‘_-..:'I ‘1'-
1
‘ Etc-u” A; if??? “S“.
Lfih wawvav‘fi .
guy; .,1.-»‘,'- 4-year: “fimfi'm

b .. , ' -g- .
A_ ,.,. o ‘$ :38 ".h 9' l. m 0 w
Jinn...» $- ' r- v.

«$0310.49! ’2': '5' Q: «infill.
tit-w v wéarb ‘ .'
. i) . . .
R24: ~ JI’_“‘l".- .r' ’4'

——.'

 

n

This is to certify that the

thesis entitled

Experimental Investigations on Age-Hardening
of Cu-lONi-6Sn Spinodal Alloy

presented by

S. Shekhar

has been accepted towards fulfillment
of the requirements for

Masters degree in Metallurgy

4! N ' Mfl‘btiéucLCW

Major professor

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

MSU
LIBRARIES
.____

 

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES will
be charged if book is
returned after the date
stamped below.

 

 

 

 

 

 

EXPERIMENTAL INVESTIGATIONS 0N AGE-HARDENING
0F Cu-lONi-GSn SPINODAL ALLOY

By

Shekhar S.

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Metallurgy, Mechanics and Materials Science

1983

Shekhar S.

ABSTRACT

The dislocation structure in as-quenched and aged specimens

of the Cu-lONi-GSn spinodal alloy, of both fine-grained and large-
grained types, was studied by transmission electron microscopy. It
was found that the deformation structure of aged specimens consisted
of curved and wavy dislocations whereas deformed as-quenched
specimens consisted of straight dislocations. This suggests that
mixed dislocations may be responsible for the hardening during
deformation of the spinodally modulated structure. It was seen that
the dislocation density decreased with increased aging time; the
dislocation multiplication seems to be hampered by the modulated
structure. It wasalso observed that usecH’large-grained samples
significantly aided hithe analysis of the dislocation structure in
the spinodally modulated alloys. The Burgers vector analysis of
dislocations in an aged and deformed specimen indicated mixed

dislocations to be responsible for the observed age hardening.

ACKNOWLEDGEMENTS

I would like to take this opportunity to sincerely thank my
advisor Dr. K. N. Subramanian, but for whose constant guidance and
encouragement this endeavour would not have ended in success. I
would also like to say special thanks to my colleagues, Tong Lee
and Apichart, my good friend Narendra, and scores of others in the
Department of Metallurgy, who sacrificed a lot of their time and
efforts to help me out.

This project is supported by the Department of Energy under
Contract Number- DE-ACOZ-BlERl0942.

List of Figures .............................................

TABLE OF CONTENTS

List of Tables ....... .......................................

I.
II.

III.
IV.

VI.
VII.

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

LITERATURE SURVEY ..................................

2.l Theory of Spinodal Decomposition ...........
2.2 Mechanical Properties in Spinodal Alloys...
2.3 Single Crystal Studies in Spinodal Alloys..
2.4 Transmission Electron Microscopic Studies
of Spinodal Alloys ........................

PURPOSE OF CURRENT STUDIES ........................

EXPERIMENTAL PROCEDURE ...... ......................

4.1 Fine-Grained Specimens .....................
4.2 Large-Grained Specimens ....................

RESULTS AND DISCUSSION ........ . ...................

5.l Fine-Grained Specimens .....................
5.2 Large-Grained Specimens ....................

CONCLUSIONS .......................................
REFERENCES ........... .............................

Page
iv
viii
1

3
3
TO
23
23
27

28

28
35

39

39
48

63
65

Figure 1:

Figure 2:

Figure 3:

Figure 4:
Figure 5:
Figure 6:

Figure 7:

Figure 8:

LIST OF FIGURES

Page

a) The free-energy versus composition curve at
temperature To. b) Binary alloy phase diagram with
miscibility gap, chemical spinodal and coherent
spinodal ............................................ . 4
The (lll) [ITO] slip system in the absence of applied
stress showing the forces on the dislocation and the
resulting configurations ........................... 15
a) screw at small amplitude for that wavelength,
b) edge at small amplitude for that wavelennth,
c) screw at large amplitude, and
d) edge at large amplitude.
Schematic representation of a mixed dislocation and
internal stress profile considered by Kato-Mori-
Schwartz. (+ and - positions show respectively maxima
and minima of the force acting on the dislocation
due to the internal stress) ........................ 20
Schematic stress-strain curves in as-quenched and aged
alloys ............................................. 22
The unit cell associated with the 0019-type superlattice. 26
Schematic of the tensile test specimen ............. 29
Schematic of tube-furnace used for homogenizing and
aging the specimens ................................ 30

Microtensile fixture used for testing in Instron

testing machine ..................................... 32

iv

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

9:

10:

ll:

12:

l3:

l4:

15:

16:

a) Photograph. Page
b) Schematic.
Schematic of single-jet electropolishing unit ............... 33
Schematic of final electropolishing unit .................... 36
Dislocation structure in a fine-grained as-quenched

specimen deformed by 5%. The foil normal is near [Oll] ..... 4O
Deformation structure in fine-grained as-quenched specimens
after l0% deformation. Foil normal is near [Oll] for
both micrographs .................................... -- ........ 4l
Dislocation structure in fine-grained specimens aged for
10 minutes at 6230K and deformed by 10%. Foil normal is
near [Tll] for (a) and [Oll] for (b) ......................... 43
Dislocation structure in fine-grained specimens aged for
20 minutes at 6230K. Foil normal is near [011] for both
micrographs ................................................. 44
a) After 5% deformation.

b) After l0% deformation.

rDislocation structure in fine-grained specimens aged for

1 hour at 6230K. Foil normal is near [Oll] for both

micrographs ................................................. 46
a) After 5% deformation.
b) After 10% deformation.

Grain-boundary precipitates in a fine-grained specimen

aged for 24 hours at 6230K ................................... 47

Page
Figure 17: Dislocation structure in a large-grained as-quenched

specimen after l0% deformation. Foil normal is near

[Ill] for all three micrographs... .................... 49

Figure l8: Dislocation structure in a large-grained specimen aged
at 623°K for l0 minutes and deformed by 5%. Foil normal

is near [Oll] for both micrographs... ................. 50

Figure 19: Dislocation structure with sharp bends and cusps in the
dislocations in a large-grained specimen aged at 623°K for
10 minutes and deformed by 5%. Foil normal is near

[Oll] for both micrographs ............................ 51

Figure 20: Dislocation structure in large-grained specimens aged at
623°K for 20 minutes and deformed by 5%. Foil normal is

near [Oll] for both micrographs. ...................... 53

Figure 21: Wavy-shaped dislocations observed in large-grained

specimens aged at 623°K for 20 minutes and deformed by 5%. 54

Figure 22: Sharp cusps and bends in dislocations observed in large-
grained Specimens aged at 623°K for 20 minutes and
deformed by 5%. Foil normal is near [Oll] for all four

micrographs ........................................... 55

Figure 23: Curved dislocations present in a large-grained specimen
aged at 623°K for 20 minutes and deformed by 5% ....... 57
a) Bright field image
b) Diffraction pattern
c) Dark field image corresponding to diffraction

spot indicated by the arrow.

vi

Figure 24:

a)

b)
C)

Page

Dislocation structure in a large-grained

specimen aged at 623°K for 20 minutes and

deformed by 5%. 3: [211] .................... 59
Same region as Figure 24a. 3 = [112] ........... 60
Same region as Figure 24a. §'= [110] ........... 5]

vii

LIST OF TABLES
Page

1) Electropolishing data for ”Dishing Technique". ............... 34
2) Electropolishing data for Final Step of thin foil preparation. 37

3) Possible values of 3.3 for the dislocations under the

three reflections in Figure524(a), 24(b), 2403) ............... 62

viii

I. INTRODUCTION

Spinodal decomposition of alloys basically involveSEIperiodic
variation in space of local concentration of alloying elements. Such
a modulation is sinusoidal in the early stages of the decomposition
and square-shaped in the later stages. For a cubic system, the early
stages of the decomposition can be expressed in terms of the following

equation:

c - c0 = A (cos 2%; x + cos §§_ y + cos fig, 2) (l)

where.

c is the local atomic concentration of a secondary element,
cO is the average atomic concentration of the secondary
element,
A is an amplitude factor, and
A is the wavelength of the composition modulation.
For a cubic system in general, the x, y and z axes are parallel to
the <100> directions.
The modulation caused by the decomposition during the aging of
a spinodal alloy accounts for increases in the yield and flow stresses
of the alloy, and this is termed as age-hardening. In this
investigation the nature of the dislocations in aged and deformed
specimens of the spinodal alloy was studied to gain a better

understanding of the mechanism of age-hardening in spinodally modulated

structures.

The Cu-lONi-GSn spinodal alloy was chosen for the experimental
work on the basis of its cubic structure, the relative ease in
controlling at desired stages of decomposition and as well as on the
basis of the availability of experimental data for mechanical

properties in bulk specimens.

II. LITERATURE SURVEY

2.1 Theory of Spinodal Decomposition

 

The spinodal phase has long been regarded as a limit beyond
which a homogeneous phase could no longer be metastable (1). But
recently it has become apparent that a phase beyond the Spinodal
phase would decompose by simple diffusional clustering mechanism
which is quite different from the nucleation and growth mechanisms
encountered for metastable phases. The theory of spinddal
decomposition, which is based on the diffusion equation modified by
thermodynamic requirements, is phenomenological, and each parameter
can be measured by independent thermodynamic or diffusion experiments.

The variation of the Helmholtz free energy F with composition
at a temperature To is considered in a binary alloy system, as shown
and C

in Figure 1(a). The two inflection points C are defined

31 32
by
2
__Ta F = F" = o (2)
3C T,v
where,

C is the atomic concentration of the second component,
and v is the volume of the binary alloy.
The point Ca] and Caz are points of common tangency to the curve and
they define the composition of the co-existing phases at T0. The
locus of points satisfying Equation 2. for different temperatures

is called the spinodal (chemical spinodal) and is shown by the dashed

A

a)

Helmholtz Free Energy, f(C)
at T0

 

  

 

 

 

Temperature

 

Miscibility
Gap

Chemical
Spinodal

Coherent
Spinodal

  
 
 
  

 

 

0

Atomic concentration of second component, C

Figure l

: a) The free-energy versus composition curve

at temperature To.

b) Binary alloy phase diagram with miscibility
gap, chemical spinodal and coherent spinodal.

Curve in Figure 1(b). The locus of the points Cal and Caz for
different temperatures is the solid line in Figure 1(b) and this line
represents the miscibility gap. The significance of the spinodal line
is as follows: alloys which become supersaturated by cooling from

the single phase solid solution region to the two phase region inside
the miscibility gap will nucleate precipitates whose morphology and
distribution depend markedly on whether the alloy is inside or outside
the spinodal line. For an alloy which lies between the phase

boundary and the spinodal line, the second derivative of the Helmholtz
free energy with reSpect to composition, 3:; , is positive and there

will be a nucleation barrier to precipitation, that is, the alloy is

stable to small composition fluctuations. For alloys which lie

2
inside the spinodal line, émg-is negative, there is, in principle,

no nucleation barrier to prggipitation and the alloy is unstable to
small composition fluctuations (3).

Although spinodal decomposition was recognized by Gibbs (4),
it is only recently that the theory of this type of precipitation
has been developed by Hillert (5), and Cahn and Hilliard (6, 7) to
an extent where it can be used to predict microstructural behavior.

These authors have shown that a solid solution inside the spinodal is

unstable to sinusoidal fluctuations of wavelength Zn/B when:

2 2
3 f'(C) 2 2n E

where, f'(c) is the free energy of a unit volume of a homogeneous

material of composition C, k is a constant determined by the surface

energy between the two phases, E is Young's modulus, v is the Poisson's
ratio, and n is the linear expansion of the lattice per unit
composition change.

Thus the pure thermodynamic condition for spinodal decomposition

2 .
a f (c)
(——2——

8C
3- which represent respectively, the energy barriers due to the

< 0) is modified by the second and third terms in Equation

creation of an additional area of interface in the lattice, and to

the volume strain energy of the misfitting phases. It can be seen
2 .

farm
3

maximum value of B to satisfy the Equation 3. and hence a certain

that for given values 0 and n, there will be a certain
minimum value of the wavelength of composition into which the alloy
can decompose. All composition fluctuations having wavelength above
this critical value, )‘c’ are also stable; but Cahn (7) has shown that
the wavelength which grows most rapidly, and hence the one which is
probably observed experimentally, is /2 Ac. The presence of a strain
energy term means that the decomposition takes account of the elastic
anisotropy of the crystal lattice since E is a minimum along <100>
in most cubic metals, three orthogonal fluctuations along <100>
directions are preferred. The microstructural result of this is a
distribution of second phase particles which consists of an ordered
array of approximately spherical particles for small volume fractions
of precipitates and an array of rods along <100> directions for larger
volume fractions.

In order to account for the effect of coherency strains, Cahn (7)

introduced an additional term in Equation 2.

F" + 2n2y = o (4)

7

where Y, in the case of <lDO> modulations, can be expressed in terms

of the elastic constants Cij as

_ 2
Y ‘ c11 * C12 ' 2 (C12/C11)° (5)

The locus of points satisfying Equation 4. Wthh always lies inside
the chemical spinodal, is defined as the coherent spinodal, and is
shown in Figure 1(b).

The initial kinetics and mechanism of spinodal decomposition in
cubic crystals has been completely described by Cahn (8) in terms of

the seven parameters 32f'(c)/3c2, k, M, n and the three elastic

constants C44, C11 and C12, where k is the gradient energy co-efficient,

and M is the mobility of atoms. According to Cahn (8), the initial
kinetics and mechanism is completely independent of crystal structure.
0f the above parameters, all but 32f'(c)/3c2 and k can be readily
determined by extrapolation of free energy data and k has been
estimated (6) from statistical mechanics.

The following predictions may be made of the initial stages of
spinodal decomposition:

(i) If (2C44 - Cll + C12) > D, spinodal decomposition should

give composition fluctuations primarily on all three {100}

planes. If (2C44 - Cll + 012) < 0, these should lie about the

four {111} planes.

(ii) The initial kinetics of decomposition are described by an

exponential increase (or decrease) in amplitude of each Fourier

component. For a given composition and temperature the

amplification factor as a function of wavelength and

orientation is completely described by 32f'(c)/3c2, k, M, n,

C44: C11 and C

12'

(iii) The kinetics are such that after a while the fastest
growing composition fluctuations predominate giving rise to
almost pure sinusoidal fluctuations which lie on the <100> or

<lll> directions and have a wavelength /2 times the critical

wavelength (Zn/BC).

(iv) The kinetics and wavelengths of the fastest growing
composition fluctuations as a function of temperature and
composition are described by the temperature and composition

dependence of the various parameters.

(v) The limit of metastability in aeolotropic cubic crystals
occurs sooner than one would expect. The spinodal decomposition
mechanism seeks out the plane where the modulation occurs most

easily.

(vi) Since various composition fluctuations do not interact
with each other, the structure at the initial stages will be
approximately represented by the composition fluctuations along
the three {100} planes or the four {111} planes. The former
resembles a simple cubic array of regions rich in one component
connected along the <100> directions by rods similarly enriched.
The body centers of this array are regions depleted in this
component connected by similarly depleted <lOO> rods.

It is possible to make some qualitative predictions about the

later stages of spinodal decomposition:

(i) When the amplitude of the plane waves becomes such that
the higher order terms in the expansion of f'(C) about Co
become imporant, there will be an interaction (7) among the
composition fluctuations in the different planes which causes
a slowing down of the rate of growth to the equilibrium
composition, and distorts the fluctuations in the different

planes.

(ii) Depending on the relative vblumes of the two phases in
equilibrium, hnperfect versions of the following morphology
are expected:
a) If the volume fraction of one phase is much smaller
than the other, the {100} habit will give a simple
cubic array of octahedral particles whose corners

are aligned along the <lOO> directions.

b) The {111} habit will give a face-centered cubic array
of particles of the minor phase. These particles should
vary from Spheres to cubes as the volume fraction

increases.

(iii) The initial spacing of the particles in the {100} habit
is equal to the wavelength of the most rapidly growing
composition fluctuation; in the {111} habit, the near neighbor

spacing of particles (in the <llD>) is Jg-times the wavelength
of the most rapidly growing fluctuation.

(iv) During the initial stages, the amplitude of the individual
composition fluctuations is only about one third for the {100}

habit (or one fourth for the {llllhabit) of the maximum

10

composition difference in the sample. A similar fraction
persists as long as coherency is maintained, so that the
observed separation of the side bands in x-ray diffraction
patterns which are due to local composition differences in

the modulated structure, will represent only a fraction of the

actual composition difference.

(v) The maximUm elastic shear strain is at the corners of the
particles (octahedral particles for the {100} habit, and
spherical to cubic particles for the {111} habit) and is of the

order of the fractional lattice parameter difference.

(vi) The reported increase in wavelength with time is probably
due to resolution of some of the particles or rods and growth of
others. The driving force for it is the reduction in surface-
free energy.
In conclusion, it must be said that spinodal decomposition differs
from nucleation and growth in that it proceeds from a stage small
in degree but large in extent, passing through stages of primarily
increasing amplitude, whereas a nucleation and growth mechanism
proceeds from a stage small in extent but large in degree, passing
through stages of primarily increasing extent. In spinodal
decomposition there is no clear division where one can say the new
phase has appeared; in nucleation and growth this is the important

nucleation event.

2.2 Mechanical Properties in Spinodal Alloys

 

There have been extensive investigationscnithe role of long-range

coherent composition fluctuations resulting from spinodal decomposition

11

on mechanical properties of cubic crystals. One of the first
theoretical studies of this nature was done by Cahn (9), who
considered first a single Fourier component of the composition
fluctuations Ac whose wave vector 8 is in the [001] direction and

whose amplitude is A(B). According to Cahn (9),

Ac = c a co = A(B) c0582 (6)

where cO is the average composition. The internal stress components

Oij produced by this plane composition fluctuation is given by

oxx = oyy = (nAcY) = AnY c0582 (7)
o = o = o = o = 0
22 xy yz zx

The force F'on a dislocation per unit length produced by a stress
field 8 is

F = (3.5) x g (8)

where, b'is the Burgers vector, and g is the unit tangent to the
dislocation line. The force on a dislocation line is always
perpendicular to E and for edge dislocations consists of both climb

and glide components. The glide component F5 is given by

F9 = (ExE) (ban) (9)

where n is the unit normal to the glide plane. Equation 9- applies
equally well to screw dislocations but since these can glide on a

number of planes it is sometimes convenient to use Equation 3.

12

which for screw dislocations becomes
+
F = --—- (b.0xb). (10)

In inhomogeneous alloys there exist several other sources of
forces on dislocations that are not present in a homogeneous alloys of
the same composition and these relate mainly to the composition
gradients. For very small gradients the self-energy y of a dislocation

is approximately given by

2
Y: Gb2~ Yb (11)

where G is the shear modulus.

If Y varies with position there will be a force on the dislocation

(10, ll) given by

~lv

-€x(9?éd Y XE)

-r|
II

+ A A
Y(df26 + 2n) (ch€)x€. (12)

 

The corresponding glide force on a plane whose unit normal is n is

+ 3£n

= - Y (

ch 3C6 + 2..) (mar?) (3x3) . (13)

 

Another source of forces in a gradient comes from the fact that after
slip through an inhomogeneous region, the two opposing faces now

differ in composition given by

Ac = 3. grad c , (l4)

13

Cahn (9) considered the forces on dislocations in the {111}

<110> slip system, which interacts with only two of the three
fluctuation components. It should, therefore, behave as if the

sample contained an assembly of pseudo-rods along [001]. In this case,
the slip plane cuts across the rods and all parallel {111} planes

encounter the same set of obstacles as do the {Ill} cross-slip planes.

Consider the equation of the slip plane to be

x + y + z = J3'd (15)

where the cartesian coordinates x, y and z are parallel to the <100>
directions, and d is the distance from the slip plane to the origin.
Rotating the [xyz] coordinate system to [x'Y'Z'] such that X' is
along [110] and Y' is along [112] in the slip plane, will provide

the following expression

JEX'=x-y
(16)
26 y' = x+y - 22 + 2 V§d
By virtue of Equation 15,
Vay' = 3x + 3y . (17)

So that the resolved force on a [110] dislocation is

+

b. .n = A b Sln ———- B ' sin ——— Bx' . 18
o 3rnlly (,5 y) (5 ) ()

14

The (111) slip plane thus resembles a rectangular checkerboard of
alternating forces, as shown in Figure 2.' The sides of the
rectangles are the locus of zero force positions and within each
rectangle the force rises or falls to an extremum in the center.

Problems of the above nature have two extremes: If
An|b|yly8<l, the dislocation line is almost straight and if
An|b|y/y8>l, the dislocation curves around all obstacles.

Cahn (9) therefore, predicted that age-hardening in spinodal
alloys is due to the motion of edge and screw dislocations. He has
predicted that the yield stress varied as A21. Explicitly, he has
stated that at applied stresses exceeding AEE§¥EE- for screws,

and flegll_9 for edges, the dislocations shoaYgBYmove continuously
throughgshe structure. But the major drawback of Cahn's theory is
that experimentally obtained values of yield stress for spinodally
modulated structures are very much higher than theoretically predicted
values, as noted by Douglass and Barbee (12), Ditchek and Schwartz

(2) and Lefevre et al (13). Moreover, the predicted AZA dependence
of the yield stress is not applicable, as noted by Butler and Thomas
(14) and Lefevre et a1 (13).

Carpenter (15) and as well as Ditchek and Schwartz (16)
considered lattice-mismatch theories to explain the age hardening
mechanism in spinodally modulated structures. They considered the
mismatch between the lower and upper half of a slip plane due to the
difference in the lattice parameter when a dislocation cuts through

the modulated structure. For example, in the experimental work on

60Au-40Pt alloys, Carpenter (15) has considered the alloy lattice

15

A’—-—--—.

 

 

I

--—-'£-—

Q!

'/
Y
11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b i
. a
I + — + I — + —
I
I
l
""'\ CI? """" sh """" sr——
1 Y I I
I 1 I c '
' 1 I I
: l I I
- I : -+ : - : -r
I I
I I | I
I l I I
I : i :
I f‘ ------ I; I\\---
F7
I
l
+ I — + -
i
l
—D

Figure 2: The (111) [1T0] slip system in the absence of applied
stress showing the fbrces on the dislocation and the
resulting configurations (9)

a) screw at small amplitude for that wavelength,
b) edge at small amplitude for that wavelength,
c) screw at large amplitude, and

d) edge at large amplitude.

16

to be a sequence of alternating gold and platinum-rich regions along
<100> in space, with average Spacing between centers of A/2. Lattice
mismatch shearing strains are caused, for example, by shearing a
Pt-rich region over a Au-rich region. The increase in work-hardening
rates at small strains is attributed to rapidly increasing
deformation-induced internal strains, resulting from shearing, by
moving dislocations, of uniformly distributed composition fluctuations
in the parent solute lattice. Similar to Cahn's (9) theory, Carpenter
related the yield stress to Azx for both screw and edge dislocations.
According to Carpenter (15) the yield stress is given as

)2

(An EZA/Zh /66b for screw dislocation, and (19)

0
II

- (An)2 EZA/Zn JEGb for edge dislocations. (20)

Q
I

But both Carpenter (l5) and as well as Ditchek and Schwartz (16)
neglected the important role of dislocation self stress. As a result
their theories cannot be considered to be complete.

Ghista and Nix (17) suggested a dislocation model of the strength
of elastically inhomogeneous crystalline materials which is based on
the elastic interactions between dislocations and periodic fluctuations
of the shear modulus. The model rests on the assumption that the
elastic energy of a dislocation in an inhomogeneous material can be
treated as if the shear modulus varies radially from the axis of the
dislocation. They assumed the variation in the shear modulus to be
represented by a Bessel function of the first kind of order either

0 or 1. The variation in the elastic energy of a dislocation with

17

position in an inhomogeneous material is accounted for by a variable
phase factor which is included in the argument of the Bessel functions,
the model suggests that the critical stress to initiate plastic

flow increases linearly with the amplitude of the shear modulus
variation, and varies inversely with the wavelength. They have Shown

that the critical shear stress required for dislocation movement is

-5
_ P ' 1.75x10

2

where, D is the average shear modulus, E = Cb ,and Plis the

force intensity on a dislocation.
But the drawbacks in their theory are as follows:
(i) Consideration of a straight dislocation and neglect of the

contribution by the internal coherency stress, and

(ii) even when the Bessel function approximation of the radial
variation of the shear modulus is permitted to appear in their
theory (18), one cannot rely on their calculations. Since the
elastic inhomogeneity is distributed periodically in their model,
the self energy should also be a completely periodic function

of the position.

Dahlgren (l9) determined that the yield strengths were proportional
to the difference in cubic lattice parameters of unstressed
precipitating phases and independent of other factors such as the
precipitate particle size and precipitate volume fractions. The
yield stress dependence on lattice parameter differences alone

indicated that coherency stresses controlled the yield strengths.

18

He obtained the yield strength for age hardened spinodal alloys as

m Aa
o = ——— Y -—— (22)
3/6 ao

where, a is the Taylor factor, and Ad and a0 are the difference in
and the average cubiclattice parameter of the precipitating phases.
The equation indicates that the yield strength is dependent only on
the internal coherency strains and independent of particle size and
precipitate volume fraction. Since Dahlgren (19) assumed a straight
dislocation and neglected the effect of dislocation self stress, his
theory is not complete.

Hanai et al (20) explained the age-hardening mechanism in
spinodal alloys based on the evaluation of an interfacial energy per
unit area of the slip plane. They proposed that new interfaces are
produced on the Slip plane when a crystal with continuous composition
fluctuations arising from spinodal decomposition is deformed by slip.
They evaluated the energycrfsuch interfaces for modulated structures,
and they concluded that the contribution of the interfacial energy is
large enough to account for the age-hardening concomitant with
Spinodal decomposition.

Hanai et al (20) pr0posed that the yield stress, resulting from
the effect of interfacial energy is proportional to the square of the
amplitude and to the inverse of the wavelength of the composition
modulation for the modulated structure. For the face-centered cubic
structure

1

o = (4/2h/9) {2UE nC nS + anz} AZA' (23)

for screw dislocation, and

19

1

O = (JEd/3) {2UE nc nS + anz} AZA' (24)

far edge dislocations
where, UE is the interchange-energy of atom power, nc is the
co—ordination number, nS is the number of atoms per unit area of the
interface and k is a constant related hathe shape of the solute rich
region.

There are some major drawbacks in the theory of Hanai et a1 (20).
They considered the interfacial energy to be the sum of chemical
interfacial energy and elastic strain energy, but interfacial energy
is defined per unit area whereas elastic strain energy is defined
per unit volume, Secondly, the assignment of interfacial energy to
be 0.30/m2 is an overestimation, since the modulated structure in
Spinodal alloys is characterized by the fluctuation of constitutive
atoms and is not brought about by an entirely different atomic
arrangement as envisaged in a grain boundary or a twin interface.

Most recently, Kato, Mori and Schwartz (21) used a dislocation
force balance equation to consider the incremental stress due to
coherency stress in a spinodally modulated structure in face-centered
cubic alloys. They considered a mixed dislocation lying mainly in
the positive regions of the internal stress field as shown in Figure
3, to be responsible for macroscopic yielding. They argued that the
resistance- to the motion of the mixed dislocation is the largest of
all possible orientations. Edge and screw dislocations will move at
lower stresses as predicted by Cahn (9) causing micro-yielding, but

inhibited by pinning, will rotate into the mixed orientation which

20

   
 
   

 

. : I : ‘
i : . 5 5
It: I I I I
--+--- 5. - . ------ i ----- +-
I I I I
I ' : 1
I : , :
I + + I — i -I— :
I : E :
: ' 1 .
--1 _______ M‘“_-‘I _____ |_--—I-'
I jg} I I I I
I 2 1 I ' '
1 l ' I I
I — i - I + : — 1
I I I
I i I : I
| : | I l
I 1 I I I
I ' f
I 0 I fix ' [ITO]—-+
I I I I
| I I I I
I I 1 I I

 

Figure 3: Schematic representation of a mixed dislocation and
internal stress profile considered by Kata-Mori-
Schwartz. (+, and - positions Show respectively
maxima and minima of the force acting on the
dislocation due to the internal stress.) (21)

21

suffers the largest resistance. The Kato-Mori-Schwartz theory

indicates that the yield stress is given by

0 =AnY l/E (25)

which indicates that it is independent of A.

In the case of Spinodal alloys, as schematically shown in
Figure 14, the yielding occurs more gradually in aged than in
as-quenched alloys. In analogy to the Pierles-Nabarro yielding, this
fact can also be attributed to the difference in the mobility between
edge or screw dislocations and mixed dislocations; that is, when the
external stress is applied in modulated alloys, screw and edge
dislocations move first resulting in micro-yielding. However, due
to pinning points, the dislocations eventually acquire an orientation
different from the orientations of either edge or screw dislocations
and reorient into a mixed orientation. Thus, the macroscopic yield
stress is determined by the movement of dislocations with mixed
character.

In the case of the Kato-Mori-Schwartz theory, both the predicted
linear dependence of the incremental yield stress on An and the
magnitude of the incremental yield stress agree well with the
experimental results within a factor of two. Considering the
uncertainties of the experimental analysis, the agreement is believed

to be very good.

22

 

Stress

aged

as-quenched

 

 

 

 

of Strain

Figure 4: Schematic stress-strain curves in as quenched and
aged alloys.

23

2.3 Single Crystal Studies on Spinodal Alloys

 

Only a very limited amount of studies have been carried out on
single crystals of spinodal alloys. Greggi and Soffa (22) have
investigated the flow and fracture stress of Cu-l.07 weight perent
Ti spinodal alloy in the form of single crystals. Single crystal

tensile specimens with the tensile axis close to the [123] were aged

at 673°K for times varying from 10 minutes to 10,000 minutes and
tensile tested at room temperature. They found that the critical
resolved shear stress increased with aging time but the total strain
decreased with aging time. The strengthening of the aged samples
was due to the periodic arrays of discrete, coherent precipitates of
the metastable Cu4 Ti phase. They also observed that the samples
deformed by primary and as well as secondary slip; they have noticed
extensive twinningirithe necked region during later stages of the

deformation.

2.4 Transmission Electron Microscopic Studies of Spinodal Alloys

 

Transmission electron microscopy (TEM) has been used to visualize
the spinodal microstructure, and to measure the wavelength of
composition modulation, waveshape and to analyze dislocation structure.
Transmission electron microscopy has demonstrated that spinodal alloys
develOp a modulated structure. The aging behavior common to many
Spinodal alloys as examined by the transmission electron microscope,
consists of a periodic structure with the periodicity along the
<100> directions as predicted by Cahn's theory (8) for anisotropic
cubic materials. This is termed as the modulated structure. In

addition, this aging behavior shows that the modulated structure

24

transforms from sinusoidal-shaped in the early stages of the
decomposition to square-shaped in the later stages. In the case of
the Cu-Ni-Sn spinodal alloy,it;is Speculated that the composition
modulations represent the separation of the aS-quenched alloy into
Sn-rich and Sn-poor regions; however, the ratio of the atomic
percentage of Cu to the atomic percentage of Ni remains the same in
both phases.

Transmission electron microscopy studies on the decomposition of
Cu-9Ni-65n Spinodal alloy were carried out by Schwartz, Mahajan and
Plewes (23). They investigated the microstructural features of
as-quenched and as well as specimens aged at 623°K for various lengths
of time. In as-quenched samples they did not observe any structural
features that could imply decomposition of the solid solution. They
concluded that the glide dislocations tend to dissociate- into Shockley
partial dislocations, separated by faulted regions and they observed
long paired dislocations which they have speculated1x>be dipoles.

In the case of Cu-9Ni-6Sn samples aged for S, 40 and 300 minutes,
the principal feature observed by Schwartz et al (23) was the
appearance of modulated regions which appeared to exhibit some order
in their arrangement along <100>; similar structural features have
been reported by Butler and Thomas (14) and Livak and Thomas (24) in
Cu-Ni-Fe alloys which also decompose spinodally. Regions of
discontinuous precipitates interspersed with regions of the modulated
structure were observed by Schwartz et al (23) in Cu-9Ni-65n Specimens
aged for eighty hours, and in specimens aged for one hundred and sixty
hours, the modulated structure was abSent and the only prominent

feature was the discontinuous precipitates.

25

Datta and Soffa (25), in their investigation on the effect of
the microstructure on the age-hardening of Cu-Ti Spinodal alloys,
concluded that the modulated structures which develop in aged alloys
result from metastable spinodal decomposition involving the
continuous transformation of a single phase into a disordered phase
and an ordered phase. They explained the age-hardening response
in the alloy in terms of the interaction of dislocations with the
internal stress field associated with the Spinodal or modulated
structures using Cahn's (9) model of spinodal hardening.

The early stages of the Spinodal decomposition in Ni-Ti alloys
have been studied by Laughlin (26) who reported that a periodic
microstructure aligned along the elastically soft directions, namely,
<100>. These modulations cannot be considered artifacts since the
diffraction patterns Show ordering spots around the fundamental
spots indicating alternating regions of Ti-rich and Ti-poor phases.
The modulations also increase in intensity with aging time. The
strain contrast (at constant wavelength) associated with the
composition modulations also increases with aging time (27) implying
that the amplitude of the modulations also increases.

The precipitation reaction of a high tin phase late in the
coarsening stage of the spinodal decomposition of Cu-lONi-GSn alloy
was studied by Ditchek and Schwartz (28). The indexing of the
diffraction ring pattern corresponding to the precipitates suggests
that they are incoherent and they have speculated these to be Ni3Sn,
which has a 0019 structure (29). The 0019 structure is an isotype of

the 0022 lattice, and is shown in Figure 5.

26

 

 

 

 

 

 

 

 

Figure 5: The unit cell associated with the 0019-tYPe
superlattice.

- Ni

- Sn

 

III. PURPOSE OF CURRENT STUDIES

Whereas most of the previous microstructural studies in
spinodal alloys were concerned with the modulated structure in aged
alloys, the current investigation involves the use of the
transmission electron microsc0py to determine whether edge and
screw dislocations, as predicted by Cahn (9), or mixed dislocations,
as predicted by Kato, Mori and Schwartz (21), are responsible for
the age-hardening behavior in spinodally decomposed Cu-lDNi-GSn
alloy. Fine grained and as well as large-grained samples were used

in these studies.

27

IV. EXPERIMENTAL PROCEDURE

The Cu-lONi-6Sn stock for the experimental studies was provided
by the 3611 Laboratories, [details in Ref. (23)]. The available stock
from which the‘fine-grained and large-grained samples were made was in

the form of strips about four millimeters in thickness.

4.1 Fine-Grained Specimens

 

The fine-grained specimens were prepared by the following steps.
The available stock was rolled down to a thickness of about 0.45 to
0.5 millimeters using a cold-rolling mill. Tensile samples with a
gage length of 13 millimeters and width of 5 millimeters were cut
out as Shown in Figure 5, These samples were solution-treated
at 1073°K in argon for 3 minutes and then drop quenched into water
so as to avoid grain growth. This homogenizing treatment results
in the relieving of all stresses induced due to prior mechanical
treatments carried out on the samples. The solution treated
samples were chemically polished in a solution of 40% nitric acid
and 60% distilled water for a Short duration to remove any surface
contamination. Specimens which were not given any further heat-
treatment are referred to as "as-quenched". In order to induce
composition fluctuation the alloy some of the Specimens were
then heat-treated at 623°K in vacuum for periods of 10 minutes, 20
minutes or 60 minutes in a tube-furnace as Shown in Figure (7). The
specimens were suspended inside the tube using a very fine wire made

of manganin.

28

29

 

 

 

 

 

11‘ r-r '7F-
12mm
, I. _
x. z T
—-) 5mm L.— 13mn 40mm

 

 

 

 

 

 

 

 

k?‘ 10mm "fl 0.4mm

Figure 6: Schematic of the tensile test specimen.

30

Electrical connections for

 

 

 

  
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t‘-—-drop—quenchinq set-up
A 1 Vacuum gage
Inert gas inlet all—‘fl —-~To vacuum pump
-] '_ ooling c0115
Thermocouple-~
\\
Three-zone
Specimen ‘ "—— furnace
heating

 

 

//////«elements
/

 

 

 

 

 

 

 

 

 

 

 

Inert gas OUtIEt I [3 Detachable lid for

L_____;:1‘**"quenching

Figure 7': Schematic of tube—furnace used for homogenizing and
aging the specimens.

31

After the aging treatment, the specimens were directly drop-
quenched into water by shorting the manganin wire by passing a
large current through it. The Specimen surfaces were cleaned in a
chemical polishing solution of 40% nitric acid and 60% distilled
water. The specimens were now deformed in tension in order to induce
some strain in the matrix.

The tensile tests on the as-quenched and aged samples were
carried out using a micro-tensile fixture attached to the Instron
testing machine Shown in Figure 8. The specimens were strained to
either 5% or 10% plastic strain. The deformed specimens were
chemically thinned down to 0.1 millimeter using a solution of 40%
nitric acid and 60% distilled water and the surfaces were cleaned
using methanol. The gage length was cut into discs of 3 millimeters
diameter using a very Sharp pair of scissors in order to avoid
inducing stresses by the cutting operation.

The central portion of the disc in each case was made
transparent to electron beams using a two-step polishing method. The
first step, where conditions used are given in Table 1, is known as the
"dishing technique" (30), and it was used to produce a preferential
polishing in the central region of the specimen using a funnel-shaped
apparatus as shown in Figure 9. After polishing for some
predetermined time (about 30 seconds) in order to create a shiny
dish-shaped concave surface on one side, the specimen was turned
over and the polising was continued on the same mode on the other side
as well. The main aim of producing concave-shaped surfaces on both

sides of the Specimen was to produce regions transparent to electrons

(a)

 

 

 

 

—_L «.— Specimen holder

Screw for J/Q @

clamping specimen

 

 

 

 

 

 

 

 

(b)
’//,, . :::h ‘—‘Specimen
Q @
L___.,l,

 

 

 

 

 

 

 

*—

Figure 8: Microtensile fixture used for testing in Instron testing
machine;

a) Photograph.
b) Schematic.

33

Polishing—e
solution

 

 

 

 

To power *‘=\\
r
d

 

 

 

 

 

 

 

 

 

 

Specimen ;;Tb power
\ / supply
fl

 

 

 

 

 

 

 

 

 

 

 

 

Platinum if ' °
. L_, J 1 ,EL, Petr1d1sh
wire :1 i with a hole
| l .
I 1 Reservo1r
1 ......... 1 I
I I
. I
I l
L_ \41 I 1
I l
I
1
1

Figure 9: Schematic of the single-jet electropolishing unit.

34

Table l: Electropolishing data for "Dishing Technique".

Composition of Electrolyte Voltage Temperature

4 parts of Methyl Alcohol
plus 1 part of Nitric Acid (d.c.)

35

in the central portion during the second step of the polishing. In
this step, the "dished" specimen was held between circular platinum
loops as Shown in Figure 10 and electropolished under conditions
given in Table 2. The cathode was a cylindrical stainless steel
sheet with Slots cut out of it. A pointed light source was used to
determine when perforation occurred in the center of the foil. The
final electropolishing time was usually a few minutes, and as soon
as the hole was formed, the sample was removed from the electrolyte
and washed thoroughly in running methanol. This procedure was
consistently successful in producing then foils suitable for

transmission electron microscopic studies.

4.2 Large-Grained Specimens

 

The large-grained speCimens were prepared by the strain annealing
method using the following steps. The available stock was rolled
down to about a millimeter in thickness and tensile strips were cut
out and homogenized at 1073°K for 3 minutes in argon to remove
strains due to prior mechanical operations and then drop-quenched
in water. These strips were then imparted a critical strain of 8%
plastic strain and annealed at 1073°K for 72 hours in vacuum to
obtain grain sizes of the order of l to 2 millimeters. Samples
approximately 4 millimeters wide were then cut out of the large-grained
specimens using a diamond saw to induce as little strain as possible.
These samples were about 30 millimeters long and they were thinned
down to about 0.4 millimeters thickness with emery papers of grades
240, 320, 400 and 600 successively, using a brass-plate substrate.

Stresses induced during any of the above operations were relieved by

36

 

 

 

 

 

 

 

 

 

 

 

To cathode.—f7 ~-—->To anode
1 - - ....... . .......

i ‘ (I ' :L' Electrolyte
Stainless
steel sheet fi__
with slots
cut out . W,,,,e—Platinum wire

‘fl,,le”””7 loops

Specimen

\ J

 

 

 

Figure 10: Schematic of final electropolishing unit.

37

Table 2: Electropolishing data for Final step of
thin foil preperation.

4 parts of Methyl Alcohol 0
8 volts 243 K
plus 1 part of Nitric Acid (d.c.)

38

solution treating the large-grained samples at 1073°K for 6 hours

in vacuum followed by drop quenching into water. These samples are,
as before, referred to as "as-quenched". Some of the as-quenched
Specimens were aged at 623°K for 10 and 20 minutes in vacuum in order
to induce composition fluctuations.

Surface contamination in the large-grained samples was removed
using a chemical polishing solution of 40% nitric acid and 60%
distilled water. The as-quenched and as well as the 10 and 20 minutes
aged samples were strained to 5% plastic strain using the micro-tensile
device shown in Figure 8.

The strained specimens were thinned down chemically to 0.1
millimeter using a 40% nitric acid 60% distilled water solution and
cleaned using methanol. Just as in the case of the fine
grained specimens, discs of 3 millimeters diameter were cut out and
electropolished using the same two-step method used for the
preparation of fine-grained foils. The "dishing technique", which
was the first step, used conditions given by Table l, and the final
electropolishing, which was the second step, used conditions given
by Table 2.

The fine-grained and as well as the large-grained samples were
examined in a transmission electron microscope operated at 100

kilovolts.

V. RESULTS AND DISCUSSION

The dislocation structure in fine-grained and large-grained
samples of the Cu-lONi-GSn spinodal alloy was studied by transmission
electron microscopy. The operating voltage of the electron
microscope was 100 kilovolts and magnification was varied for the
different micrographs by varying the intermediate lens current. The
results of the transmission electron microscopic investigations on

aS-quenched and aged samples are discussed in detail in this section.

5.1 Fine-Grained Specimens

 

Figure 11 provides the deformation structure in an as-quenched
sample that was deformed to 5% plastic strain. It is apparent that
there are two slip systems in this particular region and that each
has a set of dislocations lying approximately parallel to <112>.

The main feature of the dislocations in as-quenched specimens is that
they seem to be straight. Figures 12(a) and 12(b) show the
dislocation structure of as-quenchedsamples deformed to 10% plastic
strain; whereas Figure 12(a) is the micrograph of a region deformed

by single slip with most of the dislocations lying along one direction
namely, [211], Figure 12(b) is that of a region deformed in two slip
systems, with one set of parallel straight dislocations lying along
[011] and the other set of parallel straight dislocation lying along

[211]. Besides having straight dislocations, the micrographs of the

aS-quenched specimens do not show any modulated structure due to

spinodal decomposition, as expected, and dislocation densities seem

39

4O

 

Figure 11: Dislocation structure in a fine-grained as-quenched
opecgmen deformed by 5%. The foil normal is near
011 .

41

 

Figure 12: Deformation structure in fine-grained as-quenched
specimens after 10% deformation. Foil normal is
near [011] for both micrographs.

(b)

42

to be quite high indicating that dislocation multiplication in
homogenized specimens is relatively easy.

Figures 13(a) and 13(b) Show the deformation structure of
specimens aged for 10 minutes at 623°K and deformed by 10% plastic
strain. The modulated structure due to spinodal decomposition is
visible in both of these micrographs and it is obvious that the
contrast due to the composition modulation interferes with the contrast
due to the dislocations. The dislocations still appear to be mostly
straight, though some of them appear to be curved. In Figure 13(a)
the dislocations are present on the (111) Slip plane, and hence
appear to be long, with a set of them lying parallel to the [101]
direction whereas Figure 13(b) shows two sets of parallel dislocations,

lying along [211] and [011]. The striking feature in the micrographs

of the 10 minute aged samples as compared to the micrographs of the
as-quenched samples is a significant lowering in the density of the
dislocations, apparently due to the interference of the strain field
associated with the dislocations by the strain field associated with
the modulated structure.

Figures 14(3) and 14(b) represent the dislocation structure of
Specimens aged at 623°k for 20 minutes and deformed by 5% and 10%
plastic strain, respectively. The most important features that can
be noticed in these micrographs are the clearly visible modulated
structure due to spinodal decomposition and a large number of
dislocations which appear to be curved unlike in the case of the
deformed as-quenched specimens. This suggests that mixed

dislocations may be responsible for the hardening in spinodally

43

(a)

(b)

 

Figure 13: Dislocation structureoin fine-grained specimens aged
for 10 minutes at 623 K and deformed by 10%. Foil
normal is near [111] for (a) and [011] for (b).

44

Figure 14: Dislocation structure in fine- grained specimens a

for 20 minutes at 623°K.
for both micrographs.

a) After 5% deformation.

Foil normal is near [011

b) After 10% defbrmation.

 

oed

45

modulated structures. In Figure 14(b) the dislocations seem to be
pinned at various points which is evidenced by the observation that
these dislocations do not appear to be smooth lines. It is also
obvious that the contrast due to the modulated structure interferes
with the dislocation contrast.

Micrographs of dislocation structure in specimens aged for one
hour at 623°K and deformed by 5% and 10% are presented in Figures
15(a) and 15(b), respectively. The few dislocations that are visible
are curved indicating once again that mixed components may play a
significant role in the hardening of spinodally modulated structures.
The contrast due to the modulated structure is so strong that the
dislocations are hardly visible, apparently due to the strain field
of the modulated structure interfering with the strain field of the
dislocations. The tremendous decrease in dislocation density as
compared to as-quenched specimens also indicates that dislocation
multiplication is difficult in heavily modulated structures.

It was felt that the dislocation-structure could not be observed
in specimens aged for longer than one hour. However, a fine-grained
specimen aged at 623°K for 24 hours in vacuum was examined in the
transmission electron microscope. Figure (16) shows Spherical
particles along the grain boundaries, and they: might be due to the
precipitation reaction of a high tin phase late in the coarsening
stage of the spinodal decomposition (28). The diffraction ring pattern
corresponding to these precipitates Was indexed, and it was found to be

from crystal of body centered cubic structure.

46

(b)

I

.V

‘2 .

y .

 

Figure 15: Dislocation structure in fine-grained specimens aged
for 1 hour at 623°K. Foil normal is near [011] for

both micrographs.

a) After 5% deformation. b) After 10% deformation.

47

 

Figure 16: Grain-boundary precipitates in a fine-grained
.specimen aged for 24 hours at 623°K.

48

Another important observation was the appearance of ordering
spots around fundamental spots in aged samples and these were
absent in the diffraction patterns of homogenized Specimens. These
ordering spots may be due to the ordering of the tin rich phase

in the spinodally decomposed alloy.

5.2 Large-Grained Specimens

 

Although fine-grained specimens can provide information about
age hardening in spinodally modulated structures, they are far from
ideal to obtain crystallographic information about the dislocation
structure. Deformation structures in a large-grained as-quenched
specimen are presented in Figures 17(a), 17(b) and 17(c). The prime
features are the absence of the modulated structure, and
long straight dislocations, present in various {111} planes.

The other {111} slip planes are at an angle to the foil surface.
The dislocations present in these {111} slip planes which are
slanted to the foil normal are projected as straight lines. All
dislocations are parallel to the <110> directions and this feature
is quite different from the observations made in fine-grained
Specimens. As expected from the micrographs of fine-grained
as-quenched samples, the dislocations are neither curved nor wavy.

In the microstructures of large-grained specimens aged at
623°K for 10 minutes and deformed by 5% plastic strain presented in
Figures 18(a) and 18(b) and some straight dislocations and some
dislocations with Sharp bends are observed. The modulated structure
due to spinodal decomposition is also evident. In Figures 19(a) and

19(b), most of the dislocations present are curved and there are

 

Figure 17: Dislocation structure in a large-grained as-quenched
s ecimen after 10% deformation. Foil normal is near
11] for all three micrographs.

50

(a)

 

(b)

 

 

Figure 18: Dislocation structure in a large— grained specimen aged
at 623C K for 10 minutes and deformed by 5%. Foil
normal is near [011] for both micrographs.

(a)

(b)

 

Figure 19: Dislocation structure with sharp bends and cusps in the
dislocations in a large-grained specimen aged at 623°K
for 10 minutes and deformed by 5%. Foil normal is near
[011] for both micrographs.

52

sharp bends and cusps in them, apparently due to the dislocations
interacting with the modulated structure.

Figures 20, 21, 22 and 23 illustrate the dislocation
structure in large-grained samples aged at 623°K for 20 minutes and
deformed by 5% plastic strain. Most Of the dislocations present
are curved indicating that the mixed components may be playing a
significant role in the deformation of such Specimens. Further,
significant decrease in dislocation density in the active slip planes
(compared to as-quenched specimens) indicates that the dislocation
multiplication is difficult in aged Specimens. Navy shaped
dislocations observed in Figure 21 suggest that they are held back
at various points, but the wavelength of these wavy dislocations,
measured to be about 1,000A’ in Figure 21(a) does not correspond to
the measured wavelength of the compositional modulation in aged
Cu-10Ni-65n alloy as reported by Ditchek and Schwartz (28). They
differ by an order of magnitude. Sharp bends and cusps are observed
in the dislocations shown in Figures 22(a), 22(b), and 22(c), and
dislocation dipole like appearance caused by pinning and folding
of dislocations are observed in Figure 22(a). It can also be
noted that the dislocations in this set of micrographs are not
smooth. They appear to be wavy but the wavelength in this case is
an order of magnitude less than the ones observed in Figure 21, and
correspond very well to the measured wavelength of the composition
fluctuation by Ditchek and Schwartz (28).

In order to analyze the character of the dislocations responsible

for the age-hardening in the spinodally modulated structure, specimens

 

 

Figure 20: Dislocation structure in large-grained specimens aged at
623°K for 20 minutes and deformed by 5%. Foil normal is
near [011] for both micrographs.

54

 

 

(a) (b)

Figure 21: Navy-shaped dislocations observed in large-grained
specimens aged at 623°K for 20 minutes and deformed
by 5%.

 

E q, I, 0'25“,“
- O A 1 .

Figure 22: Sharp cusps and bends in dislocations observed in
large-grained specimens aged at 623°K for 20 minutes
and deformed by 5%. Foil normal is near [011] for
all four micrographs.

 

[(4.

 

Figure 22: (Continued).

56

0'25!!!“
r——-——I

57

 

(b)

Figure 23: Curved dislocations present in a large-grained
specimen aged at 623°K for 20 minutes and
deformed by 5%.

a) Bright field image. b) Diffraction pattern.

c) Dark field image corresponding to diffraction spot
indicated by the arrow.

-L’

58

cut from a large-grained sample aged at 623°K for 20 minutes and

deformed to 5% plastic strain were examined in a Philips EM 300

electron microscope operated at 100 kilovolts. This microsc0pe had a stage
with tilting (150°) and rotating (350°) capabilities. Such an

arrangement enabled the dislocation Burgers vector analysis by

3.5 method, where 3 is a vector normal to the reflecting plane, and

5 is the Burgers vector of the dislocation. According to this method,

the dislocation goes out of contrast when 3.5 is equal to zero and

is in contrast when 3.5 is not equal to zero. By tilting and rotating
the specimen .appropriately a series of micrographs was taken with

the 5 vector near [211], [112] and [110] respectively, as shown in
Figures 24(a), 24(b) and 24(c). One particular dislocation, which

is in contrast only in Figure 24(3) (indicated by A) but out of
contrast in Figures 24(b) and 24(C), was analyzed. This analysis is

summarized in Table 3. As can be seen from the analysis, the

Burgers vector of this dislocation is along [1T0]. When the

projections of the <llD> directions are analyzed for the [211] plane
normal, they strongly suggest that this particular dislocation

lies along [011], and the other dislocations along correSponding

<110> directions. The above observations strongly indicate that
dislocation A is of mixed character, which lies along the [011]
direction in the plane containing [211] and [011] directions. 'This is
in strong agreement with the Kato-Mori-Schwartz theory (21), which
considers that mixed dislocations which lie, on the average, parallel
to <110> and to be responsible for the age hardening of the spinodally

modulated structure.

59

 

 

Figure 24: (a) Dislocation structure in a large-grained specimen
a ed[at ]23OK for 20 minutes and deformed by 5%.
=21].

60

 

Figure 24: (5) Same region as Figure 24 (l). 7f: [112].

61

 

Figure 24: (c) Same region as Figure 24 (l). 3’: [110]-

62

m .m I m m.
oZEEE P o F P F F SE 3 a

£232:

r-IN
.
O
r—IN
mlm
mlm

SE E E

est; O .NH m- _ m m. SE 3 em

""||I'|"-'I""" """" """"Il'l-"""|'I'l""'ll"""""""|'I""|'I't"""'

(umMLucou W .W. W .m: ..N.. W
8382.5 PS: St: Soup :8: 8:: :2: e m. “mums.

T

.22; A3 ASE 8:3... 5 mcoBumCmL
woes» of .825 2338me 93 Low Pm eo moat; 3338 um mEE

VI. CONCLUSIONS

Results of the transmission electron microscopy to analyze the
dislocation structure in as-quenched and aged specimens of the
Cu-lDNi-GSn Spinodal alloy, of both fine-grained and large-grained
types, can be summarized as follows:

(i) Deformation structure of aged specimens contains more

curved dislocations compared to the straight dislocations in

deformed as-quenched specimens. This suggests that mixed
components may play a Significant role in the deformation of

aged specimens.

(ii) Dislocations present in deformed aged specimens have
sharp cusps and bends indicating that they are pinned at various

points. This feature is not observed in as-quenched specimens.

(iii) Dislocation density in aged Specimens is significantly
lower than in as-quenched specimens that have undergone the
same amount of deformation. This observation suggests that
dislocation multiplication from active sources is hampered in
the modulated structure; as a result sources present in other
regions of the specimen have to become active to accommodate

the deformation.

(iv) There have been some observations in which the dislocation
in aged specimens appear to be wavy and their wavelength is of
same order of magnitude as the measured wavelength of

compositional modulation in this alloy.

63

64

(v) Use of large-grained samples (as compared to fine-grained
Specimens) Significantly helps in the analysis of the dislocations
since the entire region of observation is usually within one

large grain.

(vi) A 3.5 analysis on a deformed large-grained sample indicated
mixed dislocations which lie parallel to <110> to be responsible
for the age hardening of the spinodally modulated structure.

This is in strong agreement with the Kato-Mori-Schwartz theory

(21).

10.

11.

12.

13.

14.

15.

REFERENCES

Cahn,(J. W3, "Spinodal Decomposition," Trans. AIME, 242, 166-180,
1968 .

Ditchek, B. and Schwartz, L. H., "Application of Spinodal Alloys,"
Annual Review of Materials Science, 9, 219-253, (1979).

Nicholson, R. B. and Tufton, P. J., "Precipitation Procedures
of Hayd Magnetic Materials," Z. Angew Physik, 2, 59-62,
1966 .

Gibbs, J. W., Collected Works, 1, (New Haven: Yale University
Press, 1948), p. 105 and p. 252.

 

Hillert, M., "A Solid-Solution Model for Inhomogeneous Systems,"
Acta Metall, 9, 525-535, (1961).

Hilliard, J. E. and Cahn, J. W., "Free Energy of a Non—Uniform
System,“ J. Chem. Phys., 28, 258-267, (1958).

Cahn, J. W., "0n Spinodal Decomposition," Acta Metall, 9,
795-801. (1961).

Cahn, J. W., "0n Spinodal Decomposition in Cubic Crystals,"
Acta Metall, 19, 179-183, (1962).

Cahn, J. W., "Hardening by Spinodal Decomposition," Acta Metall.,
‘11, 1275-1281, (1963).

Fleischer, R. L., "Solution Hardening by Interaction of Impurit
Gradients and Dislocations," Acta Metall., 8, 32-35, (1960 .

Fleischer, R. L., "Effects of Non-Uniformities on the Hardening
of Crystals," Acta Metall., 8, 598-604, (1960).

Douglass, D. L. and Barbee, T. W., "Spinodal Decomposition in
Al/Zn Alloys," J.Mater. Sci., 2, 121-129. (1959)-

Lefevre, B. G., D'Annessa, A. T., and Kalish, D., "Age-Hardening
in Cu-lSNi-BSn Alloy," Met. Transactions,_9A, 577-586, (1978).

Butler, E. P. and Thomas, 6., "Structure and Properties of
Spinodally Decomposed Cu-Ni-Fe Alloys," Acta Metall., 18,
347-365, (1970).

Carpenter, R. W., "Deformation and Fracture of Gold-Platinum
Polycrystals Strengthened by Spinodal Decomposition,"
Acta Metall., 15, 1297-1308, (1967).

65

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

66

Ditchek, B. and Schwartz, L. H., Proceedings of the Fourth
International Conference on Strength of Metals and Alloys,
8, 1319, (1976).

 

 

Ghista, D. N. and Nix, W. D., "A Dislocation Model Pertaining
to the Strength of Elastically Inhomogeneous Materials,"
Mat. Sci. and Eng., 8, 293-298, (1968/69).

Dahlgren, S. D. Ph.D. Thesis, University of California,
Berkeley, CA, (1966).

Dahlgren, S. D., "Correlaton of Yield-Strength with Internal
Coherency Strains for Age-Hardened Cu-Ni-Fe Alloys,"
Met. Transactions, 85, 347-351, (1977).

Hanai, Y., Miyazaki, T., and Mori, H., "Theoretical Estimation
of the Effect of Interfacial Energy on the Mechanical
Strength of Spinodally Decomposed Alloys," J. Mater.
Sci., 15, 599-606, (1979).

Kato, M., Mori, T., and Schwartz, L. H., "Hardening by Spinodal
Modulated Structure," Acta Metall., 88, 285-290, (1976).

Greggi, J., and Soffa, W. A., "Preliminary Observations of the
Flow and Fracture of Cu-Ti Alloy Single Crystals Containing
Coherent Precipitates," Scripta Metall., 18, 525-529, (1978).

Schwartz, L. H., Mahajan, S., and Plewes, J. T., "Spinodal
Decomposition in a Cu-9wt. % Ni- 6wt % Sn Alloy," Acta
Metall., 88, 601-609, (1974).

Livak, R. J. and Thomas, G., "Spinodally Decomposed Cu-Ni-Fe
Alloys of Asymmetrical Compositions," Acta Metall., 18,
497-505, (1971).

Datta, A. and Soffa, W. A., "The Structure and Properties of
Age-Hordened Cu-Ti Alloys," Acta Metall., 85, 987-1001,
1976 .

Laughlin, D. E., "Spinodal Decomposition in Nickel Based
Ni-Ti Alloys," Acta Metall., 84, 53-58, (1976).

Laughlin, D. E. and Cahn, J. W., "Spinodal Decomposition in
Age-Hardened Cu-Ti Alloys," Acta Metall., 88, 329-339,
1975).

Ditchek, B., and Schwartz, L.H., "Diffraction Study of Spinodal
Decomposition in Cu-lOw/oNi-6w/oSn," Acta Metall., 88,
807-822, (1980).

67

29. Barret, C. and Massalski, T. B., "Structure of Metals," 3rd Edition,
(McGraw-ifill, U.S.A,1966) p. 278.

 

30. Hirsch, P. B., Howie, A., Nicholson, R. B., Pashley, D. W.,
. and Whelan, M. J., "Electron Microscopy of Thin ngstals,"
(Butterworths, London,‘1965) p. 36.

 

MICHIGAN STATE UNIVERSITY LIBRARIES

31293

3

III III II

74 6500

111 1