Stacking fault energy determinations in hcp silver-tin alloys

STACKING

FAULT

IN HCP

ENERGY

DETERMINATIONS

SILVER-TIN

A. W. RUFF,

Jr.:

ALLOYS*?

and L. K. IVES:

Measurements of the intrinsic stacking fault energy 8s 8 function of tin solute concentration are reported throughout the r8nge of the intermediate hexagonal b-phase. Four different alloy compositions from 12 to 17 at. % tin were studied. Extended dislocation nodes and dislocation double ribbons were observed and measured. The stacking fault energy v8lues obtained from measurements on these two conflgurations were in good agreement and indiceted that the magnitude of the st8cking fault energy increased linearly with solute concentration in the hcp phase. These results are compared with those from cubic a-phase Ag-Sn alloys previously reported. The dislocation configurations in the hexagonal alloys are briefly described. DETERMINATION

DE

L’ENERGIE

DE FAUTE D’EMPILEMENT h.c. ARGENT-ETAIN

DANS

LES ALLIAGES

Les auteurs presentent des mesures de l’energie de defrtut d’empilement intrinseque en fonction de 18 concentration de l’etain dissout, dans le domeine de 18 phase intermediaire hexagonale 5. Quetre compositions differentes d’rtlliagesont QteBtudiees, de 12 8 17 “/pat. d’etain. Les auteurs ont observe des noeuds de dislocations dissocies et des doubles rubans de dislocations et les ont mesures. Les valeurs de l’energie de def8ut d’empilement observees 8 partir des mesures effectuees sur ces deux configurations sont en bon 8ccord et montrent que la valeur de l’energie de defaut d’empilement augmente lineairement avec la concentr8tion du solute dens la phase h.c.. Ces resultats sont compares 8vec ceux obtenus 8 partir de la phase cubique a des alli8ges Ag-Sn present& anterieurement. Les auteurs decrivent brievement les configurations des dislocations dens les alliages hexagonaux. BESTIMMUNG

DER

STAPELFEHLERENERGIE IN LEGIERUNGEN

HEXAGONALEN

SILBER-ZINN-

Es wird uber Messungen der intrinsischen Stapelfehlerenergie 81s Funktion der Konzentretion des gel&ten Stoffes im gesamten Bereich der hexagonelen {-Phase berichtet. Vier verschiedene Legierungen mit einem Zinngehalt zwischen 12 und 17 At. ‘A wurden untersucht. Ausgedehnte Versetzungsknoten und Versetzungsdoppelbiinder wurden beobechtet und ausgemessen. Die 8us beiden Konfigurationen bestimmten Werte w8ren in guter Ubereinstimmung und ergaben, da9 die Stapelfehlerenergie linear mit der Zinnkonzentration in der hex8gonalen Phase zunimmt. Diese Ergebnisse wurden mit kiirzlich berichteten Stapelfehlerenergiewerten der kubischen a-Phase der Ag-Sn-Legierungen verglichen. Die Versetzungskonfigurationen in den hexagonalen Legierungen werden kurz beschrieben.

intermediate

1. INTRODUCTION

Quantitative stacking been

fault

reported

Relatively hcp

measurements (SFE)

for

several

little attention

alloys.

basal

energy

planes

Dislocations

fault. packed

variation

with composition binary

fee

of have

alloys.(l)

has been paid, however, lying

in hcp materials

partial dislocations

of the

connected

on the

to

close-packed

can extend

into two

by a ribbon of stacking

This is analogous to the fee case involving closeBoth intrinsic and extrinsic { 11l} planes.

stacking faults can exist in hcp materials, intrinsic

faults are produced

The variation

in stacking

though only

by single slip processes. sequence

of close-packed

planes differs from the fee case@) as does the method of formation of arrays of extended dislocations. Several alloy systems exhibit a transition with increasing solute concentration from a terminal fee phase to an

SFE

hcp phase.

In some of these alloys, the

in the fee phase has already

A comparison

been determined.

of the SFE between these two phases is

of interest in connection

with an interpretation

of the

SFE in terms of the bulk free energy of the respective phases.

In hcp alloys it is also possible to examine

systems

having

packed. Ericsson(3) minations ments on

two

ratios

reported

of the SFE

in

Recently,

has

c/a

other

than

results

dislocations

deter-

node measure-

nickel-cobalt

Ashbee and Vassamilletc4)

extended

close-

of direct

from dislocation

hexagonal

ideal

in

alloys.

reported

a two-phase

briefly fee-hcp

copper-gallium alloy. To our knowledge, however, there has been no direct quantitative determination of the composition dependence of the SFE across extensive regions of the fee and hcp phases in a single alloy system. Previously, we have reportedt5) values for the intrinsic SFE in a series of fee silver-tin alloys

* Received December 2, 1968; revised Jrtnuary 6, 1969. t Contribution of the National Bureau of Stsndards. $ Metallurgy Division, Nation81 Bureau of Standards using Washington, D.C. 20234. 1045 ACTA METALLURGICA, VOL. 17, AUGUST 1969

the

dislocation

node method.

In that

work

ACTA

1046

METALLURGICA,

the composition ranged from pure silver to a 7.8 at. % tin alloy having a composition near the region of the fee-hop transition. This paper reports@) on the determination of the intrinsic SFE in a series of hcp silver-tin alloys. Direct measurements were made on dislocation nodes and on dislocation double ribbons in the samples. We shall also discuss some of the faulted dislocation configuration observed in the hcp alloys. Many of these configurations were similar to those found in hexagonal graphite and discussed by Amelinckx and De1avignette.c’) 2. EXPERIMENTAL

The hcp silver-tin alloys were prepared by melting the pure materials (99.999~/~ Ag and 99.999% Sn) in a graphite crucible within a vacuum induction furnace system. After holding the melt for several minutes in a vacuum of 10e5 torr to permit mixing, a drop of molten alloy was allowed to fall from the crucible onto a silver-plated copper block at room temperat,ure where it cooled quickly. This method allowed the production of several individual specimens from one alloy melt with a constant composition. The samples were then mechanically reduced in thickness and homogenized at elevated temperatures (typically 750°C) for several days. Subsequently, a series of rolling and annealing treatments reduced the samples to about 0.1 mm in thickness. The annealed sheet was then plastically deformed by a few per cent in bending to produce fresh dislocations and electropolished to obtain thin foil specimens. The foils were observed at 100 kV in an electron microscope equipped with a rotating-tilting stage. Four different alloys were prepared having concentrations of 11.9, 13.9, 16.0 and 17.2 at.% tin, as determined by chemical analysis and X-ray lattice parameter measurements. The most dilute alloy (11.9 at. %tin) lies near the lower composition limit of the hcp region. Spectrographic analysis for trace impurities on three of the alloys indicated that 1 to 10 ppm was the amount present for those detectable. The homogeneity of two different alloys (11.9 and 16 at. o/o tin) was measured using electron microprobe anaIysis. The range of variation of solute present was f0.2 at.% tin indicating a satisfactory degree of homogeneity. The original photographic plates were optically enlarged from an initial magnification of about 34,000 to 106,060 final magnification. Utilizing either line tracings or photographic enlargements of isolated dislocation nodes and double ribbons, a micrometer eyepiece in a low power optical microscope was used to measure the enlarged images to a sensitivity of about 8 A.

VOL.

17,

1969

3. DISLOCATION

STRUCTURES

Frank and Nicholas@) have discussed the fault types and dislocations expected in the hcp st~~tur~. Berghezan et .I.@) and Amelinckx and Delavingnette”) extended this analysis and applied it to zinc and hexagonal graphite, respectively. Perfect dislocations with a/3(2iiO) typo Burgers vectors lying on basal planes may extend by the reaction 43[2ilO] = ~~3[liOO] + ~~3~10~01to form a ribbon of stacking fault bounded by Shockley partial dislocations. This is analogous to the case in the fee structure. If the usual Thompson notation is applied, the reaction can be written AB 3 Aa + oB. The geometry of this confi~ration is illustra~d s~hematica~y in Fig. 1, Here the perfect stacking of close-packed planes follows the sequence ababab. The dislocation (at the left) has extended on an a-plane so that atoms formerly occupying a-positions have been shifted to e-positions and those in b-positions have moved to a-positions leaving an intrinsic stacking fault. The reverse reaction, AB -3 aI3 + Aa, where the bounding partial dislocations are interchanged, would shift atoms in the opposite direction. At the fault plane this would require an energetically unfavorable b over b stacking of atoms. However, if the latter process were to occur one plane above (or below) the present location, illustrated at the right in Fig. 1, a relatively low energy intrinsic fault would again be produced. In fact, the fault type and energy are identical in the two cases. The shear vectors describing the two faults, however, are equal in magnitude and opposite in direction. As a consequence, the contrast of the extreme fringes produced by faults inclined to the electron beam will be opposite. Figure 2 is an electron micrograph of a dislocation double ribbon obtained from the 11.9 at.% tin alloy showing this effect. Since the faults lie on adjacent planes, a relative fringe shift of one-half unit would be expected and is observed. In fee material the same contrast effect arises at adjacent intrinsic-extrinsic stacking faults.(g*ro) Many dislocation networks with extended nodes were observed in these hcp alloys. Quantitative SEE determinations were not made from such network nodes, however, information on the nature of faulted structures can be obtained from their analysis. Figure 3 shows a network from the 11.9 at. y0 tin alloy, in both stacking fault contrast and dislocation line image contrast. Burgers vector assignments are indicated. Both extended dislocation nodes (shown at A) and double ribbons (shown at B) are present. Adjacent dislocation nodes are seen to be extended by approximately equal amounts. This observation is

RUFF

_~ND IVES:

STACKIKG

FAULT

ENERGY

IS

HCP

SILVER-TIN

a

C

a

b

b

a

b

c

a

C

a

b

b

a

b

a

c

L OB

c

1047

ALLOYS

t

a

oB

A0

b

b

a

a

b

b AB-oB+An

AB -AotoB

FIG 1. Basal plane stacking sequence at extended dislocations in the hcp structure with the Burgers vectors indicated. The two stacking faults are equivalent although they lie on adjacent basal planes.

consistent faults

with the existence

on

vectors.

adjacent

having

At the cross-over

bounding

of equivalent

planes

adjacent

intrinsic

opposite

shear c/2

a jog of magnitude

exists. The dislocation structure(7)

double

shown

stacking

configuration

schematically

three partial dislocations fault ribbons

ribbon

bounding

in

Fig.

has a 4.

The

the length of the

all have the same Burgers vector.

sequence

of

close-packed

basal

The

planes

is

In principle the two stacking fault ribbons shown. could be separated in the c direction by a distance (2n + l)c/2

where n = 0, 1,2 . . . although

for large

n the contrast at the center partial dislocation probably

configuration

ribbons are separated

is also possible

when

energy

double ribbons

hcp structure

by growth or multiple

For example,

simple

produced

abab sequence. contrast

extrinsic

by the insertion

growth

faults

can be

of a c plane in any perfect

Drurnoi) has considered the diffraction

at various fault’s in hexagonal

4. METHODS

in the

slip processes.(2)

FOR STACKING DETERMINATIONS

The SFE y can be determined

crystals.

FAULT

ENERGY

from measurements

of the radius y of a circle inscribed wit’hin an extended

An the

by (2n)c/2 where n = 1, 2, 3 . . .

In that case the two faults overlap partially to a higher

separated by a distance

would

differ from that at the outside partials.

asymmetric

probably

cl2 in the c direction. More complex stacking faults can be produced

of the partial dislocations

nodes,

faults are therefore

composite

fault.c7)

have not been observed

and lead

Asymmetric in any of the

<-alloys studied here. Many examples

of extended

dislocation

loops were

found which were jogged so that faulted segments lay on adjacent example

basal planes.

imaged

in several

Figure

5 shows one such

different

reflections.

In

Fig. 5a, the stacking faults and bounding partial dislocations are imaged. In Fig. 5b all the bounding dislocations are seen while in Figs. 5c and 5d each of the pair of bounding dislocations is imaged in turn. The interchange of each partial dislocation between the outside boundary of one fault and the inside boundary of the other fault can be seen. The stacking

FIG. 2. Stacking faults on adjacent inclined basal planes in an 11.9 at. ‘A tin alloy. The fringe displacement corresponds to equal but opposite shear vectors at the two faults in the double ribbon at the right.

ACTA

1048

METALLURGICA,

VOL.

17,

1969

5%~. 3. Network of extended dislocation nodes (A) and ribbons (B) in an 11.9 tat.% tin alloy. (a) Both the stacking faults and bounding partial dislocations are shown. (b) Only two of the three bounding dislocations are in contrast at each fault.

to Brown and Th61en(12) analysis could then be made and the inner radius y measured. In fault contrast with 2 = 2200 the partial dislocations bounding a node have image contrast Gbp2 characterized by 1~~1 = 8, $, $ where n = g” 1)El, with 2 the diffraction vector and gv the partial dislocation x cos2a + Burgers vector. For a given diffraction condition, two appreciably different images are observed for x cos 2cr log, R/E (1) InI = +, depending on the side of the partial dislocation 1 on which the fault lies. This effect can be seen at the where G is the shear modulus, b, the partial dislocation adjacent extended nodes at A in Fig. 3. For the Burgers vector, Y Poisson’s ratio, CI the dislocation purpose of measurement, the sign of the operating character angle, R the outer radius of curvature of reflection used to image isolated nodes was changed the node partial dislocations, and E is a cutoff distance where necessary to produce the sharper lnf = 4 related to a dislocation core radius. The use of this image. In the high SFE alloys, this difference in relation has been discussed in detail previously(5,13) images created the impression that adjacent nodes together with the corrections required due to prowere extended by significantly different amounts. The jection distortion and diffraction contrast image In1 = $ image was sufficiently sharp for measurement shifts. In the present study, extended dislocation purposes. nodes lying on the basal planes in the hcp alloys were Dislocation double ribbons were observed in all the photographed in 2200 type reflections which give hcp alloys and were employed as an alternate constacking fault contrast and 2110 type reflections which figuration to determine the SFE. The SFE y was give dislocation line contrast. A Burgers vector determined by measurements of the ribbon width w

dislocation node.

Affording

-?!Y= O.O%(~) - o.““(&)

(o.ols(g+ 0.036(&)

RUFF

IVES:

AND

STACKING

FAULT

ENERGY

IN

Ag-15

HCP

SILVER-TIN

Sn, Ag-30

estimate

Sn and

appropriate

alloys.

The

Poisson’s

ALLOYS

we have

effective

these

for

values

to

the

hcp

reported

for

ratio were v(Ag) = 0.38 and v(Ag-15

0.39 indicating

Sn) =

only a slight increase with tin content

which is similar to the behavior alloys.

used

values

polycrystalline

1049

We therefore

of veti in the u-phase

use the value calculated(5)

for

Ag-8

Sn of vetf = 0.47 for all c-phase alloys. Several large extended dislocation loops have been found

in these alloys.

The variation

w with character

in dislocation

extension

angle a is given for a loop by the

expression w = w,[l

a

C

b

a

b

a

C

b

a

a

b

which can be used to obtain Poisson’s

b

1

values reported(r4)

Torsion

the composition reported

lOlo N/m2.

to the expressionC7) 3

GbD2 The ribbon images

2-v ~

87lw ( 1 -v

into

widths were measured

formed

in 2110 diffraction

true width is obtained making

)(

corrections

Y cos 2a 2-v

1

.

(2)

extrapolation {-phase

bounded

region

= 2.66 x

Sn) = 2.2 x of the cubic indicates

5. RESULTS

examples

that

between 2.1 and 2.3 x lOlo

N/m2. A constant value Gete = 2.3 x lOlo is used here for all [-phase alloys.

conditions. width

the

All

contain

plastic

from line contrast

to

G,,,(Ag)

by ratio G&15

the

that

AND

N/m2

DISCUSSIONS

of isolated

extended

dislocation

nodes taken from different alloys are shown in Fig. 7.

from the measured

for inclination

Assuming

of Geii is approximately

for ,u and taking Alternately,

values

Several 1-p

with the decrease in shear

dependence

Gefi is probably

Y -=--_

modulus

modulus reported for the cubic alloys.

alloy

according

The loop

= 3.08 x lOlo N/m2 and ,u(15 Sn) = 2.52 x

lOlo N/m2, we calculate

c~B+cd-Aa

ratio.

value v = 0.45.

that

Fm. 4. The basal plane stacking sequence at dislocation double ribbons is indicated. Each partial dislocation has the same Burgers vector in this symmetric configuration.

(3)

tin alloy gave the

lOlo N/m2 were consistent

c

v)]

shown in Fig. 6 in the 11.9 at.% of p(Ag)

-a PC

C

2v co9 21x/(2 -

-

other

by

ment.

Since

the thickness

produced prior

by to

of the foils was about

2000 A, the effect of surface interactions size was probably

The corrections

fault energy alloy.

to less

faults

temperature

Nodes that were distorted or too close to dislocations were not accepted for measure-

beam in the same manner as for the node inner radius. to the ribbon widths amounted

stacking at room

observation.

The

electron

intrinsic

deformation

on the node

small for all but the lowest stacking There the node radius could be as

large as 500 A and therefore not small compared to the In order to determine the SFE from values (y, CC) thickness. However we have chosen grain orientations such that the basal plane was within 10” of the surface using equation 1 or (w, a) using equation 2, appropriate orientation, so that all faulted structures are inclined values for the material constants, G, b,, and v are than 2% in all cases reported here.

required.

The values b, can be calculated

alloys from lattice parameter ever, no single crystal

data.

for all the

There are, how-

elastic constants

available

for

these hcp alloys while there are for the cubic cr-Ag-Sn alloys. For the cubic alloys, effective values for G and y were calculated from the elastic constants and used in calculating the SFE in order to account partially for the material anisotropy. Polycrystalline elastic

constants

have

been

reportedo4)

for

Ag,

only

slightly

minimize

to the surfaces.

the effect of surfaces

This should

tend

to

on the size of nodes

lying near the center of the foil. Examples of double ribbons observed in the hcp alloys are shown in Fig. 8. Since all three bounding partial dislocations have the same Burgers vector, line-contrast images with n = fl were recorded for measurement purposes. alloys where the ribbon

In the higher fault energy width was small, it was not

ACTA

METALLURGICA,

VOL.

17,

1969

FIG. 5. An extended dislocation loop in the 11.9 at. % tin alloy is shown in (a) stacking fault contrast and (b), (c), (d) line contrast with three different reflections. See text.

possible to develop dislocations. the

outer

adequately

equal contra&

However partial

at all three partial

the center partial and one of

dislocations

for measurement

could

purposes.

be

in image profile at the three partials is probably the

overlapping

specimen

due to

strain fields when the dislocations

are close-spaced. alloy has been illustrated

imaged

This variation

on

in Fig. 9.

appears that significant

the

width

of the

ribbons

is

As seen in these examples,

it

changes in ribbon width only

occur within a depth below the surface comparable

from nodes and from

double

significa,nt, difference,

ribbons

indicates

no

except for t,he highest tin alloy where the two respective 95%

confidence

intervals

do not quite overlap.

The average of all ribbon and node measurements taken as the most accurate va.lue for the WE

A study of these effects in another reported.05) An effect due to the

surface

the mean value of y obtained

to

the ribbon width. The results obtained from measurements of extended dislocation nodes and double ribbons in all four alloys are given in Table 1. The mean value

was

in each

alloy. Figure 10 shows the results for y from the four hcp alloys together with previous measurements(5) on the fee alloys. The variation of SFE with solute composition in negative values described

the hexagonal phase (plott,ed as in t,his comparison) is adequately

by a straight line as shown.

angle distribution

results obtained

The character

for the extended

for y is given together with the 95% confidence interval about the mean. The number of individual

nodes in these alloys were similar to those reportedt5) for the cubic alloys. A preference for angles between 10 and 30” was found, with few nodes approaching the edge orientation. The character angle results for the double ribbons are shown in Fig. Il. 9 strong

Ineas~lrements

preference for angles of less than 30” is found, which is

is

indicated.

comparison

between

RUFF

AND

IVES:

STACKING

FAULT

ENERGY

IN

linear

a

HCP

SILVER-TIN

dependence

of

ALLOYS

y

on

solute

1051

composition

satisfied all the data except that for the lowest fault energy alloy (7.8 at.%

tin).

large extended

in that

affected

hcp {-alloys, tration

nodes

by the specimen

It was arguedc5) that the alloy may

surfaces.

a linear dependence

are inclined

the lowest fault

In this alloy, however, as

was pointed out, both the extended ribbons

been

of y on tin concen-

fits the data well, including

energy alloy (11.9 at. O/’ tin).

have

In the present

only slightly

nodes and double to the, foil surfaces

(less than 10” in all cases) and surface effects should be minimized. equality

Examination

in the two phases. c/a ratio determined FIG. 6. An extended dislocation loop in the 11.9 at. % tin alloy used for determining Poisson’s ratio in this alloy.

similar to that reported extrinsic

by GallagheP)

for intrinsic-

fault pairs in fee silver alloys. as the solute

concentration

away from the mixed phase region.

FIG.

7. Examples

of extended

moves

In the fee region,

In that regard, we note that the from lattice parameter

measure-

ments in the c-phase is close to the ideal value in all cases, decreasing for

17.2 at.%

ideally

The SFE increases in absolute value in both the fee and hcp phases

of Fig. 10 indicates the near

of the rate of change of y with composition

from 1.636 at 11.9 at.% tin.

close-packed

The

5 alloys

tin to 1.622

are then

almost

(c/u = 1.633) over the composi-

tion range studied here. The relation between stacking faults in either fee or hcp materials

and the free energy of those phases has

dislocation nodes in the alloys (a) 11.9 (b) 13.9 (0) 16.0 (d) 17.8 at.% in determining the stacking fault energy.

tin used

ACTA

1052

FIG. 8. Examples

of dislocation

been discussed frequently.(lsl@ mation

METALLURGICA,

between

same temperature

17,

1969

double ribbons in the alloys (a) 11.9 (b) 13.9 (c) 16.0 (d) 17.8 at.% determining the stacking fault energy.

The simplest approxi-

states that the SFE equals the difference

free energy

VOL.

in

bond angles.

This relation

They find using a central-force

y(fcc, intrinsic)

is

expected to be somewhat unrealistic since the stacking

out to and including

fault in an fee matrix,

also find y(fcc,

scopically

for example,

occupies

a micro-

thin section in the crystal (two close-packed

plane thicknesses)

and cannot be properly

as a macroscopically

thick

hcp

layer.

described Hirth

and

Lothe stacking

have examined the relative energies of faults in both structures by counting bonds

between

pairs of atoms but neglecting

TABLE 1. Stacking

any effect of

frtult energy meson value y determined

approxi-

mation,

the hcp and fee phases at the

and composition.

tin used in

=

--y(hcp,

the 8th neighbor

intrinsic)

position.

= By(fcc + hcp),

being the energy per close-packed hcp crystal produced

intrinsic) They

the latter

plane of a perfect

by faulting every other plane in

In view of the conduction electron an fee crystal. contribution to the cohesive energies in metals, such an approach indicate

is not expected

to be accurate

but may

relative values.

from dislocetion

nodes and double ribbons for hcp silver-tin

alloys

_. Nodes

Double

95 0% ConComposition (at. ‘A tin)

Y (erg/cm2)

Ribbons

All

95 0% Con-

fidenoe

Standard

interval

deviation Number

(ergjfx+

Combined

95 % Con-

fidenoe

Standard

fidonce

interval

deviation

interval

(erg/cm*)

(erg/cm2)

kO.43

0.72

13

5.41

$0.3

40

(erg/cnG)

(erg/cm2)

11.9

5.51

*to.41

1.05

27

5.39

Number

(a-g;mz)

(erg/cm*)

Number

13.9

9.53

+1.5

1.19

5

10.18

10.58

1.25

20

10.05

yhO.51

25

16.0

15.8

$2.1

2.71

9

15.7

*1.2

2.23

15

15.7

kO.9

24

17.2

20.0

*

1.86

16

18.0

kO.7

1.47

21

18.9

10.6

37

1.0

RCFF

AXD

IVES:

STACKIXG

FAGLT

ESERGY

IN

HCP

SILVER-TIN

ALLOYS

x053

Alloy systems exhibit a mixed phase region between two different adjacent phases. Although the free energy of each phase varies with composition in the mixed phase region at a given temperature, only the ratio of the volume fractions of the two phases alters. The composition of each phase remains fixed. Thus the SFE cannot be dete~ined as a function of solute composition across this region. In the silver-tin system, the phase mixture (a + 5) exists from about 9 to 12 at.% tin at room temperature.os) We cannot, therefore, directly compare alloys in the two phases at even approximately the same composition. However the composition dependence of the SFE over both single-phase regions can be extrapolated into the

IO N (#I Fro. 9. An effect on the widths of double ribbons due to the foil surface is shown in two examples. The magnitude of this effect decreases .rapidly with distance from the surface.

5

0

40

20 Character

Angle

9 (d@g)

Fra. 11. The histogram of oheracter angles for the dislocation double ribbons indicating s preference for angles less than 30”.

’ 2

0. -4

\

I 4

’ 6

“< 8

’

\

12 \

-

’

14

’

16

’

18

Atomic %Tin

-8 -12 -16 -2o-

’ As

’

’

’

’

AT: % TIN

FIG. 10. The v&ation is stacking fault energy with tin eoncentr~tion is shown for the hep alloys and for a set of fee alloys (previous resultcP)). The mean value is shown together with the 95% confidence interval for each alloy studied. 9

-

mixed phase region for comparison. As seen in Fig. 10, a linear least-square curve can be fitted closely to the hcp alloy results and extrapolates to y = 0 at 9.5 at. y. tin. As discussed previously,‘5) the situation for the fee alloys is complicated by the results for the 7.8 at. y0 tin alloy. A somewhat larger value is obtained (4.2 erg/cm~(mJ~mz)) than that given by the linear relation shown (approximately 3 erg~cm2(mJ/mz)) at that composition. It is not known whether the SFE actually changes less rapidly with composition near the a-phase boundary or whether the measured value may be increased by systematic errors associated with the method, for example the surface effects previously mentioned. Assuming that the linear relations shown in Fig. 10 indicate the SFE variation in both phases, the difference in SFE (obtained by ext~polation) at one composition in the mixed phase region (for example

1064

ACTA

METALLURGICA,

9 at.% tin) is approximately 2 erg/cm2(mJ/mz). A small upward deviation in the SF% curve for the cubic alloys could reduce this difference considerably, recognizing the data for the 7.8 at.% tin alloy. Thus the maximum difference in extrapolated SFE between the two phases at the same composition is about 2 erg/cmz(mJ/m2) and may actually be less. The hypothesis that no difference exists in extrapolated SEE is also a possible interpretation of our data. The near equality of slopes between the two fitted relations (fee slope = -2.51; hcp slope = -2.55) is also of interest in this comparison. Since there is some uncertainty in the precise location of the two phase boundaries in these alloys, a comparison of the measured extreme SFE values is not particularly meaningful. There is no assurance that more or less tin in solid solution could not be accommodated in the two lowest SFE alloys. Stacking fault probabilities have been measured previously in the Ag-Sn <-phase region using X-ray diffraction line profile data.og) The stacking fault probability was found to decrease in a parabolic manner from cc = 5 X lop3 for I3 at.% tin to dc= 1 x 1O-3 for 20 at.% tin. The quantity I/a, therefore, increases with solute ~oncentr&tion and shows a similar variation to that of the SFE reported here. As discussed previously@‘) in the case of a-Ag-Sn alloys, a quantitative comparison between the results of these different methods is not justified. Stacking fault energies have been measured in adjacent phases in two other alloy systems. Eriosson(s~ measured the SFE using extended nodes in two hcp Ni-Co alloys at room temperature and found that the SFE increased in magnitude with increasing distance from the phase boundary. At the phase boundary (67% Ni) the SFE changes from y(fcc) = 15 erg/cm% @Jim2fto y(hcp)M -11 erg/em2(mJ~m2), the lat,ter value being calculated from data on the two hcp alloys. The phase boundary in this alloy exhibits a strong temperature dependence and in that regard differs considerably from the silver-tin alloys in the Ashbee and Vassamillet(~) have present work. examined one two-phase Cu-20.5 at.% Ga alloy and find extended dislocation nodes in the c-phase but not in the u-phase material. The SFE in the cc-phase could only be estimated from the widths of extended dislocations. They report ys/ys w 3 with both valuesestimated to be of the order of 1 erg~cm2(mJ~m2). No results were reported on other nearby compositions in either phase that would permit a more precise knowledge of the SFE. The results reported here together with X-ray determinations of stacking fault probabilities in

VOL.

17,

1969

hexagonal Ag-In, (lg) Au-Sn and Au-In,(21) and Cu-Ge(22) confum the increase in absolute value of the SFE with increasing solute concentration in the first intermediate hcp phase. It is now well established that the SFE in the fee terminal phase of these and other binary aIloys(s3) decreases with increasing solute These trends can be interpreted concentration. qualitatively in terms of the difference in free energy between the hcp and fee phases. However, a quantitative comparison cannot yet be made due to lack of the necessary thermodynamic data on systems such as Ag-Sn where accurate SFE values are known. It can be shown that the assumption of a parabolic variation in free energy with composition in the two phases leads to a linear increase in the magnitude of the difference in free energy (proportional to the SFE) with distance from the mixed phase region. Such a parabolic variation is however only an approximation to the expected composition dependence of the free energy in real concentrated alloys. Further detailed studies of the SFE variation about fee-hcp mixed phase regions are needed, including comparisons between materials having different c/a parameter ratios. 6. SUMMARY The intrinsic SFE of hcp silver-tin alloys was determined as a function of tin concentration and some of the faulted dislocation configurations found in these alloys were discussed. The SFE was determined from extended dislocation nodes and from dislocation double ribbons. The absolute value of the SFE increased linearly wit.h increasing solute concentration, The results were compared to previous determinations of the SFE in the fee terminal phase of this alloy. The dependence of SFE on solute concentration in the two phases was nearly equal. The lowest fault energy was found to be about 5 erg~cm2(mJ~m2) near the mixed phase region in both cases. The SFE extrapolates to zero value in the mixed phase region from both adjoining phases although not at the same composition. The maximum difference in SFE at the same composition would be about 2 erg~om2(mJ~mz~. The dislocation structures observed on the basal plane in the hcp alloys were similar to those on (111) planes in the fee phase. However all nodes in dislocation networks were usually extended in the hcp alloys and contained the same type of stacking fault. Many of these structures were similar to those observed previously in graphite and other layer substances. ACKNOWLEDGEMENTS

The authors are indebted to C. J. Bechtoldt, J. R. Baldwin, Virginia Stewart, and D. L. Vieth for

RUFF

AND

IVES:

STACKING

FAULT

efforts in characterizing the alloys and to P. A. Bayer for technical assistance. REFERENCES I. J. W. CHRISTIANand P. R. SWANN, Alloying Behaviow and Eflecte in Concentrated Solid Solutions, edited by T. B. MASSALSKI,p. 105. Gordon L Breach (1965). 2. F. C. FRANK and J. F. NICHOLAS,Phil. &fag. 44, 1213 (1953). 3. T. ERICSSON,Acta Met. 14,853 (1966). 4. K. H. G. ASIZBEEand L. F. VASSAMILLET, Acta Met. 15,481 11967\. 5. A. W. RVFF, JR. and L. K. IVES, Acta Met. 15,189 (1967). 6. Presented at AIME New York Meeting. Febrnarv 1968. 7. S. A~~EUNCKXand P. DELVICNETTE,&ectron M&oscopy and Strength of .Materiak, edited by G. THOMAS and J. WASHBURN, p. 441. Interscience (1963). 8. A. BEROHEZAN,A. FOURDEUX and S. AMELINCKX, Acta Xet.. 9, 464 (1961). 9. L. K. IVES and A. W. RDFF, JR., J. appl. Phys. %‘,I831 (1966). 10. P. C. J. GALLAGHER,Phya. Status Solidi 16,95 (1966). \----I-

ENERGY

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SILVER-TIN

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11,813

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