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
IN
HCP
SILVER-TIN
C. M. DRUM, PhiC. Msg.
11,813
ALLOYS (1965).
::: L. M. BROWN end A. R. THBLBN, Dixwe. 13, 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
1055
Faraday SW. $8, 35 (1964). P. C. J. GALLAGHEB J. appl. Phye. 57,171O (1966). B. S~BRAHMA~YAMand Bh. KRISEXAMVRTY. Indian J. pure appl. Phye. 2, 139 (1964). R. M. LATANISIO~ and A. W. RWFF, JR., J. appt. Phye. (in press). R. D. HEIDENREICHand W. SHOCKLEY,Report Conference Strenath of Solids. Bristol. D. 57 (1948). J. P: H&&s and J. Lo& ‘The&y of Dielocutions, ~eGraw.~ll (1968). M. HANSEN, C~8t~tut~~ of Einav AZloys, p. 52. &GmwHill (1958). R. P. STRATTONand W. J. KITCHINQXAN, Br. J. appt. Phys. 16, 1311 (1965). A. W. RUFF, JR., Proc. First NBS Materials Research Symposium, NBS Monograph 100, p. 554 (1967). R. P. STRATTON and W. J. KITCHINOMAN, Br. J. appt. P&8. 17, 1039 (1966). S. P. SEN GUPTA snd K. N. GOSWAX~, Br. J. appl. P&e. 18,193 (1967). P. C. J. GALLAGHER. Xra7as. Am. Iwt. Min. Enom %!& 103 (1968).