- Email: [email protected]
The structure of nickel-palladium solid solutions
THE
STRUCTURE
OF NICKEL-PALLADIUM W.
LINT
and
J.
E.
SOLID
SOLUTIONS*
SPRUIELLT
The local atomic arrangements and atomic displacements from their average positions were investigated for Ni-25, -50 and -75 at. % Pd 5110~susing the single crystal X-ray diffuse scattering technique. Analysis of the diffuse intensity revesled t.hat Ni-Pd alloys possess short wavelengt,h composition modulations along (100) directions when slowiy cooled from elevated temperatures or heat treated at relatively low temperature (~400°C) following quenching. A computer simulation was used to generate a model of t,he local atomic arrangements in the slowly cooled Xi-60 at. y0 Pd alloy. The model may be described as consisting of olusters of like atoms in the (100) planes with roughly “branched rod” shapes. Within the clusters, like atoms are linked primarily by seoond nearest bonds. Large static atomic displacements of the atoms from their average atomic sites due to the difference in atomic size were observed for all sample conditions, including quenching from high temperature. STRUCTURE
DES
SOLUTIONS
SGLIDES
NICKEL-PALLADIUM
Les ~rrangement.s atomiques locaux et les d~placements des atomes it partir de leurs positions moyennes ont et6 &udi& pour les &ages Ni-25, -50 et -757&t. Pd par “diffuse scattering” des rayons X sur un monooristal. L’analyse de l’intensite diffuse montre que les alliages Ni-Pd oontiennent des modulations de compositions 8, foibles longueurs d’onde 1%long cles directions (100) quand ils ont et6 refroidis lentement ir partir de temperatures &levees, ou quand ils ant, subiuntraitement thermique Q une temperature relativement basse (400°C) apres trempe. Une simulation B l’ordinateur a BtB utilisee pour eonstruire un mod& des arrangements atomiques locaux dam l’alliage Ni-50°/0at. Pd. Le mod& peut Btre dkcrit comme consistant en des agglomerats de quelque chose d’analogue i des atomes dans 10splans { IOO), ayant des formes rappelant grossierement des baguettes remifiees. A l’interieur des agglomerats, CRSespltces d’atomes sont lies principalemcnt per des liaisons de seconds voisins. Des d&placements importants des atomes B partir de leurs sites atomiques voisins, dOs aux differences de tailles atomiques, ant, et6 observes pour tous 1~sCBSStudies, y compris pour les echantillons trempex B par&r des temperatures Cilev&s. DIE
STRUKTUR
VON
NICKEL-PALLADIUM-LEGIlZR,UNGEX
Aus der diffusen Riintgenstreuung an Einkristallen der Ni-25, Ni-50 und Ni-75 At.% Pd-Legierungen wurden die lokale Anordnung der Atome und ihre Verschiebungen aus den mittleren Lagen be&immt. Die Antdtyse der diffusen IntensitLt ergab, da3 sowohl langssm sbgekiihlte als aueh abgeschreckte und bei relativ niedrigen Temperaturen ( ~400°C) angelsssene Ni-Pd-Legierungen periodische Schwankungen der Zusammensatzung mit kurzer Wellenliinge entlang (109).Richtungen besitzen. Mit Hilfe einer Computer-Simulation wurde ein Model1 der lokalen Atomanordnungen in der langsam abgektihlten Ni50 At.% Pd-Legierung erzeugt. Das Model1 besteht aus Clustern gleicher Atome in der Form “verzweigter St&be” in den ~lOO}-Ebenen. Innerhelb der Cluster best,ehen zwischen gleichen Atomen tibern%chster-Nachbar-Bindungen. An allen, touch an den van hohen Temperaturen abgeschreckten Proben, wurden groBe statische Verschiebungen der Atome s,us ihren mittleren Atomlagen aufgrund der verschiedenen Atomdurchmesser beobachtet.
INTRODUCTION
Although the X-ray powder diffraction study of Hultgren and Zapffee w showed that the Ni-Pd system forms a continuous series of solid solutions in which no superlattices or intermediate phases form, some authors have taken issue with these results while others have attributed anomalous behavior of physical properties t,o “nonrandom” atomic arrangements. For example, Yaeliev and Annaev@J) have reported anomalous electrical and magnetic behavior at the stoichiometric compositions NisPd and NiPd, which they attributed to the probable existence of superlattices at these compositions. Nagasawat4) also claimed the existence of superlattices at the compositions NisPd and NiPd, based on the evidence obtained through an electron diffraction study of thin, vapor deposited films. The relative thermodynamic properties of solid Ni-Pd alloys have been measured * Received April 21, 1970; revised September 29, 1970. t Department of Chemical and Metallurgical Engineering, University of Tennessee, Knoxville, Tennessee 37916. ACTA
~~ETAL~URGICA,
VOL.
19, MAY
1971
by Bidwell and Speiser(“) in the temperature range 700-12OO’C. They concluded that, if their data were interpreted in terms of quasichemical theory, Ni-Pd alloys possess short-range order or a preference for unlike neighbors at elevated temperatures and possibly long-range order at low temperatures. Bingham and Brooks(“) observed an “anomalous” rise in the heat capacity of a Ni-50 at. y0 Pd alloy 350 and 490°C a range which is well separated from the magnetic effect. They concluded that this alloy exhibits some form of local order below about 400°C. The anomalous rise in the heat capacity curve for the Ni-50 at. % Pd alloy certainly signifies some sort of structural change in the solid solution above about 350°C. However, thermodynamic and physical property data provide only indirect evidence concerning the structural state of alloys, and hence, they can be interpreted only qualitatively. It is the purpose of the present paper to report the resultzsof an X-ray diffuse scattering investigation of three Ni-Pd alloys containing 25, 50 and 75 at. % Pd. These results provide a reasonably detailed picture of the local atomic
451
ACTA
45“
arrangements
and help to clarify
thermodynamic
property
X-RAY
METALLURGICA,
the physical
and
results.
DIFFRACTION
tered from
binary
of the
of the diffuse intensity
cubic
alloys
Borieor) because
THEORY
present data is that the local order and atomic components
19,
1971
and Sparks and Borie(12) have shown that
the two components
The basic result used in the interpretation placement
VOL.
disscat-
can be expressed
as
of
their
in equation different
symmetry
The approach
used to obtain equation
the approximation atomic
of an exponential
hereafter
This
approach
X,
and X,
are the
A
and
atom
respectively, factors. the
of
components
fB are
The h’s are continuous
cal space at
fractions
and fA and
equal to one-half
reciprocal
lattice
B,
their atomic scattering coordinates
in recipro-
the usual Millar indices Relative to an points.
arbitrary origin, the integers 1, m, n define a particular lattice site according
to the relation
(2)
where z,, 6, and 2, are the translation cubic unit cell. The %mn are the Warren
short-range
vectors
of the
order param-
these
have
of finding a B atom as an
of an A atom. parameters
The Y:,~ are atomic
defined
by relationships
of
the form
(Huang)
components
must
(1) can be applied. shown
can be treated analytically
that the effect
and first order atomic displacements quadratic pansion.
term
in the above
can still be isolated,
be recovered.
series
excom-
so t’hat tc’s and y’s may
This approach is referred to hereafter as
the quadratic displacements
approximation.
The data
in the present investigation
were treated
using both
the
approximations
linear
and
quadratic
to
t’he
displacements. PROCEDURES
ingots of Ni-25,
-50 and -75 at. % Pd
alloys were prepared from high purity Ni (99.87 %) and Pd
(99.9%).
vacuum alumina
Single
crystals
were
grown
under
by the Bridgman technique in high purity crucibles. The single crystal ingots were
homogenized
for 1 week at 1100°C.
Diffuse scattering
samples in the form of discs about 0.12 in. thick and ingots.
were cut from the homogenized
These discs were crystallographically
to have a (210)
face
which
oriented
was metallographically
polished and etched after each heat treatment any where the L’s are components
of displacements
off the
X-ray
determined taken
average atomic sites,
from
measurements. from the
The
Debye-Scherrer crystals
alloys, (1) is a generalization
obtained
by Borie
of the results first obtained by Cowley(*)
and by Warren et CL(~) for the local order and the so-called “first order” atomic displacements diffuse scattering. A derivation and discussion of this equation is also given in Ref. 10.
respectively,
in
measurements
of filings
3.737,
and
-75 at. % Pd
agreement
lattice parameter vs. composition Bidwell and Speiser.(r4) The X-ray
-50,
prior to
parameters
3.635,,
Ni-25,
good
lattice patterns
were
3.820, A for the nominally
and Spark@
of
by retaining the
mentioned
They have shown that the individual
0.75 in. in diameter
Equation
be
However,
along with the local order
EXPERIMENTAL
where P rmnis the probability (lmn) neighbor
hence
and Sparksd3)
Arc melted (3)
displace-
of the thermal
thermal motion and second order static displacements
eters defined by
displacement
of the atomic
a description
removed before equation
ponents
%nn = l%+m:+nz,
and
to
approximation.
and second order static atomic displacements scattering, Borie
the
for the
is referred
as the linear displacements
The linear approximation
Here, N is the number of atoms irradiated,
(1) involves
scattered intensity by the first two terms of
ments does not include
(1)
by
involving
eiZ’G@, in the formula
displacements,
coherently
sin 2744~ + h,m + hg4.
in reciprocal
space. The U’S and y’s can then be recovered Fourier inversion of the separated intensity data.
its series expansion.
+ &&J
(1) can be separated
with
the
data reported
by
were made using crystal
monochromated CuKu radiation. Details concerning the X-ray technique are described elsewhere.(r5J6) If the data were to be analyzed by the approach based on the linear approximation to the displacements,
temperature for Xi-25, -50 and -75 at. T{ Yd ailoys after the single crystals have been furnace cooled from 11OO’C. These intensities are expressed in Laue monotonic units and have been corrected for Compton diffwe scatt,ering. The most .&king characteristic of each of these diEuse int,ensity d~str~but~ou~is the concentration of diffuse intensity near t,he Bragg
Frc. 1.
oorrections for temperature diffuse scattering were applied by making the me~urements at two temperatures (room ~m~rature and 78OKf and extrapolating linearly to 0°K. The intensity measurements were converted to absolute units (electron units per atem) by comparison with the scattering from polystyrene (C&H,) at 30 = 100”. The Compton scattering was calculated and subtracted from the data after conversion to a.bsolute units. For the quantitative determination of the Warren order pm&meters, CQ~%,and atomic disp~aceme~t.s coeficients, yEmn,the diffuse intensity was measured at each of 2106 points looated on a3cubic grid throughout the volume element in reciprooal space shown heavily outlined in Fig. 1. Dab in this volume are sufficient to permit one to make the three-d~~nensional atomic displacements z+xeparationby the procedure of Sparks and Rorie.cl2) The separation based on the quadratic approximation was used for data taken on the h&O plane of reciprocal space. RESULTS
and DISCUSSION
Figure 2 shows the intensity distributions in the h,h20 plane of reciprocal space measnred at room
FIG. 2. Effuse intensity distributions on the &h& plane of reciprocal space for (a) 25 at. % Pd, fb) 50 at. % Pd, fo) 75 at,.“/;; Pd. Samples were furnace cooled fram llOO”C. The quantity p&ted is I,&VXAX,(f, -f&F,
ACTA Fundamental Diffuse
METALLURGICA,
VOL.
19,
have proved
Reflections
1971
separated
component
was
compared
based
for separating
the
from the local order linear
technique
displacements
distribution data
in Fig.
based on the quadratic
distribution.
The
resulting
for the local order component
in Fig. 4(b).
should be
shown
was also applied to this two-dimension-
intensity
distribution
The extrapolation
intensity
is presented
under the Bragg peak
has not been carried out for these data, but it can be seen that a very similar intensity
FIG. 3. Schematic representation of the diffuse intensity distribution in reciprocal space for slowly cooled Ni-50 at. ‘A Pd single crystal.
reflections,
shown
In
three-dimensions consists
of
lobes
represented
schematically
diffuse lobes occurring on the indices type reflections,
permits
4(a)
based
on
intensity
intensity
of
diffuse
intensity
reflections
in the absence
might
caused
as
in Fig. 3. The number
of
near each Bragg peak depends for hO0
reflection-one
two for hk0 type reflections,
and three
distribution
atomic displacements) The two intensity
plotted
along
of diffuse intensity
shown
in Fig.
fundamental
These
reflections.
diffuse
lobes
of
intensity extend down along the [OOi] direction in the lattice and cut the h,h20 plane with about
reciprocal
the same order of intensity (300) position. The diffuse
as that near the (100) and
The
separated
equation
(l)]
distributions,
particularly
those for the 75 at. % Pd alloy, are very similar to that by Moss (17)and Moss and Averbach
for an
the
distribution
with respect to the Bragg reflections, suggested
that this unusual
was due to atomic
intensity
displacements
and a
space
is
alloy;
h sin h dependence
it [see
the origin of the asymWhen the atomic
are algebraically
component,
the
added to
observed
broad
occurs to the low angle side of the
that
the
or fluctuation modulation
peak.
local
order
diffuse
scattering
along the (100)
axes in
space implies that some form of composition
composition separation
ation techniques which have been employed in analyzing the present diffuse intensity distributions
modulations
crystals.
be
Although the atomic displacements alone can produce an asymmetric diffraction pattern, the separ-
a
modulation
Ni-50 at. % Pd
is concentrated
modulation
in which rich,
displacements
the expected
in the alloy
clustering type of local atomic arrangements to
data taken throughout
5 for the
order
The fact
regions along (100) directions alternately, in Au and Ni.
tended
in Figs. 4(a)
This result suggests
(200) reflection.
reciprocal
the distribution
atomic
diffuse maximum
(100) axes in reciprocal these authors
shown
intensity distribution.
local
component
of
static
space for this alloy.
and illustrates
experimental
Au-40 at. y0 Ni crystal quenched from 890°C. Because of the concentration of the diffuse intensity along the space and the asymmetry
which
order
metry about the (200) Bragg peak (h, = 1.0) in the displacements
intensity
(second
the h,OO line in reciprocal
clearly exhibits
diffuse
of the Bragg
to use the linear displacement
for treating
The intensity contours shown near the (110) and (310) positions in Fig. 2 are due to the concentrations
approximation
of the order
and thermal diffuse scattering.
it is adequate
approximation
to that
separation
of any interference
Huang
distributions
volume in reciprocal
with the (111) and (311)
quadratic
and (b) are in good agreement. that
The
in the vicinity
by
for hkl type reflections.
associated
the
one to see the shape
be
distribution
is obtained.
diffuse
Bragg reflections,
of the Bragg
Fig.
the
on the (100) axes and just to the low angle
side of each of the fundamental
in
technique
along the (100) type axes in the reciprocal
distributions
obtained
the
with the unseparated
approximation
centered
on
This intensity
2(b). The separation
lattice.
modulations
used to obtain Fig. 4(a) for the Ni-50 at. %
alloy
approximation.
000
are not
4 shows the
of diffuse intensity
The procedure
atomic displacements
al
Figure
alloys.
local order component
for the three alloys.
Pd
arrangements
that the atomic
random in these Ni-Pd
intensity
exists along (100) directions
The mean wavelength may be estimated
of the diffuse maximum
Interpreted
in terms
of the
from the
from the Bragg
of such
a model,
the
broad, weak diffuse maxima observed in Figs. 4(b) and (c) for the Ni-50 and 75 at. ‘A Pd. alloys indicate that
the
composition
modulations
have
average
wavelengths of about 5.7 and 6.6 A, respectively. The intensity distribution for the 25 at. ok Pd. alloy,
LTN
STRUCTURE
SPRUIELL:
ANI)
OF
Xi-Pd
SOI,ID
455
SOLUTIONS
lb)
FIG 4. Local order component of diffuse intensity for Ni-Pd alloys in hi&O plane. (a) and (b) 50 at. % I’d, (c) 75 at.% Pd, (d) 25 at. % Pd. (a) is obtained using linear approximation, (b)-(d) are obtained using quadrat’ic approximation.
Fig. 4(d), with its slight peaking lattice
position,
may
indicate
at the usual supera tendency
to form
extremely thin platelet shaped regions parallel to (100) planes within which the local atomic3 arrange-
6-
ments
are tending
distribution
toward
ordering.
that only very slight deviations involved. the
other
The intensity
for this alloy is so nearly flat, however, from randomness
are
The nature of the atomic arrangements
for
two
alloys,
alloy, will be considered of the temperature
particularly
the
further following
dependence
of the
50 at. % Pd a discussion short-range
structure.
In
0
(b) Temperature dependence of the short-range ” 0 2
1”
04
0.6
1
II
0.8
”
1.0
”
1.2
”
1.4
h4
Atomic displacements modulation along the hi00 line in reciprocal space for the slowly cooled Ni-50 at. % Pd alloy. FIG.
5.
structure of nickel-palladium The response of the Ni-Pd was investigated
by making
alloys
alloys to heat treatments intensity
measurements
along the hL,OOline in reciprocal space in the vicinity of the (200) reflection. Figure 6 presents a graphical
ACTA
456
METALLURGICA,
VOL.
19,
1971
8.0 -
o0.4
0.6
0.5
0.8
0.7
o-
09
0.4
0.5
07
06
0.8
0.9
h,
h,
(a)
, -- -- .- *mded
96 hrs at CIOO’C, furwxe cooled to r.t. 2 - - Quenched from 7OO’C ,“to rt water 3 ---Annealed 132 hrs ot 550% qwnckd into r.t. water 4 ---Annealed 29 dovs ot 491°C. quenched Into r I wqter -----.. Annealed 56 hr; at 370%. i”;“aCe cooled t0 r.t. -.-Anneolad 224 hrs ot 300% furnace cooled t0 rt. - Guuenched fro”, 963’c ,nto rt water -A”neoled 24 hrs ot 37O’C, quenched into rt water (b) -----Quenched fro”, 996’C ,n+o r t. water Annealed 15 hrs ot 5lO’C. quenched into rt water - -Annealed 20 hrs ot 405’C, quenched into rt. water ---Annealed 24 hrs at 305’C, quenched into r 1. water Annealed 24 hrs. ot 3OO’C, furrmce cooled to r t
.,....
-
OL------I 0.4 0.5 FIG. 6. Diffuse intensity
summary
0.6
0.7
0.8
0.9
of some of these measurements. only for Compton
profiles
can be divided
The data
measured
intervals
in the
range from 350 to 545°C [these measurements
are not
scattering.
shown
into two main
When the sample was heat treated below groups. about 370°C or when it was slowly cooled from higher temperature, distinct
“hump”
fundamental maximum observed
profile exhibited
a
to the low angle side of the (200)
reflection
corresponding
shown in Fig. 2(b). when the sample
from temperatures intensity
the diffraction
to the diffuse
No distinct hump was
was aged and quenched
above 49O”C, although
remained
asymmetric
about
in the diffuse indicate
intensity
Bingham
profile
with
and Brook@)
observed in the same temperature range for this alloy. In order to investigate the temperature dependence of this
structure
change,
the
diffuse
was
lowered
intensity
was
showed
range ; there was no indication
that
the
gradually
in this
as
temperature
of a sharp change at a
specific temperature.
On the basis of these data it is
concluded
amplitude
that
modulations decreases
the
in this X-50
with increasing
the range 350490°C. hump
was
of the
composit,ion
at. y0 Pd alloy quenching
gradually
temperature
in
Since the position of the diffuse
unaffected
by
heat
treatment,
is not affected
(200)
at. ‘A Pd alloy is occurring
that
data
the
between 370 and 490°C. This change in short-range structure is apparently responsible for the anomalous capacity
These
concluded that the mean wavelength
that a change in the short-
range structure of the X-50
6(a)].
20°C
in the diffuse hump increased
temperature
Behavior
The changes
rise in heat
in Fig.
intensity the
at approximately
the diffuse
reflection. heat treatment
(a) 50 at. ‘A Pd,
units and
Note that in Fig. 6(a) for the Ni-50 at. % Pd alloy the intensity
ot t16O”C, furnace cooled to r 1. from 980°C into r 1. water from 7OO’C into rt wqter
along the hi00 line in reciprocal space after various heat treatments. (b) 75 at.% Pd, (c) 25 at. % Pd.
shown in this figure are in Laue monotonic have been corrected
Annealed It6 hrs.
-.Ouenched -----Quenched
it was
of the modulation
by the heat treatments
investigated.
similar to that for the Ni-50 at. % Pd alloy
was observed
for the Ni-75 at. % Pd alloy [Fig. 6(b)J,
but the Ni-25 at. % Pd alloy was not as responsive heat treatment heat treatment
[Fig. 6(c)]. is probably
to
This lack of response to due to the low degree of
local order in this alloy and associated in both local order and atomic heat treatment.
small changes
displacements
upon
Above about 490°C the intensity distribution
for all
three alloys is dominated
by the atomic displacements
1,Xx
AND SPRUIELI,
: STRUCTURE
component which persists to the highest quenching temperatures investigated. This was readily demonstrated by performing the separation of the local order and atomic displacements diffuse scattering on samples quenched from high temperatures, Similar analyses also showed that the atomic displacements parameters are functions of the heat treatment; the atomic displacements parameters are significantly greater in the slow-cooled condition than in the quenched condition. This is probably a result of the changes in local atomic arrangements with heat treatment [see equation (4)], but, could be partially due to a change in the actual atomic displacements as well. (c) illeasuremelrt of the &fuse
intensity throughout a
voluble in r~c~~ro~l space and 2s ~nter~re~at~o~
In order to recover adequate values of the Warren order parameters, aims, and the atomic displacements parameters, J&,,,, measurements throughout a volume in reciprocal space are required. Considering the results presented in Figs, 4(a) and (b), it was decided that the separation based on the linear approximation was adequate for the K-50 at. % Pd alloy and intensity measurements tl~rougl~out the volume ofFig. 1 were made for this crystal after a heat treatment of 100 hr at 370°C followed by slowly cooling to room temperature at a rate of 12°C per hour. The Warren order parameters obtained from Fourier inversion of the separated local order diffuse scattering are presented in column 2 of Table 1. A model for the local atomic arrangements in the TABLE 1. Comparison of the order parameters cakwlated from model with the experimental values for X-60 at. % Pd alloy --_
Computer generated model 1 na ?L 000 110 200 211 220 3 10 222 321 400 411 330 420 332 422 4 3 I 440 433 442 444
Experimental
3-shell
5-shell
1.533 0.005 0.184 -0.069 -0.012 0.021 -0.030 -0.010 0.013 -0.006 -0.005 - 0.009 -0.005 -0.003 --0.002 -0.015 0.000 0.007 0.003
1.000 0.005 0.184 -0.069 0.049 0.011 0.018 -0.009 0.040 0.014 -0.017 0.020 0.001 0.011 -0.004 -0.007 -0.003 0.008 0.005
1.000 0.005 0.184 -0.069 -0.012 0.020 -0.030 - 0.006 0.032 -0.009 0.021 0.002 0.005 -0.002 0.004 -0.001 -0.003 -0.002 0.005 --
OF
Ni-Pd
SOLID
SOLUTIONS
457
alloy which is consistent with the experimental local order parameters may be derived using a computer simulation as was first done by Gehlen and Cohen.ugj The two kinds of atoms in the model are rearranged until the order parameters for the model fit some specified number of experimental parameters. Such a computer simulation was carried out for the present data using a program recently developed by Williams. This program, described in detail elsewhere,@*) appears to give essentially the same results as that due to Gehlen and Cohen, although it is based on different algorithms. Whereas Gehlen and Cohen’s program interchanges unlike atoms chosen at random if such an interchange will cause the first three computed order parameters to change toward the experimental set, Williams’ program examines the at,om sites sequentially in a pseudo-random manner such that no site can be missed and the identity of a given site is changed if the composition will remain within set design limits and if the vector sum of the local order parameters being monitored moves closer to the experimental value. The results of two computer simulations using an 8000 atom model are shown in Table 1. In one case only the first three alphas, namely 110, 200 and 211, were monitored; in the second case the 220 and 222 were monitored in addition to the first three. Comparison of the list of calculated alphas with the experimental values shows considerably better agreement among the higher order values for the !&shell model than for the 3-shell model, as is to be expected. The diffuse intensity on the k&,0 plane synthesized for the &hell computer generated model from the first 40 order parameters is shown in Fig. 7 ; this figure may be compared to the experimental result shown in Fig. 4(a) or (b). If allowance is made for a small, flat, parasitic scattering in the experimental data ~~~~~ # l.OO), the s-shell results are in excellent agreement. with experiment. The distributions of Pd atoms in the first and second coordination shells about a Pd atom as origin in the &shell model for the IocalIy ordered alloy are shown and compared to similar quantities for a random alloy in Fig. 8. The distribution in the model for the first coordination shell is not appreciably shifted relative to the random model, although it is broadened slightly. The distribution for the second ~oord~ation shell is shifted to higher numbers of 200 neighbors in the model. This means that there are many more Pd atoms in the model for the locally ordered alloy with four or more Pd atom second nearest neighbors than in the random case, The model was also searched for several types of special configurations such as 110 Pd atom triplets and
ACTA
45s
METALLUKGICA,
VOL.
19,
1971
210
010
FIG.
7. The
diffuse
intensity
distribution
on the
h,h,O plane
generated
quadruplets.
None
of
these
present
in numbers
number
present in the random
figuration involved
200 Pd-Pd
In order to obtain atomic
configurations
significantly
arrangements,
a better
different
from
regions
the
criterion
and to examine
regions.
The
case unless the conconcept
in
the
model
of the local
to try to isolate
I
0
0.3 x _z 5 x 0.2
regions
e a.
region”
some
information
specified
indicated Hence,
investigate
Figure 9 shows
(100) planes of the computer
designate
the
Pd
Boundary
in which
atoms lines
the Pd atoms
model
Symbols
and
are
some
a criterion
this possibility
regions.
for the Ni-50 at. % Pd alloy.
respectively. criterion.
meet
was occurring.
was chosen which would
and
Ni
drawn
1
atoms, around
meet the following
A Pd atom is defined to be in a “clustered
if there are 4, 5, 6, 7, or 8 Pd atoms in its 110 shell and 4, 5, or 6 Pd atoms in its 200 shell.
0.1
0
computer
the size and shape of such
and isolate such “clustered” generated
I
which
available
form of clustering
two consecutive 0.4
for the &shell
was
bonds.
it is useful
synthesized
model.
In general the appearance
1 2 3 4 5 6 7 6 9 10 11 12 Number of Pd Neighbors in First Shell Around Pd Atoms
alloy tend to form roughly several
04 (b)
branches
along
rod-shaped
(100)
type
clusters with directions.
In
most cases, the clusters of rods lying in a given (100)
,-Model
plane do not extend
0.3 a .c.z z 0.2 e P 0.1
below.
to the plane above
or the one
Their shape and size vary from one plane to
another. Although small clusters and rods can also be found in the model for random configuration, their sizes are much smaller compared to those found in the locally ordered model. That is, the number of Pd atoms which satisfy the definition of an atom inside a
0
0 I 2 3 4 5 6 Number of Pd Neighbors in Second Shell Around Pd Atoms FIG. 8. Distribution of Pd neighbors in the first second coordination shells around a Pd atom.
of the regions as shown in
Fig. 10 is such that the Pd atoms in the Ni-50 at. % Pd
0
cluster in the model and
for the locally
ordered
alloy is
much larger than that in the random case. The ratio of the former to the latter is about 1.4. When a
LIN
AND
SPRUIELL:
STRUCTURE
OF
Ni-Pd
SOLID
459
SOLUTIONS
the computer model is that it gives a very detailed physical picture of the nature of these modulations. The importance of the large atomic displacement modulations in controlling the appearance of the total diffuse intensity was illustrated in Fig. 5. We now consider the physical significance of these atomic displacement modulations. The atomic displacement parameters for the Ni-50 at. ‘A Pd alloy, determined from the separated intensity data, are shown in Table 2. We may obtain an estimate of the actual nearest-neighbor atomic displacements using a treatment given by Rudman and Averbach. This treatment that the atomic displacements are assumes parallel to the interatomic vectors and that L&t (Lfi + L$$/2 = 0. With these assumptions we find that Jzp = -0.013 @r/2 + d,/2), 61P;bPd = $0.013 (Z,f2 + C&/2) and ag$d = 0.000. This result, which indicates that in order to conserve the volume of the alloy the amount of shrinkage in the Ni-Ni distance is balanced by expansion of the Pd-Pd distance with essentially no difference between the Ni-Pd distance and the average interatomic distance, seems reasonable in this alloy with equal number of Ni and Pd atoms. Based on a hard sphere model in which the atoms in the alloy were assumed to retain their pure state size, the displacements were calculated to be JEp = -0.059 f&/2 + &,/2), @&sd = 0.038 (Gil2 + &z/2) and c!$$‘~ = 0.010 @i/2 + &s/2). These values are considerably larger than the experimental values for the alloy, and comparison with the experimental results indicates that the Ni atom is effectively 4.8 per cent larger and Pd atom is 2.4 per cent smaller in the Ni-50 at. o/oPd alloy than its pure state size. Because the Pd atom has the largest atomic scattering factor and also the largest atomic size, we expect that the 75 at. y0 Pd alloy will exhibit the largest atomic displacement modulations of these alloys. This should be true even though the actual atomic displacements are no larger in the 75 at. y0 Pd
ql1loo1ooooloo1o1l1l 0000000111 1 la0 0000100111 0 0 10 0 0 0 0 0 1 1 1 0 0 0 0n 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 ~1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 111111 0
0
o-o 0
1
1
0 0
1 Cl 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 R0 0 1 0 1 0 1 111100 0 0 lMlll0 0
)I0
q
dl
0
1 0 1
0 1
1 0
0 0
1 0
1 0
1 1
1 0
0
0
IZI
0
1 0
1 0
0
0 1 1 0 1 0 1
~1 1
0 0
10 0 0 1 0 0 1 0 0 0 1 0 1 0 0
0
~ 0
0 0
0
0 1
1 1
0
u 1
1
0 0 0
0
0 tt 1
0 0 0
0 1
J.
1
0
0
0
1 1
1 1 0~ 0
0
1 0
1 0 ~1 1 0 cl 1 1 0 1 1 0 0 1 1
0
0
1 1
0
1
0
0
1
0
0
0
olLl0
0
0
1
0
1
0
0
1
1
;El;0;1
1
1 0
110
Ml
II1
0 0
0 1 111 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0
1
0
1 0
1
1
1
1
0 0
0
1
0
1
1~1000
OIZI 1 0 1 1 1 0 1 1 IZI 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 .l 0 1 0 1 1 0 0 1 1 1 0 0 0 M 0
FIG. 9. Two consecutive (100) planes of the compu~r model generated for W-50 at. ‘A Pd &oy.
slightly different criterion was used to define an atom in a clustered region, the result was clusters of slightly different size (depending on how restrictive the criterion). The general characteristics of the fine structure, however, remained the same. It should be remembered that, while the ~onfi~rations have been discussed in terms of the Pd atoms in the 50-50 Ni-Pd alloy, the same results would be obtained for the Ni atoms. The fine structure of the Xi-50 at.% Pd solid solution can then be described as consisting of clusters of like atoms in the (100) planes with roughly branched rod shapes ; witXhin these clusters like atoms are linked together primarily by second-nearest neighbor bonds. The verbal description of the computer model is therefore consistent with the idea previously stated that the alloy contains very short wavelength oomposition moduIations along (100) directions. The value of
TABLE 2. First-order size effect parameters for Ni-50 at. % Pd alloy slowly cooled from 370°C 1 ?n @, 000 110 200 211 220 3 10 222 321
t Ymtn
Y&l
YElnwi -_____
0.000 0.240 -0.326 -0.014 -0.003 -0.102 0.042 0.017
0.000 0.240 0.000 0.091 -0.004 0.022 0.042 0.000
0.000 0.000 0.000 0.091 0.000 0.000 0.042 0.021
ACTA
460
MIETALLURGICA,
alloy, because of the dependence of the atomic displacement parameters on composition and scattering factor ratios. This trend was indeed observed, although not to the extent expected. Such comparisons indicated that the atomic displacements are somewhat smaller in both the Ni-25 and -75 at. % Pd alloys than in the K-50 at. % Pd alloy. (d) Fu~~-~~~~e ~~~~~c~~onenergies and ~~n~~~r~~~o~~ energy for the Xi-50 at. y0 Pd allow It is of interest to apply one of the approximate theories of pair correlations in binary alloys to evaluate the pair-wise interaction energies and configurational energy from the measured local order parameters for the N-50 at. % Pd alloy. Because of the importance of second neighbor interactions in the present alloy, the nearest neighbor theories are obviously useless. Clapp and Moss(a2) have recently developed a theory which is easily applied and which holds for an arbitrary range of interaction. We have chosen to use this theory to interpret our data. According to the Clapp-Moss theory, the pair-wise interaction energies are related to the measured local order parameters through 2 c v*&$ = j
2
.
(6)
A B
Here aoi is the correlation between an atom at the origin and one at the site i. This is given in terms of the sum over the product of the interaction energies V,$ between the origin and thej neighbors ofi, and the correlations uj, between j and i. The energy V,,, is given by
where V$*, VzB and VtB are interaction energies between AA, BB and AB pairs, respectively. In applying the Clapp-Moss theory to the present data, it was assumed that the net ~~raction energies beyond the t*hirdcoordination shell could he neglected. Using this assumption the values of V,, V, and V, (first, second and third coordination shells) were obtained by solving three simultaneous equations of the form of equation (6), using experimental order parameters for the first thirteen shells. Since the theory assumes thermod~amic equilibrium, the proper temperature to use in the calculations is the temperature at which the sample would have the measured local atomic arrangements under equilibrium conditions. Because the present measurements were made on an alloy slowly cooled to room temperature, the appropriate temperature for the calculation is the temperature at which the local
VOL.
19,
1971
atomic arrangements were “frozen-in”. This temperature was estimated to be 35O’C from the diffuse scattering data measured as a function of quenching and from the heat capacity vs. temperature temperature data of Bingham and Brooks.@) The resulting interaction energies were l’, = -24k, V, = -215k and V, = 43k. It is difficult to assess the accuracy of these values due to the complex procedures and assumptions involved in their calculation : a probable error of about 20 per cent is reasonable, however. With the calculated interaction energies, we can estimate the configurational energy of the alloy at, 35O’C relative t,o the random state; (7) where Zi is the coordination number of the ith shell. This calculation gives 640 & 200 J/mole which may be compared with the value of 900 & 400 J/mole estimated by Bingham and Brooks from their heat capacity data. Within the rather large experimental error, the two estimates of the configurational energy are in agreement. Note that reasonable agreement would be impossible using only a nearest neighbor theory. SUMMARY
AND
CONCLUSIONS
The short-range structures of Ni-Pd alloys containing 25, 50 and 75 at. “/, Pd were investigated using the single crystal X-ray diffuse scattering technique. It was concluded that these alloys, when slowly cooled or heat treated below about 450-500°C. contain very short wavelength composition modulations along (100) directions and static displacements of the atoms from their average sites. A computer simulation of the 50 at. % Pd alloy showed that the composition modulations in this alloy may be described more specifically as consisting of clusters of like atoms in the (100) planes with roughly “branohed rod” shapes. Within the clusters, like atoms are linked primarily by second nearest neighbor bonds. The detailed structure of the composition modulations in the 75 at. ‘A Pd alloy is quite similar to that in the 50 at. % Pd alloy, although the wavelength of the modulations is slightly longer. The deviation from randomness was small in the 25 at. % Pd alloy, but there was some evidence of a tendency to form one or two plane thick regions parallel to (106] ptanes within which the Iocal atomic arrangements tend toward ordering. The N-50 and -75 at. % Pd aIloys are quite responsive to heat treatment in the temperature range between 350 and 490°C. This was shown to be due to a decrease in the amplitudes of the composition
Lx??
ArjD
SPRUIELL:
STRUCTURE
modulations with increasing temperature within this range. This structural change is probably responsible for anomalous physical property results observed for these alloys, such as the anomalous rise in heat capacity of the X-50 at. % Pd alloy observed by Bingham and Brooks.tQ Alloys quenched from above about 490°C are essentially random but still exhibit large static atomic displacements from their average lattice sites. The Clapp-Moss approximate theory of pair correlations was applied to the Ni-50 at. % Pd results. The configurational enthalpy obtained agreed with t,he value estimated from the heat capacity data of Bingham and Brooks. The net interaction energy between second nearest neighbors was almost an order of magnitude larger than for first nearest neighbors in this alloy; thus it was concluded that for application to such systems, nearest neighbor theories are inadequate. ACKNOWLEDGEMENTS
The authors acknowledge with gratitude the help of R. 0. W~liams with the computer simulation and the many helpful discussions with R. 0. Williams, C. J. Sparks, J. E. Epperson and B. S. Borie. The support of this research by the National Aeronautics and Space Administration is appreciated.
OF
Xi-Pd
SOLID
SOLUTIONS
461
2. R. G. AHNAEV and S. YAZLIEV,Iza.Akad. ~Nauk turkmen. &S-R 6, 3 (1957). 3. YAZLIEV,Izv.Akad. Naul; turkmen. SSR, Ser. Fiz.-Teckh., Khim. i Geol Nauk 5, 14 (1961). 81, 1215 (1966). 4. A. NAGASA~~A,J.~~~~.SOC.J~?~~~ 5. L.R.BIDwELL~,~~ R. S~~1~~~,ActaMet.13,61(1965). and C. R. BROOKS,J. phys.Chem. Solids 6. R. E. BIXGHAM SO, 2365 (1969). 7. B. S. BORIE and C. J. SPARKS,JR.,Acta ~~~~l~gr. 17,827 (1964). 8. J. I@. COWLEY, .J. a&. Fhya. 15, 24 (1%50). AVERBACH and B. W.ROBERTS,J. 9. B.E.WARREN,B.L. appl. Phys. 22, 1493 (1951). Addison-Wesley 10. B. E. WARREN, X-ray Diffraction. (1968). 14,472 (1961). 11. B. S.BORIE,Acta crystallogr. 12. C. J. SPARKS, JR. and B. S. BORIE,Local Atomic Arrangements Studied by X-ray Lti,ffra&on, IvfetallurgicalSociety Conf. 36, editedbyJ.B. COHE~~~~~ J. E. HILLIARD,pp. 5-46. Gordon and Breach (1966). 13. B. S. BORIE and C. J. SPARKS,JR.,Actacrz&aElogr.to be published. 14. L. R. BIDWELL and R. SEISERP, Acta crystallogr. 17, 1473 (1964). 15. J.E. EPPERSON and J.E. SPRUIELL, J.phys.Chem.Solids 30, 1733 (1969). 16. WEE LIN, Ph.D. Dissertation, University of Tennessee (1969). 17. S. C. Moss, Local Atomic Arrangement8 Smudge by XT-ray ~~ffra~t~o~, ~et~llurgieal Societ.y Conf. 36, edited by J. B. COHEN and J. E. HILLIARD,pp. 95-122. Gordon and
Breach (1966). 18. S. C. Moss and B. L. AVERBACH, Small Angle Scattering, editod by IX. BRUMBERGER, pp. 336-350. Gordon and
Breach (1967).
19. P. C. GERLEN and J. B. COHEN, Phys. Rev. 139, AS44 (1966). REFERENCES 20. R. 0. WILLIAMS,ORNL Report T&I-2866 (1970). 1. E. HULTGREN and C. ZAPFFE, Tmns. Am. Inst..&I&. 21. P. S. RUDSIAN and B. L. A~ERBACE, Acta h-let. 5,65 (1957). 22. P. C. CLAPP and S. C. Moss, Pkys. Rev. 142, 418 (1966). E%gf% 183, 58 (1939).
STRUCTURE
OF NICKEL-PALLADIUM W.
LINT
and
J.
E.
SOLID
SOLUTIONS*
SPRUIELLT
The local atomic arrangements and atomic displacements from their average positions were investigated for Ni-25, -50 and -75 at. % Pd 5110~susing the single crystal X-ray diffuse scattering technique. Analysis of the diffuse intensity revesled t.hat Ni-Pd alloys possess short wavelengt,h composition modulations along (100) directions when slowiy cooled from elevated temperatures or heat treated at relatively low temperature (~400°C) following quenching. A computer simulation was used to generate a model of t,he local atomic arrangements in the slowly cooled Xi-60 at. y0 Pd alloy. The model may be described as consisting of olusters of like atoms in the (100) planes with roughly “branched rod” shapes. Within the clusters, like atoms are linked primarily by seoond nearest bonds. Large static atomic displacements of the atoms from their average atomic sites due to the difference in atomic size were observed for all sample conditions, including quenching from high temperature. STRUCTURE
DES
SOLUTIONS
SGLIDES
NICKEL-PALLADIUM
Les ~rrangement.s atomiques locaux et les d~placements des atomes it partir de leurs positions moyennes ont et6 &udi& pour les &ages Ni-25, -50 et -757&t. Pd par “diffuse scattering” des rayons X sur un monooristal. L’analyse de l’intensite diffuse montre que les alliages Ni-Pd oontiennent des modulations de compositions 8, foibles longueurs d’onde 1%long cles directions (100) quand ils ont et6 refroidis lentement ir partir de temperatures &levees, ou quand ils ant, subiuntraitement thermique Q une temperature relativement basse (400°C) apres trempe. Une simulation B l’ordinateur a BtB utilisee pour eonstruire un mod& des arrangements atomiques locaux dam l’alliage Ni-50°/0at. Pd. Le mod& peut Btre dkcrit comme consistant en des agglomerats de quelque chose d’analogue i des atomes dans 10splans { IOO), ayant des formes rappelant grossierement des baguettes remifiees. A l’interieur des agglomerats, CRSespltces d’atomes sont lies principalemcnt per des liaisons de seconds voisins. Des d&placements importants des atomes B partir de leurs sites atomiques voisins, dOs aux differences de tailles atomiques, ant, et6 observes pour tous 1~sCBSStudies, y compris pour les echantillons trempex B par&r des temperatures Cilev&s. DIE
STRUKTUR
VON
NICKEL-PALLADIUM-LEGIlZR,UNGEX
Aus der diffusen Riintgenstreuung an Einkristallen der Ni-25, Ni-50 und Ni-75 At.% Pd-Legierungen wurden die lokale Anordnung der Atome und ihre Verschiebungen aus den mittleren Lagen be&immt. Die Antdtyse der diffusen IntensitLt ergab, da3 sowohl langssm sbgekiihlte als aueh abgeschreckte und bei relativ niedrigen Temperaturen ( ~400°C) angelsssene Ni-Pd-Legierungen periodische Schwankungen der Zusammensatzung mit kurzer Wellenliinge entlang (109).Richtungen besitzen. Mit Hilfe einer Computer-Simulation wurde ein Model1 der lokalen Atomanordnungen in der langsam abgektihlten Ni50 At.% Pd-Legierung erzeugt. Das Model1 besteht aus Clustern gleicher Atome in der Form “verzweigter St&be” in den ~lOO}-Ebenen. Innerhelb der Cluster best,ehen zwischen gleichen Atomen tibern%chster-Nachbar-Bindungen. An allen, touch an den van hohen Temperaturen abgeschreckten Proben, wurden groBe statische Verschiebungen der Atome s,us ihren mittleren Atomlagen aufgrund der verschiedenen Atomdurchmesser beobachtet.
INTRODUCTION
Although the X-ray powder diffraction study of Hultgren and Zapffee w showed that the Ni-Pd system forms a continuous series of solid solutions in which no superlattices or intermediate phases form, some authors have taken issue with these results while others have attributed anomalous behavior of physical properties t,o “nonrandom” atomic arrangements. For example, Yaeliev and Annaev@J) have reported anomalous electrical and magnetic behavior at the stoichiometric compositions NisPd and NiPd, which they attributed to the probable existence of superlattices at these compositions. Nagasawat4) also claimed the existence of superlattices at the compositions NisPd and NiPd, based on the evidence obtained through an electron diffraction study of thin, vapor deposited films. The relative thermodynamic properties of solid Ni-Pd alloys have been measured * Received April 21, 1970; revised September 29, 1970. t Department of Chemical and Metallurgical Engineering, University of Tennessee, Knoxville, Tennessee 37916. ACTA
~~ETAL~URGICA,
VOL.
19, MAY
1971
by Bidwell and Speiser(“) in the temperature range 700-12OO’C. They concluded that, if their data were interpreted in terms of quasichemical theory, Ni-Pd alloys possess short-range order or a preference for unlike neighbors at elevated temperatures and possibly long-range order at low temperatures. Bingham and Brooks(“) observed an “anomalous” rise in the heat capacity of a Ni-50 at. y0 Pd alloy 350 and 490°C a range which is well separated from the magnetic effect. They concluded that this alloy exhibits some form of local order below about 400°C. The anomalous rise in the heat capacity curve for the Ni-50 at. % Pd alloy certainly signifies some sort of structural change in the solid solution above about 350°C. However, thermodynamic and physical property data provide only indirect evidence concerning the structural state of alloys, and hence, they can be interpreted only qualitatively. It is the purpose of the present paper to report the resultzsof an X-ray diffuse scattering investigation of three Ni-Pd alloys containing 25, 50 and 75 at. % Pd. These results provide a reasonably detailed picture of the local atomic
451
ACTA
45“
arrangements
and help to clarify
thermodynamic
property
X-RAY
METALLURGICA,
the physical
and
results.
DIFFRACTION
tered from
binary
of the
of the diffuse intensity
cubic
alloys
Borieor) because
THEORY
present data is that the local order and atomic components
19,
1971
and Sparks and Borie(12) have shown that
the two components
The basic result used in the interpretation placement
VOL.
disscat-
can be expressed
as
of
their
in equation different
symmetry
The approach
used to obtain equation
the approximation atomic
of an exponential
hereafter
This
approach
X,
and X,
are the
A
and
atom
respectively, factors. the
of
components
fB are
The h’s are continuous
cal space at
fractions
and fA and
equal to one-half
reciprocal
lattice
B,
their atomic scattering coordinates
in recipro-
the usual Millar indices Relative to an points.
arbitrary origin, the integers 1, m, n define a particular lattice site according
to the relation
(2)
where z,, 6, and 2, are the translation cubic unit cell. The %mn are the Warren
short-range
vectors
of the
order param-
these
have
of finding a B atom as an
of an A atom. parameters
The Y:,~ are atomic
defined
by relationships
of
the form
(Huang)
components
must
(1) can be applied. shown
can be treated analytically
that the effect
and first order atomic displacements quadratic pansion.
term
in the above
can still be isolated,
be recovered.
series
excom-
so t’hat tc’s and y’s may
This approach is referred to hereafter as
the quadratic displacements
approximation.
The data
in the present investigation
were treated
using both
the
approximations
linear
and
quadratic
to
t’he
displacements. PROCEDURES
ingots of Ni-25,
-50 and -75 at. % Pd
alloys were prepared from high purity Ni (99.87 %) and Pd
(99.9%).
vacuum alumina
Single
crystals
were
grown
under
by the Bridgman technique in high purity crucibles. The single crystal ingots were
homogenized
for 1 week at 1100°C.
Diffuse scattering
samples in the form of discs about 0.12 in. thick and ingots.
were cut from the homogenized
These discs were crystallographically
to have a (210)
face
which
oriented
was metallographically
polished and etched after each heat treatment any where the L’s are components
of displacements
off the
X-ray
determined taken
average atomic sites,
from
measurements. from the
The
Debye-Scherrer crystals
alloys, (1) is a generalization
obtained
by Borie
of the results first obtained by Cowley(*)
and by Warren et CL(~) for the local order and the so-called “first order” atomic displacements diffuse scattering. A derivation and discussion of this equation is also given in Ref. 10.
respectively,
in
measurements
of filings
3.737,
and
-75 at. % Pd
agreement
lattice parameter vs. composition Bidwell and Speiser.(r4) The X-ray
-50,
prior to
parameters
3.635,,
Ni-25,
good
lattice patterns
were
3.820, A for the nominally
and Spark@
of
by retaining the
mentioned
They have shown that the individual
0.75 in. in diameter
Equation
be
However,
along with the local order
EXPERIMENTAL
where P rmnis the probability (lmn) neighbor
hence
and Sparksd3)
Arc melted (3)
displace-
of the thermal
thermal motion and second order static displacements
eters defined by
displacement
of the atomic
a description
removed before equation
ponents
%nn = l%+m:+nz,
and
to
approximation.
and second order static atomic displacements scattering, Borie
the
for the
is referred
as the linear displacements
The linear approximation
Here, N is the number of atoms irradiated,
(1) involves
scattered intensity by the first two terms of
ments does not include
(1)
by
involving
eiZ’G@, in the formula
displacements,
coherently
sin 2744~ + h,m + hg4.
in reciprocal
space. The U’S and y’s can then be recovered Fourier inversion of the separated intensity data.
its series expansion.
+ &&J
(1) can be separated
with
the
data reported
by
were made using crystal
monochromated CuKu radiation. Details concerning the X-ray technique are described elsewhere.(r5J6) If the data were to be analyzed by the approach based on the linear approximation to the displacements,
temperature for Xi-25, -50 and -75 at. T{ Yd ailoys after the single crystals have been furnace cooled from 11OO’C. These intensities are expressed in Laue monotonic units and have been corrected for Compton diffwe scatt,ering. The most .&king characteristic of each of these diEuse int,ensity d~str~but~ou~is the concentration of diffuse intensity near t,he Bragg
Frc. 1.
oorrections for temperature diffuse scattering were applied by making the me~urements at two temperatures (room ~m~rature and 78OKf and extrapolating linearly to 0°K. The intensity measurements were converted to absolute units (electron units per atem) by comparison with the scattering from polystyrene (C&H,) at 30 = 100”. The Compton scattering was calculated and subtracted from the data after conversion to a.bsolute units. For the quantitative determination of the Warren order pm&meters, CQ~%,and atomic disp~aceme~t.s coeficients, yEmn,the diffuse intensity was measured at each of 2106 points looated on a3cubic grid throughout the volume element in reciprooal space shown heavily outlined in Fig. 1. Dab in this volume are sufficient to permit one to make the three-d~~nensional atomic displacements z+xeparationby the procedure of Sparks and Rorie.cl2) The separation based on the quadratic approximation was used for data taken on the h&O plane of reciprocal space. RESULTS
and DISCUSSION
Figure 2 shows the intensity distributions in the h,h20 plane of reciprocal space measnred at room
FIG. 2. Effuse intensity distributions on the &h& plane of reciprocal space for (a) 25 at. % Pd, fb) 50 at. % Pd, fo) 75 at,.“/;; Pd. Samples were furnace cooled fram llOO”C. The quantity p&ted is I,&VXAX,(f, -f&F,
ACTA Fundamental Diffuse
METALLURGICA,
VOL.
19,
have proved
Reflections
1971
separated
component
was
compared
based
for separating
the
from the local order linear
technique
displacements
distribution data
in Fig.
based on the quadratic
distribution.
The
resulting
for the local order component
in Fig. 4(b).
should be
shown
was also applied to this two-dimension-
intensity
distribution
The extrapolation
intensity
is presented
under the Bragg peak
has not been carried out for these data, but it can be seen that a very similar intensity
FIG. 3. Schematic representation of the diffuse intensity distribution in reciprocal space for slowly cooled Ni-50 at. ‘A Pd single crystal.
reflections,
shown
In
three-dimensions consists
of
lobes
represented
schematically
diffuse lobes occurring on the indices type reflections,
permits
4(a)
based
on
intensity
intensity
of
diffuse
intensity
reflections
in the absence
might
caused
as
in Fig. 3. The number
of
near each Bragg peak depends for hO0
reflection-one
two for hk0 type reflections,
and three
distribution
atomic displacements) The two intensity
plotted
along
of diffuse intensity
shown
in Fig.
fundamental
These
reflections.
diffuse
lobes
of
intensity extend down along the [OOi] direction in the lattice and cut the h,h20 plane with about
reciprocal
the same order of intensity (300) position. The diffuse
as that near the (100) and
The
separated
equation
(l)]
distributions,
particularly
those for the 75 at. % Pd alloy, are very similar to that by Moss (17)and Moss and Averbach
for an
the
distribution
with respect to the Bragg reflections, suggested
that this unusual
was due to atomic
intensity
displacements
and a
space
is
alloy;
h sin h dependence
it [see
the origin of the asymWhen the atomic
are algebraically
component,
the
added to
observed
broad
occurs to the low angle side of the
that
the
or fluctuation modulation
peak.
local
order
diffuse
scattering
along the (100)
axes in
space implies that some form of composition
composition separation
ation techniques which have been employed in analyzing the present diffuse intensity distributions
modulations
crystals.
be
Although the atomic displacements alone can produce an asymmetric diffraction pattern, the separ-
a
modulation
Ni-50 at. % Pd
is concentrated
modulation
in which rich,
displacements
the expected
in the alloy
clustering type of local atomic arrangements to
data taken throughout
5 for the
order
The fact
regions along (100) directions alternately, in Au and Ni.
tended
in Figs. 4(a)
This result suggests
(200) reflection.
reciprocal
the distribution
atomic
diffuse maximum
(100) axes in reciprocal these authors
shown
intensity distribution.
local
component
of
static
space for this alloy.
and illustrates
experimental
Au-40 at. y0 Ni crystal quenched from 890°C. Because of the concentration of the diffuse intensity along the space and the asymmetry
which
order
metry about the (200) Bragg peak (h, = 1.0) in the displacements
intensity
(second
the h,OO line in reciprocal
clearly exhibits
diffuse
of the Bragg
to use the linear displacement
for treating
The intensity contours shown near the (110) and (310) positions in Fig. 2 are due to the concentrations
approximation
of the order
and thermal diffuse scattering.
it is adequate
approximation
to that
separation
of any interference
Huang
distributions
volume in reciprocal
with the (111) and (311)
quadratic
and (b) are in good agreement. that
The
in the vicinity
by
for hkl type reflections.
associated
the
one to see the shape
be
distribution
is obtained.
diffuse
Bragg reflections,
of the Bragg
Fig.
the
on the (100) axes and just to the low angle
side of each of the fundamental
in
technique
along the (100) type axes in the reciprocal
distributions
obtained
the
with the unseparated
approximation
centered
on
This intensity
2(b). The separation
lattice.
modulations
used to obtain Fig. 4(a) for the Ni-50 at. %
alloy
approximation.
000
are not
4 shows the
of diffuse intensity
The procedure
atomic displacements
al
Figure
alloys.
local order component
for the three alloys.
Pd
arrangements
that the atomic
random in these Ni-Pd
intensity
exists along (100) directions
The mean wavelength may be estimated
of the diffuse maximum
Interpreted
in terms
of the
from the
from the Bragg
of such
a model,
the
broad, weak diffuse maxima observed in Figs. 4(b) and (c) for the Ni-50 and 75 at. ‘A Pd. alloys indicate that
the
composition
modulations
have
average
wavelengths of about 5.7 and 6.6 A, respectively. The intensity distribution for the 25 at. ok Pd. alloy,
LTN
STRUCTURE
SPRUIELL:
ANI)
OF
Xi-Pd
SOI,ID
455
SOLUTIONS
lb)
FIG 4. Local order component of diffuse intensity for Ni-Pd alloys in hi&O plane. (a) and (b) 50 at. % I’d, (c) 75 at.% Pd, (d) 25 at. % Pd. (a) is obtained using linear approximation, (b)-(d) are obtained using quadrat’ic approximation.
Fig. 4(d), with its slight peaking lattice
position,
may
indicate
at the usual supera tendency
to form
extremely thin platelet shaped regions parallel to (100) planes within which the local atomic3 arrange-
6-
ments
are tending
distribution
toward
ordering.
that only very slight deviations involved. the
other
The intensity
for this alloy is so nearly flat, however, from randomness
are
The nature of the atomic arrangements
for
two
alloys,
alloy, will be considered of the temperature
particularly
the
further following
dependence
of the
50 at. % Pd a discussion short-range
structure.
In
0
(b) Temperature dependence of the short-range ” 0 2
1”
04
0.6
1
II
0.8
”
1.0
”
1.2
”
1.4
h4
Atomic displacements modulation along the hi00 line in reciprocal space for the slowly cooled Ni-50 at. % Pd alloy. FIG.
5.
structure of nickel-palladium The response of the Ni-Pd was investigated
by making
alloys
alloys to heat treatments intensity
measurements
along the hL,OOline in reciprocal space in the vicinity of the (200) reflection. Figure 6 presents a graphical
ACTA
456
METALLURGICA,
VOL.
19,
1971
8.0 -
o0.4
0.6
0.5
0.8
0.7
o-
09
0.4
0.5
07
06
0.8
0.9
h,
h,
(a)
, -- -- .- *mded
96 hrs at CIOO’C, furwxe cooled to r.t. 2 - - Quenched from 7OO’C ,“to rt water 3 ---Annealed 132 hrs ot 550% qwnckd into r.t. water 4 ---Annealed 29 dovs ot 491°C. quenched Into r I wqter -----.. Annealed 56 hr; at 370%. i”;“aCe cooled t0 r.t. -.-Anneolad 224 hrs ot 300% furnace cooled t0 rt. - Guuenched fro”, 963’c ,nto rt water -A”neoled 24 hrs ot 37O’C, quenched into rt water (b) -----Quenched fro”, 996’C ,n+o r t. water Annealed 15 hrs ot 5lO’C. quenched into rt water - -Annealed 20 hrs ot 405’C, quenched into rt. water ---Annealed 24 hrs at 305’C, quenched into r 1. water Annealed 24 hrs. ot 3OO’C, furrmce cooled to r t
.,....
-
OL------I 0.4 0.5 FIG. 6. Diffuse intensity
summary
0.6
0.7
0.8
0.9
of some of these measurements. only for Compton
profiles
can be divided
The data
measured
intervals
in the
range from 350 to 545°C [these measurements
are not
scattering.
shown
into two main
When the sample was heat treated below groups. about 370°C or when it was slowly cooled from higher temperature, distinct
“hump”
fundamental maximum observed
profile exhibited
a
to the low angle side of the (200)
reflection
corresponding
shown in Fig. 2(b). when the sample
from temperatures intensity
the diffraction
to the diffuse
No distinct hump was
was aged and quenched
above 49O”C, although
remained
asymmetric
about
in the diffuse indicate
intensity
Bingham
profile
with
and Brook@)
observed in the same temperature range for this alloy. In order to investigate the temperature dependence of this
structure
change,
the
diffuse
was
lowered
intensity
was
showed
range ; there was no indication
that
the
gradually
in this
as
temperature
of a sharp change at a
specific temperature.
On the basis of these data it is
concluded
amplitude
that
modulations decreases
the
in this X-50
with increasing
the range 350490°C. hump
was
of the
composit,ion
at. y0 Pd alloy quenching
gradually
temperature
in
Since the position of the diffuse
unaffected
by
heat
treatment,
is not affected
(200)
at. ‘A Pd alloy is occurring
that
data
the
between 370 and 490°C. This change in short-range structure is apparently responsible for the anomalous capacity
These
concluded that the mean wavelength
that a change in the short-
range structure of the X-50
6(a)].
20°C
in the diffuse hump increased
temperature
Behavior
The changes
rise in heat
in Fig.
intensity the
at approximately
the diffuse
reflection. heat treatment
(a) 50 at. ‘A Pd,
units and
Note that in Fig. 6(a) for the Ni-50 at. % Pd alloy the intensity
ot t16O”C, furnace cooled to r 1. from 980°C into r 1. water from 7OO’C into rt wqter
along the hi00 line in reciprocal space after various heat treatments. (b) 75 at.% Pd, (c) 25 at. % Pd.
shown in this figure are in Laue monotonic have been corrected
Annealed It6 hrs.
-.Ouenched -----Quenched
it was
of the modulation
by the heat treatments
investigated.
similar to that for the Ni-50 at. % Pd alloy
was observed
for the Ni-75 at. % Pd alloy [Fig. 6(b)J,
but the Ni-25 at. % Pd alloy was not as responsive heat treatment heat treatment
[Fig. 6(c)]. is probably
to
This lack of response to due to the low degree of
local order in this alloy and associated in both local order and atomic heat treatment.
small changes
displacements
upon
Above about 490°C the intensity distribution
for all
three alloys is dominated
by the atomic displacements
1,Xx
AND SPRUIELI,
: STRUCTURE
component which persists to the highest quenching temperatures investigated. This was readily demonstrated by performing the separation of the local order and atomic displacements diffuse scattering on samples quenched from high temperatures, Similar analyses also showed that the atomic displacements parameters are functions of the heat treatment; the atomic displacements parameters are significantly greater in the slow-cooled condition than in the quenched condition. This is probably a result of the changes in local atomic arrangements with heat treatment [see equation (4)], but, could be partially due to a change in the actual atomic displacements as well. (c) illeasuremelrt of the &fuse
intensity throughout a
voluble in r~c~~ro~l space and 2s ~nter~re~at~o~
In order to recover adequate values of the Warren order parameters, aims, and the atomic displacements parameters, J&,,,, measurements throughout a volume in reciprocal space are required. Considering the results presented in Figs, 4(a) and (b), it was decided that the separation based on the linear approximation was adequate for the K-50 at. % Pd alloy and intensity measurements tl~rougl~out the volume ofFig. 1 were made for this crystal after a heat treatment of 100 hr at 370°C followed by slowly cooling to room temperature at a rate of 12°C per hour. The Warren order parameters obtained from Fourier inversion of the separated local order diffuse scattering are presented in column 2 of Table 1. A model for the local atomic arrangements in the TABLE 1. Comparison of the order parameters cakwlated from model with the experimental values for X-60 at. % Pd alloy --_
Computer generated model 1 na ?L 000 110 200 211 220 3 10 222 321 400 411 330 420 332 422 4 3 I 440 433 442 444
Experimental
3-shell
5-shell
1.533 0.005 0.184 -0.069 -0.012 0.021 -0.030 -0.010 0.013 -0.006 -0.005 - 0.009 -0.005 -0.003 --0.002 -0.015 0.000 0.007 0.003
1.000 0.005 0.184 -0.069 0.049 0.011 0.018 -0.009 0.040 0.014 -0.017 0.020 0.001 0.011 -0.004 -0.007 -0.003 0.008 0.005
1.000 0.005 0.184 -0.069 -0.012 0.020 -0.030 - 0.006 0.032 -0.009 0.021 0.002 0.005 -0.002 0.004 -0.001 -0.003 -0.002 0.005 --
OF
Ni-Pd
SOLID
SOLUTIONS
457
alloy which is consistent with the experimental local order parameters may be derived using a computer simulation as was first done by Gehlen and Cohen.ugj The two kinds of atoms in the model are rearranged until the order parameters for the model fit some specified number of experimental parameters. Such a computer simulation was carried out for the present data using a program recently developed by Williams. This program, described in detail elsewhere,@*) appears to give essentially the same results as that due to Gehlen and Cohen, although it is based on different algorithms. Whereas Gehlen and Cohen’s program interchanges unlike atoms chosen at random if such an interchange will cause the first three computed order parameters to change toward the experimental set, Williams’ program examines the at,om sites sequentially in a pseudo-random manner such that no site can be missed and the identity of a given site is changed if the composition will remain within set design limits and if the vector sum of the local order parameters being monitored moves closer to the experimental value. The results of two computer simulations using an 8000 atom model are shown in Table 1. In one case only the first three alphas, namely 110, 200 and 211, were monitored; in the second case the 220 and 222 were monitored in addition to the first three. Comparison of the list of calculated alphas with the experimental values shows considerably better agreement among the higher order values for the !&shell model than for the 3-shell model, as is to be expected. The diffuse intensity on the k&,0 plane synthesized for the &hell computer generated model from the first 40 order parameters is shown in Fig. 7 ; this figure may be compared to the experimental result shown in Fig. 4(a) or (b). If allowance is made for a small, flat, parasitic scattering in the experimental data ~~~~~ # l.OO), the s-shell results are in excellent agreement. with experiment. The distributions of Pd atoms in the first and second coordination shells about a Pd atom as origin in the &shell model for the IocalIy ordered alloy are shown and compared to similar quantities for a random alloy in Fig. 8. The distribution in the model for the first coordination shell is not appreciably shifted relative to the random model, although it is broadened slightly. The distribution for the second ~oord~ation shell is shifted to higher numbers of 200 neighbors in the model. This means that there are many more Pd atoms in the model for the locally ordered alloy with four or more Pd atom second nearest neighbors than in the random case, The model was also searched for several types of special configurations such as 110 Pd atom triplets and
ACTA
45s
METALLUKGICA,
VOL.
19,
1971
210
010
FIG.
7. The
diffuse
intensity
distribution
on the
h,h,O plane
generated
quadruplets.
None
of
these
present
in numbers
number
present in the random
figuration involved
200 Pd-Pd
In order to obtain atomic
configurations
significantly
arrangements,
a better
different
from
regions
the
criterion
and to examine
regions.
The
case unless the conconcept
in
the
model
of the local
to try to isolate
I
0
0.3 x _z 5 x 0.2
regions
e a.
region”
some
information
specified
indicated Hence,
investigate
Figure 9 shows
(100) planes of the computer
designate
the
Pd
Boundary
in which
atoms lines
the Pd atoms
model
Symbols
and
are
some
a criterion
this possibility
regions.
for the Ni-50 at. % Pd alloy.
respectively. criterion.
meet
was occurring.
was chosen which would
and
Ni
drawn
1
atoms, around
meet the following
A Pd atom is defined to be in a “clustered
if there are 4, 5, 6, 7, or 8 Pd atoms in its 110 shell and 4, 5, or 6 Pd atoms in its 200 shell.
0.1
0
computer
the size and shape of such
and isolate such “clustered” generated
I
which
available
form of clustering
two consecutive 0.4
for the &shell
was
bonds.
it is useful
synthesized
model.
In general the appearance
1 2 3 4 5 6 7 6 9 10 11 12 Number of Pd Neighbors in First Shell Around Pd Atoms
alloy tend to form roughly several
04 (b)
branches
along
rod-shaped
(100)
type
clusters with directions.
In
most cases, the clusters of rods lying in a given (100)
,-Model
plane do not extend
0.3 a .c.z z 0.2 e P 0.1
below.
to the plane above
or the one
Their shape and size vary from one plane to
another. Although small clusters and rods can also be found in the model for random configuration, their sizes are much smaller compared to those found in the locally ordered model. That is, the number of Pd atoms which satisfy the definition of an atom inside a
0
0 I 2 3 4 5 6 Number of Pd Neighbors in Second Shell Around Pd Atoms FIG. 8. Distribution of Pd neighbors in the first second coordination shells around a Pd atom.
of the regions as shown in
Fig. 10 is such that the Pd atoms in the Ni-50 at. % Pd
0
cluster in the model and
for the locally
ordered
alloy is
much larger than that in the random case. The ratio of the former to the latter is about 1.4. When a
LIN
AND
SPRUIELL:
STRUCTURE
OF
Ni-Pd
SOLID
459
SOLUTIONS
the computer model is that it gives a very detailed physical picture of the nature of these modulations. The importance of the large atomic displacement modulations in controlling the appearance of the total diffuse intensity was illustrated in Fig. 5. We now consider the physical significance of these atomic displacement modulations. The atomic displacement parameters for the Ni-50 at. ‘A Pd alloy, determined from the separated intensity data, are shown in Table 2. We may obtain an estimate of the actual nearest-neighbor atomic displacements using a treatment given by Rudman and Averbach. This treatment that the atomic displacements are assumes parallel to the interatomic vectors and that L&t (Lfi + L$$/2 = 0. With these assumptions we find that Jzp = -0.013 @r/2 + d,/2), 61P;bPd = $0.013 (Z,f2 + C&/2) and ag$d = 0.000. This result, which indicates that in order to conserve the volume of the alloy the amount of shrinkage in the Ni-Ni distance is balanced by expansion of the Pd-Pd distance with essentially no difference between the Ni-Pd distance and the average interatomic distance, seems reasonable in this alloy with equal number of Ni and Pd atoms. Based on a hard sphere model in which the atoms in the alloy were assumed to retain their pure state size, the displacements were calculated to be JEp = -0.059 f&/2 + &,/2), @&sd = 0.038 (Gil2 + &z/2) and c!$$‘~ = 0.010 @i/2 + &s/2). These values are considerably larger than the experimental values for the alloy, and comparison with the experimental results indicates that the Ni atom is effectively 4.8 per cent larger and Pd atom is 2.4 per cent smaller in the Ni-50 at. o/oPd alloy than its pure state size. Because the Pd atom has the largest atomic scattering factor and also the largest atomic size, we expect that the 75 at. y0 Pd alloy will exhibit the largest atomic displacement modulations of these alloys. This should be true even though the actual atomic displacements are no larger in the 75 at. y0 Pd
ql1loo1ooooloo1o1l1l 0000000111 1 la0 0000100111 0 0 10 0 0 0 0 0 1 1 1 0 0 0 0n 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 ~1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 111111 0
0
o-o 0
1
1
0 0
1 Cl 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 R0 0 1 0 1 0 1 111100 0 0 lMlll0 0
)I0
q
dl
0
1 0 1
0 1
1 0
0 0
1 0
1 0
1 1
1 0
0
0
IZI
0
1 0
1 0
0
0 1 1 0 1 0 1
~1 1
0 0
10 0 0 1 0 0 1 0 0 0 1 0 1 0 0
0
~ 0
0 0
0
0 1
1 1
0
u 1
1
0 0 0
0
0 tt 1
0 0 0
0 1
J.
1
0
0
0
1 1
1 1 0~ 0
0
1 0
1 0 ~1 1 0 cl 1 1 0 1 1 0 0 1 1
0
0
1 1
0
1
0
0
1
0
0
0
olLl0
0
0
1
0
1
0
0
1
1
;El;0;1
1
1 0
110
Ml
II1
0 0
0 1 111 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0
1
0
1 0
1
1
1
1
0 0
0
1
0
1
1~1000
OIZI 1 0 1 1 1 0 1 1 IZI 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 .l 0 1 0 1 1 0 0 1 1 1 0 0 0 M 0
FIG. 9. Two consecutive (100) planes of the compu~r model generated for W-50 at. ‘A Pd &oy.
slightly different criterion was used to define an atom in a clustered region, the result was clusters of slightly different size (depending on how restrictive the criterion). The general characteristics of the fine structure, however, remained the same. It should be remembered that, while the ~onfi~rations have been discussed in terms of the Pd atoms in the 50-50 Ni-Pd alloy, the same results would be obtained for the Ni atoms. The fine structure of the Xi-50 at.% Pd solid solution can then be described as consisting of clusters of like atoms in the (100) planes with roughly branched rod shapes ; witXhin these clusters like atoms are linked together primarily by second-nearest neighbor bonds. The verbal description of the computer model is therefore consistent with the idea previously stated that the alloy contains very short wavelength oomposition moduIations along (100) directions. The value of
TABLE 2. First-order size effect parameters for Ni-50 at. % Pd alloy slowly cooled from 370°C 1 ?n @, 000 110 200 211 220 3 10 222 321
t Ymtn
Y&l
YElnwi -_____
0.000 0.240 -0.326 -0.014 -0.003 -0.102 0.042 0.017
0.000 0.240 0.000 0.091 -0.004 0.022 0.042 0.000
0.000 0.000 0.000 0.091 0.000 0.000 0.042 0.021
ACTA
460
MIETALLURGICA,
alloy, because of the dependence of the atomic displacement parameters on composition and scattering factor ratios. This trend was indeed observed, although not to the extent expected. Such comparisons indicated that the atomic displacements are somewhat smaller in both the Ni-25 and -75 at. % Pd alloys than in the K-50 at. % Pd alloy. (d) Fu~~-~~~~e ~~~~~c~~onenergies and ~~n~~~r~~~o~~ energy for the Xi-50 at. y0 Pd allow It is of interest to apply one of the approximate theories of pair correlations in binary alloys to evaluate the pair-wise interaction energies and configurational energy from the measured local order parameters for the N-50 at. % Pd alloy. Because of the importance of second neighbor interactions in the present alloy, the nearest neighbor theories are obviously useless. Clapp and Moss(a2) have recently developed a theory which is easily applied and which holds for an arbitrary range of interaction. We have chosen to use this theory to interpret our data. According to the Clapp-Moss theory, the pair-wise interaction energies are related to the measured local order parameters through 2 c v*&$ = j
2
.
(6)
A B
Here aoi is the correlation between an atom at the origin and one at the site i. This is given in terms of the sum over the product of the interaction energies V,$ between the origin and thej neighbors ofi, and the correlations uj, between j and i. The energy V,,, is given by
where V$*, VzB and VtB are interaction energies between AA, BB and AB pairs, respectively. In applying the Clapp-Moss theory to the present data, it was assumed that the net ~~raction energies beyond the t*hirdcoordination shell could he neglected. Using this assumption the values of V,, V, and V, (first, second and third coordination shells) were obtained by solving three simultaneous equations of the form of equation (6), using experimental order parameters for the first thirteen shells. Since the theory assumes thermod~amic equilibrium, the proper temperature to use in the calculations is the temperature at which the sample would have the measured local atomic arrangements under equilibrium conditions. Because the present measurements were made on an alloy slowly cooled to room temperature, the appropriate temperature for the calculation is the temperature at which the local
VOL.
19,
1971
atomic arrangements were “frozen-in”. This temperature was estimated to be 35O’C from the diffuse scattering data measured as a function of quenching and from the heat capacity vs. temperature temperature data of Bingham and Brooks.@) The resulting interaction energies were l’, = -24k, V, = -215k and V, = 43k. It is difficult to assess the accuracy of these values due to the complex procedures and assumptions involved in their calculation : a probable error of about 20 per cent is reasonable, however. With the calculated interaction energies, we can estimate the configurational energy of the alloy at, 35O’C relative t,o the random state; (7) where Zi is the coordination number of the ith shell. This calculation gives 640 & 200 J/mole which may be compared with the value of 900 & 400 J/mole estimated by Bingham and Brooks from their heat capacity data. Within the rather large experimental error, the two estimates of the configurational energy are in agreement. Note that reasonable agreement would be impossible using only a nearest neighbor theory. SUMMARY
AND
CONCLUSIONS
The short-range structures of Ni-Pd alloys containing 25, 50 and 75 at. “/, Pd were investigated using the single crystal X-ray diffuse scattering technique. It was concluded that these alloys, when slowly cooled or heat treated below about 450-500°C. contain very short wavelength composition modulations along (100) directions and static displacements of the atoms from their average sites. A computer simulation of the 50 at. % Pd alloy showed that the composition modulations in this alloy may be described more specifically as consisting of clusters of like atoms in the (100) planes with roughly “branohed rod” shapes. Within the clusters, like atoms are linked primarily by second nearest neighbor bonds. The detailed structure of the composition modulations in the 75 at. ‘A Pd alloy is quite similar to that in the 50 at. % Pd alloy, although the wavelength of the modulations is slightly longer. The deviation from randomness was small in the 25 at. % Pd alloy, but there was some evidence of a tendency to form one or two plane thick regions parallel to (106] ptanes within which the Iocal atomic arrangements tend toward ordering. The N-50 and -75 at. % Pd aIloys are quite responsive to heat treatment in the temperature range between 350 and 490°C. This was shown to be due to a decrease in the amplitudes of the composition
Lx??
ArjD
SPRUIELL:
STRUCTURE
modulations with increasing temperature within this range. This structural change is probably responsible for anomalous physical property results observed for these alloys, such as the anomalous rise in heat capacity of the X-50 at. % Pd alloy observed by Bingham and Brooks.tQ Alloys quenched from above about 490°C are essentially random but still exhibit large static atomic displacements from their average lattice sites. The Clapp-Moss approximate theory of pair correlations was applied to the Ni-50 at. % Pd results. The configurational enthalpy obtained agreed with t,he value estimated from the heat capacity data of Bingham and Brooks. The net interaction energy between second nearest neighbors was almost an order of magnitude larger than for first nearest neighbors in this alloy; thus it was concluded that for application to such systems, nearest neighbor theories are inadequate. ACKNOWLEDGEMENTS
The authors acknowledge with gratitude the help of R. 0. W~liams with the computer simulation and the many helpful discussions with R. 0. Williams, C. J. Sparks, J. E. Epperson and B. S. Borie. The support of this research by the National Aeronautics and Space Administration is appreciated.
OF
Xi-Pd
SOLID
SOLUTIONS
461
2. R. G. AHNAEV and S. YAZLIEV,Iza.Akad. ~Nauk turkmen. &S-R 6, 3 (1957). 3. YAZLIEV,Izv.Akad. Naul; turkmen. SSR, Ser. Fiz.-Teckh., Khim. i Geol Nauk 5, 14 (1961). 81, 1215 (1966). 4. A. NAGASA~~A,J.~~~~.SOC.J~?~~~ 5. L.R.BIDwELL~,~~ R. S~~1~~~,ActaMet.13,61(1965). and C. R. BROOKS,J. phys.Chem. Solids 6. R. E. BIXGHAM SO, 2365 (1969). 7. B. S. BORIE and C. J. SPARKS,JR.,Acta ~~~~l~gr. 17,827 (1964). 8. J. I@. COWLEY, .J. a&. Fhya. 15, 24 (1%50). AVERBACH and B. W.ROBERTS,J. 9. B.E.WARREN,B.L. appl. Phys. 22, 1493 (1951). Addison-Wesley 10. B. E. WARREN, X-ray Diffraction. (1968). 14,472 (1961). 11. B. S.BORIE,Acta crystallogr. 12. C. J. SPARKS, JR. and B. S. BORIE,Local Atomic Arrangements Studied by X-ray Lti,ffra&on, IvfetallurgicalSociety Conf. 36, editedbyJ.B. COHE~~~~~ J. E. HILLIARD,pp. 5-46. Gordon and Breach (1966). 13. B. S. BORIE and C. J. SPARKS,JR.,Actacrz&aElogr.to be published. 14. L. R. BIDWELL and R. SEISERP, Acta crystallogr. 17, 1473 (1964). 15. J.E. EPPERSON and J.E. SPRUIELL, J.phys.Chem.Solids 30, 1733 (1969). 16. WEE LIN, Ph.D. Dissertation, University of Tennessee (1969). 17. S. C. Moss, Local Atomic Arrangement8 Smudge by XT-ray ~~ffra~t~o~, ~et~llurgieal Societ.y Conf. 36, edited by J. B. COHEN and J. E. HILLIARD,pp. 95-122. Gordon and
Breach (1966). 18. S. C. Moss and B. L. AVERBACH, Small Angle Scattering, editod by IX. BRUMBERGER, pp. 336-350. Gordon and
Breach (1967).
19. P. C. GERLEN and J. B. COHEN, Phys. Rev. 139, AS44 (1966). REFERENCES 20. R. 0. WILLIAMS,ORNL Report T&I-2866 (1970). 1. E. HULTGREN and C. ZAPFFE, Tmns. Am. Inst..&I&. 21. P. S. RUDSIAN and B. L. A~ERBACE, Acta h-let. 5,65 (1957). 22. P. C. CLAPP and S. C. Moss, Pkys. Rev. 142, 418 (1966). E%gf% 183, 58 (1939).