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The influence of annealing on the electrical properties of cold-worked Ag-Pd alloys
THE
INFLUENCE PROPERTIES
OF ANNEALING ON THE OF COLD-WORKED Ag-Pd
WEI-KONG
CHENt
and
ELECTRICAL ALLOYS*
M. E. NICHOLSON7
The influence of annealing on the electrical resistivity and Hall constant of cold-worked silverp:~ll~ium alloys has been de~rmined. In addition, a study was nlade of t,he effect of cold working on the magnetic suscept,ibilit~ and thermoelectric power of t,hese alloys. Two processes occur during annealing. One causes an increase m resistivit,y. This appears to be due to a decrease in the number of conduction electrons as indicated by t.he Hall constant becoming more negative. This is attributed to the reestablishment of short-range order which is destroyed by cold working. The other process causes a decrease in resistivity. This is probably due to the elimination of lat&e defects, principally vacancies, which results in a reduction of electron scattering. These opposing processes are influenced to different degrees by the amount of prior plastic deformation and the annealing temperature. The magnetic suscteptibility of a 9.5 “/,and of a 41.8 oA Pd alloy is not appreciably altered by cold work. These alloys are diamagnetic and exhibit no change in magnetic susceptibility between -196OC and room temperature. The relative change in absolute thermoelectric power produced by cold working deviates negatively for all compositions from that of pure silver. These observations support the hypothesis that short-range order exists in the annealed alloys and that it is destroyed by cold working. The effect of short-range order on resistivity, Hall oonst~ant and thermoelectric power is discussed in terms of both Gibson’s theory and the supereone concept. INFLUENCE
D’IJN RECUIT ALLIAGES
SUR LES PROPRI~T.ES ELECTRIQUES Ag-Pd DEFORMES A FROID
DES
Les auteurs ont Btudie l’influence d’un recuit sur la resistivite Bleotrique et la constante de Hall d’alliages argent-palladium deform&s a froid. En outre, ils ont Btudie l’influence de la deformation a froid sur la susceptibilite magn&ique et, le pouvoir thermoelectrique de ces &ages. Deux processus ~tervienneI~t au tours du recuit. L’un d’eux provoque un accrois~ment de resistivite. Ce phenomene semble dO 8, une diminution du nombre des Qlectrons de conduction, ee qui est suggere par le fait que la constants de Hall devient plus negative. Ceci est attribui? a une reconstitution de l’ordre it petite distance qui est detruit par la deformation a froid. L’autre processus provoqua une diminution de resistivite. Ce phenomene est probablement d6 a l’elimination des defauts reticulaires, principalement des lacunas. Ces processus opposes sont influences a differents degres par le taux de deformation plastique et la temperatur de recuit , La eusceptibilite magnetique des alliages a 9,5 % et a 41,8 % I’d n’est pas modifiee de man&e a,ppreeiable par une deformation 8. froid. Ces alliages sont diamagn~tiqlles et ne montrent* pas de changement. de la susceptibility magnetique entre - 196°C et la temperature ambiante. La modification relat,ive produite par la deformation a froid sur le pouvoir therrno~le~t~~que absolu d&vie n~gativeme~t par rapport, a celle de l’argent pur, pour toutes les compositions. Ces observations appuient l’hypothese qu’il existe un ordre & petite distance dans les &ages recuits, et que oet ordre est detruit par la deformation a froid. Les auteurs discutent l’influcnee de l’ordre a petite distance sur la r&istivite, sur la con&ante de Hall et le pouvoir thermoelectrique, a la lumi&e de la thirorie de Gibson et du concept de la superzone. DIE
ANDERUNG
DER
E~~~~TRISCHE~
Rg-Pd.LEGIERUNGEN
EIGE~SC~,~FT~N VON BEIM ANLASSEN
K.~LTVERFORMT~N
Es wurde der EinfluIj des Anlassens auf den elektrischen Widerstand und die Hall-Konst,ante von kaltbearbeiteten Silber-Palladium-Legierungen bestimmt Zusatzlich wurde untersueht, wie die Kaltbearbeitung die magnotische Suszeptibilitat und die Thermokraft dieser Legierungen beeinfluflt. Zwei Prozesse laufen wiihrend des Anlassens ab. Der einu fiihrt zu einer Erhiihung des elekt,risohen Widerstandes. Dies schaint auf einer Abnahme der Zahl der Leitungselektronen zu beruhen, da die Hall-Konstante dabei starker nogativ wird. ills Ursache wird die Wiederherstellung der Nahordnung zmgesehen, die bei der Kaltbearbeitung zerstiirt wird. Der andere Prozess verursaeht eine Abnahme des ~Viderst~des. Diese beruht wahrscheinli~h auf dem VeI,s~hwinden von Gitterfehlern, haupts~~~~llich Leerstellen, und der damit verbundenen Verringerun~ der ~~ektrone~st.reuung. Diese gegenlaufigen Proeesse werden in verschiedenem MaBe durch die Starke der vorhergehenden plastischen Verformung und die Anlaatemperatur beeinfb&t~. Die magnetische Suszoptibilitiit von Legierungen mit 9,5 % bzw. 41,8 T/,Pd wird durch Keltbearbeitung nicht wesentlich geiind?rt. Diese Legierungen sind diamagnctisch und zeigen zwisehen - 196’C: und R~~umtemperatur keine Anderung der magnet&hen Suszeptibili~t. Die dureh die Kaltbear. beitung hervorgerufene relative Anderung der absoluten Ther~lokraft weicht van der des reinen Silbers lbei allen Zusammense~ungen in negativer Richung ab. Diese Beobachtungen stiitzen die Hypothese, da13 bei den gegliihten Legierungen Nahordnung vorhanden ist und da6 sie durch Kaltbearbeitung zerstiirt wird. Der Einflul3 der Nahordnung auf Widerstand, Hall-Konstante und Thermokraft wird einmal im Rahmen der Theorie von Gibson, sum andern auf der Grundlagc der Supsrzonen-Vorstellung diskutiert. * Received September 9, 1963. This paper is based on the Ph.D. thesis of W. K. Chen submitted to the Department Metallurgy in January 1963. j Department of metallurgy, University of Minnesota, Minneapolis, ~inr~esot~. ACTA
M~~~ALL~~RGICA,
VOL.
12, JUNE
1964
687
of
ACTA
68X
METALLURGICA,
1. INTRODUCTION
Plastic deformation in the electrical because
generally
resistivity
of the increased
fections.
However,
is observed.
melted in high purity recrystallized
conductors
in vacua by induction
of metallic number
alloys
of lattice
impereffect
have observed
the electrical
resistivity
decreases upon plastic deformation. A number of proposals for this effect.
have been made to account
et aZ.(7) proposed that a deformation dislocation a way
potential around a
produces local shifts of Fermi level in such
that
electrons
alloys, Logie
tbe
sd
is partly
scattering
of the
suppressed.
heating.
were made by rolling. were
annealed
contents
analysis. graphic spectrographically 0.01%
After forming,
at 800°C
were determined by A typical impurity showed the following:
Au O.OOl-O.Ol%,
Mg 0.001%.
produced the density
at this
alloys have suggested that the
Fermi distribution
by
cold
in interatomic
working,
which
may
of states near the top
of the
by a shift in the relative centers of
of the s-p and d-bands.
gravity
Si O.OOl%,
Actual analyses may be found in Ref. 9.
2.2. Electrical resistivity measurements
values of resistance
increase
The
spectroanalysis
Rh O.OOl-
Ca
in the study of Cu-Pd distances
the specimens
conduction
In arriving
is due to a change
were
8 hr in vacua.
for
using a standard potentiometric
effect
After homogenizing
made by swaging and wire drawing, and foil specimens
point, they have implicitly assumed the existence of vacant states in the d-band. Jaumot and Sawatzky(2) observed
metals were
alumina crucibles
one week at 900°C in vacua the wire specimens
palladium
From a study of Au-Pd
Mixtures of the constituent
an increase
in a few cases the opposite
binary
12, 1964
respectively.
produces
Several investigators’r-*)
that in some
VOL.
Aarts and Houston-
Electrical
resistivity
measurements
were obtained
drop across the specimen
through
the
specimen
was determined
drop across a Rubicon eliminate the junction
The
made
by measuring
potential
specimen.
were
method in which the the
and the current
current
through
the
by measuring the potential
standard resistor. potentials,
In order to
measurements
were
MacMillanc4) explained that the increased conductivity
also made with current reversed.
in the cold-worked
were set on a bakelite board and fixed at the ends by
in the number distortion
Ag-Pd
alloys is due to an increase
of conduction
of the Brillouin
deformation.
electrons zones
as a result of
caused
by plastic
Several other investigators(3~5~6~s) attri-
screws
on
the
current
The wire specimens
fixed separation.
The specimen
with the knife edges by leaf springs.
short-range
foil
Although
these investigators
processes for the explanation, is a certain fundamental
offer different
they all agree that there
change in electronic structure
of alloys which produces negative resistivity
atomic
change in electrical
upon cold working.
In order to develop
of the
possible atomic processes which are responsible
for the
effect, this series of studies has been made. involved electric
The work
a study of the effect of cold work on the Hall the magnetic
susceptibility
power of Ag-Pd
annealing
on
the
and the thermo-
electrical
temperature
resistivity
Ag-Pd
and
alloys.
electrons
2. EXPERIMENTAL
temperature.
and
cm.
Exact
less negative
by cold working.
Industries,
about
by
“clover-leaf”
thickness
of the specimen
The
300 A/cm2.
magnetic
as
primary
shaped
foil was
was measured density
magnet
indirectly
of protons,
using
is 5100 G.
of was
with 5-in.
pole gap was used.
calibrated
resonance
current
A permanent
and current measurements
Inc.
der
Mod. 1000 gage with the accuracy
pole pieces and l&in. strength,
van
Pauw,(lO)
The specimen thickness was about 5 x 10-a
METHODS
Engelhard
A
employed.
Alloys were prepared from 99.99+ % Ag and 99.9+ % Pd sponge obtained from American Platinum and Company
as
Hall
The effect
2.1. Specimen preparation
Silver
Milli-Microvoltmeter
suggested
This result indicates an increase in
the number of conduction
measure-
low thermal
specimen,
They observed that the
alloys becomes
six-dial
The Hall constant for these alloys was measured at room
2.5 x 1O-5 in.
of Ag-Pd
was immersed in
2.3. Hall constant measurements
Westerlund
Hall constant
a
null indicator.
by a Sheffield
with cold working.
using
Potential
ments were made by Rubicon
of cold work on the Hall constant has been reported by and Nicholson.(g)
bath.
with Keithly
made
In all measurements
the entire specimen holder assembly the constant
In the case of
were
of van der Pauw.o”)
with a
of
alloys and the influence
constant of the cold-worked
method
measurements
potentiometer
a further understanding
constant,
specimen,
potential
contacts
was held in contact
bute this effect to the change in the degree of atomic order upon plastic deformation.
The
terminals.
probes were stainless steel knife-edge
The field nuclear Potential
were made using the same
equipment used for electrical resistivity measurements. For accurate measurements of the Hall voltage, the spurious potentials due to Nernst effect and RighiLeduc effect were eliminated by making measurements
CHEN
APU‘I>
NICHOLSON:
EL~G~~~ICAL
PROPERTIES
with primary current reversed. The potentials due to IR drop were eliminated by reversing the magnetic field.
The magnetic susceptibility was measured by the Gouy method. The force on the specimen induced by magnetic field was measured by a modified Ainsworth Chainom~~tic balance. The details of the balance are described elsewhere.(n) During th.e measurement the entire balance assembly and specimen were kept in ~~~0. The possible error in force measurement was estimated to be & 1%. A Varian electromagnet with 4-in. pole pieces was used. The magnetic field at the center of the pole pieces was eali~~ratedas a function of exciting current indirectly by the nuclear magnetic resonance of protons. Correct8ions for possible ferromagnetic impurities were made by Honda’s method in whioh the true Sus~eI~t~bilitywas found by plotting values of apparent susceptibility against the corresponding values of reciprocal field strength, and extrapolating the plot to infinite field. The method of least squares was used for the extrapolation.
Wire spee~me~s ranging from 0.2 to 0.3 mm dia. with various degrees of cold working were spot welded to annealed 0.3mm dia. copper wires. The copper wires were drawn from spectrographic grade oopper rod of 99.999 *%purity obtained from American Smelting and Refining Company. A copper-constantan thermocouple which was calibrated at three points, i.e. liquid nitrogen, a slush of solid carbon dioxide and acetone mixture, and melting point of ice, was used for all measurements. One junction of the speeimen couple was immersed in an ice bath and the other junction with the calibrated thermocouple was placed in the small hole at the center of an aluminium block. The aluminium block was fitted into the Dewar-flask, and its temperature was allowed to rise slowly from - 196°C to room temperat~lre. The warming rate was about 25”C/hr. Alternate reading of copper-constantan e.m.f. and that of the specimen with respect to copper were made at five to ten degree intervals. The e.m.f.s were measured using the instruments mentioned above. The thermoelectric power relative to copper was obtained from the slope of the thermal e.m.f. of the specimen against temperature. The relative thermoelectric power was converted to absolute thermoelectric power using the values of the absolute thermoelectric power of copper given by Borelius.us)
OF
CO~~~W~Rl~~D
Ag-Pd
ALLOYS
6s9
2.6. Ann~~~~n~of ~~~-~~r~~~ specimens The recovery behavior of electrical ~esistivity and Hall constant was studied on the cold-worked Two types of annealing, isochronal specimens. annealing and isothermal annealing, were employed. In isochronal annealing, the cold-worked wire specimens were annealed for 30 min at successively higher telnperatur~a and then quenched to room temperature. The annealing was made in a water bath for tem~ratures up to 100°C and in a silicone oil bath for temperatures between 100°C and 275% Higher temperature annealing was performed in a furnace where the specimen was protected by a puri~ed helium gas atmosphere. In isothermal annealing, the specimens were annealed for various times at 3OO”C, 350°C and 400°C. The cold-worked wire specimens were annealed in a neutral salt bath where specimens were protected in vacua. After annealing for a certain period of time, the specimen was quenched to room temperature and the resistivity was measured at 0°C. The cold-rolled foil s~~imens were annealed in a furnace with helium atmosphere. The Hall constant and resistivity of foil specimens were measured at room temperature. 3, EXPERIMENTAL
RESULTS
3.1. The effect of cold work on the magnetic s~~ce~t~b~l~t~ Since change in the d-band structure by cold working has been suggested(‘) as a cause of the anomalous resistivity effect, the effect of cold work on the magnetic susceptib~ity was studied, Results of this measurement for two alloys, 9.5 % Pd and 41.8 % Pd, are shown in Table 1. measurements were made at both room tem~rature and liquid nitrogen temperature using fields ranging from 6160 to 7800G. The specimen was deformed by wire drawing at room temperature in the case of 9.5 % Pd alloy and by simple tension at liquid nitrogen temperature for 41.8% Pd alloy. The results in Table 1 show no appreciable effect on magnetic susceptibility due to cold working. The difference in the observed values is within the experimental error (ri; 1 ‘A). In addition, since the susceptibility is temperature independent, it may be concluded TABLE 1. Ma~atic mass susceptibil~t~~of Ag-Pd aIIoys at annealed and cold-warkad states (in c.g.s. units times 106) ---._.““_c_ Temp. R.T. - 196°C R.T. -196°C \Alloy __-._-Au&led 22 % R.A. --._ 9.5% Pd -0.176 -0.177 -0.173 -0.177 .l_l..__-__X_.I.-___l.ll_____.. Annealed 9 % B.A. ___41.3% Pd -0.172 -0.169 -0.171 -0.170 ---.-l___l___
690
ACTA
that there is no component magnetism,
characterized
inversely proportional
of palladium
and since it was temperature
completely
by cold
independent,
that in these alloys, both in the
filled.
Therefore,
state, 4d-band the
theoretical
based on the change in s-d scattering
for the anomalous
resistivity
work is not applicable
behavior
to the Ag-Pd
3.2. InJluence of annealing
due to cold
1 illustrates
on the electrical resistivity
the resistivity,
12,
increases.
1964
Finally,
liquid
nitrogen
I
I
I
39.0-
deformation,
41.8 % Pd ,/f
-
sition
range from
absolute
at liquid
change
deformed
!I.8
y
!I.6
5 0
specimens
z 0 CD ‘0
!I.4 !I.2
v-
16.2
respectively
The resistivity
temperature. in
specimens
temperature
generally
work.t4)
at room temperature
but these specimens
after
the
final extension
were brought
show a larger
same
strain.
at liquid
for
about
18 hr.
and The
were made again at liquid
temperature.
resistivity
was observed except for pure silver.
No about
significant 40%
change
in
In the
of the increase
in
was recovered. the
anomalous mainly
The
nitrogen
nitrogen
case of pure silver,
The
show less
to room temperature
temperature
measurements
The
the
of previous
for
at by
41.8%
effect
Pd
(Fig.
concentrated
alloy
shows
the
l), the annealing on
this
greatest
study
was
composition.
Wire specimens for the annealing studies were deformed by
t
wire drawing
10.8 Q
and foil specimens
by rolling at room
temperature. Figure 2 shows the change in resistivity
10.6
of a cold-
worked 41.8 ‘A Pd alloy (9 % R.A.) after heating for 30
10.4
6.2
nitrogen
in resistivity
resistivity
of
b I I.0
16.0
nitrogen
the results
at that
Since
?I.0
16.4
at and
Pd were deformed
resistivity
deformed
resistivity ,
in
at liquid
with
kept 38.6
0 to 54%
simple tension up to 2OoA elongation.
temperature,
!2.0
38.8
tension
two sets of the specimens in the compo-
specimens,
12.2
specimens
by simple
liquid nitrogen and room temperature
decrease
75 % Pd
values.
measured resistivity at that temperature. In order to compare the effect of the temperature
agrees
p, at 0°C as a
the annealed
They deformed
temperature
strain hardening,
39.2
it exceeds
This behavior is similar to that observed by Aarts and
was measured
alloys.
and Hall constant of cold-worked alloys Figure
VOL.
Houston-MacMillan.(4)
was not changed
annealed state and in the cold-worked is
being
to temperature.
it may be concluded
interpretation
type para-
by its susceptibility
Since the susceptibility working,
METALLURGICA,
min at successively 6.0
The resistivity
higher temperatures
recovers
as indicated.
in two steps.
It increases
gradually as a result of heating at above room temperature.
5.6 20
IO
0
30
PERCENT FIG. 1. Resistivity
function
40
50
REDUCTION
7;R.A. for five alloys.
The resistivity temperature.
the
resistivity
90
the
100
in cross-sectional
250°C
increase and
takes place in
375°C
(step
I).
A
area,
was also measured The absolute
at
change in
at 0°C.
is All
except the 75 ‘A Pd alloy, qualitatively same
between
of cold-drawing
the same as that measured resistivity
decreases
The most significant
range
AREA
measured at liquid nitrogen temperature
compositions, show
IN
80
A,, - A = ~ x 100, -%I
liquid nitrogen essentially
70
plotted as a function for Ag-Pd alloys.
of percent reduction
resistivity
60
behavior.
First,
for a strain of about 20%
the R.A.
and then increases as the degree of plastic deformation
-U)r
0
100
200 ANNEALING
300
400
TEMPERATURE,
500
600
700
“C
FIG. 2. Change in resistivity resulting from a 30 min isochronal annealing of a Ag-41.8 % Pd alloy cold-drawn 9% R.A. Ap = p - pO, where p = measured resistivity and p,, = resistivity of fully annealed alloy.
CHEX
AND NICHOLSOX:
ELECTRICAL
PROPERTIES
ANNEALING
TIME,
OF
COLD-WORKED
Sg-Pd
ALLOYS
691
MIN.
Change in resistivity resulting from isothermal annealing of a Ag-41.8 % 0 where p = measured resistivity and Pd alloy cold-drawn 9 % R.A. ap = p p0 = rosistivity of fu Ply annealed alloy. FIG.
3.
maximum, which is above annealed value, is reached at about 375°C. Above this temperature resistivity decreases (step II) and finally reaches the annealed value at about 450°C. Raot13) made a similar study on a Ag-40% Pd alloy. His results were essentially the same as those shown in Fig. 2. Specimens with the same thermal and mechanical history as those above were annealed isothermally at 305°C and 355°C. Figure 3 shows that at 355°C the resistivity first increases with time and after reaching a maximum, decreases asymptotically toward the annealed value. At 305”C, no maximum is observed. The resistivity increases continuously for the duration of the test (170 hr). This behavior indicates that in this temperature range there are two processes occurriu~, i.e. one tends to increase the resistivity, and the other to decrease the resistivity. The observed behavior appears to be a consequence of the differential effect of two processes. Figure 4 shows the
similar isothermal annealing of the 41.8% Pd alloy cold-reduced to 32% R.A. The resistivity recovery behavior is similar to Fig. 3 at 305°C and 350°C. At 395°C the rates of two processes are sufficiently equal, so that no distinct maximum is observed. In heavily deformed specimens the resistivity is proportionally higher than in the lightly deformed specimen, as shown in Fig. 1. The cold-worked resistivity generally exceeds the annealed resistivity at about 40-50x R.A. For example, the resistivity in the 41.8 % Pd alloy after 87 % R.A. is more than 3 % greater than its annealed value. Upon isothermal annealing at 300400% the resistivity of this specimen was observed to decrease continuously (Fig. 5). The rate of recovery decreased initially with time, then increased and finally again decreased. This indicates that, in addition to a process which causes a decrease in resistivity there is a second process occurring which tends to increase the resistivity. The decrease in
20 Ag- 41.0 x X R.A. = 32
w
0
303*c
x A
350.C 395’C
0’
z ;I0 1
/
’ ’ ’ ““” ’ ’ “““’ ’ ’ ’ ““” ’ ’ ‘rlrid 10000 100
ANNtiLING
TIME,
1000
MIN.
FIG. 4. Change in resistivity resulting from isothermal annealing of a ilg-41.8 % Pd alloy cold-drawn 32% R.A. Ap = p - pO.
ACTA
092
METALLURGICA,
VOL.
12, 1964
60 z ..
-30
x k
420
FIQ. 5. Change in resistivity resulting from isothermal annealing of a Ag-41.8 %
Pd alloy cold-drawn 87 % R.A. Ap = p - pO.
resistivit~
occurs
more rapidly
in the heavily
cold-
worked alloys because the high cou~entrat~on of defects in the cold-worked alloys accelerates the rate of annihilation of these defects as in recovery. During these thermal treatments no softening occurs, In fact, no s~gn~cant softening occurs below about 550°C. Thus it appears that the processes associated with the recovery of electricaf resistivity do not. involve significant dislocation rearrangement. Instead they must involve either short range solute diffusion and/or vacancy migration and annihilation. The hypothesis that two processes are occurring during annealing of the bold-worked specimen is
supported by the simultaneous study of the recovery behavior of resistivity and Hall constant in coldrolled foil specimen. Figures 6 and 7 show the plot of electrical resistivity, p, and Hall constant, R, in terms of annealing time for isothermal annealing at 350°C of cold-rolled (30 % R-A.1 21.4% Pd and 41.8 % Pd alloys respectively. In these measurements the absolute value of p and R may be in error of the order of 1 ‘A due to error in specimen thickness measurements. However? uncertainty in the relative value measured on one specimen would not exceed 0.05% for p, and 0.1% for R. In both cases the resistjvity versus time shows a maximuu~ as does the
FIG. 6. Resist;tivity(p) and Ha.11constant (R) of a Ag-21.4% Pd alloy cold-rolled 30 % R.A. platted a.3 a function of annealing time at 350°C.
CHEN
P*‘ICHOLSON:
AND
ELECTRICAL
PROPERTIES
OF COLD-WORKED
Ag-Pd
ALLOYS
693
.o -
3
-
5 -
T>. 61. c.,
ANNEALING FIG.
wire specimen
(Figs. 3-5).
Hall
becomes
constant
On the other hand,
increasingly
time and tends to approach
resistivity
MIN.
negative
to a constant
the with
value after
predicted
that the relative change in absolute thermo-
electric power is equal to the relative electrical resistivity. sensitive
prolonged annealing. The result supports observed
TIME,
Resistivity (p) and Hall constant (R) of a Ag-41.8 % Pd alloy cold-rollecl 30% R.A. plotted as & function of annealing time at 35O’C.
7.
the
explanation
behavior
that
the
is due to the combined
effect of two processes having opposite
effects on the
process quite
to
the
detailed
nature
as well as electronic sensitive
change in the
Since the thermoelectric of the
structure,
to the atomic
power is scattering
it should
Rrrangement
alloys.
One process which is predominant resistivity. during the first step of the isochronal recovery of the
for pure silver and five alloys
electrical
is
cold-worked
one which causes a change in the Hall constant.
A
21.4 % Pd and 41.8 % Pd, the thermoelectric
possible
of
was measured as a function
resistivity process
short-range
(i.e. the increase in resistivity)
involved
order
which
state and was destroyed Since
there
is no
is a re-establishment existed
in
the
appreciable
effect
on
The absolute
annealed
in the course of cold working. the
Hall
of
in arrangement
second
step of the isochronal
resistivity fact
recovery
(i.e. the decrease in resistivity)
the annihilation The
of constituent
atoms
in the
The other process which dominates
of the excess vacancies
that
this process
is not
the
of electrical is probably in the lattice.
accompanied
by
R.A.)
power
was mea,sured
in the annealed
conditions.
power, X,, of annealed of composition
Taylor
and
Coles. u7)
dependence
by cold working.
In
all
compositions
Figure 9 illustrates the temperature
of S for two typical alloys, 21.4 % Pd and
41.8 % Pd.
It is interesting
produces
to note that cold working
no change on the S for the 21.4 % Pd alloy
in the temperature
range studied.
the relative change in thermoelectric
Figure
power
10 shows
power, AS//X,,],
at 0°C as a function
on the thermoelectric
the
dependence
pure silver, 21.4 % Pd and 41.8 % Pd.
work
in
of S is only slightly altered
have little effect on the Hall constant. of cold
power
of cold work.
change in the Hall constant implies that the vacancies
3.3. The effect
and
For two alloys,
Fig. 8. It shows an excellent agreement with the work temperature
change
(90%
The absolute thermoelectric
constant upon cold working or subsequent annealing of
solid solution.
thermoelectric
alloys at 0°C is plotted as a function
pure metals,(14~i5) this effect must originate
from the
be
in the
of percent reduction
in area for Some of the
data for pure silver are calculated from the results of Druyvesteyn and Menson, and plotted for compari-
Cold working usually causes a positive change in thermoelectric power of pure metals. Hirone and
son.
Adachiu6)
against composition in Fig. 11. A&‘/lfl,l produced by cold working for all alloys deviates negatively from
have
estimated
the
change
in thermo-
electric power due to cold working, based perturbing potential of an edge dislocation.
on the They
The
A&‘/l~5’,1 at 0°C due to 90%
the value
of pure
silver.
R.A.
The maximum
is plotted
negative
ACTA
694
I
I
I
I
I
(
METALLURGICA,
dislocation
I
1
I
VOL.
I-“,
1964
contribution,
IO 0
THIS
WORK
x
TAYLOR
From the foregoing
l----t-
best be explained alloys. Positive
u 8
X-ray
Measurement
-20
evidence alloys
probably
because short-range measurable these
-30
reason
due
factors
a diffuse
tion.
However,
Recently, IO
Ag
30
20
40
50
60
70
00
90
Pd
ATOMIC PERCENT PALLADIUM FIG. 8. Absolute thermoelectric power (S,) of annealed Ag-Pd alloys at 0°C plotted as a function of composition. is observed
studied.
negatively suspect tions
in the 41.8 % Pd among
Since
from
AS/jS,l
that
for
that any positive
and other
working
must
lattice be
alloys suggested
for all alloys
pure
silver,
defects
deviate
one
opposed
resulting
by
other
would
from
sensitive means of detecting
cold
phenomena
in their study
that thermoelectric
increasingly
the
change in S due to disloca-
affecting S. Jaumot and Sawatzky,@)
became
has never
-
-3
‘1.
the
similarity
For this
This could
these
in a part of this investiga-
order
may
occur
in this
and Nicholson,(21) I
I
system.
using
I
X-ray
I
(01 Ag-21.4%
Pd
-
“1.
t.z n-4
-
0
;
.\,.
a-5 I v)
\ -6
‘\,,
-
-7 -190
I -160
of Cu-Pd
‘;\
I
I -120
-60
-40
TEMPERATURE,
“C
0
power could be a
0 %
case.
study
They found that S as a function of cold
exhibit short-range
that the destruction
of
atomic of
o
latter
the
order.
negative
Hyatt,t3)
scattering
of
scattering
working in both ordered and quenched samples, which and
attempted
X-ray
presumably Klokholm
been
of silver and palladium.
I
-2
reported.
: a
deviation alloys
to
Copeland
-I
order in
been
one may infer from thermodynamic
data(rgysO) that -5C
never
order would have little effect, if
alloys was not undertaken
-
order in the
for short-range
has
at all, on the diffuse X-ray
alloys
scattering -4c b
results, it appears
in terms of short-range
silver-palladium
* . up
experimental
that the primary effect of cold work on the electrical resistivity of silver-rich silver-palladium alloys can
-10
$
change
4. DISCUSSION
ETAL.
0
y
and the net negative
in S is observed.
order as suggested by
with
less
change
be interpreted
of both
range order tend to produce
as indicating
long-range a negative
in the
AS
ANNEALED R.A.
= 9.4
= %R.A.
= 30
x % R.A.
= 90
and shortchange in S.
Our 41.8 % Pd alloy exhibits similar behavior to their results, S in 32.8% negative
Pd and 76% Pd alloys also show
change by heavy deformation.
The present
result can be explained
that the effect of dislocations
by assuming
and other lattice defects
tend to cause a positive change in S, while the effect of the destruction of short-range order tends to produce a negative change in S. In alloys with dilute concentration of solute, dislocation contribution dominates over the short-range order effect. In the high alloy range,
short-range
order
effect
dominates
over
the
-20 -22
’ -160
I -160
I -120
I
I -60
TEMPERATURE,
-40
0
-2
FIG. 9. Absolute thermoelectric power (S) of Ag-21.4% Pd and Ag-41.8 % Pd alloys after various degrees of cold work. In the 21.4 ‘A Pd alloy the thermoelectric power was independent of the degree of cold work.
CHEN
30
_
I
I
. 20
ELECTRICAL
AND NICHOLSON:
Ag
1
I
I
(~RUYVESTEYN
A
Ag- 9.5%
x
Ag - 21.4%Pd
o
Ag -41.6%
PROPERTIES
I
1
OF
COLD-WORKED
atomic distribution
I
I’d
and
also
that
in
by
Slater(24) new
superlattice,
superzone)
boundaries
first Brillouin
IO
and
with the
Nicholas(26)
Brillouin
are formed
the extra Bragg reflections.
Pd
695
It was first pointed out by Muto@)
discussed a
ALLOYS
can also be understood
superzone concept.
ETAL.)
Ag-Pd
zone
(i.e.
corresponding
to
As a result, the original
zone characteristic
of random
distri-
bution of atoms is split into two or more superzones.
8
The density
m
of states curves, N(E)
istic of the original first Brillouin
go
be replaced
is 4
by a density
vs. E, characterzone will therefore
of states curve made up of
two or more zones having over-lapping Disordering
-10
the atomic arrangement
is equivalent
to destroying
energy levels.
by cold working
the superzone
structure.
If the Fermi surface lies well inside the Brillouin zone -20
boundary
for
superzone,
the destruction
effective -30
I
IO
0
I
I
I
I
I
I
I
I
20
30
40
50
60
70
60
90
PERCENT
REDUCTION
bute 100
IN AREA
the random
number
existence
of
Au40% alloy
short-range
Pd was
techniques,
alloy.
Since gold.-palla,dium vity
behavior
order
The
effectively
demonstrated in
short-range
destroyed
to that found
cold
The
same
model
struction
of short-range
this system, the
behavior
concept
resistivity
of
behavior
“‘7
30
Muto,(s3)
order may
solution
depending
position
and Brillouin
zone boundary
and for the superlattice.
solid
between for the
random
lattice
extimate
based on the electronic structure proposed by
Mott(26) and short-range
IO
Slater(24) and
that the short-range
on the relative
may
of Gibson(22) or
of a binary
-10
A rough
the thermoelectric
as energy dependence
r2k2T 1
al
Ziman,(2s) power,
X,
of mean free
1 aA,
m+laaE:
’
I
(1)
> E=Ep
F
’
order parameter measured by
with short-range order for Ag,Pd alloy. destruction of short-range order by cold decrease in the resistivity.
The change in electronic structure which produces the change in the conduction process due to change in
‘:I \
-20
Cowley(27) for Cu,Au quenched from 500°C shows that the Gibson’s theory predicts an increase in
working produces
the observed
Following
2C
or increase the resistivity
resistivity Therefore,
The
path and area of the Fermi surface, i.e.
order exists in
decrease
surface
measurement.(s)
power.
in the silver-palladium
that short-range
Nicholas.(25) Gibson(2J) predicted
Fermi
and contri-
in this
a similar resisti-
in terms of the theory
superzone
the
order present in the annealed
the anomalous
be explained
metal
can be expressed
has the same origin, i.e. the de-
alloys. On the assumption
to
This has been
can also explain
change in thermoelectric
working.
system, one may assume that the anomalous in the two systems
the
annealed
order
by
alloys exhibit
the
close
electrons
in resistivity.
by the Hall effect
in an isotropic scattering
and
Hall constant becomes less negative upon cold working.
FIG, 10. Relative change in absolute thermoelectric power of Ag and Ag-Pd alloys at 0°C plotted as a function of the degree of cold work (reduction in area).
diffuse
of conduction
to the decrease
confirmed
state
of order will increase the
; FLt
k
I
‘_
-3c Ag
IO
20
ATOMIC
30
40
/I
I’
50
PERCENT
60
70
80
90
Pd
PALLADIUM
FIG. 11. Relative changes in absolute thermoelectric power of cold-worked (90% R.A.) Ag-Pd alloys at 0°C plotted as a function of composition.
ACTA
696
METALLURGICA,
where E’, is the energy on the Fermi surface, 1 is the electron and A,
mean free path of the conduction
is
the area of the Fermi surface. the
more
energetic
should
electrons
easily scattered than the slow ones. would
depend
on the relative
be
between
the
zone boundary.
In
state the first Brillouin zone boundary
considered
However, touch
to
be
Since there is no
spherical.
of the Fermi
Therefore,
surface
boundary
a In a,,./aE is negative spherical
in such a way that
or less positive
Th us, S in the ordered
case.
negative
than in the disordered
picture,
the negative
state.
deviation
than
the
state is less Based on this
of S due
to
cold
working could be explained. In addition
to providing
the short-range
order
experimental
hypothesis
two
support
system.
proposed
for
of the fore-
going results tend to cast doubt upon the validity the hypothesis
of
by Logie et al. for the Ag-Pd
Implicit in their hypothesis
is the assumption
that vacant states exist in the d-band of these alloys. The
magnetic
Ag41.8
susceptibility
% Pd alloys
of Ag-21.4
% Pd
shows no indication
and
of vacant
states in the d-band either before or after deformation. Second,
the
recovery
of
occurs in a temperature far
below
recovery
the
the
annealed
resistivity
range of 250-375°C
temperature
at
which
which is
mechanical
occurs (550°C). 5. CQNCLUSIONS
From annealing studies of Ag-Pd alloys it is concluded that the anomaly in the electrical resistivity change accompanying Ag-Pd
alloys
short-range supported
cold working in the silver-rich
can best be explained in terms of a This postulate is order mechanism.
by
measurements
of
Hall
and
short-range
thermoelectric
order
on
power.
the electronic
of these alloys can be explained in terms of
both Gibson’s
theory and the superzone
concept.
ACKNOWLEDGMENTS
The authors are indebted to the U.S. Atomic Energy Commission contract
for
its
support
of
this
work
under
AT-11-l-1009.
The authors wish to thank Professor J. M. Sivertsen for many helpful discussions.
energy
area is positive.
in the ordered state, the Fermi surface may
the superzone
of
be less
between the two, the Fermi surface may
dependence
12, 1964
susceptibility
effect
The second term
lies well outside the Fermi surface. interaction
be positive
would
position
Fermi surface and the Brillouin the disordered
magnetic The
conduction
The first term in the bracket since
VOL.
constant,
REFERENCES 1. J. 0. LINDE, AppZ. Sci. Res., Hague B4, 73 (1954).
2. F. E. JAUMOT, Jr. and A. SAWATZKY, Acta Met. 4, 127 (1956). 3. E. KLOKROLM and B. HYATT, Trans. Amer. Inst. Min. (Metall.) Engrs. 215,792 (1959). 4. W. H. AARTS and A. S. HOUSTON-MACMILLAN,Acta Met. 5, 525 (1957). 5. B. M. KOREVAAR, Acta Met. 6, 572 (1958). 6. J. H. AALBERTS, Acta Met. 9, 894 (1961). 7. H. J. LOQIE, J. JACKSON, J. C. ANDERSON and F. R. N. NABARRO, Acta Met. 9, 707 (1961). 8. W. KOSTER and T. HALPERN, 2. Met&k. 52, 821 (1961). 9. R. WESTERLUND and M. E. NICHOLSON, to be published. 10. L. J. VAN DER PAUW, Philips Res. Reports 13, 1 (1958). 11. W. K. CHEN, F. B. KOCH and J. M. SIVERTSEN,Rev. Sci. Instmm. 32, 1157 (1960). 12. G. BORELIUS, Handbuch der Metallphysik I Der Metallisch Zustand der Materie, Leipzig (1935). 13. K. K. RAO, Acta Met. 10,900 (1962). 14. B. WIENER and G. GROETZINGER,J. AppZ. Phys. 23, 441 (1952). 15. W. K~STER and W. SCH~~LE,2. MetaZZk. 48, 634 (1957). 16. T. HIRONE and K. ADACHI, Sci. Rep. Res. Inst. Tohoku Univ. A3, 454 (1951). 17. J. C. TAYLOR and B. R. COLES, Phys. Rev. 102,27 (1956). 18. M. J. DRUYVESTEYN and H. MENSON, AppZ. Sci. Res., Hague 4B, 388 (1954). 19. J. P. CHAN, P. D. ANDERSON, R. L. 0~~andR. HULTQREN, Technical Report Mineral Res. Lab. University of California ( 1959). 20. R. ORIANI and W. K. MURPHY, Actn Met. 10,879 (1962). 21. W. D. COPELAND and M. E. NICHOLSON, to be published. 22. J. B. GIBSON, J. Phys. Chem. Solids 1,27 (1956). 23. T. MUTO, Sci. paper Inst. Phys. Ghem. Res., Tokyo 34, 377 (1938). 24. .?. C.’ %&ER, Phys. Rev. 84, 179 (1951). 25. J. F. NICHOLAS, Proc. Phys. Sot. Lond. A68, 201 (1953). 26. N. F. MOTT, Proc. Phvs. Sot. Lond., A47, 571 (1936). 27. J. M. COWL~Y, J. ApjZ. Phys. 21, 24 (1950). 28. J. M. ZIMAN, EZectrons and Phonons, Oxford University Press, London (1960).
INFLUENCE PROPERTIES
OF ANNEALING ON THE OF COLD-WORKED Ag-Pd
WEI-KONG
CHENt
and
ELECTRICAL ALLOYS*
M. E. NICHOLSON7
The influence of annealing on the electrical resistivity and Hall constant of cold-worked silverp:~ll~ium alloys has been de~rmined. In addition, a study was nlade of t,he effect of cold working on the magnetic suscept,ibilit~ and thermoelectric power of t,hese alloys. Two processes occur during annealing. One causes an increase m resistivit,y. This appears to be due to a decrease in the number of conduction electrons as indicated by t.he Hall constant becoming more negative. This is attributed to the reestablishment of short-range order which is destroyed by cold working. The other process causes a decrease in resistivity. This is probably due to the elimination of lat&e defects, principally vacancies, which results in a reduction of electron scattering. These opposing processes are influenced to different degrees by the amount of prior plastic deformation and the annealing temperature. The magnetic suscteptibility of a 9.5 “/,and of a 41.8 oA Pd alloy is not appreciably altered by cold work. These alloys are diamagnetic and exhibit no change in magnetic susceptibility between -196OC and room temperature. The relative change in absolute thermoelectric power produced by cold working deviates negatively for all compositions from that of pure silver. These observations support the hypothesis that short-range order exists in the annealed alloys and that it is destroyed by cold working. The effect of short-range order on resistivity, Hall oonst~ant and thermoelectric power is discussed in terms of both Gibson’s theory and the supereone concept. INFLUENCE
D’IJN RECUIT ALLIAGES
SUR LES PROPRI~T.ES ELECTRIQUES Ag-Pd DEFORMES A FROID
DES
Les auteurs ont Btudie l’influence d’un recuit sur la resistivite Bleotrique et la constante de Hall d’alliages argent-palladium deform&s a froid. En outre, ils ont Btudie l’influence de la deformation a froid sur la susceptibilite magn&ique et, le pouvoir thermoelectrique de ces &ages. Deux processus ~tervienneI~t au tours du recuit. L’un d’eux provoque un accrois~ment de resistivite. Ce phenomene semble dO 8, une diminution du nombre des Qlectrons de conduction, ee qui est suggere par le fait que la constants de Hall devient plus negative. Ceci est attribui? a une reconstitution de l’ordre it petite distance qui est detruit par la deformation a froid. L’autre processus provoqua une diminution de resistivite. Ce phenomene est probablement d6 a l’elimination des defauts reticulaires, principalement des lacunas. Ces processus opposes sont influences a differents degres par le taux de deformation plastique et la temperatur de recuit , La eusceptibilite magnetique des alliages a 9,5 % et a 41,8 % I’d n’est pas modifiee de man&e a,ppreeiable par une deformation 8. froid. Ces alliages sont diamagn~tiqlles et ne montrent* pas de changement. de la susceptibility magnetique entre - 196°C et la temperature ambiante. La modification relat,ive produite par la deformation a froid sur le pouvoir therrno~le~t~~que absolu d&vie n~gativeme~t par rapport, a celle de l’argent pur, pour toutes les compositions. Ces observations appuient l’hypothese qu’il existe un ordre & petite distance dans les &ages recuits, et que oet ordre est detruit par la deformation a froid. Les auteurs discutent l’influcnee de l’ordre a petite distance sur la r&istivite, sur la con&ante de Hall et le pouvoir thermoelectrique, a la lumi&e de la thirorie de Gibson et du concept de la superzone. DIE
ANDERUNG
DER
E~~~~TRISCHE~
Rg-Pd.LEGIERUNGEN
EIGE~SC~,~FT~N VON BEIM ANLASSEN
K.~LTVERFORMT~N
Es wurde der EinfluIj des Anlassens auf den elektrischen Widerstand und die Hall-Konst,ante von kaltbearbeiteten Silber-Palladium-Legierungen bestimmt Zusatzlich wurde untersueht, wie die Kaltbearbeitung die magnotische Suszeptibilitat und die Thermokraft dieser Legierungen beeinfluflt. Zwei Prozesse laufen wiihrend des Anlassens ab. Der einu fiihrt zu einer Erhiihung des elekt,risohen Widerstandes. Dies schaint auf einer Abnahme der Zahl der Leitungselektronen zu beruhen, da die Hall-Konstante dabei starker nogativ wird. ills Ursache wird die Wiederherstellung der Nahordnung zmgesehen, die bei der Kaltbearbeitung zerstiirt wird. Der andere Prozess verursaeht eine Abnahme des ~Viderst~des. Diese beruht wahrscheinli~h auf dem VeI,s~hwinden von Gitterfehlern, haupts~~~~llich Leerstellen, und der damit verbundenen Verringerun~ der ~~ektrone~st.reuung. Diese gegenlaufigen Proeesse werden in verschiedenem MaBe durch die Starke der vorhergehenden plastischen Verformung und die Anlaatemperatur beeinfb&t~. Die magnetische Suszoptibilitiit von Legierungen mit 9,5 % bzw. 41,8 T/,Pd wird durch Keltbearbeitung nicht wesentlich geiind?rt. Diese Legierungen sind diamagnctisch und zeigen zwisehen - 196’C: und R~~umtemperatur keine Anderung der magnet&hen Suszeptibili~t. Die dureh die Kaltbear. beitung hervorgerufene relative Anderung der absoluten Ther~lokraft weicht van der des reinen Silbers lbei allen Zusammense~ungen in negativer Richung ab. Diese Beobachtungen stiitzen die Hypothese, da13 bei den gegliihten Legierungen Nahordnung vorhanden ist und da6 sie durch Kaltbearbeitung zerstiirt wird. Der Einflul3 der Nahordnung auf Widerstand, Hall-Konstante und Thermokraft wird einmal im Rahmen der Theorie von Gibson, sum andern auf der Grundlagc der Supsrzonen-Vorstellung diskutiert. * Received September 9, 1963. This paper is based on the Ph.D. thesis of W. K. Chen submitted to the Department Metallurgy in January 1963. j Department of metallurgy, University of Minnesota, Minneapolis, ~inr~esot~. ACTA
M~~~ALL~~RGICA,
VOL.
12, JUNE
1964
687
of
ACTA
68X
METALLURGICA,
1. INTRODUCTION
Plastic deformation in the electrical because
generally
resistivity
of the increased
fections.
However,
is observed.
melted in high purity recrystallized
conductors
in vacua by induction
of metallic number
alloys
of lattice
impereffect
have observed
the electrical
resistivity
decreases upon plastic deformation. A number of proposals for this effect.
have been made to account
et aZ.(7) proposed that a deformation dislocation a way
potential around a
produces local shifts of Fermi level in such
that
electrons
alloys, Logie
tbe
sd
is partly
scattering
of the
suppressed.
heating.
were made by rolling. were
annealed
contents
analysis. graphic spectrographically 0.01%
After forming,
at 800°C
were determined by A typical impurity showed the following:
Au O.OOl-O.Ol%,
Mg 0.001%.
produced the density
at this
alloys have suggested that the
Fermi distribution
by
cold
in interatomic
working,
which
may
of states near the top
of the
by a shift in the relative centers of
of the s-p and d-bands.
gravity
Si O.OOl%,
Actual analyses may be found in Ref. 9.
2.2. Electrical resistivity measurements
values of resistance
increase
The
spectroanalysis
Rh O.OOl-
Ca
in the study of Cu-Pd distances
the specimens
conduction
In arriving
is due to a change
were
8 hr in vacua.
for
using a standard potentiometric
effect
After homogenizing
made by swaging and wire drawing, and foil specimens
point, they have implicitly assumed the existence of vacant states in the d-band. Jaumot and Sawatzky(2) observed
metals were
alumina crucibles
one week at 900°C in vacua the wire specimens
palladium
From a study of Au-Pd
Mixtures of the constituent
an increase
in a few cases the opposite
binary
12, 1964
respectively.
produces
Several investigators’r-*)
that in some
VOL.
Aarts and Houston-
Electrical
resistivity
measurements
were obtained
drop across the specimen
through
the
specimen
was determined
drop across a Rubicon eliminate the junction
The
made
by measuring
potential
specimen.
were
method in which the the
and the current
current
through
the
by measuring the potential
standard resistor. potentials,
In order to
measurements
were
MacMillanc4) explained that the increased conductivity
also made with current reversed.
in the cold-worked
were set on a bakelite board and fixed at the ends by
in the number distortion
Ag-Pd
alloys is due to an increase
of conduction
of the Brillouin
deformation.
electrons zones
as a result of
caused
by plastic
Several other investigators(3~5~6~s) attri-
screws
on
the
current
The wire specimens
fixed separation.
The specimen
with the knife edges by leaf springs.
short-range
foil
Although
these investigators
processes for the explanation, is a certain fundamental
offer different
they all agree that there
change in electronic structure
of alloys which produces negative resistivity
atomic
change in electrical
upon cold working.
In order to develop
of the
possible atomic processes which are responsible
for the
effect, this series of studies has been made. involved electric
The work
a study of the effect of cold work on the Hall the magnetic
susceptibility
power of Ag-Pd
annealing
on
the
and the thermo-
electrical
temperature
resistivity
Ag-Pd
and
alloys.
electrons
2. EXPERIMENTAL
temperature.
and
cm.
Exact
less negative
by cold working.
Industries,
about
by
“clover-leaf”
thickness
of the specimen
The
300 A/cm2.
magnetic
as
primary
shaped
foil was
was measured density
magnet
indirectly
of protons,
using
is 5100 G.
of was
with 5-in.
pole gap was used.
calibrated
resonance
current
A permanent
and current measurements
Inc.
der
Mod. 1000 gage with the accuracy
pole pieces and l&in. strength,
van
Pauw,(lO)
The specimen thickness was about 5 x 10-a
METHODS
Engelhard
A
employed.
Alloys were prepared from 99.99+ % Ag and 99.9+ % Pd sponge obtained from American Platinum and Company
as
Hall
The effect
2.1. Specimen preparation
Silver
Milli-Microvoltmeter
suggested
This result indicates an increase in
the number of conduction
measure-
low thermal
specimen,
They observed that the
alloys becomes
six-dial
The Hall constant for these alloys was measured at room
2.5 x 1O-5 in.
of Ag-Pd
was immersed in
2.3. Hall constant measurements
Westerlund
Hall constant
a
null indicator.
by a Sheffield
with cold working.
using
Potential
ments were made by Rubicon
of cold work on the Hall constant has been reported by and Nicholson.(g)
bath.
with Keithly
made
In all measurements
the entire specimen holder assembly the constant
In the case of
were
of van der Pauw.o”)
with a
of
alloys and the influence
constant of the cold-worked
method
measurements
potentiometer
a further understanding
constant,
specimen,
potential
contacts
was held in contact
bute this effect to the change in the degree of atomic order upon plastic deformation.
The
terminals.
probes were stainless steel knife-edge
The field nuclear Potential
were made using the same
equipment used for electrical resistivity measurements. For accurate measurements of the Hall voltage, the spurious potentials due to Nernst effect and RighiLeduc effect were eliminated by making measurements
CHEN
APU‘I>
NICHOLSON:
EL~G~~~ICAL
PROPERTIES
with primary current reversed. The potentials due to IR drop were eliminated by reversing the magnetic field.
The magnetic susceptibility was measured by the Gouy method. The force on the specimen induced by magnetic field was measured by a modified Ainsworth Chainom~~tic balance. The details of the balance are described elsewhere.(n) During th.e measurement the entire balance assembly and specimen were kept in ~~~0. The possible error in force measurement was estimated to be & 1%. A Varian electromagnet with 4-in. pole pieces was used. The magnetic field at the center of the pole pieces was eali~~ratedas a function of exciting current indirectly by the nuclear magnetic resonance of protons. Correct8ions for possible ferromagnetic impurities were made by Honda’s method in whioh the true Sus~eI~t~bilitywas found by plotting values of apparent susceptibility against the corresponding values of reciprocal field strength, and extrapolating the plot to infinite field. The method of least squares was used for the extrapolation.
Wire spee~me~s ranging from 0.2 to 0.3 mm dia. with various degrees of cold working were spot welded to annealed 0.3mm dia. copper wires. The copper wires were drawn from spectrographic grade oopper rod of 99.999 *%purity obtained from American Smelting and Refining Company. A copper-constantan thermocouple which was calibrated at three points, i.e. liquid nitrogen, a slush of solid carbon dioxide and acetone mixture, and melting point of ice, was used for all measurements. One junction of the speeimen couple was immersed in an ice bath and the other junction with the calibrated thermocouple was placed in the small hole at the center of an aluminium block. The aluminium block was fitted into the Dewar-flask, and its temperature was allowed to rise slowly from - 196°C to room temperat~lre. The warming rate was about 25”C/hr. Alternate reading of copper-constantan e.m.f. and that of the specimen with respect to copper were made at five to ten degree intervals. The e.m.f.s were measured using the instruments mentioned above. The thermoelectric power relative to copper was obtained from the slope of the thermal e.m.f. of the specimen against temperature. The relative thermoelectric power was converted to absolute thermoelectric power using the values of the absolute thermoelectric power of copper given by Borelius.us)
OF
CO~~~W~Rl~~D
Ag-Pd
ALLOYS
6s9
2.6. Ann~~~~n~of ~~~-~~r~~~ specimens The recovery behavior of electrical ~esistivity and Hall constant was studied on the cold-worked Two types of annealing, isochronal specimens. annealing and isothermal annealing, were employed. In isochronal annealing, the cold-worked wire specimens were annealed for 30 min at successively higher telnperatur~a and then quenched to room temperature. The annealing was made in a water bath for tem~ratures up to 100°C and in a silicone oil bath for temperatures between 100°C and 275% Higher temperature annealing was performed in a furnace where the specimen was protected by a puri~ed helium gas atmosphere. In isothermal annealing, the specimens were annealed for various times at 3OO”C, 350°C and 400°C. The cold-worked wire specimens were annealed in a neutral salt bath where specimens were protected in vacua. After annealing for a certain period of time, the specimen was quenched to room temperature and the resistivity was measured at 0°C. The cold-rolled foil s~~imens were annealed in a furnace with helium atmosphere. The Hall constant and resistivity of foil specimens were measured at room temperature. 3, EXPERIMENTAL
RESULTS
3.1. The effect of cold work on the magnetic s~~ce~t~b~l~t~ Since change in the d-band structure by cold working has been suggested(‘) as a cause of the anomalous resistivity effect, the effect of cold work on the magnetic susceptib~ity was studied, Results of this measurement for two alloys, 9.5 % Pd and 41.8 % Pd, are shown in Table 1. measurements were made at both room tem~rature and liquid nitrogen temperature using fields ranging from 6160 to 7800G. The specimen was deformed by wire drawing at room temperature in the case of 9.5 % Pd alloy and by simple tension at liquid nitrogen temperature for 41.8% Pd alloy. The results in Table 1 show no appreciable effect on magnetic susceptibility due to cold working. The difference in the observed values is within the experimental error (ri; 1 ‘A). In addition, since the susceptibility is temperature independent, it may be concluded TABLE 1. Ma~atic mass susceptibil~t~~of Ag-Pd aIIoys at annealed and cold-warkad states (in c.g.s. units times 106) ---._.““_c_ Temp. R.T. - 196°C R.T. -196°C \Alloy __-._-Au&led 22 % R.A. --._ 9.5% Pd -0.176 -0.177 -0.173 -0.177 .l_l..__-__X_.I.-___l.ll_____.. Annealed 9 % B.A. ___41.3% Pd -0.172 -0.169 -0.171 -0.170 ---.-l___l___
690
ACTA
that there is no component magnetism,
characterized
inversely proportional
of palladium
and since it was temperature
completely
by cold
independent,
that in these alloys, both in the
filled.
Therefore,
state, 4d-band the
theoretical
based on the change in s-d scattering
for the anomalous
resistivity
work is not applicable
behavior
to the Ag-Pd
3.2. InJluence of annealing
due to cold
1 illustrates
on the electrical resistivity
the resistivity,
12,
increases.
1964
Finally,
liquid
nitrogen
I
I
I
39.0-
deformation,
41.8 % Pd ,/f
-
sition
range from
absolute
at liquid
change
deformed
!I.8
y
!I.6
5 0
specimens
z 0 CD ‘0
!I.4 !I.2
v-
16.2
respectively
The resistivity
temperature. in
specimens
temperature
generally
work.t4)
at room temperature
but these specimens
after
the
final extension
were brought
show a larger
same
strain.
at liquid
for
about
18 hr.
and The
were made again at liquid
temperature.
resistivity
was observed except for pure silver.
No about
significant 40%
change
in
In the
of the increase
in
was recovered. the
anomalous mainly
The
nitrogen
nitrogen
case of pure silver,
The
show less
to room temperature
temperature
measurements
The
the
of previous
for
at by
41.8%
effect
Pd
(Fig.
concentrated
alloy
shows
the
l), the annealing on
this
greatest
study
was
composition.
Wire specimens for the annealing studies were deformed by
t
wire drawing
10.8 Q
and foil specimens
by rolling at room
temperature. Figure 2 shows the change in resistivity
10.6
of a cold-
worked 41.8 ‘A Pd alloy (9 % R.A.) after heating for 30
10.4
6.2
nitrogen
in resistivity
resistivity
of
b I I.0
16.0
nitrogen
the results
at that
Since
?I.0
16.4
at and
Pd were deformed
resistivity
deformed
resistivity ,
in
at liquid
with
kept 38.6
0 to 54%
simple tension up to 2OoA elongation.
temperature,
!2.0
38.8
tension
two sets of the specimens in the compo-
specimens,
12.2
specimens
by simple
liquid nitrogen and room temperature
decrease
75 % Pd
values.
measured resistivity at that temperature. In order to compare the effect of the temperature
agrees
p, at 0°C as a
the annealed
They deformed
temperature
strain hardening,
39.2
it exceeds
This behavior is similar to that observed by Aarts and
was measured
alloys.
and Hall constant of cold-worked alloys Figure
VOL.
Houston-MacMillan.(4)
was not changed
annealed state and in the cold-worked is
being
to temperature.
it may be concluded
interpretation
type para-
by its susceptibility
Since the susceptibility working,
METALLURGICA,
min at successively 6.0
The resistivity
higher temperatures
recovers
as indicated.
in two steps.
It increases
gradually as a result of heating at above room temperature.
5.6 20
IO
0
30
PERCENT FIG. 1. Resistivity
function
40
50
REDUCTION
7;R.A. for five alloys.
The resistivity temperature.
the
resistivity
90
the
100
in cross-sectional
250°C
increase and
takes place in
375°C
(step
I).
A
area,
was also measured The absolute
at
change in
at 0°C.
is All
except the 75 ‘A Pd alloy, qualitatively same
between
of cold-drawing
the same as that measured resistivity
decreases
The most significant
range
AREA
measured at liquid nitrogen temperature
compositions, show
IN
80
A,, - A = ~ x 100, -%I
liquid nitrogen essentially
70
plotted as a function for Ag-Pd alloys.
of percent reduction
resistivity
60
behavior.
First,
for a strain of about 20%
the R.A.
and then increases as the degree of plastic deformation
-U)r
0
100
200 ANNEALING
300
400
TEMPERATURE,
500
600
700
“C
FIG. 2. Change in resistivity resulting from a 30 min isochronal annealing of a Ag-41.8 % Pd alloy cold-drawn 9% R.A. Ap = p - pO, where p = measured resistivity and p,, = resistivity of fully annealed alloy.
CHEX
AND NICHOLSOX:
ELECTRICAL
PROPERTIES
ANNEALING
TIME,
OF
COLD-WORKED
Sg-Pd
ALLOYS
691
MIN.
Change in resistivity resulting from isothermal annealing of a Ag-41.8 % 0 where p = measured resistivity and Pd alloy cold-drawn 9 % R.A. ap = p p0 = rosistivity of fu Ply annealed alloy. FIG.
3.
maximum, which is above annealed value, is reached at about 375°C. Above this temperature resistivity decreases (step II) and finally reaches the annealed value at about 450°C. Raot13) made a similar study on a Ag-40% Pd alloy. His results were essentially the same as those shown in Fig. 2. Specimens with the same thermal and mechanical history as those above were annealed isothermally at 305°C and 355°C. Figure 3 shows that at 355°C the resistivity first increases with time and after reaching a maximum, decreases asymptotically toward the annealed value. At 305”C, no maximum is observed. The resistivity increases continuously for the duration of the test (170 hr). This behavior indicates that in this temperature range there are two processes occurriu~, i.e. one tends to increase the resistivity, and the other to decrease the resistivity. The observed behavior appears to be a consequence of the differential effect of two processes. Figure 4 shows the
similar isothermal annealing of the 41.8% Pd alloy cold-reduced to 32% R.A. The resistivity recovery behavior is similar to Fig. 3 at 305°C and 350°C. At 395°C the rates of two processes are sufficiently equal, so that no distinct maximum is observed. In heavily deformed specimens the resistivity is proportionally higher than in the lightly deformed specimen, as shown in Fig. 1. The cold-worked resistivity generally exceeds the annealed resistivity at about 40-50x R.A. For example, the resistivity in the 41.8 % Pd alloy after 87 % R.A. is more than 3 % greater than its annealed value. Upon isothermal annealing at 300400% the resistivity of this specimen was observed to decrease continuously (Fig. 5). The rate of recovery decreased initially with time, then increased and finally again decreased. This indicates that, in addition to a process which causes a decrease in resistivity there is a second process occurring which tends to increase the resistivity. The decrease in
20 Ag- 41.0 x X R.A. = 32
w
0
303*c
x A
350.C 395’C
0’
z ;I0 1
/
’ ’ ’ ““” ’ ’ “““’ ’ ’ ’ ““” ’ ’ ‘rlrid 10000 100
ANNtiLING
TIME,
1000
MIN.
FIG. 4. Change in resistivity resulting from isothermal annealing of a ilg-41.8 % Pd alloy cold-drawn 32% R.A. Ap = p - pO.
ACTA
092
METALLURGICA,
VOL.
12, 1964
60 z ..
-30
x k
420
FIQ. 5. Change in resistivity resulting from isothermal annealing of a Ag-41.8 %
Pd alloy cold-drawn 87 % R.A. Ap = p - pO.
resistivit~
occurs
more rapidly
in the heavily
cold-
worked alloys because the high cou~entrat~on of defects in the cold-worked alloys accelerates the rate of annihilation of these defects as in recovery. During these thermal treatments no softening occurs, In fact, no s~gn~cant softening occurs below about 550°C. Thus it appears that the processes associated with the recovery of electricaf resistivity do not. involve significant dislocation rearrangement. Instead they must involve either short range solute diffusion and/or vacancy migration and annihilation. The hypothesis that two processes are occurring during annealing of the bold-worked specimen is
supported by the simultaneous study of the recovery behavior of resistivity and Hall constant in coldrolled foil specimen. Figures 6 and 7 show the plot of electrical resistivity, p, and Hall constant, R, in terms of annealing time for isothermal annealing at 350°C of cold-rolled (30 % R-A.1 21.4% Pd and 41.8 % Pd alloys respectively. In these measurements the absolute value of p and R may be in error of the order of 1 ‘A due to error in specimen thickness measurements. However? uncertainty in the relative value measured on one specimen would not exceed 0.05% for p, and 0.1% for R. In both cases the resistjvity versus time shows a maximuu~ as does the
FIG. 6. Resist;tivity(p) and Ha.11constant (R) of a Ag-21.4% Pd alloy cold-rolled 30 % R.A. platted a.3 a function of annealing time at 350°C.
CHEN
P*‘ICHOLSON:
AND
ELECTRICAL
PROPERTIES
OF COLD-WORKED
Ag-Pd
ALLOYS
693
.o -
3
-
5 -
T>. 61. c.,
ANNEALING FIG.
wire specimen
(Figs. 3-5).
Hall
becomes
constant
On the other hand,
increasingly
time and tends to approach
resistivity
MIN.
negative
to a constant
the with
value after
predicted
that the relative change in absolute thermo-
electric power is equal to the relative electrical resistivity. sensitive
prolonged annealing. The result supports observed
TIME,
Resistivity (p) and Hall constant (R) of a Ag-41.8 % Pd alloy cold-rollecl 30% R.A. plotted as & function of annealing time at 35O’C.
7.
the
explanation
behavior
that
the
is due to the combined
effect of two processes having opposite
effects on the
process quite
to
the
detailed
nature
as well as electronic sensitive
change in the
Since the thermoelectric of the
structure,
to the atomic
power is scattering
it should
Rrrangement
alloys.
One process which is predominant resistivity. during the first step of the isochronal recovery of the
for pure silver and five alloys
electrical
is
cold-worked
one which causes a change in the Hall constant.
A
21.4 % Pd and 41.8 % Pd, the thermoelectric
possible
of
was measured as a function
resistivity process
short-range
(i.e. the increase in resistivity)
involved
order
which
state and was destroyed Since
there
is no
is a re-establishment existed
in
the
appreciable
effect
on
The absolute
annealed
in the course of cold working. the
Hall
of
in arrangement
second
step of the isochronal
resistivity fact
recovery
(i.e. the decrease in resistivity)
the annihilation The
of constituent
atoms
in the
The other process which dominates
of the excess vacancies
that
this process
is not
the
of electrical is probably in the lattice.
accompanied
by
R.A.)
power
was mea,sured
in the annealed
conditions.
power, X,, of annealed of composition
Taylor
and
Coles. u7)
dependence
by cold working.
In
all
compositions
Figure 9 illustrates the temperature
of S for two typical alloys, 21.4 % Pd and
41.8 % Pd.
It is interesting
produces
to note that cold working
no change on the S for the 21.4 % Pd alloy
in the temperature
range studied.
the relative change in thermoelectric
Figure
power
10 shows
power, AS//X,,],
at 0°C as a function
on the thermoelectric
the
dependence
pure silver, 21.4 % Pd and 41.8 % Pd.
work
in
of S is only slightly altered
have little effect on the Hall constant. of cold
power
of cold work.
change in the Hall constant implies that the vacancies
3.3. The effect
and
For two alloys,
Fig. 8. It shows an excellent agreement with the work temperature
change
(90%
The absolute thermoelectric
constant upon cold working or subsequent annealing of
solid solution.
thermoelectric
alloys at 0°C is plotted as a function
pure metals,(14~i5) this effect must originate
from the
be
in the
of percent reduction
in area for Some of the
data for pure silver are calculated from the results of Druyvesteyn and Menson, and plotted for compari-
Cold working usually causes a positive change in thermoelectric power of pure metals. Hirone and
son.
Adachiu6)
against composition in Fig. 11. A&‘/lfl,l produced by cold working for all alloys deviates negatively from
have
estimated
the
change
in thermo-
electric power due to cold working, based perturbing potential of an edge dislocation.
on the They
The
A&‘/l~5’,1 at 0°C due to 90%
the value
of pure
silver.
R.A.
The maximum
is plotted
negative
ACTA
694
I
I
I
I
I
(
METALLURGICA,
dislocation
I
1
I
VOL.
I-“,
1964
contribution,
IO 0
THIS
WORK
x
TAYLOR
From the foregoing
l----t-
best be explained alloys. Positive
u 8
X-ray
Measurement
-20
evidence alloys
probably
because short-range measurable these
-30
reason
due
factors
a diffuse
tion.
However,
Recently, IO
Ag
30
20
40
50
60
70
00
90
Pd
ATOMIC PERCENT PALLADIUM FIG. 8. Absolute thermoelectric power (S,) of annealed Ag-Pd alloys at 0°C plotted as a function of composition. is observed
studied.
negatively suspect tions
in the 41.8 % Pd among
Since
from
AS/jS,l
that
for
that any positive
and other
working
must
lattice be
alloys suggested
for all alloys
pure
silver,
defects
deviate
one
opposed
resulting
by
other
would
from
sensitive means of detecting
cold
phenomena
in their study
that thermoelectric
increasingly
the
change in S due to disloca-
affecting S. Jaumot and Sawatzky,@)
became
has never
-
-3
‘1.
the
similarity
For this
This could
these
in a part of this investiga-
order
may
occur
in this
and Nicholson,(21) I
I
system.
using
I
X-ray
I
(01 Ag-21.4%
Pd
-
“1.
t.z n-4
-
0
;
.\,.
a-5 I v)
\ -6
‘\,,
-
-7 -190
I -160
of Cu-Pd
‘;\
I
I -120
-60
-40
TEMPERATURE,
“C
0
power could be a
0 %
case.
study
They found that S as a function of cold
exhibit short-range
that the destruction
of
atomic of
o
latter
the
order.
negative
Hyatt,t3)
scattering
of
scattering
working in both ordered and quenched samples, which and
attempted
X-ray
presumably Klokholm
been
of silver and palladium.
I
-2
reported.
: a
deviation alloys
to
Copeland
-I
order in
been
one may infer from thermodynamic
data(rgysO) that -5C
never
order would have little effect, if
alloys was not undertaken
-
order in the
for short-range
has
at all, on the diffuse X-ray
alloys
scattering -4c b
results, it appears
in terms of short-range
silver-palladium
* . up
experimental
that the primary effect of cold work on the electrical resistivity of silver-rich silver-palladium alloys can
-10
$
change
4. DISCUSSION
ETAL.
0
y
and the net negative
in S is observed.
order as suggested by
with
less
change
be interpreted
of both
range order tend to produce
as indicating
long-range a negative
in the
AS
ANNEALED R.A.
= 9.4
= %R.A.
= 30
x % R.A.
= 90
and shortchange in S.
Our 41.8 % Pd alloy exhibits similar behavior to their results, S in 32.8% negative
Pd and 76% Pd alloys also show
change by heavy deformation.
The present
result can be explained
that the effect of dislocations
by assuming
and other lattice defects
tend to cause a positive change in S, while the effect of the destruction of short-range order tends to produce a negative change in S. In alloys with dilute concentration of solute, dislocation contribution dominates over the short-range order effect. In the high alloy range,
short-range
order
effect
dominates
over
the
-20 -22
’ -160
I -160
I -120
I
I -60
TEMPERATURE,
-40
0
-2
FIG. 9. Absolute thermoelectric power (S) of Ag-21.4% Pd and Ag-41.8 % Pd alloys after various degrees of cold work. In the 21.4 ‘A Pd alloy the thermoelectric power was independent of the degree of cold work.
CHEN
30
_
I
I
. 20
ELECTRICAL
AND NICHOLSON:
Ag
1
I
I
(~RUYVESTEYN
A
Ag- 9.5%
x
Ag - 21.4%Pd
o
Ag -41.6%
PROPERTIES
I
1
OF
COLD-WORKED
atomic distribution
I
I’d
and
also
that
in
by
Slater(24) new
superlattice,
superzone)
boundaries
first Brillouin
IO
and
with the
Nicholas(26)
Brillouin
are formed
the extra Bragg reflections.
Pd
695
It was first pointed out by Muto@)
discussed a
ALLOYS
can also be understood
superzone concept.
ETAL.)
Ag-Pd
zone
(i.e.
corresponding
to
As a result, the original
zone characteristic
of random
distri-
bution of atoms is split into two or more superzones.
8
The density
m
of states curves, N(E)
istic of the original first Brillouin
go
be replaced
is 4
by a density
vs. E, characterzone will therefore
of states curve made up of
two or more zones having over-lapping Disordering
-10
the atomic arrangement
is equivalent
to destroying
energy levels.
by cold working
the superzone
structure.
If the Fermi surface lies well inside the Brillouin zone -20
boundary
for
superzone,
the destruction
effective -30
I
IO
0
I
I
I
I
I
I
I
I
20
30
40
50
60
70
60
90
PERCENT
REDUCTION
bute 100
IN AREA
the random
number
existence
of
Au40% alloy
short-range
Pd was
techniques,
alloy.
Since gold.-palla,dium vity
behavior
order
The
effectively
demonstrated in
short-range
destroyed
to that found
cold
The
same
model
struction
of short-range
this system, the
behavior
concept
resistivity
of
behavior
“‘7
30
Muto,(s3)
order may
solution
depending
position
and Brillouin
zone boundary
and for the superlattice.
solid
between for the
random
lattice
extimate
based on the electronic structure proposed by
Mott(26) and short-range
IO
Slater(24) and
that the short-range
on the relative
may
of Gibson(22) or
of a binary
-10
A rough
the thermoelectric
as energy dependence
r2k2T 1
al
Ziman,(2s) power,
X,
of mean free
1 aA,
m+laaE:
’
I
(1)
> E=Ep
F
’
order parameter measured by
with short-range order for Ag,Pd alloy. destruction of short-range order by cold decrease in the resistivity.
The change in electronic structure which produces the change in the conduction process due to change in
‘:I \
-20
Cowley(27) for Cu,Au quenched from 500°C shows that the Gibson’s theory predicts an increase in
working produces
the observed
Following
2C
or increase the resistivity
resistivity Therefore,
The
path and area of the Fermi surface, i.e.
order exists in
decrease
surface
measurement.(s)
power.
in the silver-palladium
that short-range
Nicholas.(25) Gibson(2J) predicted
Fermi
and contri-
in this
a similar resisti-
in terms of the theory
superzone
the
order present in the annealed
the anomalous
be explained
metal
can be expressed
has the same origin, i.e. the de-
alloys. On the assumption
to
This has been
can also explain
change in thermoelectric
working.
system, one may assume that the anomalous in the two systems
the
annealed
order
by
alloys exhibit
the
close
electrons
in resistivity.
by the Hall effect
in an isotropic scattering
and
Hall constant becomes less negative upon cold working.
FIG, 10. Relative change in absolute thermoelectric power of Ag and Ag-Pd alloys at 0°C plotted as a function of the degree of cold work (reduction in area).
diffuse
of conduction
to the decrease
confirmed
state
of order will increase the
; FLt
k
I
‘_
-3c Ag
IO
20
ATOMIC
30
40
/I
I’
50
PERCENT
60
70
80
90
Pd
PALLADIUM
FIG. 11. Relative changes in absolute thermoelectric power of cold-worked (90% R.A.) Ag-Pd alloys at 0°C plotted as a function of composition.
ACTA
696
METALLURGICA,
where E’, is the energy on the Fermi surface, 1 is the electron and A,
mean free path of the conduction
is
the area of the Fermi surface. the
more
energetic
should
electrons
easily scattered than the slow ones. would
depend
on the relative
be
between
the
zone boundary.
In
state the first Brillouin zone boundary
considered
However, touch
to
be
Since there is no
spherical.
of the Fermi
Therefore,
surface
boundary
a In a,,./aE is negative spherical
in such a way that
or less positive
Th us, S in the ordered
case.
negative
than in the disordered
picture,
the negative
state.
deviation
than
the
state is less Based on this
of S due
to
cold
working could be explained. In addition
to providing
the short-range
order
experimental
hypothesis
two
support
system.
proposed
for
of the fore-
going results tend to cast doubt upon the validity the hypothesis
of
by Logie et al. for the Ag-Pd
Implicit in their hypothesis
is the assumption
that vacant states exist in the d-band of these alloys. The
magnetic
Ag41.8
susceptibility
% Pd alloys
of Ag-21.4
% Pd
shows no indication
and
of vacant
states in the d-band either before or after deformation. Second,
the
recovery
of
occurs in a temperature far
below
recovery
the
the
annealed
resistivity
range of 250-375°C
temperature
at
which
which is
mechanical
occurs (550°C). 5. CQNCLUSIONS
From annealing studies of Ag-Pd alloys it is concluded that the anomaly in the electrical resistivity change accompanying Ag-Pd
alloys
short-range supported
cold working in the silver-rich
can best be explained in terms of a This postulate is order mechanism.
by
measurements
of
Hall
and
short-range
thermoelectric
order
on
power.
the electronic
of these alloys can be explained in terms of
both Gibson’s
theory and the superzone
concept.
ACKNOWLEDGMENTS
The authors are indebted to the U.S. Atomic Energy Commission contract
for
its
support
of
this
work
under
AT-11-l-1009.
The authors wish to thank Professor J. M. Sivertsen for many helpful discussions.
energy
area is positive.
in the ordered state, the Fermi surface may
the superzone
of
be less
between the two, the Fermi surface may
dependence
12, 1964
susceptibility
effect
The second term
lies well outside the Fermi surface. interaction
be positive
would
position
Fermi surface and the Brillouin the disordered
magnetic The
conduction
The first term in the bracket since
VOL.
constant,
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