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Thermodynamic properties of solid palladium-silver alloys
THERMODYNAMIC
PROPERTIES
OF SOLID
K. M.
PALLADIUM-SILVER
ALLOYS*
MYLESt
The vapor pressure of silver over solid silver end over nine palladium-silver alloys has been measured by the torsion-effusion method in the temperature range 1100-1300°K. The chemical activities, a8 well as the free energies, entropies, and enthalpies of formation of the alloys at 1200°K have been computed from the vapor pressure data. The activities of silver exhibit large negative deviations from ideal behavior over the entire compositional range. The activities of palladium. computed by graphical integration of the Gibbs-Duhem relation, deviate positively in the palladium-rich alloys and negatively in the silver-rich alloys. The thermodynamic properties are considered in terms of existing thermodynamic data. The excess entropies and enthalpies, both of which are negative, are discussed in relation to the changes that occur in the characteristic properties of palladium and silver upon alloying. PROPRIETES
THERMODYNAMIQUES D’ALLIAGES PALLADIUM-ARGENT CONSIDERES A L’ETAT SOLIDE
La pression de vapeur de l’argent sur l’argent solide et sur neuf alliages palladium-argent a & mesuree par la methode de torsion-effusion dans le domaine de temperature 1lOO-1300°K. L’auteur a calcule B pertir des don&es de pression de vapeur, les activites chimiques, ainsi que les energies libres, entropies et enthalpies de formation des ellieges B 1200°K. Lesactivitesde l’argent manifestentdegrandes deviations negatives par rapport au comportement ideal dans lrt gamme entiere des compositions. Les sctivites du palladium, calculees par integration grephique de la relation Gibbs-Duhem, verient positivement dans les alliages riches en palladium, et negativement dans les alliages riches en argent. Les proprietes thermodynamiques sont consider&es en fonction des donnees thermodynamiques existantes. Les variations d’entropie et d’enthelpie, toutes deux negatives, dont discutees en relation avec la modification apparaissant dans les proprietes caracteristiquea du palladium et de l’argent 8, l’etat allie. THERMODYNAMISCHE
EIGENSCHAFTEN FESTER LEGIERUNGEN
PALLADIUM-SILBER-
Mittels einer Torsions-Ausstromungsmethode wurde der Silber-Dampfdruck tiber festem Silber und iiber neon Palladium-Silber-Legierungen im Temperaturgebiet llOO-1300°K gemessen. Aus den Dampfdruckmessungen wurden die chemischen Aktivitiiten sowie die freien Energien, Entropien und Enthalpien fiir die Bildung der Legierungen bei 1200°K berechnet. Die Aktivitiit des Silbers zeigt im gesamten Zusammensetsungsbereich starke negative Abweichungen vom idealen Verhalten. Die Aktivitiit des Palladiums wurde durch graphische Integration der Gibbs-Duhem-Besiehung bestimmt, ihre Abweichung ist positiv bei den palladiumreichen, negativ bei den silberreichen Legierungen. Die thermodynamischen Eigenschaften werden im Rahmen bereits vorhandener thermodynamischer Messungen betrachtet, Die UberschuB-Entropien und -Enthalpien-beide negativ-werden diskutiert im Hinblick auf die Anderungen, die bei den cherakteristischen Eigenschaften von Palladium und Silber beim Legieren auftreten.
solid
1. INTRODUCTION
The small disparities between the atomic sizes of the transition allow
elements
for
with the same crystal
interesting
nonconligurational namic
properties
in the
electronic
contributions band
contributions that
and
upon
These
system
alloy system
other
the
pertinent
when is
the
known.
was selected
band
for
structure
information
is
related
to the properties of the electrons is available. In addition, the reliability of the entropy and the enthalpy
values
derived
temperature
energies
calculated
from the experimentally
dependences
could be evaluated
formation previously Palladium
of
the
alloys
by calorimetric
have
of
been
methods.
and silver form a continuous
series of
This work was performed under the auspices of the U.S. Atomic Energy Commission. t Alloy Properties Group, Metallurgy Division, Argonne National Laboratory, Argonne, Illinois. METALLURGICA,
VOL.
Pd-25wl.
13, FBRUARY
at about
There is 700°K near
%Agt2). TECHNIQUES
method
in preference
because
the desired
transition-metal
alloys,
fering side reactions vapor
pressures
ciently
in the galvanic
A tantalum located
is induced
1965
for
by inter-
tell.(3)
As the
and of silver are suffi-
in magnitude,
from a fine tungsten orifices.
particularly
masked
the torsion-effusion
that has been used in previous
was employed.
strain
e.m.f.,
is often
of palladium
different
apparatus
the free energies
to an electromotive-force
studies(4-6)
effusion cell that has two
orifices is suspended
vertically
wire in which an elastic torsional
as the vapor
effuses through
the
The vapor pressure p is related to the angle
8 through which the cell rotates by the expression p = 2rtl/JZAdf. Here r is the torsion constant of the wire, A is the cross-sectional
* Received June 18, 1964.
ACTA
temperatures.“) order
An effusion method for determining
was adopted
eccentrically
free
since the enthalpies
palladium-silver
determined
of
all
2. EXPERIMENTAL
alloying.
resolved
the composition
thermodychanges
best
at
of short-range
the
with
alloy
since
structure study
the
the
investigation
known
to
often of
The palladium-silver this
to
are associated
structure
are
structure
opportunities
solutions
evidence
the
horizontal
distance
suspension axis, and
f
of
area of the orifice, d is the
orifice
is the Freeman-Searcy
tion factor for an orifice of nonzero length.(‘) 109
from
the
correc-
110
ACTA
METALLURGICA,
The alloys were prepared by arc-melting on a water-cooled copper hearth in a helium-argon atmosphere the requisite amounts of 99.9 wt.% pure pa~adium and silver. The specimens were homogenized near the solidus, quenched, and machined into coarse turnings that were cleaned and loaded into the tantalum cells. All of the alloys were chemically analyzed following the heat treatment. As the weight loss during a run did not exceed 0.2%, the compositional changes of a specimen were considered negligible. Chemical analysis indicated that the concentration of palladium in the effusate was less than the limits of detection (about 0.01 wt”/$ 3. RESULTS
The measured values of the vapor pressure of silver over pure silver and over’ the palladium-silver alloys, derived from at least two separate runs per specimen, were fitted to linear equations of the form logp =f (l/T) by the method of least squares. The constants of the equations are given in Table 1 together with the probable errors for 95% confidence limits. Values of AH&s for pure silver, calculated by means of the third-law test equation, showed no systematic deviations with temperature from the average value of 67 kcal/g atom. The molecular composition of the vapor phase must be known to calculate activities from vapor pressure data. Several workers(*pg) have reported large percentages of polymeric species in silver vapor while others(i0-14) have found that polyatomic were essentially absent at 1200°K complexes (Ag,/Ag = 5-8 x lOA). In the present work, an attempt was made to determine the molecular weight of silver vapor at 1200*K by combining the torsioneffusion results with those of Knudsen measurements. A tungsten Knudsen cell, fitted with a thin tantalum orifice plate, was carefully positioned in the furnace to approximate the experimental conditions experienced by the torsion-effusion cell. The temperature
VOL.
13,
1965
of the Knudsen cell was inde~ndently calibrated against the e.m.f. of the working thermocouple. The results tended to indicate that negligible amounts of polymers were present in the vapor. The activities of silver in the alloys, with pure silver as the reference state, were calculated from the vapor pressure data at 1.100, 1200, and 1300°K. The activities of palladium, relative to pure palladium, were determined with the Gibbs-Duhem relation. From the activities, the partial and integral free energies, entropies, and enthalpies of formation at 1200’K were computed; they are assembled in Table 2. The precision of the activities is estimated to be about f3% and that of the integral free energies about f 150 oalfg atom. The integral entropies and enthalpies are less precise ; reasonable estimates, the basis for which will become evident later, are about f0.3 Cal/g atom-deg for the entropies and about f500 Cal/g atom for the enthalpies. 4. DISCUSSION
As seen in Fig. 1, the activities of silver exhibit fairly large negative deviations from ideality. The activities of palladium in the silver-rich alloys are characterized by negative deviations, and in the palladium-rich alloys by positive deviations. Good qualitative agreement exists between these activities of palladium and those found by Schmahl,05) who measured the activity of palladium in the composition range NAg = 0.58 to 0.80 at 956°K by an oxygenequilibria method. There is no agreement between the present results and those calculated by PrattW from e.m.f. measurements made at 1000’K. Although reproducible at lOOO*K, the e.m.f. data exhibited a tendency to drift to lower values at higher temperatures, which made it impossible to calculate entropies or enthalpies with any certainty. The integral free energies, entropies, and enthalpies are shown in Fig. 2. As predicted by the activities,
TABLE 1. Vrtpor prerrsures of silver over palladium-silver alloys
10~2, (mm Hg) = m/T + b
Temp. range NArr
b
??a
F)
No. of points
1 .ooo 0.897 0.802 0.697 0.587 0.490
-13696 -13759 -13795 -13793 -13904 -14201
+ 83 f 90 j: 78 rt: 30 j, 111 i: 81
8.727 8.736 6.649 8.527 8.436 8.549
rit:0.070 jc 0.078 rt: 0.067 I: 0.025 & 0.091 * 0.066
1128-1212 1093-1201 1092-1221 1135-1232 1127-1264 1174-1273
14 11 15 13 15 19
0.386 0.280 0.189 0.093
-14294 -14275 -14308 -14049
i: 79 rt: 53 j, 111 * 80
8.513 0.064 8.396 f& 0.042 8.300 rt: 0.089 7.871 f 0.063
1186-1286 1199-1297 1204-1313 1199-1311
:f 12 14
MYLES:
I---
THERMODYNAMIC
-
0.895
0.705 0.513 0.356 0.258 0.200 0.163 0.122 0.075
0.018 0.071 0.186 0.369 0.550 0.680 0.764 0.839 0.908
-265 -833 -- 1592 --2463 -3231 -3838 -- 4340 --5016 -6176
A.&a
A&,
@-I'd
(Cal/g atom-deg)
(cal/g atom)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
-0.020 0.325 0.955 1.285 0.800 0.995 1.485 1.935 3.880
-9571 - 6305 -4012 -2378 - 1423 -920 -641 -418 -230
Pd-Ag
A%,,
Ai?, --
111
ALLOYS
AP
(Cal/g atom)
4.420 3.035 1.075 0.445 1.030 0.990 0.735 0.615 0.276
-289
-443 -446 -921 -2271 -2644 -2558 -2694 -1520
-4267 -2663 - 2722 -1844 -187 268 241 320 100
AH
(cat/g atom) -1196 -1927 -2318 - 2429 -2327 -2os7 -1751 -1338 - 825
AS (Cal/g atom-deg)
-687 -887 -x129 -1290 -1229 -897 -599 -283 -62
0.424 0.867 0.991 0.949 0.915 0.992 0.960 0.879 0.636
the excess entropy at 298°K are plotted in Fig. 3. The electronic and lattice vibrational contributions were estimated from low temperature specific heat data(s0) by the relationship X (electronic) = yT, where y is the electronic specific heat coefficient and the Debye theory of lattice speciSc heat.(21’ No corrections were made for (C, - C,) terms or for the limitations in the Debye theory. The magnetic
0.8
a
OF
TABLE 2. Thermodynamic properties of palladium-silver alloys at 1200°K _ _..-.z.-
AFAP,
0.9
PROPERTIES
0.6
a2
0
0.2
0.4
0.6
0.8
1.0
FIG. 1. Activities of pal~i~rn and silver at 1200°K. 0 experimental; 0 calculated; A Schmahl(ls’ 956°K.
is had between the free energies and those computed by Pratt. Hultgren et c&(17) and Oriani and Murphy (l*) have measured enthalpies of formation of several palladium-silver alloys at 1000°K and at 915’K, respectively, by means of liquid-tin solution calorimetry. The present results agree quite favorably with these data although the lack of heat capacities between 915’K and 1200°K makes an exact comparison difficult. When the enthaipies reported at 1000°K sre combined in the GibbsHelmholtz relationship with the free energies determined at 12OO”K, the resulting entropies, plotted in Fig. 2, are in moderately good accord with those of the present study. Several workers(16-1s)have estimated and discussed the various contributions to the excess quantities, which show the deviations from ideal behavior, in solid palladium-silver alloys. Although short-range ordering may exist at lower temperatures, there is no evidence that any deviations from random mixing occur at 1200°K. Thus, the configurational entropy and enthalpy, which are associated with nonrandomness. are considered to be negligible. The estimated nonconfigur&tional contributions to no agreement
0
0.2
0.4
OS
0.8
I,0
NAg Fru. 2. Integral free energies, 0, entropies, A, and enthalpies, [:I, of formation of palladium-silver alloys at 1200’K. A AH, Hultgren et CZ~.,~~~) 1000°K; vTAS from AH, Hultgren et al.,“” 1000°K and AP, present work, 1200°K.
ACTA
METALLURCICA,
VOL.
13,
1965
where pPd, the effective atomic moment of palladium in Bohr magnetons, is about 1.44.(a5)* For the alloys that have a full 4&band, (Npd < 0.4),@7) the effective atomic moment of palladium in the alloy, pall,_,, equals zero. Where the 4d-band is only partially filled, (Nr, > 0.4) p,,,,, is approximated by the relation 2.4ONr, - 0.96, if it is assumed that pallor varies linearly with the decrease in palladium concentration. The electronic and lattice vibrational contributions to the enthalpy, computed at 298°K from the electronic specific heat coefllcients and Debye temperatures, are quite small and negative as seen in Fig. 4.
CONTRIBUYIONS
Fm. 3. Estimated nonconfigurational contributions to the excess entropy of palladium-silver alloys at 298°K and values derived from experimental data of present work at 1200°K. I vibrational (electronic + lattice), II magnetic (a, paramagnetio palladium with randomly orientated moments; b, diamagnetic silver; c, hypothetical paramagnetic palladium with no moments).
entropy is dependent upon the change that occurs upon alloying in the degree of rando~e~ in the orientation of the atomic magnetic moments assoeiated with the palladium atoms. By applying classical Boltzmann statistics, Weiss and Tauer(s2)have derived an expression that describes the limiting value of the magnetic entropy for metals that obey a localized electron model. Unfortunately, this relation is not applicable for palladium at ambient temperatures, which is best described in terms of a collective electron model,@@) governed by the statistics of Fermi-Dime. In spite of the fact that at ~m~ratures considerably above the degeneracy temperature, (T, N 13OO’K for Pd(%j), the classical limit to the Fermi-Dirac statistics is effectively reached, it is unlikely that either electron model accurately describes the behavior of palladium at 12OO’K. In view of this dilemma and in the absence of an expression for the magnetic entropy based on Fermi-Dirac statistics, the magnetic entropy for the palladiumsilver alloys has been estimated by means of a simple expansion of the relationship of Weiss and Tauer. The resulting values are considered larger in magnitude than the true magnetic contribution to the entropy. Accordingly, near the solidus, AS (magnetic) approaches as a limit
NAQ FIG. 4. Estimated-vibration&l contribution ta the enthalpy of palladium-silver alloys at 296°K and values derived from experimental data of present work at 1200’K.
The enthalpy t,erm associated with the decrease in the relative Fermi energy, E, alloy - N,,,E, rd as a result of the transfer of electrons NAgEf AP upon alloying from the 5s-band of silver to the 4d-band of palladium is negative.t16z17)The minimum in the enthalpies at approximately 60 at.% Ag is indicative, if the band structure is rigid,izo) of the maximum negative deviation in the relative Fermi energy at that composition. The good agreement between the enthalpies measured by calorimetric methods and those computed from the vapor pressure data suggests that the entropies of the present work are also fairly reliable. However, as noted in Fig. 3, the estimated contributions to the entropy are several times larger than the experimental values. This discrepancy may be rationalized in part by assu~ng that the negative * From Ref. 25, pra = 2.827 O1/a where C is the paramagnetic Curie constant, expressed in e.m.u.-deg/mole, derived from the magnetic susceptibility data of Ref. 26. This value of prp is in statistical agreement with the relationships developed in Ref. 22.
MYLES:
THERMODYNAMIC
PROPERTIES
vibrational contributions to the entropy and the enthalpy, as approximated from low ~rn~rature specific heat data, are considerably too large numerically. If this assumption is correct, then, as may be seen in Fig. 4, the bulk of the enthalpy must be attribut,ed to contributions arising from alterations in the electron distribution upon alloying. 5. SUMMARY
The interesting correlation between the results of this investigation and the proposed band structure of palladium-silver alloys(27) tends to demonstrate the importance of nonconfigurational and nonvibrational contributions to the thermodynamics associated with the formation of transition-metal alloys. Further, the agreement between the enthalpy values of this study and those found by calorimetric methods suggests that entropy and enthalpy data ~loula~d from the temperature dependences of vapor pressures can be quite reliable. ACKNOWLEDGMENTS
The author wishes to thank Dr. M. V. Nevitt, Dr. A. T. Aldred and Dr. D. J. Lam of the Argonne National Laboratory, for their helpful discussions and for reading the manuscript. REFERENCES 1. R. RUER, Z.~~~~.C~e~. 51, 315 (1906). 2. C. N. RAO and K. K. RAO, Phil. Mtxg. 9, 527 (1964).
OF
Pd-Ag
ALLOYS
113
sndE. L. EVANS, MetaZZurgicaE Them3. 0. KUBASCHEWSKI chem~et~. Pergamon Press, Now York, N.Y. (1958). 4. K. M. MYLES, Argollne Nstional Lsboratory, Argonne. Ill., ANL-6657 (1963). 5. K. M. MYLES rendA. T. ALDILED,J. Phys. Chem. 68, 64 (1964). 0 o. A. T. ALDREDand K. M. MYLES, Trans. Amer. Inst. Min. (Met&.) Engra. 230, 736 (1964). 7. R. D. FREEMANand A. W. SEARCY, J. Ch.em. Phys. 22, 762 (1954). 8. A. W. SEARCY, R. D. FREEMAN and M. C. MOREL, J. Amer. Chem. Sot. ‘X%,4050 (1954). P. SCHISSEL, $1.Chem. Phys. 26, 1276 (1957). W. A. CRUPKAand M. G. INGHRAM,J. Phw. Chem. 59, 100 (1955). 11. J. DROWAR~ and R. E. HONIG, J. Chem. Phys. 25, 581 (1956). 12. Yu. V. KORNEV and E. Z. V~KT~IKI~~,Sow. Phys. Dok2. 1, 203 (1956). 13. G. M. MARTYNOVICH.Vestnik Moskov. Gos. Univ., Ser Mat. Mekh. A&r. Fir: Khim., No. 2, 151 (1955). 14. M. B. PANISH, J. Chem. Eng. Data 6, 592 (1961). 15. N. G. SCHMAHL,2. anorg. Chem. 286, 1 (1951). 16. J. N. PRATT, Trans. FaTad. Sot. 56, 975 (1960). 17. J. P. GHAN, P. D. ANDERSON,R. L. ORR snd R. HULTCREN, 4th Tech. Rept., Miner& Research Lsborotory, Berkeley, Cslif., October 1, 1959. 18. R. ORIANI rendW. K. MURPHY, Acta Met. IO, 879 (1962). IQ. 0. J. KLEPPA, paper contributed to Colloquium on The Structure of Metallic Solid Solutions, Orsrty, France, Julv Q-11. 1962. 20. F. 8. Ho& and B. Yates, Proc. Roy. Sot. A240,42 (1957). 21. ~~~dol~-~~r~ete~n 2, 742 (1961). 22. R. J. WEISS and K. J. TAVER, P&/s. Eev. 102.1490 (1956). 23. M. SHIMIZU,J. Phy. SW. Joga% i5, 376 (1960). 24. P. RHODESand E. P. WOE~FARTH. Proc. Row. SW. A273. 247 (1963). S. ~RAJ~ (private communication). !Z: J. WUCHER, C.R. Acad. SC?:. Paris 242, 1143 (1956). 27. F. E. HOARE, in Electronic Structure and AEZoy Chemistry of the T~a~~t~~ Elem&s. Interscience, New York, N.Y. (1963).
10”:
PROPERTIES
OF SOLID
K. M.
PALLADIUM-SILVER
ALLOYS*
MYLESt
The vapor pressure of silver over solid silver end over nine palladium-silver alloys has been measured by the torsion-effusion method in the temperature range 1100-1300°K. The chemical activities, a8 well as the free energies, entropies, and enthalpies of formation of the alloys at 1200°K have been computed from the vapor pressure data. The activities of silver exhibit large negative deviations from ideal behavior over the entire compositional range. The activities of palladium. computed by graphical integration of the Gibbs-Duhem relation, deviate positively in the palladium-rich alloys and negatively in the silver-rich alloys. The thermodynamic properties are considered in terms of existing thermodynamic data. The excess entropies and enthalpies, both of which are negative, are discussed in relation to the changes that occur in the characteristic properties of palladium and silver upon alloying. PROPRIETES
THERMODYNAMIQUES D’ALLIAGES PALLADIUM-ARGENT CONSIDERES A L’ETAT SOLIDE
La pression de vapeur de l’argent sur l’argent solide et sur neuf alliages palladium-argent a & mesuree par la methode de torsion-effusion dans le domaine de temperature 1lOO-1300°K. L’auteur a calcule B pertir des don&es de pression de vapeur, les activites chimiques, ainsi que les energies libres, entropies et enthalpies de formation des ellieges B 1200°K. Lesactivitesde l’argent manifestentdegrandes deviations negatives par rapport au comportement ideal dans lrt gamme entiere des compositions. Les sctivites du palladium, calculees par integration grephique de la relation Gibbs-Duhem, verient positivement dans les alliages riches en palladium, et negativement dans les alliages riches en argent. Les proprietes thermodynamiques sont consider&es en fonction des donnees thermodynamiques existantes. Les variations d’entropie et d’enthelpie, toutes deux negatives, dont discutees en relation avec la modification apparaissant dans les proprietes caracteristiquea du palladium et de l’argent 8, l’etat allie. THERMODYNAMISCHE
EIGENSCHAFTEN FESTER LEGIERUNGEN
PALLADIUM-SILBER-
Mittels einer Torsions-Ausstromungsmethode wurde der Silber-Dampfdruck tiber festem Silber und iiber neon Palladium-Silber-Legierungen im Temperaturgebiet llOO-1300°K gemessen. Aus den Dampfdruckmessungen wurden die chemischen Aktivitiiten sowie die freien Energien, Entropien und Enthalpien fiir die Bildung der Legierungen bei 1200°K berechnet. Die Aktivitiit des Silbers zeigt im gesamten Zusammensetsungsbereich starke negative Abweichungen vom idealen Verhalten. Die Aktivitiit des Palladiums wurde durch graphische Integration der Gibbs-Duhem-Besiehung bestimmt, ihre Abweichung ist positiv bei den palladiumreichen, negativ bei den silberreichen Legierungen. Die thermodynamischen Eigenschaften werden im Rahmen bereits vorhandener thermodynamischer Messungen betrachtet, Die UberschuB-Entropien und -Enthalpien-beide negativ-werden diskutiert im Hinblick auf die Anderungen, die bei den cherakteristischen Eigenschaften von Palladium und Silber beim Legieren auftreten.
solid
1. INTRODUCTION
The small disparities between the atomic sizes of the transition allow
elements
for
with the same crystal
interesting
nonconligurational namic
properties
in the
electronic
contributions band
contributions that
and
upon
These
system
alloy system
other
the
pertinent
when is
the
known.
was selected
band
for
structure
information
is
related
to the properties of the electrons is available. In addition, the reliability of the entropy and the enthalpy
values
derived
temperature
energies
calculated
from the experimentally
dependences
could be evaluated
formation previously Palladium
of
the
alloys
by calorimetric
have
of
been
methods.
and silver form a continuous
series of
This work was performed under the auspices of the U.S. Atomic Energy Commission. t Alloy Properties Group, Metallurgy Division, Argonne National Laboratory, Argonne, Illinois. METALLURGICA,
VOL.
Pd-25wl.
13, FBRUARY
at about
There is 700°K near
%Agt2). TECHNIQUES
method
in preference
because
the desired
transition-metal
alloys,
fering side reactions vapor
pressures
ciently
in the galvanic
A tantalum located
is induced
1965
for
by inter-
tell.(3)
As the
and of silver are suffi-
in magnitude,
from a fine tungsten orifices.
particularly
masked
the torsion-effusion
that has been used in previous
was employed.
strain
e.m.f.,
is often
of palladium
different
apparatus
the free energies
to an electromotive-force
studies(4-6)
effusion cell that has two
orifices is suspended
vertically
wire in which an elastic torsional
as the vapor
effuses through
the
The vapor pressure p is related to the angle
8 through which the cell rotates by the expression p = 2rtl/JZAdf. Here r is the torsion constant of the wire, A is the cross-sectional
* Received June 18, 1964.
ACTA
temperatures.“) order
An effusion method for determining
was adopted
eccentrically
free
since the enthalpies
palladium-silver
determined
of
all
2. EXPERIMENTAL
alloying.
resolved
the composition
thermodychanges
best
at
of short-range
the
with
alloy
since
structure study
the
the
investigation
known
to
often of
The palladium-silver this
to
are associated
structure
are
structure
opportunities
solutions
evidence
the
horizontal
distance
suspension axis, and
f
of
area of the orifice, d is the
orifice
is the Freeman-Searcy
tion factor for an orifice of nonzero length.(‘) 109
from
the
correc-
110
ACTA
METALLURGICA,
The alloys were prepared by arc-melting on a water-cooled copper hearth in a helium-argon atmosphere the requisite amounts of 99.9 wt.% pure pa~adium and silver. The specimens were homogenized near the solidus, quenched, and machined into coarse turnings that were cleaned and loaded into the tantalum cells. All of the alloys were chemically analyzed following the heat treatment. As the weight loss during a run did not exceed 0.2%, the compositional changes of a specimen were considered negligible. Chemical analysis indicated that the concentration of palladium in the effusate was less than the limits of detection (about 0.01 wt”/$ 3. RESULTS
The measured values of the vapor pressure of silver over pure silver and over’ the palladium-silver alloys, derived from at least two separate runs per specimen, were fitted to linear equations of the form logp =f (l/T) by the method of least squares. The constants of the equations are given in Table 1 together with the probable errors for 95% confidence limits. Values of AH&s for pure silver, calculated by means of the third-law test equation, showed no systematic deviations with temperature from the average value of 67 kcal/g atom. The molecular composition of the vapor phase must be known to calculate activities from vapor pressure data. Several workers(*pg) have reported large percentages of polymeric species in silver vapor while others(i0-14) have found that polyatomic were essentially absent at 1200°K complexes (Ag,/Ag = 5-8 x lOA). In the present work, an attempt was made to determine the molecular weight of silver vapor at 1200*K by combining the torsioneffusion results with those of Knudsen measurements. A tungsten Knudsen cell, fitted with a thin tantalum orifice plate, was carefully positioned in the furnace to approximate the experimental conditions experienced by the torsion-effusion cell. The temperature
VOL.
13,
1965
of the Knudsen cell was inde~ndently calibrated against the e.m.f. of the working thermocouple. The results tended to indicate that negligible amounts of polymers were present in the vapor. The activities of silver in the alloys, with pure silver as the reference state, were calculated from the vapor pressure data at 1.100, 1200, and 1300°K. The activities of palladium, relative to pure palladium, were determined with the Gibbs-Duhem relation. From the activities, the partial and integral free energies, entropies, and enthalpies of formation at 1200’K were computed; they are assembled in Table 2. The precision of the activities is estimated to be about f3% and that of the integral free energies about f 150 oalfg atom. The integral entropies and enthalpies are less precise ; reasonable estimates, the basis for which will become evident later, are about f0.3 Cal/g atom-deg for the entropies and about f500 Cal/g atom for the enthalpies. 4. DISCUSSION
As seen in Fig. 1, the activities of silver exhibit fairly large negative deviations from ideality. The activities of palladium in the silver-rich alloys are characterized by negative deviations, and in the palladium-rich alloys by positive deviations. Good qualitative agreement exists between these activities of palladium and those found by Schmahl,05) who measured the activity of palladium in the composition range NAg = 0.58 to 0.80 at 956°K by an oxygenequilibria method. There is no agreement between the present results and those calculated by PrattW from e.m.f. measurements made at 1000’K. Although reproducible at lOOO*K, the e.m.f. data exhibited a tendency to drift to lower values at higher temperatures, which made it impossible to calculate entropies or enthalpies with any certainty. The integral free energies, entropies, and enthalpies are shown in Fig. 2. As predicted by the activities,
TABLE 1. Vrtpor prerrsures of silver over palladium-silver alloys
10~2, (mm Hg) = m/T + b
Temp. range NArr
b
??a
F)
No. of points
1 .ooo 0.897 0.802 0.697 0.587 0.490
-13696 -13759 -13795 -13793 -13904 -14201
+ 83 f 90 j: 78 rt: 30 j, 111 i: 81
8.727 8.736 6.649 8.527 8.436 8.549
rit:0.070 jc 0.078 rt: 0.067 I: 0.025 & 0.091 * 0.066
1128-1212 1093-1201 1092-1221 1135-1232 1127-1264 1174-1273
14 11 15 13 15 19
0.386 0.280 0.189 0.093
-14294 -14275 -14308 -14049
i: 79 rt: 53 j, 111 * 80
8.513 0.064 8.396 f& 0.042 8.300 rt: 0.089 7.871 f 0.063
1186-1286 1199-1297 1204-1313 1199-1311
:f 12 14
MYLES:
I---
THERMODYNAMIC
-
0.895
0.705 0.513 0.356 0.258 0.200 0.163 0.122 0.075
0.018 0.071 0.186 0.369 0.550 0.680 0.764 0.839 0.908
-265 -833 -- 1592 --2463 -3231 -3838 -- 4340 --5016 -6176
A.&a
A&,
@-I'd
(Cal/g atom-deg)
(cal/g atom)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
-0.020 0.325 0.955 1.285 0.800 0.995 1.485 1.935 3.880
-9571 - 6305 -4012 -2378 - 1423 -920 -641 -418 -230
Pd-Ag
A%,,
Ai?, --
111
ALLOYS
AP
(Cal/g atom)
4.420 3.035 1.075 0.445 1.030 0.990 0.735 0.615 0.276
-289
-443 -446 -921 -2271 -2644 -2558 -2694 -1520
-4267 -2663 - 2722 -1844 -187 268 241 320 100
AH
(cat/g atom) -1196 -1927 -2318 - 2429 -2327 -2os7 -1751 -1338 - 825
AS (Cal/g atom-deg)
-687 -887 -x129 -1290 -1229 -897 -599 -283 -62
0.424 0.867 0.991 0.949 0.915 0.992 0.960 0.879 0.636
the excess entropy at 298°K are plotted in Fig. 3. The electronic and lattice vibrational contributions were estimated from low temperature specific heat data(s0) by the relationship X (electronic) = yT, where y is the electronic specific heat coefficient and the Debye theory of lattice speciSc heat.(21’ No corrections were made for (C, - C,) terms or for the limitations in the Debye theory. The magnetic
0.8
a
OF
TABLE 2. Thermodynamic properties of palladium-silver alloys at 1200°K _ _..-.z.-
AFAP,
0.9
PROPERTIES
0.6
a2
0
0.2
0.4
0.6
0.8
1.0
FIG. 1. Activities of pal~i~rn and silver at 1200°K. 0 experimental; 0 calculated; A Schmahl(ls’ 956°K.
is had between the free energies and those computed by Pratt. Hultgren et c&(17) and Oriani and Murphy (l*) have measured enthalpies of formation of several palladium-silver alloys at 1000°K and at 915’K, respectively, by means of liquid-tin solution calorimetry. The present results agree quite favorably with these data although the lack of heat capacities between 915’K and 1200°K makes an exact comparison difficult. When the enthaipies reported at 1000°K sre combined in the GibbsHelmholtz relationship with the free energies determined at 12OO”K, the resulting entropies, plotted in Fig. 2, are in moderately good accord with those of the present study. Several workers(16-1s)have estimated and discussed the various contributions to the excess quantities, which show the deviations from ideal behavior, in solid palladium-silver alloys. Although short-range ordering may exist at lower temperatures, there is no evidence that any deviations from random mixing occur at 1200°K. Thus, the configurational entropy and enthalpy, which are associated with nonrandomness. are considered to be negligible. The estimated nonconfigur&tional contributions to no agreement
0
0.2
0.4
OS
0.8
I,0
NAg Fru. 2. Integral free energies, 0, entropies, A, and enthalpies, [:I, of formation of palladium-silver alloys at 1200’K. A AH, Hultgren et CZ~.,~~~) 1000°K; vTAS from AH, Hultgren et al.,“” 1000°K and AP, present work, 1200°K.
ACTA
METALLURCICA,
VOL.
13,
1965
where pPd, the effective atomic moment of palladium in Bohr magnetons, is about 1.44.(a5)* For the alloys that have a full 4&band, (Npd < 0.4),@7) the effective atomic moment of palladium in the alloy, pall,_,, equals zero. Where the 4d-band is only partially filled, (Nr, > 0.4) p,,,,, is approximated by the relation 2.4ONr, - 0.96, if it is assumed that pallor varies linearly with the decrease in palladium concentration. The electronic and lattice vibrational contributions to the enthalpy, computed at 298°K from the electronic specific heat coefllcients and Debye temperatures, are quite small and negative as seen in Fig. 4.
CONTRIBUYIONS
Fm. 3. Estimated nonconfigurational contributions to the excess entropy of palladium-silver alloys at 298°K and values derived from experimental data of present work at 1200°K. I vibrational (electronic + lattice), II magnetic (a, paramagnetio palladium with randomly orientated moments; b, diamagnetic silver; c, hypothetical paramagnetic palladium with no moments).
entropy is dependent upon the change that occurs upon alloying in the degree of rando~e~ in the orientation of the atomic magnetic moments assoeiated with the palladium atoms. By applying classical Boltzmann statistics, Weiss and Tauer(s2)have derived an expression that describes the limiting value of the magnetic entropy for metals that obey a localized electron model. Unfortunately, this relation is not applicable for palladium at ambient temperatures, which is best described in terms of a collective electron model,@@) governed by the statistics of Fermi-Dime. In spite of the fact that at ~m~ratures considerably above the degeneracy temperature, (T, N 13OO’K for Pd(%j), the classical limit to the Fermi-Dirac statistics is effectively reached, it is unlikely that either electron model accurately describes the behavior of palladium at 12OO’K. In view of this dilemma and in the absence of an expression for the magnetic entropy based on Fermi-Dirac statistics, the magnetic entropy for the palladiumsilver alloys has been estimated by means of a simple expansion of the relationship of Weiss and Tauer. The resulting values are considered larger in magnitude than the true magnetic contribution to the entropy. Accordingly, near the solidus, AS (magnetic) approaches as a limit
NAQ FIG. 4. Estimated-vibration&l contribution ta the enthalpy of palladium-silver alloys at 296°K and values derived from experimental data of present work at 1200’K.
The enthalpy t,erm associated with the decrease in the relative Fermi energy, E, alloy - N,,,E, rd as a result of the transfer of electrons NAgEf AP upon alloying from the 5s-band of silver to the 4d-band of palladium is negative.t16z17)The minimum in the enthalpies at approximately 60 at.% Ag is indicative, if the band structure is rigid,izo) of the maximum negative deviation in the relative Fermi energy at that composition. The good agreement between the enthalpies measured by calorimetric methods and those computed from the vapor pressure data suggests that the entropies of the present work are also fairly reliable. However, as noted in Fig. 3, the estimated contributions to the entropy are several times larger than the experimental values. This discrepancy may be rationalized in part by assu~ng that the negative * From Ref. 25, pra = 2.827 O1/a where C is the paramagnetic Curie constant, expressed in e.m.u.-deg/mole, derived from the magnetic susceptibility data of Ref. 26. This value of prp is in statistical agreement with the relationships developed in Ref. 22.
MYLES:
THERMODYNAMIC
PROPERTIES
vibrational contributions to the entropy and the enthalpy, as approximated from low ~rn~rature specific heat data, are considerably too large numerically. If this assumption is correct, then, as may be seen in Fig. 4, the bulk of the enthalpy must be attribut,ed to contributions arising from alterations in the electron distribution upon alloying. 5. SUMMARY
The interesting correlation between the results of this investigation and the proposed band structure of palladium-silver alloys(27) tends to demonstrate the importance of nonconfigurational and nonvibrational contributions to the thermodynamics associated with the formation of transition-metal alloys. Further, the agreement between the enthalpy values of this study and those found by calorimetric methods suggests that entropy and enthalpy data ~loula~d from the temperature dependences of vapor pressures can be quite reliable. ACKNOWLEDGMENTS
The author wishes to thank Dr. M. V. Nevitt, Dr. A. T. Aldred and Dr. D. J. Lam of the Argonne National Laboratory, for their helpful discussions and for reading the manuscript. REFERENCES 1. R. RUER, Z.~~~~.C~e~. 51, 315 (1906). 2. C. N. RAO and K. K. RAO, Phil. Mtxg. 9, 527 (1964).
OF
Pd-Ag
ALLOYS
113
sndE. L. EVANS, MetaZZurgicaE Them3. 0. KUBASCHEWSKI chem~et~. Pergamon Press, Now York, N.Y. (1958). 4. K. M. MYLES, Argollne Nstional Lsboratory, Argonne. Ill., ANL-6657 (1963). 5. K. M. MYLES rendA. T. ALDILED,J. Phys. Chem. 68, 64 (1964). 0 o. A. T. ALDREDand K. M. MYLES, Trans. Amer. Inst. Min. (Met&.) Engra. 230, 736 (1964). 7. R. D. FREEMANand A. W. SEARCY, J. Ch.em. Phys. 22, 762 (1954). 8. A. W. SEARCY, R. D. FREEMAN and M. C. MOREL, J. Amer. Chem. Sot. ‘X%,4050 (1954). P. SCHISSEL, $1.Chem. Phys. 26, 1276 (1957). W. A. CRUPKAand M. G. INGHRAM,J. Phw. Chem. 59, 100 (1955). 11. J. DROWAR~ and R. E. HONIG, J. Chem. Phys. 25, 581 (1956). 12. Yu. V. KORNEV and E. Z. V~KT~IKI~~,Sow. Phys. Dok2. 1, 203 (1956). 13. G. M. MARTYNOVICH.Vestnik Moskov. Gos. Univ., Ser Mat. Mekh. A&r. Fir: Khim., No. 2, 151 (1955). 14. M. B. PANISH, J. Chem. Eng. Data 6, 592 (1961). 15. N. G. SCHMAHL,2. anorg. Chem. 286, 1 (1951). 16. J. N. PRATT, Trans. FaTad. Sot. 56, 975 (1960). 17. J. P. GHAN, P. D. ANDERSON,R. L. ORR snd R. HULTCREN, 4th Tech. Rept., Miner& Research Lsborotory, Berkeley, Cslif., October 1, 1959. 18. R. ORIANI rendW. K. MURPHY, Acta Met. IO, 879 (1962). IQ. 0. J. KLEPPA, paper contributed to Colloquium on The Structure of Metallic Solid Solutions, Orsrty, France, Julv Q-11. 1962. 20. F. 8. Ho& and B. Yates, Proc. Roy. Sot. A240,42 (1957). 21. ~~~dol~-~~r~ete~n 2, 742 (1961). 22. R. J. WEISS and K. J. TAVER, P&/s. Eev. 102.1490 (1956). 23. M. SHIMIZU,J. Phy. SW. Joga% i5, 376 (1960). 24. P. RHODESand E. P. WOE~FARTH. Proc. Row. SW. A273. 247 (1963). S. ~RAJ~ (private communication). !Z: J. WUCHER, C.R. Acad. SC?:. Paris 242, 1143 (1956). 27. F. E. HOARE, in Electronic Structure and AEZoy Chemistry of the T~a~~t~~ Elem&s. Interscience, New York, N.Y. (1963).
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