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The low-temperature specific-heats of several palladium-rich palladium-antimony alloys
J. Phys. Chem. Solids
Petgamon Press 1970. Vol. 3 1, pp. 2735-2739.
Printed in Great Britain.
THE LOW-TEMPERATURE SPECIFIC-HEATS OF SEVERAL PALLADIUM-RICH PALLADIUMANTIMONY ALLOYS* PAUL J. TSANG Michigan State University East Lansing, Mich. 68823 and IBM, East Fishkill Facility, Hopewell Junction, N.Y. 12533, U.S.A.
and J. B. DABBY, Jr. Argonne National Laboratory Argonne, III. 60439, U.S.A. (Received 6 February 1970) Abstract-The low-temperature specific-heat coefficients y and the corresponding Debye temperatures 0 were determined for four palladium-rich terminal solid-solution alloys containing 3,6,9 and 12 at.% antimony. The specific-heat results can be correlated with the room-temperature magnetic susceptability and the vacant d-states of palladium decrease as the solute concentration increases but at a reduced rate when compared with noble metal-palladium systems. Comparison with Mossbauer results obtained over the same concentration range of the palladium-antimony system and optical data on noble mew-p~l~iurn alloys suggest that a screening model, in which each atomic cell is eiectricalty neutral, is a more appropriate description than a charge transfer model.
THE ELECTRONIC structure
of several binary palladium alloys has been investigated extensively by a variety of techniques. These alloys are of interest because pure palladium has a nearly filled d-band, with high density of states at the Fermi level, that decreases rapidly as noble metals or polyvalent solutes are dissolved in pahadium. Thus, several macroscopic properties of pahadium alloys, such as the magnetic susceptibility and electronic specific heat, show large variations with composition and provide a definitive basis for the comparison of experimental results among the various palladium-base alloy systems. A large quantity of magnetic susceptibility data are available on p~la~urn alloys. The susceptibi~ty results for a variety of binary systems (including Pd-Ag[ 11, Pd-Au [2], Pd-Cu[3], Pd-Al[4], Pd-Cd[5], Pd-In[fi], Pd-Sb [5], and Pd-Sn [7]) lie more or less on a common curve, when plotted as a function of *Work performed under the auspices ofthe U.S. Atomic Energy Commission.
the electron concentration e/u. The rate of change of the susceptibility is approximately proportional to the effective valency of the solute. If the spin paramaguetic susceptibility of the electrons in the 4d-band of palladium is the principal contribution to the total susceptibility of the alloys, then the electron concentration at which the transition from paramagnetic to di~agnetic behavior occurs should correspond to the complete filling of the vacant 4d holes of palladium. Electronic specific-heat measurements have been made on only a few of the palladium alloys, i.e. the complete series of solid solutions in the Pd-Ag system[ 11, the 52 at.% Sn in palladium [S] , and a few alloys in the Pd-Th and Pd-U systems[8]. When the electronic specific-heat coefilcient y is plotted vs. electron concentration ela for the alloys in the four systems, a common curve is obtained when effective valencies of 4, 4 and 6 are assigned to tin, thorium, and uranium, respectively. The y values for the Pd-Ag system[l] decrease abruptly to low values at the same ela ratio at which the d-holes in Pd are filled,
2735
2736
P. J. TSANG
and J. B. DARBY,
as indicated by the susceptibility results. A rigid-band interpretation for the various properties of palladium-base alloys appears to be inadequate in view of theoretical calculations [9] of the electron-magnon interactions and recent de Haas-van Alphen measurements on pure palladium [ lo]. Thus, experimental y values give only a qualitative indication of the variation of the density of states of alloys with composition, and an accurate assessment of the various interactions are required to obtain the true density-of-states curve. The experimentally determined Fermi surface of palladium from Vuillemin’s measurements [8], confirmed by the calculations of Mueller and Priestley [ 111, clearly indicate that the d-band of p~ladium contains 0.36 holes rather than the 0.6 hole predicted from rigid-band arguments. While a theoretical basis for relating thermodynamic properties, such as heats of formation, to the electronic structure of alloys does not exist, a correlation between the electronic structure and the heats of formation has been suggested for a few alloy systems [ 121. The heats of formation AHf at 298°K were determined for the p~la~um-~ch solid solutions in the Pd-Cd, Pd-In, Pd-Sn and Pd-Sb systems [ 131. When the heats-of-formation values are plotted as a function of electron concentration e/a (assuming the group valence for the solutes), the values for the systems containing the solutes Cd, In, or Sn lie essentially on a common curve, while the Pd-Sb values are substanti~ly above the curve. It has been observed[l4] that antimony does not always display the group valence of five in compounds. Also, the room-temperature magnetic susceptibility vs. e/a curve for palladium-rich Pd-Sb terminal solid-solution alloys [5] deviates from the curve for the Pd-Ag system above 5 at.% antimony. Low-temperature specific-heat data for the Pd-Sb system were not available to compare with the trend observed in the susceptibility results. The present investigation was initiated to determine if the y values for the palladium-rich
Jr.
Pd-Sb alloys would superimpose on the y vs. e/a curve for Pd-Ag alloys derived from lowtemperature specific-heat measurements. 2. EXPERIMENTAL
TECHNIQUES
The low-temperature specific-heat measurements were made on four palladium alloys cont~ning 3, 6, 9 and 12 at.% ~timony, respectively. To compensate for the reduction in specific heat as the antimony concentration increased, the specimen mass appropriate for low-temperature calorimetry studies varied from approximately 37 g for the 3 at.% antimony alloy to 113 g for the 12 at.% alloy. The alloys were prepared by arc-melting the requisite amounts of 99.99 + % pure palladium and 99995% pure antimony on a water-cooled copper hearth in a helium-argon atmosphere, Several of the individual buttons produced by arc melting (mass of 15-20 g each) were charged into a high-purity recrystallized alumina crucible and remelted in an induction furnace under a high-purity (99.999%) argon atmosphere to produce an ingot approaching a right-circular cylinder. The ingot was completely enclosed in an envelope of molybdenum foil, sealed in an evacuated quartz capsule, and annealed at 1000°C for 24 hr; followed by an anneal at 1100°C for 72 hr to continue the homogenization process. The annealing was terminated by a water quench without breaking the capsule. The ingot was then machined, without any lubricants, into a three-quarter-inch diameter right-circular cylinder. All surfaces were ground with emery paper to remove surface conta~nation, cleaned in acetone, and given a ilnal rinse in alcohol. A strain-relief anneal followed for 1 hr at 1100°C and the specimen was furnace cooled to room temperature. A metallographic examination confirmed that the alloys consisted of a single phase and were free of segregation. The low-tem~rature specific-heat measurements were carried out between 1.4 and 4.2X in a 4He cryogenic facility [ 153. Each alloy ingot was cut into two specimens of equal
THE LOW-TEMPERATURE
volume. One surface of each specimen was ground and polished to ensure good thermal contact with the heater-thermometer assembly. The sample and heater-thermometer assembly con8guration was similar to that described by Wei etal.[16]. A semiconducting carbon resistor, with a nominal resistance of 6OfI at room temperature, was employed as a thermometer. The thermometer was calibrated against the NBS (1958) 4He Temperature Scale prior to each experiment, and the data were fitted to the equation (In R/T)‘j2 = A + BlnR.
(1)
2737
SPECIFIC-HEATS
Table 1. Values of the electronic specificheat coeficient and the Debye temperature of palladium-rich Pd-Sb alloys Alloy composition (at.% Sb)
yx l(r (cal/molede@)
3 6 9 12
17.78 13.86 10.21 5.78
280.1 278.6 249.1 250.2
241 20
The coefficients A and B, determined by the least-squares method, were -1M6643 and O-624630, respectively. The maximum rootmean-square deviation of the experimental points from the thermometer calibration curve, fitted to equation (l), is O-05 per cent, while the maximum total calibration error is less than l-5 per cent [ 171. 3. RESULTS
At least 40 heat-capacity values were determined for each alloy between l-4 and 4*2”K and gave a good fit to the heat-capacity equation C,IT=
y+/3T2.
By extrapolation of a least-squares fit of the experimental CJT vs. T2 curves to absolute zero, the electronic specific-heat coefficients y for the four alloys were obtained, and the corresponding Debye temperatures 8 were calculated from the slope of the curves. The y and 19values are tabulated in Table 1 and the CJT vs. T2 curves are shown in Fig. 1. In Fig. 2, the electronic specific-heat coefficients y for the Pd-Sb alloys are plotted as a function of electron concentration e/a. The e/a ratio for a given alloy was obtained by assuming that the total number of 5s and 5p electrons of Sb contributed to the alloy was five.
0
4
6 p,
.g
I6
20
Fig. 1. C,/T vs. T* plot for palladium-rich alloys.
The y values reported by Hoare et al. [l] for a major portion of the Pd-Ag system are included in Fig. 2 for comparison. 4. DISCUSSION
The assumption that the five conduction electrons of antimony are transferred to the empty d holes in palladium may not be valid, since the y values for the Pd-Sb alloys lie above the y vs. e/a curve for the Pd-Ag system; although the general trend that y decreases as the solute concentration increases is noted for both the Pd-Ag and Pd-Sb values. If the y values from the present measurements are superimposed on the curve for the Pd-Ag system, the number of electrons of antimony transferred can be inferred, neglecting en-
2738
P. J. TSANG
mPd-Ag,
Hoare et
A Pd-Rh, 0 Pd-Sb,
0 96
3 ’ 98
I
’ 100
’
’ 102 e/a
’
and J. B. DARBY, Jr.
Present work
’ IO.4
’
’ 106
’ IO-8
Fig. 2. Electronic specific-heat coefficients versus electron concentration for palladium-rich Pd-Sb and Pd-Rh alloys and for the Pd-Ag binary system.
hancement effects, by projecting the experimental values onto the abscissa. The extrapolation indicates that approximately 3.7 electrons would be transferred. Although the value derived from the extrapolation is not exact, since interactions that may enhance the y quantities have been ignored, the apparent number of conduction electrons of antimony that would participate in a chargetransfer interpretation would be less than five. Hence, the specific-heat measurements appear to correlate with the observations from ma~etic-susceptibility studies. Magnetic susceptib~ity me~urements have been carried out on the palladium-rich solid solutions of the Pd-Cd[S], Pd-In[6], Pd-Sn [7], and Pd-Sb [5] systems. The susceptibility results for the Pd-Ag and Pd-Cd alloys superimpose essentially on a common curve when plotted as a function of electron concentration. The remaining three systems also lie on the same general curve (assuming rigid-band behavior) up to approximately 8.8, 5.5 and 2.6 at.% indium, tin, or antimony, respectively, and then progressively deviate from the curve as the solid-solubility limit is approached. The deviations indicate that the ‘apparent valency’ of the three solutes decreases, with concen-
tration, from the valence assigned according to the group number in the periodic table. In order for the susceptibility values to coincide with the Pd-Ag values at higher concentrations, the apparent valence of tin or antimony would be approximately three or four, respectively. In terms of the electronic state of free atoms, the three polyvalent solutes indium, tin, and antimony are likely to display p-like as well as s-like character, and Harris et al. [7f have suggested that the susceptibility deviations may indicate the formation of localized p states. A model has been proposed by Montgomery et al.@] for palladium alloys, with noble or polyvalent elements as solutes, that provides an interesting alternative to the requirement of charge transfer for the rigid-band model. It is assumed that every atomic cell in an alloy is electrically neutral and differences in the nuclear charges are essentially screened by the itinerant electrons,* i.e. a charge of Z-conduction electrons is associated with a solute site. The effect of a polyvalent solute ‘is to induce the palladium matrix to convert some of its own s electrons into d electrons’ until the n~ber of d holes in palladium decreases to zero at an e/a ratio of approximately O-6. The model is attractive in that it is not necessary to correlate the critical e/a ratio with the number of d holes in elemental palladium, nor the solute valency 2 with the rate at which the d band fills. Therefore, the model is consistent with the de Haas-van Alphen results that indicate O-36 d holes in pure palladium, and with the abrupt changes observed at the critical e/a ratio in the average properties, such as specific heats and magnetic susceptibilities. Some information has been obtained on the conduction-electron density at tin (l”Sn) or *Experimental justification is the fact that the tetrago4 phase (a’) in the pahadium-rich Pd-Cd system reverts to a face-centered-cubic modification by mechanical working of the aIloy[lB]. Also, the compound Pd$n has a face-cente~d-tet~on~ structure that can be converted to a face-centered-cubic form by deformation f 191. Hence, the ordering energy is much smaher than the Madelung energy in an ionic crystal.
THE LOW-TEMPERATURE
SPECIFIC-HEATS
2739
antimony ( 121Sb)nuclei in binary palladium results show a correlation between the rate alloys from the isomer shifts in the Miissbauer at which the d band fills and the solute valency spectra[7,203. The isomer shifts are derived in palladium-antimony alloys. The correlation from a change in the charge radius of the is, at most, qualitative and it appears that a nucleus when a ‘y-ray is emitted and the shifts screening model, in which the solute atoms vary linearly with the electron density at the are nearly perfectly screened by conduction electrons, is compatible with the measurenuclear site. Harris and Cordey-Hayes[7] reported negative values for the llgSn isomer ments of various properties of palladium shifts for the pahadium-rich solid solutions alloys. that indicate Ss-electron density about the tin Acknowledgements-The authors are indebted to Dr. C. nuclei is less than in /3-Sn, and suggested the T. Wei, Michigan State University, for providing the facilities and for fruitful discussions. Mr. results are consistent with a simple rigid-band experimental Paul Paulikas provided experimental assistance in the model. Montgomery and Ruby[20] measured preparationof the alloys. We thank Dr. H. Montgomery the isomer shifts in palladium-rich Pd-Sb and Dr. F. M. Mueller for useful discussions and suggesalloys and found a close correlation with the tions. Pd-Sn results. If a ch~ge-transfer inter1. HOARE F . E., MATTHEWS J. C. and WALLING pretation is applied, the ‘apparent valency’ of J. C., Proc. R. Sot. A216,502 (1953); HOARE F. E. and YATES B.. Proc. R. Sot. AZW 42 (1957). antimony in the Pd-Sb alloys is somewhat . ’ 2. VOGT E., Ann: Phys. 14,l (1932). less than 4. However, Montgomery and Ruby 3. SVENSSON B., Ann. Phys. 14,699 (1932). [20] qu~itatively explain the isomer shifts for 4. GERSTENBERG D.,Ann. P&s. 2,236 (1958). 5. LAM D. J. and MYLES K. M., J. phys. Sot. Japan the Pd-Sb and Pd-Sn alloys in terms of a 21,1503 (1966). screening model. To a first approximation 6. HARRIS I. R., NORMAN M. and BRYANT A. each atomic cell in the alloys is electrically W., J. less-common Metals 16,427 (1968). neutral as suggested by Friedel’s theory [2 1J, 7. HARRIS I. R. and CORDEY-HAYES M., J. Zesscommon Metals 16,223 f 1968). and the d-band level of palladium is filled by the 8. MONTGOMERY H., PELLS 0. P. and WRAY conversion of s electrons into d electrons E. M.. Proc. R. Sot. A301.261 (1967). within the palladium cells. However, the de- 9. MUELLER F. M., FREEMAN A.‘J., DIMMOCK J. 0. and FURDYNA A. EA., Phys. Rev. (In press). tailed mechanism by which the solute atoms 10. WINDMILLER L. R. and KETTERSON J. B.. perturb the d band of palladium remains unPhys. Rev. Lett. 21, 1076 (1968). 11. MUELLER F. M. and PRIESTLEY M. G.. Phvs. resolved. Rev. 148,638 (1966). Further support for the screening model of 12. DARBY J. B. Jr., Acta Metall. 14,265 (1966). Montgomery and Ruby is found in the mea- 13. DARBY J. B. Jr., MYLES K. M. and PRATT J. N., Acta MetaN. (In press). surements of the optical absorption spectrum by Myers er al. [22] in alloys of palladium in 14. PAULING L., The Nature of the Chemical Bond. Cornell University Press, New York (1960). copper, silver, or gold. The results show that 15. For details of the system see WE1 C. T., Ph.D. Thesis, University of Illinois 1958, and TSANG P. J. the d-electrons of both silver and palladium and WE1 C. T. (To be uublished). atoms in silver-palladium alloys may be con- 16. WE1 C. T., CHANG-C. H. and BECK P. A., Phys. sidered as occupying bound states over the Rev. 120,426 (1960). entire composition range and no significant 17. TSANG P. J., Ph.D. Thesis, Michigan State Uni(1968). overlap occurs either in energy or space, con- 18. versity PRATT J. N., MYLES K. M., DARBY J. B. Jr. trary to the requirements of a rigid-band and MUELLER M. H., J. less-common Metals 14, 427 (1968). model. The distribution of conduction-elecPRATT 1. N., University of Birmingham, Birmingtron charge density was very nonunifo~ and 19. ham, England (private ~o~uni~tion). associated totally with the silver atoms in 20. MONTGOMERY H. and RUBY S., Phys. Reu. Bl, 2948 (1970). alloys containing less than 40 at.% palladium. 21. FRIEDEL J., Adv. Phys. 3,446 (1954). In summary, the electronic specific-heat 22. MYERS H. P., WALLDEN L. and KARLSSON coefficients and the magnetic susceptibility A., Phil. Mag. 18,725 (1968).
Petgamon Press 1970. Vol. 3 1, pp. 2735-2739.
Printed in Great Britain.
THE LOW-TEMPERATURE SPECIFIC-HEATS OF SEVERAL PALLADIUM-RICH PALLADIUMANTIMONY ALLOYS* PAUL J. TSANG Michigan State University East Lansing, Mich. 68823 and IBM, East Fishkill Facility, Hopewell Junction, N.Y. 12533, U.S.A.
and J. B. DABBY, Jr. Argonne National Laboratory Argonne, III. 60439, U.S.A. (Received 6 February 1970) Abstract-The low-temperature specific-heat coefficients y and the corresponding Debye temperatures 0 were determined for four palladium-rich terminal solid-solution alloys containing 3,6,9 and 12 at.% antimony. The specific-heat results can be correlated with the room-temperature magnetic susceptability and the vacant d-states of palladium decrease as the solute concentration increases but at a reduced rate when compared with noble metal-palladium systems. Comparison with Mossbauer results obtained over the same concentration range of the palladium-antimony system and optical data on noble mew-p~l~iurn alloys suggest that a screening model, in which each atomic cell is eiectricalty neutral, is a more appropriate description than a charge transfer model.
THE ELECTRONIC structure
of several binary palladium alloys has been investigated extensively by a variety of techniques. These alloys are of interest because pure palladium has a nearly filled d-band, with high density of states at the Fermi level, that decreases rapidly as noble metals or polyvalent solutes are dissolved in pahadium. Thus, several macroscopic properties of pahadium alloys, such as the magnetic susceptibility and electronic specific heat, show large variations with composition and provide a definitive basis for the comparison of experimental results among the various palladium-base alloy systems. A large quantity of magnetic susceptibility data are available on p~la~urn alloys. The susceptibi~ty results for a variety of binary systems (including Pd-Ag[ 11, Pd-Au [2], Pd-Cu[3], Pd-Al[4], Pd-Cd[5], Pd-In[fi], Pd-Sb [5], and Pd-Sn [7]) lie more or less on a common curve, when plotted as a function of *Work performed under the auspices ofthe U.S. Atomic Energy Commission.
the electron concentration e/u. The rate of change of the susceptibility is approximately proportional to the effective valency of the solute. If the spin paramaguetic susceptibility of the electrons in the 4d-band of palladium is the principal contribution to the total susceptibility of the alloys, then the electron concentration at which the transition from paramagnetic to di~agnetic behavior occurs should correspond to the complete filling of the vacant 4d holes of palladium. Electronic specific-heat measurements have been made on only a few of the palladium alloys, i.e. the complete series of solid solutions in the Pd-Ag system[ 11, the 52 at.% Sn in palladium [S] , and a few alloys in the Pd-Th and Pd-U systems[8]. When the electronic specific-heat coefilcient y is plotted vs. electron concentration ela for the alloys in the four systems, a common curve is obtained when effective valencies of 4, 4 and 6 are assigned to tin, thorium, and uranium, respectively. The y values for the Pd-Ag system[l] decrease abruptly to low values at the same ela ratio at which the d-holes in Pd are filled,
2735
2736
P. J. TSANG
and J. B. DARBY,
as indicated by the susceptibility results. A rigid-band interpretation for the various properties of palladium-base alloys appears to be inadequate in view of theoretical calculations [9] of the electron-magnon interactions and recent de Haas-van Alphen measurements on pure palladium [ lo]. Thus, experimental y values give only a qualitative indication of the variation of the density of states of alloys with composition, and an accurate assessment of the various interactions are required to obtain the true density-of-states curve. The experimentally determined Fermi surface of palladium from Vuillemin’s measurements [8], confirmed by the calculations of Mueller and Priestley [ 111, clearly indicate that the d-band of p~ladium contains 0.36 holes rather than the 0.6 hole predicted from rigid-band arguments. While a theoretical basis for relating thermodynamic properties, such as heats of formation, to the electronic structure of alloys does not exist, a correlation between the electronic structure and the heats of formation has been suggested for a few alloy systems [ 121. The heats of formation AHf at 298°K were determined for the p~la~um-~ch solid solutions in the Pd-Cd, Pd-In, Pd-Sn and Pd-Sb systems [ 131. When the heats-of-formation values are plotted as a function of electron concentration e/a (assuming the group valence for the solutes), the values for the systems containing the solutes Cd, In, or Sn lie essentially on a common curve, while the Pd-Sb values are substanti~ly above the curve. It has been observed[l4] that antimony does not always display the group valence of five in compounds. Also, the room-temperature magnetic susceptibility vs. e/a curve for palladium-rich Pd-Sb terminal solid-solution alloys [5] deviates from the curve for the Pd-Ag system above 5 at.% antimony. Low-temperature specific-heat data for the Pd-Sb system were not available to compare with the trend observed in the susceptibility results. The present investigation was initiated to determine if the y values for the palladium-rich
Jr.
Pd-Sb alloys would superimpose on the y vs. e/a curve for Pd-Ag alloys derived from lowtemperature specific-heat measurements. 2. EXPERIMENTAL
TECHNIQUES
The low-temperature specific-heat measurements were made on four palladium alloys cont~ning 3, 6, 9 and 12 at.% ~timony, respectively. To compensate for the reduction in specific heat as the antimony concentration increased, the specimen mass appropriate for low-temperature calorimetry studies varied from approximately 37 g for the 3 at.% antimony alloy to 113 g for the 12 at.% alloy. The alloys were prepared by arc-melting the requisite amounts of 99.99 + % pure palladium and 99995% pure antimony on a water-cooled copper hearth in a helium-argon atmosphere, Several of the individual buttons produced by arc melting (mass of 15-20 g each) were charged into a high-purity recrystallized alumina crucible and remelted in an induction furnace under a high-purity (99.999%) argon atmosphere to produce an ingot approaching a right-circular cylinder. The ingot was completely enclosed in an envelope of molybdenum foil, sealed in an evacuated quartz capsule, and annealed at 1000°C for 24 hr; followed by an anneal at 1100°C for 72 hr to continue the homogenization process. The annealing was terminated by a water quench without breaking the capsule. The ingot was then machined, without any lubricants, into a three-quarter-inch diameter right-circular cylinder. All surfaces were ground with emery paper to remove surface conta~nation, cleaned in acetone, and given a ilnal rinse in alcohol. A strain-relief anneal followed for 1 hr at 1100°C and the specimen was furnace cooled to room temperature. A metallographic examination confirmed that the alloys consisted of a single phase and were free of segregation. The low-tem~rature specific-heat measurements were carried out between 1.4 and 4.2X in a 4He cryogenic facility [ 153. Each alloy ingot was cut into two specimens of equal
THE LOW-TEMPERATURE
volume. One surface of each specimen was ground and polished to ensure good thermal contact with the heater-thermometer assembly. The sample and heater-thermometer assembly con8guration was similar to that described by Wei etal.[16]. A semiconducting carbon resistor, with a nominal resistance of 6OfI at room temperature, was employed as a thermometer. The thermometer was calibrated against the NBS (1958) 4He Temperature Scale prior to each experiment, and the data were fitted to the equation (In R/T)‘j2 = A + BlnR.
(1)
2737
SPECIFIC-HEATS
Table 1. Values of the electronic specificheat coeficient and the Debye temperature of palladium-rich Pd-Sb alloys Alloy composition (at.% Sb)
yx l(r (cal/molede@)
3 6 9 12
17.78 13.86 10.21 5.78
280.1 278.6 249.1 250.2
241 20
The coefficients A and B, determined by the least-squares method, were -1M6643 and O-624630, respectively. The maximum rootmean-square deviation of the experimental points from the thermometer calibration curve, fitted to equation (l), is O-05 per cent, while the maximum total calibration error is less than l-5 per cent [ 171. 3. RESULTS
At least 40 heat-capacity values were determined for each alloy between l-4 and 4*2”K and gave a good fit to the heat-capacity equation C,IT=
y+/3T2.
By extrapolation of a least-squares fit of the experimental CJT vs. T2 curves to absolute zero, the electronic specific-heat coefficients y for the four alloys were obtained, and the corresponding Debye temperatures 8 were calculated from the slope of the curves. The y and 19values are tabulated in Table 1 and the CJT vs. T2 curves are shown in Fig. 1. In Fig. 2, the electronic specific-heat coefficients y for the Pd-Sb alloys are plotted as a function of electron concentration e/a. The e/a ratio for a given alloy was obtained by assuming that the total number of 5s and 5p electrons of Sb contributed to the alloy was five.
0
4
6 p,
.g
I6
20
Fig. 1. C,/T vs. T* plot for palladium-rich alloys.
The y values reported by Hoare et al. [l] for a major portion of the Pd-Ag system are included in Fig. 2 for comparison. 4. DISCUSSION
The assumption that the five conduction electrons of antimony are transferred to the empty d holes in palladium may not be valid, since the y values for the Pd-Sb alloys lie above the y vs. e/a curve for the Pd-Ag system; although the general trend that y decreases as the solute concentration increases is noted for both the Pd-Ag and Pd-Sb values. If the y values from the present measurements are superimposed on the curve for the Pd-Ag system, the number of electrons of antimony transferred can be inferred, neglecting en-
2738
P. J. TSANG
mPd-Ag,
Hoare et
A Pd-Rh, 0 Pd-Sb,
0 96
3 ’ 98
I
’ 100
’
’ 102 e/a
’
and J. B. DARBY, Jr.
Present work
’ IO.4
’
’ 106
’ IO-8
Fig. 2. Electronic specific-heat coefficients versus electron concentration for palladium-rich Pd-Sb and Pd-Rh alloys and for the Pd-Ag binary system.
hancement effects, by projecting the experimental values onto the abscissa. The extrapolation indicates that approximately 3.7 electrons would be transferred. Although the value derived from the extrapolation is not exact, since interactions that may enhance the y quantities have been ignored, the apparent number of conduction electrons of antimony that would participate in a chargetransfer interpretation would be less than five. Hence, the specific-heat measurements appear to correlate with the observations from ma~etic-susceptibility studies. Magnetic susceptib~ity me~urements have been carried out on the palladium-rich solid solutions of the Pd-Cd[S], Pd-In[6], Pd-Sn [7], and Pd-Sb [5] systems. The susceptibility results for the Pd-Ag and Pd-Cd alloys superimpose essentially on a common curve when plotted as a function of electron concentration. The remaining three systems also lie on the same general curve (assuming rigid-band behavior) up to approximately 8.8, 5.5 and 2.6 at.% indium, tin, or antimony, respectively, and then progressively deviate from the curve as the solid-solubility limit is approached. The deviations indicate that the ‘apparent valency’ of the three solutes decreases, with concen-
tration, from the valence assigned according to the group number in the periodic table. In order for the susceptibility values to coincide with the Pd-Ag values at higher concentrations, the apparent valence of tin or antimony would be approximately three or four, respectively. In terms of the electronic state of free atoms, the three polyvalent solutes indium, tin, and antimony are likely to display p-like as well as s-like character, and Harris et al. [7f have suggested that the susceptibility deviations may indicate the formation of localized p states. A model has been proposed by Montgomery et al.@] for palladium alloys, with noble or polyvalent elements as solutes, that provides an interesting alternative to the requirement of charge transfer for the rigid-band model. It is assumed that every atomic cell in an alloy is electrically neutral and differences in the nuclear charges are essentially screened by the itinerant electrons,* i.e. a charge of Z-conduction electrons is associated with a solute site. The effect of a polyvalent solute ‘is to induce the palladium matrix to convert some of its own s electrons into d electrons’ until the n~ber of d holes in palladium decreases to zero at an e/a ratio of approximately O-6. The model is attractive in that it is not necessary to correlate the critical e/a ratio with the number of d holes in elemental palladium, nor the solute valency 2 with the rate at which the d band fills. Therefore, the model is consistent with the de Haas-van Alphen results that indicate O-36 d holes in pure palladium, and with the abrupt changes observed at the critical e/a ratio in the average properties, such as specific heats and magnetic susceptibilities. Some information has been obtained on the conduction-electron density at tin (l”Sn) or *Experimental justification is the fact that the tetrago4 phase (a’) in the pahadium-rich Pd-Cd system reverts to a face-centered-cubic modification by mechanical working of the aIloy[lB]. Also, the compound Pd$n has a face-cente~d-tet~on~ structure that can be converted to a face-centered-cubic form by deformation f 191. Hence, the ordering energy is much smaher than the Madelung energy in an ionic crystal.
THE LOW-TEMPERATURE
SPECIFIC-HEATS
2739
antimony ( 121Sb)nuclei in binary palladium results show a correlation between the rate alloys from the isomer shifts in the Miissbauer at which the d band fills and the solute valency spectra[7,203. The isomer shifts are derived in palladium-antimony alloys. The correlation from a change in the charge radius of the is, at most, qualitative and it appears that a nucleus when a ‘y-ray is emitted and the shifts screening model, in which the solute atoms vary linearly with the electron density at the are nearly perfectly screened by conduction electrons, is compatible with the measurenuclear site. Harris and Cordey-Hayes[7] reported negative values for the llgSn isomer ments of various properties of palladium shifts for the pahadium-rich solid solutions alloys. that indicate Ss-electron density about the tin Acknowledgements-The authors are indebted to Dr. C. nuclei is less than in /3-Sn, and suggested the T. Wei, Michigan State University, for providing the facilities and for fruitful discussions. Mr. results are consistent with a simple rigid-band experimental Paul Paulikas provided experimental assistance in the model. Montgomery and Ruby[20] measured preparationof the alloys. We thank Dr. H. Montgomery the isomer shifts in palladium-rich Pd-Sb and Dr. F. M. Mueller for useful discussions and suggesalloys and found a close correlation with the tions. Pd-Sn results. If a ch~ge-transfer inter1. HOARE F . E., MATTHEWS J. C. and WALLING pretation is applied, the ‘apparent valency’ of J. C., Proc. R. Sot. A216,502 (1953); HOARE F. E. and YATES B.. Proc. R. Sot. AZW 42 (1957). antimony in the Pd-Sb alloys is somewhat . ’ 2. VOGT E., Ann: Phys. 14,l (1932). less than 4. However, Montgomery and Ruby 3. SVENSSON B., Ann. Phys. 14,699 (1932). [20] qu~itatively explain the isomer shifts for 4. GERSTENBERG D.,Ann. P&s. 2,236 (1958). 5. LAM D. J. and MYLES K. M., J. phys. Sot. Japan the Pd-Sb and Pd-Sn alloys in terms of a 21,1503 (1966). screening model. To a first approximation 6. HARRIS I. R., NORMAN M. and BRYANT A. each atomic cell in the alloys is electrically W., J. less-common Metals 16,427 (1968). neutral as suggested by Friedel’s theory [2 1J, 7. HARRIS I. R. and CORDEY-HAYES M., J. Zesscommon Metals 16,223 f 1968). and the d-band level of palladium is filled by the 8. MONTGOMERY H., PELLS 0. P. and WRAY conversion of s electrons into d electrons E. M.. Proc. R. Sot. A301.261 (1967). within the palladium cells. However, the de- 9. MUELLER F. M., FREEMAN A.‘J., DIMMOCK J. 0. and FURDYNA A. EA., Phys. Rev. (In press). tailed mechanism by which the solute atoms 10. WINDMILLER L. R. and KETTERSON J. B.. perturb the d band of palladium remains unPhys. Rev. Lett. 21, 1076 (1968). 11. MUELLER F. M. and PRIESTLEY M. G.. Phvs. resolved. Rev. 148,638 (1966). Further support for the screening model of 12. DARBY J. B. Jr., Acta Metall. 14,265 (1966). Montgomery and Ruby is found in the mea- 13. DARBY J. B. Jr., MYLES K. M. and PRATT J. N., Acta MetaN. (In press). surements of the optical absorption spectrum by Myers er al. [22] in alloys of palladium in 14. PAULING L., The Nature of the Chemical Bond. Cornell University Press, New York (1960). copper, silver, or gold. The results show that 15. For details of the system see WE1 C. T., Ph.D. Thesis, University of Illinois 1958, and TSANG P. J. the d-electrons of both silver and palladium and WE1 C. T. (To be uublished). atoms in silver-palladium alloys may be con- 16. WE1 C. T., CHANG-C. H. and BECK P. A., Phys. sidered as occupying bound states over the Rev. 120,426 (1960). entire composition range and no significant 17. TSANG P. J., Ph.D. Thesis, Michigan State Uni(1968). overlap occurs either in energy or space, con- 18. versity PRATT J. N., MYLES K. M., DARBY J. B. Jr. trary to the requirements of a rigid-band and MUELLER M. H., J. less-common Metals 14, 427 (1968). model. The distribution of conduction-elecPRATT 1. N., University of Birmingham, Birmingtron charge density was very nonunifo~ and 19. ham, England (private ~o~uni~tion). associated totally with the silver atoms in 20. MONTGOMERY H. and RUBY S., Phys. Reu. Bl, 2948 (1970). alloys containing less than 40 at.% palladium. 21. FRIEDEL J., Adv. Phys. 3,446 (1954). In summary, the electronic specific-heat 22. MYERS H. P., WALLDEN L. and KARLSSON coefficients and the magnetic susceptibility A., Phil. Mag. 18,725 (1968).