THE RELATIVE THERMODYNAMIC SOLID NICKEL-PALLADIUM L. R. PROPERTIES ALLOYS* OF and R. SPEISER$ BIDWELL? The relative thermodynamic properties of solid nickel-palladium alloys were determined in the temperature range 700-1200°C using a galvanic cell with a solid electrolyte. Within experimental error, the relative partial molar free energies of nickel were linear functions of the temperature, signifying that AC, above 700°C is essentially zero and that the specific heats at elevated temperatures can be approximated by the Kopp-Neumann rule. Nickel-rich solutions were found to exhijit endothermic enthalpies of mixing and positive deviations from Raoult’s law for the activity of the solvent and negative deviations for the activity of the solute. palladium-rich solutions, on the other hand, exhibit exothermic enthalpies of mixing and negative deviations from Raoult’s law for the activity of the solvent and solute alike. The excess entropies of mixing are positive for all compositions. This is considered to be primarily a result of the ferromagnetic properties of the alloys. From a consideration of magnetic, electronic, vibrational, and lattice distortional factors it has been concluded that nickel-palladium alloys, particularly those rich in palladium, exhibit significant short-range order. PROPRIETES THER~~ODYNAMIQUES DES ALLIAGES NICKELPALLADIUM Les auteurs ont Btudie les propriirtcs thermodynamiques relatives des atliages nickel-paladin B, l’etat so&de, dans le domaine de temperature de 700 B. 12OO”C, en utilisant une cellule Zt electrolyte solide. Dans les limites des erreurs experimentales, ils ont observe que les energies libres molaires partie&s du nickel etaient des fonctions lineaires de la temperature, ce qui implique que AC, est essentiellament nul au-dessus de 7OO”C, et qu’on peut obtenir, de man&e approchee, les chaleurs specifiques aux temperatures Blevees en utilisant la regle de Kopp-Neumann. Les autcurs ont observe que les solutions riches en nickel montraient des enthalpies de melanges endothermiques, des deviations positives de la loi de Raoult pour l’activitb du solvant et des deviations negatives pour l’activite du solute. D’autre part, les solutions riches en palladium montrent des enthalpies de melange exothermiques et des deviations negatives de la loi de Raoult aussi bien pour la solvant que pour lc solute. L’exces de l’entropie de Ces proprietes semblent &re au premier chef une melange est positif pour toutes les compositions. consequence des proprietes ferromagnetiques des alliages. En prenant en consideration les facteurs magnetiques, electroniques, vibratoires, et la distorsion du reseau, les auteurs concluent que les alliages nickel-palladium, et particulierement ceux riches en palladium, possedent un ordre rl petite distance significatif. DIE RELATIVEN THERMODYNAMISCH~~ EIGENSCHAFTEN PALLADIUM-LEGIERUNGEN FESTER NICKEL- Die relativen thermodynamischen Eigenschaften fester Nickel-Palladium-Legierungen wurden im Temperaturbereich 700-1200°C mit Hilfe einer galvanischen Zelle mit festem Elektrolyt bestimmt. Innerhalb der Fehlergrenzen warm die relativen partiellen molaren freien Energien von Nickel linearo Funktionen der Temperatur. Dies bedeutet, d& AC, oberhalb 700°C im wesentlichen Null ist und daB die spezifischen Warmen bei hohen Temperaturen durch die Kopp-Neumann-Regel approximiert werden k&men. Nickelreiche Legierungen zeigten endotherme ~~hungsenthalpien, positive Abweichungen vom Raoult’schen Gesetz fdr die Aktivitat des Lijsungsmittels und negative Abweichungen fur die Aktivitiit dss gel&ten Stoffes. Palladiumreiche Legierungen zeigten andererseits exotherme Mischungsenthalpien und negative Abweichungen vom Raoultschen Gesetz fur die Aktivitat sowohl des Losungsmittels als such des geliisten Stoffes. Die Uberschuflmisohungsentropien sind fur alla Zusammensetzungen positiv. Dies wird in erster Linie auf die ferromagnetischen Eigenschaften der Legierungen zurtickgefiihrt. Es wird auf Grund &nor Betrachtung dsr magnet&hen, elektronischen, Schwingungs- und Gitter-Ve~rrun~fak~~n geschlossen, de0 in Nickel-Pall~i~-Legierungen, insbesondere in den pall~iu~eichen, starke Nahordnung auftritt. INTRODUCTION THE nickel-palladium system, unlike the closely related Fe-I’d, Fe-P& Co-Pt, and Ni-Pt systems, has generally been regarded as a complete series of solid solutions in which no superlattices are formed.(l) The most prominent evid,enoe for the absence of ordering in the system is the careful X-ray diffraction work of Hulgtren and Zapffe.f2) Using a series of * Received May 4, 1964; revised June 22, 1964. This paper is based in part on a dissertation submitted by L. R. Bidwell to the Ohio State University in partial fulfillment of the requirements for the Ph.D. degree. t Aerosuace Research Laboratories. Office of Aerosnace Rekearch,-Wright-Patterson Air Force ‘Base, Ohio. * $ Department of Met.a~~gieal Engineering, The Ohio State University, Columbus, Ohio. ACTA METALLURGICA, VOL. 13, FEBRUARY 1965 well homogenized alloys that had been annealed for periods up to 2 weeks at 600°C and 3 weeks at 4OO”C, they found that the cell Dimensions followed a smooth curve as a function of composition with a considerable positive deviation from Vegard’s law.8 They could not 6nd any evidence for the existence of ordering or for a miscibility gap that had been suggested earlier by Fraenkel and Stern.t4) In recent years, however, several Russian investigate have noted anomalous electrical and magnetic behavior at the stoichiometric composition NiPd, which they conclude is due to the existence of a superstructure at that composition. Among the effects observed are 5 X-ray studies by the authors confirm this observation.(3’ 61 62 ACTA METALLURGICA, a satellite peak in the variation of the thermoelectrio force as a function of longitudinal and transverse magnetic field strength ;(S) a small but sharp variation in the Curie temperature and a maximum in the temperature coefficient of the longitudinal galvanomagnetic effect;@*‘) a sharp change in the magnitude of the odd Nernst-Ettingshausen effect;(s)* and a sharp change in magnetostriction in both longitudinal and transverse magnetic [email protected]) Although it is questionable whether or not these observations are related to the presence of a superlattice, particularly in view of the negative but more direct X-ray results, they do suggest that a tendency toward ordering, perhaps in the form of increased short-range order, may exist in palladium-rich alloys. This possibility becomes especially attractive when the nickelpalladium system is compared with the iron-palladium system. While iron has a larger number of positive holes in the d-band than nickel, there are many obvious similarities between the two systems, e.g., their small difference in atomic size, the conformation of their phase diagrams,“) and their deviations from Vegard’s law. t2) The iron-palladium system shows strong ordering effects, with superlattices stable to SOO-900°C being formed at compositions roughly corresponding to FePd and FePd,. It was expected that a knowledge of the solution properties of solid nickel-palladium alloys would contribute substantially to a better understanding of their alloying behavior and might also provide further insight into the question of ordering in the system. EXPERIMENTAL PROCEDURE The relative thermodynamic properties of solid nickel-palladium alloys were derived from measurements of the reversible potential of the solid galvanic cell Pt 1Ni, NiO 10.85Zr0, * 0.15CaO 1Ni-Pd, NiO 1Pt as a function of composition and temperature. Solid galvanic cells employing calcia stabilized ziroonia as the electrolyte have been used with considerable success by Kiukkola and Wagner(lO~ll) in determining the standard free energies of formation of several oxides at elevated temperatures and by Rapp and Maak(12) in an investigation of the thermodynamic properties of solid copper-nickel alloys. It can be shownds) that under conditions of pure anionic conductivity of the electrolyte, the activity (aNi) and relative partial molar free energy (Apx,) of nickel in the nickel-palladium alloy can be obtained directly * Reference 8 refers to Ni,Pd, however, the experimental data clearly indicate that Ni Pd, is intended. VOL. 13, 1965 from the open circuit potential of the cell using the relation E= -Elna, 2F = _A’Ni 21r” (1) where E is in volts, T is the absolute temperature, R is the gas constant, and F is the Faraday oonstant. The standard state for this case is solid nickel saturated with oxygen. However, since the solubility of oxygen in nickel is less than 0.08 at.% in the 700-1200°C temperature range covered,(i) this is essentially equivalent to a standard state corresponding to pure solid nickel. The nearly pure anionic conductivity of the electrolyte in this temperature range and in the range of oxygen partial pressures imposed by the electrodes (Ni-NiO equilibria for 0.04 < aNi < 1.0) has been well established by Kingery et uZ.(13) and by Schmalzried.04) According to the relative values of the standard free energies of formation of ZrO,, NiO, and Pd0,d5) mixed potentials arising from displacement reactions involving the cell components would not be expected. The cell apparatus consists of a cell holder and an impervious mullite reaction tube that serves as a gas-tight furnace enclosure for maintaining the cell in an inert environment, The reaction tube is graded to Pyrex joints at each end and.is encased in electrically grounded platinum foil in order to shield the measuring circuits from induced a.c. potentials. The essential features of the cell holder, which is a modification of the configuration employed by Schmalzried,06) are shown in Fig. 1. The tapered brass fixture serves as the seal for one end of the mullite reaction tube and as an exit for the electrical leads. In addition, it aligns the two small concentric mullite tubes which clamp the galvanic cell. A portion of the outer tube, which is held to the brass fixture under spring tension, is cut away to facilitate placement of the cell and to provide a seat for the alundum thrust block. The inner tube, which acts as a pushrod, is positioned via a compression spring by a hollow threaded screw located in the brass fixture. The hross Towed Ground Alignment Fixture Mullitr Tuber to fit Pyrex Gloss Joint FIG. 1. Schematic diagram of galvanic cell holder. BIDWELL AND SPEISER: THERMODYNAMICS tablets and platinum electrodes which make up the cell are held against the alundum thrust block by applying a moderate pressure with the pushrod. The cell, which consists of a stabilized zirconia electrolyte tablet sandwiched between metal plus nickel oxide electrodes backed with platinum contacts, is roughly 4 mm long by 8 mm dia., thus minimizing the effects of thermal gradients. The cell assembly was heated by a tubular resistance furnace which was held to within f 1.5”C by a proportional band controller. Cell temperatures were measured by means of a Pt-13% Rh thermocouple placed in the alunclum thrust block, l-2 mm from the alloy electrode. The thermocouple used for this purpose was calibrated against the melting points of pure zinc and gold. Cell potentials were measured with a Leeds and Northrup K-3 potentiometer and a high sensitivity galvanometer using a three wire circuit in which the platinum leg of the thermocouple acted as the positive lead to the galvanic cell. The negative lead to the cell was grounded through a 0.01 ,uF capacitor as a further precaution against the introduction of induced potentials. The alloys were prepared at nominal 10 at.% intervals from high purity carbonyl nickel and commercial high purity palladium sponge by induction melting in vacua. The alloy ingots were cold forged and then homogenized in vacua beginning with 5 hr at 1075”C, followed by successively higher temperatures, and ending with a 1 hr treatment within 100°C of the solidus. Chemical analyses of the alloys indicated that they contained less than 200 ppm impurities, exclusive of oxygen. The electrode tablets were prepared from reagent grade NiO and from metal powder ground from the homogenized ingots with a tungsten carbide dental drill. Prio; to use, the NiO was heated in purified helium several hours at 1000°C in order to free it of excess oxygen. Tablets 6 mm dia. by 2 mm thick were cold-pressed at 5000 psi in a hardened steel die. It was f0und from experience that metal to oxide ratios of 5 : 1 to 10: 1 were preferable to lower ratios because of the improved sensitivity in the measurements made possible by the lower circuit resistance. The electrolyte tablets were prepared from high purity Wah Chang (99.98%) zirconia and reagent grade calcium carbonate. The appropriate mixtures of zirconia and calcium carbonate were compacted by cola-pressing ad calcinecl at 1300°C for 12 hr. The calcined material was ground in a boron carbide mortar, cold-pressed into tablets 1-2 mm thick by 9 mm dia., and then sinterecl in air at 1750°C for 36 hr. OF Ni-Pd ALLOYS 63 In starting an experiment, the mull&e reaction tube was alternately evacuated with a mechanical pump and purged with purifiecl helium several times in order to obtain a clean system. The helium was purified by passing it over anhydrous magnesium perchlorate, ascarite, hydrogen-reduced copper catalyst at 15O”C, oxidized copper catalyst at 15O”C, again over anhydrous magnesium perchlorate and ascarite, and finally through a liquid-nitrogen cold trap. In a few of the earlier experiments the cell was heated to 700°C and data recorded with increasing temperature. In all subsequent ones however, the initial equilibration of the cell was hastened by making the first measurements at 1100°C. The cells were usually allowed to equilibrate 8-12 hr (overnight) at this temperature. After the initial equilibration period, the cdl potential was measured to the nearest 0.01 mV every 10-20 min over a period of several hours. When the voltage had attained a constant value the furnace temperature was lowered and the cell allowed to equilibrate at the new temperature. Data on the nominal 20, 40, 60 and 80 at.% compositions were recorded both on cooling and heating. The data on the nominal 10, 30, 50, 70 and 90 at.% compositions were checked with measurements on a duplicate cell. The time required for the cells to reach equilibrium, for all but the initial equilibration, varied from 1 to 2 hr at the higher temperatures to 4 to 8 hr at the lower temperatures. EXPERIMENTAL RESULTS AND DISCUSSION Within experimental error, the cell potentials were linear functions of the temperature. Values taken from the smoothed experimental data at even 100°C intervals are shown in Table 1. The overall reproducibility of the experimental measurements was exceptionally good. In the earlier experiment,s, where only normal precautions were observed in the preparation and manipulation of the cell components and in the assembly of the cell, the scatter in the data was generally less than &2.5%. In later experiments, where improved techniques were employed, the scatter was in all cases considerably less than f 1 Oh. In general, the observed cell voltages were very stable over’ long periods of time. For example, the pot.ential of a cell containing a 47.4 at. y. Pa electrode equilibrated at 12OO”C, changed by only 0.04 mV in over 28 hr. However, cells involving 77.7 and 86.5 at.% Pd electrodes were exceptions to this rule at temperatures of 1000°C and above. After one of these cells appeared to reach equilibrium, the voltage drifted downward, continuously, at the rate of several hundredths of a millivolt per hour. In all cases the 64 ACTA METALLURGICA, VOL. 13, 1965 TABLE 1. Cell potentials for nickel-palladium alloys Cell potential (mV) NPd 700°C 800°C 900°C 1ooo”c llOO°C 1200°C 0.107 0.191 0.287 3.51 6.25 10.45 4.09 7.32 12.30 4.64 8.39 14.15 6.27 9.47 15.98 6.86 10.55 17.83 6.45 11.63 19.68 0.382 0.474 0.564 17.43 26.75 41.40 20.13 30.40 46.40 22.76 34.00 51.40 25.41 37.66 56.35 28.03 41.30 61.35 30.69 44.90 66.35 0.681 0.777 0.866 66.30 93.40 132.85 73.05 102.15 144.05 79.80 110.86 155.10 86.50 119.55 166.25 93.30 128.20 177.26 100.05 136.90 188.35 NiO content at the electrolyte interface appeared to decrease on the alloy side and to increase on the nickel side. This behavior was attributed to concentration polarization of the electrodes due to the small but finite electron conduction in the electrolyte. By allowing these cells to remain at 1000°C and above only long enough to achieve practical equilibrium, the drop in potential attributable to polarization could be held well within the limits of reproducibility dictated by the other experimental errors. Although there is no direct experimental criterion for cell reversibility, reproducibility is generally accepted as a strong indication of it. Cells were checked for thermal reversibility by recording potential measurements with increasing as well as decreasing temperature. They were also checked for electrical reversibility by momentarily unbalancing the potentiometer, causing a small current of several microamps to flow according to the direction of unbalance. When the cells were displaced from equilibrium in this manner, they rapidly returned to their initial voltage, usually within a matter of minutes. The activities (aNi) and relative partial molar free energies (ApNi) of nickel, taken relative to solid nickel saturated with oxygen, were calculated from equation (1). The corresponding quantities for palladium were evaluated from a graphical integration of the Gibbs-Duhem equation in the form : Nm 1% yPd = @NilNNiNPd - s aNi dNPd, (2) other but have been spread out somewhat in order to show the number of measurements. Figures 3 and 4 illustrate the manner in which the activities and relative molar free energies change with temperature from 700 to 12OOW. From a consideration of the phase diagram, i.e., the absence of miscibility gaps, compounds, or superlattices, and the similarities in the atomic size and electronic structure of nickel and palladium, the small deviations of the activities from ideal solution behavior seen in Fig. 3 are not surprising. However, the details of the observed deviations are noteworthy, particularly in the case of nickel, which exhibits both positive and negative departures from Raoult’s law. Although this type of behavior is unusual, it is not without precedent in systems involving transition metals with nearly or completely filled d-shells. Similar behavior has been observed by Weibke and Matthea in Cu-Pt alloys, Schmahl(ls) in Au-Pd alloys, Orianios) in Co-Pt alloys, and by Aukrust and Muant20)in Fe-Pd alloys. The relative partial molar entropies of nickel (A&) were calculated from the slopes of potentialtemperature curves using the relation =2p p.Npd aE [ 6'T P,Npd' (3' I The values for palladium were determined in a similar manner from the slopes of APpd-temperature curves (Fig. 5). The relative partial molar enthalpies were evaluated from equations of the form : 1 where the Ni are the appropriate mole fractions, ypd is the activity coefficient of palladium (apd/Npd), and aNi E log yNi/NPd2 (see Tables 2 and 3). The activities of nickel and palladium calculated from the smoothed data at 900°C are shown in Fig. 2. Also included in this figure are the values for a,, calculated directly from the experimental data. In most cases these values fall nearly on top of each A& = AFi + TA& (4) Like the activities, the enthalpies of mixing exhibit rather unusual behavior (Fig. 6) in that they are endothermic for nickel-rich solutions and exothermic for palladium-rich solutions. It is worthy of note, although no explanation can be offered, that the partial enthalpies of mixing of nickel and palladium pass through maximum positive and negative values, BIDWELL SPEISER: AND THERMODYNAMICS TABLE 2. Activities -_ in nickel-palladium oPd !PC 0.107 0.191 0.287 0.382 0.474 0.564 0.681 0.777 0.865 700 0.920 0.862 0.779 0.660 0.528 0.373 0.206 0.108 0.042 0.072 0.105 0.145 0.201 0.272 0.372 0.530 0.680 0.824 1000 0.908 0.841 0.749 0.629 0.503 0.358 0.207 0.113 0.048 0.068 0.106 0.154 0.217 0.292 0.400 0.556 0.701 0.833 0.107 0.191 0.287 0.382 0.474 0.564 0.681 0.777 0.865 800 0.915 0.854 0.766 0.647 0.518 0.367 0.206 0.110 0.044 0.070 0.104 0.148 0.206 0.278 0.381 0.540 0.687 0.827 1100 0.906 0.837 0.740 0.623 0.498 0.355 0.207 0.115 0.050 0.067 0.106 0.157 0.221 0.298 0.408 0.565 0.705 0.835 0.107 0.191 0.287 0.382 0.474 0.564 0.681 0.777 0.865 900 0.912 0.847 0.756 0.638 0.510 0.362 0.206 0.112 0.047 0.068 0.105 0.151 0.211 0.284 0.390 0.548 0.694 0.830 1200 0.903 0.833 0.733 0.617 0.493 0.352 0.207 0.116 0.051 0.066 0.106 0.160 0.225 0.303 0.413 0.570 0.709 0.836 _ -214 -387 -653 -1050 - 1569 -2372 -3682 -5112 -7156 - A Fm -6255 -5255 -4407 -3626 -2930 -2194 -1405 -851 -435 aNi molar quantities for nickel-palladium aPd alloys at 900°C cal/deg-mole AFJf -860 -1317 -1731 -2034 -2214 -2271 -2132 -1801 -1342 Ai& Ai& 0.271 0.497 0.852 1.222 1.678 2.302 3.110 4.614 5.131 5.652 4.406 3.220 2.522 1.902 1.315 0.825 0.516 0.336 Cal/mole AS” AHNI 0.847 1.243 1.531 1.719 1.784 1.746 1.554 1.296 0.983 104 195 346 384 399 329 -34 -403 -1138 0.4 in nickel-palladium alloys at 900°C. 65 alloys aNi AFm Fm. 2. Activities ALLOYS T”C Cal/mole 0.107 0.191 0.287 0.382 0.474 0.564 0.681 0.777 0.865 Ni-Pd NPd TABLE 3. Relative h’d OF AHpd AH= 375 -87 -630 -668 -699 -652 -437 -246 -39 133 141 66 -18 -121 -225 -309 -281 -189 0.6 0.0 FIG 3. Temperature variation of the activities in nickelpalladium alloys. ACTA METALLURGICA, VOL. 13, 1965 ---- Idea1Solution NPd FIG. 4. Tempemture variation of the relative integrtal molar free energy of nickel-palladium alloys. FIG. 5. Relative molar entropies of nicked-palladium alloys in the range XK-1200°C. FICX.6. Rebtive molar enthalpiss of nickel-palladium aIloys in the range ?oO-1200°C. BIDWELL AND SPEISER: THERMODYNAMICS respectively, at about 45 at.% Pd, which corresponds to the Gom~osition of the ~nimum in the phase diagram. The relative molar entropies and enthalpies are listed in Table 3. Since the oell potentials at constant composition were, within experimental error, linear factions of the ~mperature, the relative molar entropies and enthalpies listed can be regarded as constant over the entire 700-1200°C temperature range. It follows therefore, that AC, g 0 and within this temperature range the specific heat of the alloys can be approxima~ by the ~opp-Neumann rule. Although electroche~oal methods are generally considered to be inferior to calorimetric methods in obtaining enthalpy data, the excellent reproducibility of the potintial measurements and the minimization of side-reactions made possible by the use of a solid rather than a liquid electrolyte, permitted an accuracy which is considered to be comparable with that obtainable by calorimetry. On the basis of the scatter in the data, the limits of error are estimated to be less than: 10.005 for the activities; f20 Cal/mole for + 100 Cal/mole for AH= ; and fO.1 calfdegf AF=; mole for AL?. GENERAL DISCUSSION The characteristic features of the thermod~amic functions obtained for nickel-pa~di~ alloys are best described by referring to the appropriate excess properties (Fig. 7) obtained by subtracting the properties for an ideal solution from the observed properties. Thus, the excess entropies of mixing (ASExs) are small and positive and the heats of mixing are small and change from positive to negative with increasing palladium content. The positive ASEX’ indicates the important role of non-configurational factors in determining thermodynamic properties that has been stressed in recent years by a number of investigators, particularly [email protected] Any deviation from ideal (random) mixing such as clustering or ordering leads necessarily to a negative contribution to the excess entropy of mixing. In order to assess the con~ational aspects of the mixing process in the nickel-palladium system, non-configurational factors such as the magnetic, electronic, and lattice vibrational contributions to the thermodynamic properties must be taken into account. Although specific heat data for the system are not available, the order of magnitude of these contributions can be crudely estimated from other considerations. One would expect a magnetic contribution to ASExs due to the ferromagnetic properties of nickelpalladium alloys at lower temperatures. Saturation OF Ni-Pd ALLOYS 67 FIG. 7. Relative integral molar excess properties of nickel-palladium alloys at 900°C. magnetization measurements(a2-M) on these alloys have shown that the average magnetic moment per atom is larger than can be accounted for by nickel alone. This means that in the ferromagnetic state a greater degree of electron spin ordering is present in the alloys than in the corresponding amounts of pure nickel and pa~~ium. Con~quently, at 700°C and above, where both the alloys and pure nickel are in the paramagnetic state, the alloys will have a positive magnetic entropy of mixing due to their larger relative magnetic entropy of disordering. According to Gugge~e~,(~) the statistical mechanical value for the molar magnetic entropy in changing from the ferromagnetic to the paramagnetic state is given by S (magnetic) = R In (2s + I), (5) where s is the resultant spin quantum number of the unpaired electrons and (2s + 1) is the multiplicity of states. In applying this relationship to nickelpalladium alloys a question arises as to whether one should consider the d-electrons collectively or as bound to specific atoms. On the basis of the former one concludes from magnetic measurements that niokel and palladium both contain approximately 0.6 electrons in the s-band and an equal number of positive holes in the d-band. In the case of nickel, the 68 ACTA d-band is completely holes are present has suggested number polarized, in one that and only the relative and nickel-palladium Equally attractive, however, the d-electrons regarded the electrical is the of generalized by Van Vleck.(2s) a band In this but are Nickel is considered to be 0.6 moles of magnetic with moment a magnetic In addition of one to yielding for nickel in remarkably atoms, each Bohr magneton a magnetic entropy close agreement with experi- ment,@a) this model does not require the use of nonhalf-integral spin numbers by the authors. model is assumed (5) that palladium and is therefore If the number to entropy alloy can be obtained S (magnetic) = alloy, both taken at 0°K. from the expression expressions of nickel magnetization The product represents the mole fraction By combining (6) magnetization and 5, is the relative saturation 3ds state. as for a nickel- cO,uBRIn 2, where pB is the saturation equation in this on alloying, for the band model, it follows the magnetic of the <ohs in this of atoms in the (6) with the corresponding for the pure components shown that the magnetic entropy it can readily be of mixing is given by the relation ASM saturation remarkably result data accounts well. from N,i) In 2. (7) (7) using from of Sadron(22) to 0°K are compared ASEXS in Fig. 8.* (magnetic) - calculated (magnetic) experimental netic) = ,@(10 magnetization WentJ2s) extrapolated ASM ASEXS (nonmagnetic), Fig. 8. the same (Fig. The negative the loss values of ASM (magof ferromagnetism at Although the differences between 97 at.% Pd. ASExs and ASM (magnetic) may be trivial in view of the uncertainties in each, they represent values of * If one ignores the requirement for half-integral spin numbers and somewhat arbitrarily uses the expression (pB + 1) for the multiplicity of states as has been done in some instances,‘sl-ss’ we obtain the relation AS”(magnetic) = R[ln (&,1ug+ 1) - NNi In (,u~ + l)]. This leads to values of AS”(magnetic) that are slightly larger (less than 10 per cent in all cases) than those shown in Fig. 8. as the for nickel curve enthalpy since the magnetic at temperatures for AHM rich solutions rich solutions. may only be coincidental unexpected curve in that this curve exhibits features for palladium similarity and Although this it is not totally contribution to the well above the Curie point is essentially zero(34) and AHM (nonmagnetic) s Apv. The contribution to ASEx’ and AHM arising from changes in the electronic and vibrational heat on mixing cannot be satisfactorily absence of low-temperature specific from Stoner’s ferromagnetic ya = of the former relation heat coefficient [y = C, Jf!L[(l for the electronic pure While ferromagnetic, the assumption approximate,(36) 50 )1’s] 9 (8) for the alloy and component respectively. of a parabolic this equation of a band shape?) + 50)1’s + (1 - where ya and y. are the coefficients the Howcan be (electronic)/T] alloy with a parabolic 2113 specific evaluated in the specific heat data. ever, the order of magnitude and ASEx’ general 7), i.e. positive negative with the It can be seen that for the observed shown as the dotted It is worth noting estimated ASM (magnetic) The NPd FIG. 8. Comparison of calculated relative magnetic entropies with experimental relative excess entropies of nickel-palladium alloys well above the Curie temperature. preferred of s-electrons be constant suggested by Wohlfarth from -0.2 - of 3ds and 3d1° states such that one mole of atoms contains (s = +). holes coefficients(28) do not form as quasi bound. a mixture the alloys. Heisenberg model introduced model Hall 0.6 This model has to explain ordinary 1965 constant of positive is changed. been used quite successfully resistivities(27) remains distribution 13, Wohlfarth(26) and palladium, in the s-band in the two half d-bands VOL. i.e. all of the positive half-band. on alloying of electrons METALLURGICA, band predicts is only a reasonable value of y for pure palladium(35) and might therefore be expected to approximate the value of y for alloys. Using the 5, determined from the data of Sadron’22) and Went(23) the values predicted change specific in the electronic for Ay, i.e., the heat coefficient mixing, are positive and less than 2.5 mole for nickel-rich solutions for solutions. palladium-rich x on 10-a cal/deg2/ and 10H4 cal/deg2/mole If by is assumed HIDWELL independent butions of temperature, to AS”s” THERMODYNAMICS ANI) SPEISER: contri- deviations are less are many the corresponding (900°C) and AHM (900°C) OF Ni-Pd of the activities times from ideal solution behavior larger and at least solutions palladium alloys. long-range order is the most 0.1 cal/deg/mole mole for palladium-rich Although solutions. a suitable method vibrational contributions properties is not available, that a positive low temperatures-and enthalpy at for estimating to the lattice to expect to the specific hence the heat lower therefore temperature, seems stable the and The above result from evaluation the nickel-palladium use of various theoretical made system. It must be recognized, palladium. An idea of the magnitude evidence cannot be distortional energy, often termed the misfit energy,(21) can be shown that of the lattice at the composition It and tempera- The current suspicion permit models regarded present only qualitative at best. free palladium the solid. If it is assumed does not change greatly able assumption that the entropy on melting, and solidus curves suggest difference solid, in the A(AH’f) misfit energy coordination heat = number and the lattice roughly AH” AH”(‘), and reflects the different heat the ASEXS and and asymmetric with maximum 0.3 cal/deg/mole to be and toward negative 800 Cal/mole aspects by X-ray temperature AND indicates nickel Raoult’s law. The magnitude those obtained remaining ASESS leave the and AHM even more negative, If these quantities are interpreted statistical and nearest-neighbor theories, alloys, it might be concluded particularly short-range possibly atures. energy order in terms of the usual chemical interaction that nickel-palladium palladium-rich at even long-range elevated would solutions, temperatures possess and order at much lower temper- A comparison of the activity and excess free data with those for solid and liquid iron- palladium possibility alloys(20) casts some doubt on the latter however. In the iron-palladium system, the course of t,he activity and excess free energy curves is strikingly similar to those shown in Figs. 2 and 7. However. even for liquid alloys, the negative iron-palladium (iii) The small and Palladium-rich alike. diagram, the exhibit solutions, data Aukrust which deviations negative deviations activity by in the activities solutions solvent solute evaluated, phase exhibit negative of solid by an electrochemical the Nickel-rich for the for the solute. properties determined solid solubility, and palladium measurements. a solid electrolyte. with complete deviations were range 700-1200°C that employed of the such as might CONCLUSIONS alloys (ii) Consistent helium analysis of the alloys, thermodynamic nickel-palladium minimum, a liquid diffuse scattering SUMMARY (i) The relative A more above the ferromagnetic and an experimental hand, exhibit be as configurational be obtained this of the nickel- from to temperatures The deletion of vibrational contrirespectively. butions, which are assumed to be positive but whose cannot require, transformation factors which is presumed would measurements temperatures method and electronic are negative solutions than liquid of the solid and liquid. with composition, remaining less of the and the slightly misfit’ energy, palladium-rich values - of magnetic parabolic in the atomic system specific in the liquid and solid, AHM(s) _ AHMU). The of mixing of the lattice In the absence in the liquidus similarities AHcM’) of mixing which is a reason- since the flat minima and electronic configurations then AF.=SYS _ AFE=U) i for that reservation. of refinement, AFEXS(‘) = 612 Cal/mole, i.e. the excess energy indirect are not above state conclusions of by the order in the however, of alloy solutions and in their behavior without definite analysis of the alloying behavior than length provides AFEXS(“) - is 612 Cal/mole more negative if at temperature of short-range ture ofthe minimum in the phase diagram, of the liquid that possible models, for the existence due to Wagner.t3*) likely configuration of the alloying system, evidence by methods energy for nickel- critical the lattice distortions(37) caused by the 10% mean difference in the atomic diameters of nickel and can be obtained free than of time. at entropy temperatures-will some It excess negative may be too low for it to occur in a reasonable thermodynamic it is reasonable contribution higher and 70 cal/ more the than 0.3 cal/deg/ mole and 170 Cal/mole for nickel-rich and less than five times 69 ALLOYS positive deviations on the other for the solvent are very and of from similar Muant20) for and to the system. relative partial molar nickel are, within experimental of the temperature, signifying free energies of error, linear functions that AC, above 760°C is essentially zero and that the specific heats of alloys at elevated temperatures the Kopp-Neumann (iv) The heats thermic can be approximated of mixing for nickel-rich negative i.e. coincident diagram. values, with are small and are endo- solutions palladium-rich solutions. of nickel and palladium and by rule. and exothermic respectively, the for The partial heats of mixing attain maximum positive minimum at 45 at.% in the Pd, phase 70 ACTA METALLURGICA, (v) The excess entropies of mixing are small and positive and pass through a maximum also coincident with the composition of the phase diagram minimum. 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