J. Phys. Chem. 1996, 100, 1159-1163
1159
Activity Measurements in Nickel-Platinum Alloys F. Lantelme* and A. Salmi Laboratoire d’Electrochimie,† Case 51, UniVersite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France ReceiVed: May 16, 1995; In Final Form: July 12, 1995X
The thermodynamic properties of Ni-Pt metallic alloys, in the temperature range 500-720 °C, are measured from energy dispersive analysis of the X-ray of alloys prepared by fused salt electrolysis at constant potentials in the cell: Ni-Pt alloy|fused electrolyte + NiCl2|Ni. For nickel-rich alloys, the partial entropy of nickel exhibits a nearly ideal behavior. For a molar fraction of nickel between 0.4 and 0.6, a rapid change in the thermodynamic properties occurs. A minimum in the entropy of mixing is found at xNi = 0.5. The departure from ideality of the Gibbs energy is mainly due to the negative value of the molar enthalpy of mixing; ∆H0.5 ) -10.5 kJ mol-1. This behavior, which results from the preferential interaction Pt-Ni, is linked to an order-disorder transformation around the equiatomic composition.
1. Introduction The interest in platinum alloys stems from the frequent use of platinum in high-temperature chemistry and electrochemistry of molten salts or metallic oxides. For instance, when a platinum crucible is used, a small part of the metal (such as Ni, Co, Nb, Ta, Ti, etc.) is lost from oxide or salt phases by alloying with the crucible material.1 Moreover, alloys are formed during metal deposition at a platinum electrode in fused salt electrolysis.2 Since, at high temperatures, most of the research works on the metal electrodeposition have been carried out using platinum working electrodes, it was important to determine the role of the alloy formation. The purpose of the present work was to measure the thermodynamic properties of the nickelplatinum alloys. The Ni-Pt system was attractive for this investigation, since nickel and platinum form a complete series of solid solutions; two superlattices are formed near the composition Ni3Pt and NiPt at 580 and 645 °C, respectively.3 The only thermodynamic properties of the system published in the literature are the activity and excess Gibbs energy values at temperatures above 1000 °C.1,4 Since most of the experiments concerning fused salts electrolysis have been performed over the temperature range 450-750 °C, determinations at lower temperatures were needed. The activities and Gibbs energies of formation for a series of solid Ni-Pt alloys were measured from the surface analysis of alloys electrochemically generated at constant potentials. 2. Principle of the Measurements The alloys were prepared by electrolysis at constant potentials in fused electrolytes such as LiCl-KCl or NaCl-KCl. The following cell was used:
Q Ni|fused electrolyte + NiCl2|alloy Pt-Ni x
(1)
When an external voltage, E, is applied to such a cell, the activity of metallic nickel at the alloy surface is given by
aNi ) exp(-2FE/RT)
The composition of the alloy surface was determined from the energy dispersive analysis of X-ray (EDAX),5 which gives the atomic fraction, xNi. The activity coefficient of nickel is defined by
γNi )
aNi xNi
To obtain acceptable results, it was necessary to maintain the electrolysis for a time long enough to reach a constant concentration over a certain thickness at the electrode surface. The electron beam penetrates into the sample, and the intensity of the emitted X-ray depends on the distance to the surface according to the curves in Figure 1. The abcissae, δ, of the gravity center of the emitting profile depends on the electron energy and on the alloy components.5 For the Ni-Pt system, δ is about 1.5 × 10-5 cm. In the region near the alloy surface, it is essential that the variation of the alloy composition be small. This requirement is achieved when the mean diffusion path, x2Dt, is much greater than δ. D is the diffusion coefficient and t the duration of the electrolysis. At 720 °C, a typical value for D is 10-12 cm2 s-1.6 A few hours are sufficient to obtain a significant thickness of alloy at the electrode surface. For smaller values of D (lower temperatures), the concentration profile near the interface can be taken into account to calculate the surface concentration, c* Ni, from the concentration, cNi(δ, t), given by EDAX. The concentration is related to the atomic fraction by the equation
cNi )
xNiFNi-Pt xNiMNi + (1 - xNi)MPt
Unite´ de Recherche No. 430 Associe´e au CNRS. X Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-1159$12.00/0
(4)
FNi-Pt being the alloy-specific mass and MNi and MPt the atomic masses of nickel and platinum. It is assumed that EDAX gives the composition of the alloy at a distance δ. At time t, the concentration profile of nickel, cNi(x,t), into the platinum matrix is given by7
cNi(x,t) ) c* Ni erfc
(2)
†
(3)
x 2xDt
(5)
erfc is the complement error function. For a mean path of the diffusing species greater than the analysis distance, δ, a simplified equation is used to obtain the surface concentration from the © 1996 American Chemical Society
1160 J. Phys. Chem., Vol. 100, No. 4, 1996
Lantelme and Salmi
Figure 1. Energy dispersive analysis of the X-ray. Penetration of electrons and profile intensitysdistance of the emitted X-ray. Equiatomic Ni-Pt alloy.
3. Experimental Section
out under a dry and oxygen-free argon atmosphere. The temperature was maintained at a fixed value, (0.5 °C, by an electrical furnace fitted with a PID controller.9 The electrodes were made of a sheet of pure nickel and a rod of platinum (diameter 1 mm). The metals were supplied by Johnson Matthey. A nickel wire, placed in a separate compartment, was used as the reference electrode. It was checked that the potential separation between the two nickel electrodes was less than 2 mV. The voltage, E, was obtained from a Tacussel PRT 20-2X potentiostat.
The fused electrolyte was an eutectic mixture LiCl (59 mol %)-KCl (41 mol %) or an equimolar mixture NaCl-KCl. The mixtures were prepared from R.P. NORMAPUR reagents (Prolabo). They were purified in a quartz vessel according to a procedure involving high-vacuum desiccation, chlorine bubbling, argon flushing, and filtering.8 The nickel chloride, NiCl2, 6H2O, R.P. NORMAPUR, was dehydrated by heating at 120 °C; the temperature was raised slowly up to 400 °C under vacuum and then to 500 °C in a chlorine atomsphere. A weighted amount of anhydrous nickel chloride was introduced in the electrolyte to obtain a concentration of about 0.1-0.3 mol L-1. The electrochemical cell consisted of an outer Pyrex or Hastelloy (Cabot Corp.) envelope, at the base of which was a glassy carbon crucible containing the molten salt. The components of the apparatus were selected to achieve a vacuumtight cell at elevated temperature. The experiments were carried
4. Results Since the redox properties of nickel and platinum are very different, it was possible to determine the composition of alloys formed in a very large potential range. For instance, in NaClKCl at 720 °C, the standard potentials of nickel and platinum are -1.105 and -0.247 V vs the standard Cl2/Cl- electrode, respectively.10 For a concentration of NiCl2 of 0.1 mol L-1, at a cell voltage as positive as 0.5 V, the concentration of platinum ions, Pt2+, at the positive electrode was about 5 × 10-8 mol cm-3. The thickness of the diffusion layer in the liquid phase being about 10-2 cm, the flux of platinum ions remained very small, around 0.15 × 10-9 mol cm2 s-1. It results that the concentration of Pt2+ ions in the bulk of the electrolyte was always negligible, and EDAX showed that no detectable amount of platinum appeared at the surface of the nickel electrode. An order of magnitude of the accuracy of the results is given by the scatter of measurements performed at fixed voltage. The
concentration, cNi(δ,t), given by the analysis
c*Ni )
cNi(δ,t) 1 - δ/xπDt
(6)
Usually, the denominator is very close to unity and the uncertainties arising from the concentration profile were negligible with respect to the errors in the analysis itself (see below).
Activity Measurements in Nickel-Platinum Alloys
J. Phys. Chem., Vol. 100, No. 4, 1996 1161
TABLE 1: Results Obtained by Emf Measurements 500 °C
720 °C
xNi
E, (mV)
xNi
E, (mV)
0.75 0.72 0.66 0.64 0.59 0.55 0.51 0.49 0.38 0.13 0.10 0.03 0.02
22.5 29.0 41.0 48.0 60.5 92.0 102.0 110.0 170.0 200.0 248.0 350.0 405.0
0.81 0.71 0.64 0.62 0.59 0.55 0.45 0.40 0.36 0.24 0.22 0.16 0.14 0.06 0.04 0.03 0.02
18.8 36.6 53.0 63.0 71.0 103.5 126.0 151.0 170.0 188.0 200.0 236.0 250.0 300.0 334.0 429.0 440.0
Figure 2. Activities of Ni and Pt in Ni-Pt alloys. Continuous line, 500 °C, broken line, 720 °C.
error on the alloy composition is ∆xNi = (0.015. However, for alloys containing a small amount of nickel (xNi < 0.1), a large scatter in the results was obtained, ∆xNi = (0.025. At 500 °C, the diffusion coefficient in the nickel-rich alloys becomes as small as 10-14 cm2 s-1,6 and a very long time, about a few hundred hours, was needed to obtain a penetration distance much greater than δ. However, since the thermodynamic properties do not rapidly vary with the temperature, the alloy was prepared at high temperature (720 °C). Then, the electrode was maintained at the lower temperature for 1 or 2 days to equilibrate the surface concentration. The error in the surface composition was minimized by using the correction of concentration described above (eqs 5 and 6). The additional error is estimated to be ∆xNi = (0.005. The compositions of the alloys prepared at various voltages and temperatures are shown in Table 1. The activity-concentration curves are reported in Figure 2. For a further exploitation of the results, it is useful to obtain an algebraic representation of the activity coefficient. Usually, for systems forming a solid solution over the entire concentration range, such as Au-Cu,11 the activity coefficient (eq 3) obeys the Margules equation:12
R2 R3 R4 ln γNi ) (1 - xNi)2 + (1 - xNi)3 + (1 - xNi)4 + ... 2 3 4 (7) where Ri are constant coefficients. In the present study, eq 7 fits well the experimental data for the nickel-rich alloys. Over the concentration range 1 g xNi > 0.65, the activity coefficient obeys the equation
ln γNi ) A(1 - xNi)2
(8)
The inflection point in the ln γNi-concentration curves around the equiatomic composition (Figure 3) shows that the Margules equation is not obeyed for nickel concentrations lower than 0.65. For platinum-rich alloys, an empirical equation is used:
ln γNi ) B1 +
B2 xNi +
(9)
In the intermediate region, 0.65 > xNi > 0.4, the activity coefficient is given by a weighted average of the two equations (eqs 8 and 9). The weighting factors are conveniently represented by the functions 0.5{1 - erf[Ψ(xNi - X)]} and 0.5{1 + erf[Ψ(xNi - X)]}. Now, over the entire concentration range,
Figure 3. Naperian logarithm of the activity coefficient of nickel in Ni-Pt alloys.
TABLE 2: Values of the Parameters A, B1, B2, X, Ψ, and E for Calculating the Value of ln γNi via Eq 10 temp, °C
A
B1
B2
X
Ψ
500 720
-6.7 -5.3
-2.98 -1.77
-0.101 -0.202
0.54 0.50
10.0 4.8
0.010 0.017
the activity coefficient is given by
1 + erf[Ψ(xNi - X)] ln γNi ) A(1 - xNi)2 + 2 B2 1 - erf[Ψ(xNi - X)] B1 + (10) xNi + 2
{
}
The six parameters A, B1, B2, X, Ψ, and were calculated by a least-squares method to obtain the best fit with the experimental values. The values of the parameters at 500 and 720 °C are shown in Table 2. The value of X is close to the concentration at the inflection point. A rapid change in the activity coefficient occurs around the concentration X. The slope of the curve ln γNi vs xNi at concentration X is proportional to Ψ. This parameter delimits the transition region in which the representation of the activity coefficient changes from eq 8 to eq 9. For example, the concentration interval, δx, in which the weighting factor changes from 0.1 to 0.9, is given by
δx )
0.9 Ψ
(11)
1162 J. Phys. Chem., Vol. 100, No. 4, 1996
Lantelme and Salmi
At a concentration xNi ) X + δx/2, eq 8 contributes 90% to the value of ln γNi and eq 9 10%. At a concentration xNi ) X - δx/2, eq 8 contributes 10% to the value of ln γNi and eq 9 90%. According to the values in Table 2, the δx interval is 0.09 at 500 °C. At 720 °C, a larger interval is obtained, δx = 0.18, which shows that, at high temperatures, the change in the activity coefficient around the equiatomic composition is less abrupt. 5. Thermodynamic Properties The nickel activities for the Ni-Pt system exhibit a negative deviation from ideality over the entire concentration range in agreement with the previous studies carried out at higher temperatures.1,4 This behavior is consistent with the tendencies for ordering which give rise to the formation of superlattices.13 Although the maximum temperature of equilibrium existence of an ordered phase is 645 °C,3 it has been shown that its influence remains at higher temperatures.1,4 At 500 °C (present work), the rapid change in the NiPt equiatomic region is due to the presence of the ordered phase. At 720 °C, the change is merely softened (Figure 3). Over the composition range 0.65 < xNi e 1, eq 8 shows that the Ni-Pt solid solutions behave like a regular solution.14 The A factor (eq 8) is sometimes termed the R function.15 The regular solution model is applicable to solutions whose components are randomly mixed regardless their disparity in size. Stronger mutual bounding energies are not to be expected, since the metal atoms have substantially the same electron configuration and the same polarizability. The negative departure to ideality arises from the fact that the platinum-nickel interaction energy, EPt-Ni, is greater than the mean value of the platinumplatinum, EPt-Pt, and nickel-nickel, ENi-Ni, interaction energies. The difference is probably due to the difference in the electronegativities of nickel and platinum,16 which give rise to a higher attractive force in the heterogeneous pairs, Pt-Ni. According to theory,12 the excess interaction energy, Ω, is linked to the A factor
Ω ) EPt-Ni - 0.5(EPt-Pt + ENi-Ni) )
RTA Z
(12)
Z is the coordination number; both nickel and platinum have a fcc structure, Z ) 12. In agreement with the theory of regular solutions, Ω is independent of the temperature. The value of Ω is -3.6 kJ mol-1. This model does not hold for atomic fractions of platinum greater than 0.35; the departure to ideality is greater than predicted from eq 8. It is assumed that the partial enthalpy of nickel, ∆H h Ni, is constant over the temperature interval 500-720 °C. ∆H h Ni is obtained from the activity measurements at two temperatures, T1 (773 K) and T2 (993 K). From the Gibbs-Helmoltz equation, it follows that
ln aNi,T2 - ln aNi,T1
∆H h Ni ) R
1 1 T2 T1
(13)
The excess partial entropy of nickel is calculated from ∆H h Ni E and from the excess partial Gibbs energy,17 ∆G h Ni ) RT ln γNi E ∆ShNi ) E T∆ShNi ,
∆H h Ni T
- R ln γNi E ∆G h Ni
(14)
The values of ∆H h Ni, and are shown in Figure E , and ∆H h Ni, around xNi ) 0.5, 4. The negative peaks for T∆ShNi
Figure 4. Partial molar enthalpy, entropy, and Gibbs energy of nickel in Ni-Pt alloys at 500 °C.
reflect the formation of the ordered phase. The negative value of the excess partial entropy balances the ideal term, R ln xNi; the partial entropy, ∆ShNi, remains small, which indicates that the mixing of Ni and Pt is not fully random in this region. A large contribution to the partial Gibbs energy arises from the enthalpy term due to the interaction energy Ni-Pt (eq 12) and structure change. The curves for activities of platinum appearing in Figure 2 were determined by use of the Gibbs-Duhem equation12
(
ln γPt ) -
∫0x
Ni
)
xNi ∂ ln γNi dxNi 1 - xNi ∂xNi
(15)
This equation was integrated by parts:
(
ln γPt ) -
∫0x
Ni
ln γNi (1 - xNi)
2
)
dxNi -
xNi ln γNi (16) 1 - xNi
The integral in eq 16 was evaluated by the Simpson method.18 It has been pointed out12 that the accuracy of the values indirectly calculated from (16) was not very good since (16) involves quotients of the form ln γNi/(1 - xNi)2. However, it was shown that, for small values of (1 - xNi), eq 8 is wellobeyed and the limit of the quotient, ln γNi/(1 - xNi)2, remains well-defined when xNi tends toward unity. The main error arises from the uncertainties of ln γNi for the small values of xNi, which are probably due to the presence of traces of oxides at the electrode surface. The partial molar enthalpy, ∆H h Pt, and the E , were calculated from the temperexcess partial entropy, ∆ShPt ature dependence of the partial molar Gibbs energy. The values of the integral molar Gibbs energy, enthalpy, and entropy of mixing are calculated. These quantities are related to the formation of one gram-atom of alloy. They are sometimes called the integral free energy, heat of formation, and entropies of formation of the alloy.12 They are calculated from the relations existing between molar and partial molar quantities
h Ni + xPt∆G h Pt ∆G ) xNi∆G
(17)
∆H ) xNi∆H h Ni + xPt∆H h Pt
(18)
∆S ) xNi∆ShNi + xPt∆ShPt
(19)
Accordingly, the excess integral molar entropy equals
∆SE ) ∆S + R(xNi ln xNi + xPt ln xPt)
(20)
The curves for these quantities as a function of the atomic
Activity Measurements in Nickel-Platinum Alloys
J. Phys. Chem., Vol. 100, No. 4, 1996 1163 low nickel activities, abnormally large amounts of nickel are present at the electrode surface. It results in very low activity coefficients for nickel in platinum-rich alloys which may be due to the presence of traces of oxides at the electrode surface. However, this effect could be correlated to the phenomenon of underpotential deposition of nickel pointed out by Hills et al.,20 who have shown that, at 400 °C in fused LiCl-KCl-NiCl2, nickel-rich layers are formed at the surface of a platinum electrode at potentials much more positive than predicted by Nernst’s law. It is believed that, at higher temperatures, this surface structure extends into the bulk material. Acknowledgment. We are grateful to Dr. Beaunier and Mrs. S. Borensztajn (UPR 15, CNRS) for energy dispersive analysis of the X-ray. References and Notes
Figure 5. Molar enthalpy, Gibbs energy, and entropy of mixing in Ni-Pt alloys at 500 °C. The dotted curve represents ideal entropy of mixing.
fraction, xNi, are presented in Figure 5. The integral heats of formation for the Ni-Pt system are exothermic over most of the concentration range. This is in agreement with measurements carried out at room temperature (∆H298 0.5 ) -9.0 kJ mol-1).4 In the temperature range 500-720 °C, the integral heat of formation becomes slightly endothermic for platinumrich alloys. This tendency toward positive values for platinumrich alloys seems to be more marked at higher temperatures, as pointed out by Walker and Darby.4 This change in the value of ∆H questions the application of the Neumann-Kopp’s rule,19 which assumes the constancy of the enthalpy of mixing. 6. Conclusion In contrast with the Au-Cu system,11 the order-disorder transformation in the Ni-Pt system has a significant influence on the thermodynamic properties of the system. At low temperature (500 °C), a negative shift in the excess Gibbs energy occurs around the equiatomic composition NiPt. A similar shift occurs at higher temperatures, although the change around the equiatomic composition is less pronounced. The excess entropy of mixing remains positive over the whole concentration range; however a minimum, ∆SE = 0, occurs at xNi ) 0.5, which is in agreement with the existence of an ordered phase in this region. This hypothesis is also supported by the large negative value of the enthalpy of mixing (∆H0.5 ) -10.5 kJ mol-1) due to the preferential Ni-Pt interactions. It was also shown that, for very
(1) Schwerdtfeger, K.; Muan, A. Acta Metall. 1965, 13, 509. (2) Lantelme, F.; Salmi, A. J. Electrochem. Soc. 1995, 142, 3451. (3) Hansen, M.; Anderko, K. Constitution of Binary Alloys, 2nd ed.; McGraw-Hill: New York, 1958; p 1032. (4) Walker, K. R. A.; Darby, J. B., Jr. Acta Metall. 1970, 18, 1261. (5) Agius, B.; Froment, M. Surfaces, Interfaces et Films minces; Dunod: Paris, 1990; pp 85-108. (6) Lantelme, F.; Salmi, A. To be published. (7) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon: Oxford, 1979; pp 11-21. (8) Vargas, T.; Inman, D. J. Appl. Electrochem. 1987, 17, 270. (9) Lantelme, F.; Inman, D.; Lovering, D. G. Molten Salt Techniques; Plenum: New York, 1984; Vol. 2, pp 203-208. (10) Lantelme, F.; Berghoute, Y. J. Electrochem. Soc. 1994, 141, 3306. (11) Lantelme, F.; Belaidouni, S.; Chemla, M. J. Chim. Phys. 1979, 76, 423. (12) Wagner, C. Thermodynamics of Alloys; Addison-Wesley: Reading, MA, 1952; pp 8-35. (13) Dahmani, C. E.; Cadeville, M. C.; Sanchez, J. M.; Mora´n-Lo´pez, J. L. Phys. ReV. Lett. 1985, 55, 1208. (14) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand Reinhold: New York, 1970; p 3. (15) Darken, L. S.; Gurry, R. W. Physical Chemistry of Metals; McGraw-Hill: New York, 1953. (16) Handbook of Chemistry and Physics, 74th ed.; Lide, D. R., Ed.; CRC: Boca Raton, FL, 1993; Section 10, p 181. (17) According to the IUPAC recommendations, the free enthalpy must be called Gibbs energy: IUPAC Manual of Symbols and Terminology for Physico-chemical Quantities and Units; Mills, I. M., Ed.; Blackwells: Oxford, 1988. (18) Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions, 9th printing; Dover: New York, 1972; p 886. (19) Kubaschewski, O.; Alcock, C. B.; Spencer, P. J. Materials Thermochemistry, 6th ed.; Pergamon: Oxford, 1993; p 167. (20) Hills, G. J.; Schiffrin, D. J.; Thompson, J. J. Electrochem. Soc. 1973, 120, 157.
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