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The thermodynamic properties of palladium were reviewed by the author in 1995 (1). At that time the value for the enthalpy of fusion was considered to be tentative since it differed significantly from the only known experimental value. Newly considered enthalpy of fusion values now indicate that the original selected value was almost certainly incorrect and a more likely value has been suggested which leads to a major alteration to the selected values for the liquid phase. Additional measurements of the vapour pressure do not alter the selected enthalpy of sublimation value of 377 kJ mol^–1 but the accuracy can now be refined to give a 95% confidence value of ±4 kJ mol^–1.

Selected values in the low-temperature region as given in the previous review (1) were based mainly on the specific heat values of Boerstoel et al. (2), Clusius and Schachinger (3) and Mitacek and Aston (4) and continue to be considered satisfactory. However only limited information was given in the original review which above 50 K consisted of specific heat values at 10 K intervals from 50 to 100 K and at 20 K intervals from 100 to 280 K and with the value at 298.15 K also included. This is now considered to be far too little information and instead a comprehensive review of the low-temperature thermodynamic properties is given in Table I.

In the high-temperature solid region closely agreeing specific heat values derived from the enthalpy measurements of Cordfunke and Konings (5) (528 to 848 K) and the direct specific heat measurements of Miiller and Cezairliyan (6) (1400 to 1800 K) were selected since they were in excellent agreement with an extrapolation of the selected low-temperature values and allowed a single smooth specific heat curve to represent both the low- and high-temperature regions. More recent high-temperature specific heat values by Milošević and Babić (7) (248 to 1773 K) differ significantly from the selected values showing a trend from 1.3% lower at 323 K to 3.9% lower at 723 K to 2.3% lower at 1223 K to 5.9% lower at 1773 K. However, at the low-temperature change over point at 270 K the measurements of Milošević and Babić show a sharp change in the slope of the specific heat curve compared to the selected low-temperature values, indicating that these high-temperature measurements are incompatible with those obtained at low temperatures. On these grounds the original high-temperature values were retained and can be represented by Equation (i) to cover the range from 298.15 K to the accepted melting point at 1828.0 K:

Equivalent enthalpy and entropy equations are given in Table II and derived thermodynamic values are given in Table III.

In comparison with the selected equations the specific heat values of Vollmer and Kohlhaas (8) (300 to 1825 K) trend from 2.6% lower at 300 K to 5.3% lower at 800 K to an average of 1.5% higher above 1600 K (Figure 1). Enthalpy measurements of Holzmann (9) (575 to 1177 K) trend from 0.4% higher to 1.7% higher whilst those of Jaeger and Veenstra (10) (573 to 1772 K) scatter from 0.7% lower to 1.4% lower with an average of 1.1% lower (Figure 2). More recent enthalpy measurements of Cagran and Pottlacher (11) (1550 to 1828 K) determined using the rapid pulse heating technique trend from 1.4% to 3.7% lower in the solid range (Figure 3).

Fig. 1.

Fig. 2.

Fig. 3.

Drop calorimetry enthalpy measurements by Treverton and Margrave (12) were initially determined over the range 1846 to 2334 K on the International Practical Temperature Scale of 1948 (IPTS-48) but a short note added in the proof indicated further corrections for radiation losses and a conversion to the temperature scale IPTS-68. However only the amended liquid specific heat value and the liquid enthalpy at the melting point (given as 1827 K) were given. After correction for atomic weight, to the melting point of 1828.0 K and to the International Temperature Scale of 1990 (ITS-90), the liquid enthalpy at the melting point is H°_T – H°_{298.15 K} = 63,151 J mol^–1 which in combination with the enthalpy of the solid at the melting point leads to an enthalpy of fusion of 16.08 ± 0.74 kJ mol^–1. This is notably lower than actual experimental values of 17.64 kJ mol^–1 determined by Nedumov (13) using differential thermal analysis and rapid pulse heating values of 17.4 ± 2.0 kJ mol^–1 determined by Seydel et al. (14, 15) and 16.98 kJ mol^–1 determined by Cagran and Pottlacher (11). The reason why the indirect determination of the enthalpy of fusion was low is not known but may be due to either an overestimation of the enthalpy values for the solid or, more likely, to the fact that even the revised values of Treverton and Margrave had still not accounted for all of the systematic errors that may have been present in their measurements. Not including the measurement of Seydel et al. because of the large uncertainty, the two other enthalpy values were equivalent to entropy of fusion values of 9.65 J mol^–1 K^–1 and 9.29 J mol^–1 K^–1 respectively. Kats and Chekhovskoi (16) noted that for a particular structure type the entropies of fusion (ΔS_M) could be linearly related to the melting points (T_m) by means of the equation ΔS_M = a T_m + b where a and b are constants. For the face-centred cubic platinum group metals rhodium, iridium and platinum selected entropy of fusion values of 12.21 ± 0.38 J mol^–1 K^–1 at a melting point of 2236 K for rhodium (17), 15.20 ± 0.41 J mol^–1 K^–1 at a melting point of 2719 K for iridium (18) and 10.83 ± 0.46 J mol^–1 K^–1 at a melting point of 2041.3 K for platinum (19) when fitted to the above equation extrapolated to 9.52 J mol^–1 K^–1 for palladium, in excellent agreement with the above experimental entropy values. The two experimental entropy values for palladium were therefore combined with the values for rhodium, iridium and platinum and were fitted to the equation: ΔS_M = 6.4574 × 10^–3 T_m – 2.3211 with the derived value for palladium as 9.483 ± 0.40 J mol^–1 K^–1 where the error is assigned to match those obtained for the other elements. The derived enthalpy of fusion value is rounded to 17.34 ± 0.73 kJ mol^–1 and leads to an enthalpy for the liquid at the melting point of 64,411 J mol^–1, suggesting that even with corrections applied the enthalpy measurements of Treverton and Margrave were 2.0% too low. This confirms the suggestion that other liquid enthalpy measurements obtained by Treverton and Margrave also appear to be systematically low with, for example, the values obtained for vanadium (20) being on average 2.4% lower than the preferred values of Berezin et al. (21) and Lin and Frohberg (22).

The liquid specific heat determined by Treverton and Margrave (12) on IPTS-68 corrected to the value 41.20 ± 1.38 J mol^–1 K^–1 on ITS-90 which is notably higher than the value for the liquid of 37.3 J mol^–1 K^–1 determined by Cagran and Pottlacher (11) (1828 to 2900 K) using rapid pulse heating. However, it is noted that Cagran and Pottlacher obtained a specific heat value for the solid which is some 10% to 16% lower than the selected values. Therefore, the value of Treverton and Margrave was selected on the assumption that the apparently lower enthalpy values obtained are due to a constant systematic error. Over the range 1828 to 3300 K the actual enthalpy can be expressed as (Equation (ii)):

Equivalent specific heat and entropy equations are also given in Table II whilst derived thermodynamic properties are given in Table III. The more recent liquid enthalpy measurements of Cagran and Pottlacher (11) trend from 3.3% lower at 1828 K to 5.8% lower at 2900 K.

Selected values are based on the 143 energy levels selected by Engleman et al. (23). The thermodynamic properties were calculated using the method of Kolsky et al. (24) and the 2014 Fundamental Constants selected by Mohr et al. (25, 26). Derived thermodynamic values based on a one bar standard state pressure are given in Table IV.

Because of a general lack of detail as to what temperature scales were used and problems associated with the exact measurement of temperature, no attempt was made to correct vapour pressure measurements to ITS-90 from what would have been contemporary scales. For results given in the form of the Clausius-Clapeyron equation, log(p) = A + B/T (where p is pressure and T is temperature), the enthalpy of sublimation was calculated at the two temperature extremes and averaged. For the measurements of Walker et al. (27), Lindscheid and Lange (28) and Chegodaev et al. (29) no temperature ranges were given and therefore these measurements were not included. From Table V, in view of possible systematic errors in the earlier measurements, only the twelve determinations from Taberko et al. (42, 43) to Ferguson et al. (51) were considered. The unweighted average value of 377 kJ mol^–1 is assigned an accuracy of ±4 kJ mol^–1 which is equivalent to a 95% confidence level (two standard deviations).

The vapour pressure equations as given in Table VI were evaluated for the solid from free energy functions for the solid and the gas at 50 K intervals from 900 K to 1800 K and the melting point and for the liquid at the melting point and at 50 K intervals from 1850 to 3300 K and were fitted to the following equation (Equation (iii)):