Introduction

The thermodynamic properties of osmium were reviewed by the author in 1995 (1) with a further review in 2005 (2) to estimate a most likely value for the melting point at 3400 ± 50 K to replace the poor quality experimental values which were being quoted in the literature. More recently Burakovsky et al. (3) have estimated a value of 3370 ± 75 K in good agreement with the above selected value. In the 1995 review the enthalpy of fusion was unknown but was estimated from a relationship between the entropy of fusion and the melting point which showed a high degree of correlation for the platinum group metals (pgms). However the derived entropy of fusion value for osmium was based on values for the other pgms available at that time but since then the values for both palladium and platinum have been revised so that the entropy of fusion value for osmium would also be revised leading to a new estimate of 68.0 ± 1.7 kJ mol⁻¹ for the enthalpy of fusion. This would then require the thermodynamic properties of the liquid phase to also be updated. A comment is included on an independent much lower estimate of the enthalpy of fusion. Wherever possible measurements have been corrected to the International Temperature Scale (ITS-90) and to the currently accepted atomic weight of 190.23 ± 0.03 (4).

Low Temperature Solid Phase

Selected values in the normal and superconducting states are based on the specific heat measurements of Okaz and Keesom (0.18 K to 4.2 K) (5) including a superconducting transition temperature of 0.638 ± 0.002 K, an electronic specific heat coefficient (γ) of 2.050 ± 0.003 mJ mol⁻¹ K⁻² and a limiting Debye temperature (Θ_D) of 467 ± 6 K. Specific heat values up to 5 K in both the normal and superconducting states are given in Table I.

Above 4 K selected specific heat values are initially based on the measurements by Naumov et al. (6 K to 316 K) (6). However above 280 K these measurements show an abrupt increase of 0.5 J mol⁻¹ K⁻¹ and a further abrupt increase of 0.3 J mol⁻¹ K⁻¹ above 300 K. Naumov et al. attempted to accommodate these values but the selected specific heat curve showed an unnatural sharp change in slope above 270 K. Therefore the selected values of Naumov et al. above 250 K were rejected and instead specific heat values to 298.15 K were obtained by joining smoothly with the high temperature enthalpy measurements of Ramanauskas et al. (7). In the original review of the low temperature data only the specific heat values were given consisting above 50 K of 10 K intervals to 100 K and then 20 K intervals above this temperature as well as the value at 298.15 K. This minimalist approach is now considered to be unsatisfactory and therefore comprehensive low temperature thermodynamic data are now given at 5 K intervals from 5 K to 50 K and at 10 K intervals above this temperature up to 290 K and then the value at 298.15 K as given in Table II.

High Temperature Solid Phase

In the high temperature region, after correction for temperature scale and atomic weight, the enthalpy measurements of Ramanauskas et al. (1155 K to 2961 K) (7) were fitted to the following equation with an overall accuracy of ± 200 J mol⁻¹ (0.4%) (Equation (i)):

(i)

This equation was used to represent selected enthalpy values from 298.15 K to 3400 K. Equivalent specific heat and entropy equations corresponding to the above equation are given in Table III, the free energy equations in Table IV, transitions values associated with the free energy functions in Table V and derived thermodynamic values in Table VI. The actual equation given by Ramanauskas et al. to represent the enthalpy measurements over the experimental temperature range agrees with Equation (i) to within 0.2%.

The only other enthalpy measurements were obtained by Jaeger and Rosenbohm (693 K to 1877 K) (8) and compared to the selected values vary from 1.6% low at 693 K to an estimated 1.2% low at 1600 K to 1.4% low at 1877 K.

Liquid Phase

Selected values of the enthalpies and entropies of fusion of the Groups 8 to 10 elements with a close-packed structure are given in Table VII. Only the enthalpy of fusion of osmium is unknown. References (10–14) represent the latest reviews on the thermodynamic properties of the pgms by the present author. From an evaluation of the entropies of fusion of the elements, Chekhovskoi and Kats (15) proposed that the entropy of fusion (ΔSº_M) and the melting point (T_M) could be related by the equation ΔSº_M = A T_M + B. In the previous review (1) different values were proposed for the entropies of fusion of palladium (8.80 J mol⁻¹ K⁻¹) and platinum (10.45 J mol⁻¹ K⁻¹) leading to an estimate of the entropy of fusion for osmium of 20.6 J mol⁻¹ K⁻¹. With the revised values it is clear that, although of the right order, the entropy of fusion of nickel is discrepant and has therefore been disregarded. The other six values were fitted to the equation with A = 6.6954 × 10⁻³ and B = −2.7630 and a standard deviation of the fit of ± 0.193 J mol⁻¹ K⁻¹. However in order that the derived entropy of fusion of osmium has a similar accuracy to those of the input values then the accuracy is expanded to a 95% confidence level leading to an entropy of fusion of 20.0014 ± 0.387 J mol⁻¹ K⁻¹ and based on a melting point 3400 ± 50 K to an enthalpy of fusion of 68,005 ± 1653 J mol⁻¹. Based on neighbouring elements then a liquid specific heat of 50 J mol⁻¹ K⁻¹ was proposed in the original paper (1) and therefore the enthalpy of liquid osmium can now be expressed as Equation (ii):

(ii)

Equivalent specific heat and entropy equations corresponding to the above equation are given in Table III, the free energy equation in Table IV and derived thermodynamic values in Table VI. It should now be possible to accurately determine the melting point and enthalpy of fusion of osmium since the metal is available in high purity in a coherent form whilst the enthalpies of fusion of other high melting point elements such as rhenium (3458 K) and tungsten (3687 K) have been successfully determined.

Gas Phase

Based on a standard state pressure of 1 bar the thermodynamic properties of the monatomic gas were calculated from the 295 energy levels listed by Van Kleef and Klinkenberg (16) and Gluck et al. (17) using the method outlined by Kolsky et al. (18) together with the 2018 Fundamental Constants (19). Derived thermodynamic values are given in Table VIII.

Enthalpy of Sublimation

No temperature scales were given with the measurements of the vapour pressures by Panish and Reif (20) and Carrera et al. (21). Normally the experimental temperature values would therefore be accepted but in the case of such values above 2000 K the difference from the current scale, ITS‐90, becomes significant. Since the measurements were carried out in 1962 and 1964 then they would ultimately be associated with the International Practical Temperature Scale (IPTS-1948) and were therefore corrected to the ITS-90 scale on this basis. Derived enthalpies of sublimation are given in Table IX. The selected enthalpy of sublimation of 788 ± 4 kJ mol⁻¹ is basically an unweighted average but slightly biased towards the measurements of Carrera et al. (21).

Vapour Pressure Equations

The vapour pressure equations are given in Table X. For the solid the evaluation was for free energy functions for the solid and the gas at 50 K intervals from 1700 K to 3400 K and for the liquid at 50 K intervals from 3400 K to 5600 K and were fitted to Equation (iii):

(iii)

A review of the vapour pressure data is given in Table XI.

Discussion of Alternative Estimates of the Enthalpy of Fusion of Osmium

Based on various assumptions Fokin et al. (22) proposed that the enthalpy of fusion for osmium was only in the range 30 kJ mol⁻¹ to 40 kJ mol⁻¹ or half of the above derived value. One of the main arguments was that by using the Chekhovskoi-Kats equation the entropy of fusion for rhenium was estimated to be 20.0 J mol⁻¹ K⁻¹ whereas the actual value is only 9.85 J mol⁻¹ K⁻¹ (23) and therefore if the estimate for rhenium was so completely wrong then it would also be possible that the estimate for the neighbouring element osmium at 19.0 J mol⁻¹ K⁻¹ could also be wrong. However, Fokin et al. completely misunderstood how the estimated values were arrived at. It was initially assumed that Group 7 rhenium would behave like Groups 8 to 10 (the pgms) whereas all that the experimental value proved was that Group 7 elements behaved completely independently of Groups 8 to 10 and therefore showed the same deviations as other transition metal groups. For example, the entropies of fusion of Group 5 elements vanadium, niobium and tantalum at 10.46 J mol⁻¹ K⁻¹, 11.13 J mol⁻¹ K⁻¹ and 10.25 J mol⁻¹ K⁻¹ (24) showed no trend with temperature whilst the entropies of fusion of the Group 6 elements chromium, molybdenum and tungsten at 13.89 J mol⁻¹ K⁻¹, 13.53 J mol⁻¹ K⁻¹ and 13.66 J mol⁻¹ K⁻¹ (24) were virtually identical. Therefore it would not be surprising if Group 7 elements would also behave completely independently. In fact for the transition metals only the Groups 8 to 10 elements showed a high degree of correlation with the Chekhovskoi-Kats equation. However in order to prove their point that osmium does behave differently to the other pgms, Fokin et al. used the equation: σ_M = Z ΔH_M ρ_SM d where σ_M is the surface tension at the melting point, ΔH_M is the enthalpy of fusion, ρ_SM is the density of the solid at the melting point and d is the interatomic distance. This equation was applied to a number of elements but there is virtually no correlation for the values of Z with values varying between 1.2 to 3.3. For osmium Fokin et al. selected an arbitrary rounded value of Z = 2 for osmium and values of surface tension and liquid density determined by Paradis et al. (25) to arrive at an enthalpy of fusion of only 32 kJ mol⁻¹ which is considerably less than the value of 39.0 ± 1.4 kJ mol⁻¹ (9) selected for the analogue element ruthenium whereas for the other pgms the enthalpy of fusion is always greater for the heavier analogue. This much lower value for the enthalpy of fusion would suggest that the thermal properties of osmium should then be distinct from those of the other pgms but this is not the case. For example, the specific heat values of ruthenium (10) and osmium at reduced temperature (T/T_M) as indicated in Figure 1 are very similar and show virtually the same behaviour suggesting that they are genuine analogues of each other whilst the extrapolated melting point of osmium obtained by applying the same incremental difference as between iridium and platinum agrees closely with the selected value and again suggesting a common Groups 8 to 10 behaviour.

Further, the chemical properties of ruthenium and osmium are virtually identical forming the same type of compounds with similar properties. These are examples where osmium behaves exactly like the other pgms and on these grounds it is suggested that the very low value for the enthalpy of fusion as suggested by Fokin et al. is inconsistent with this behaviour and that osmium would obey the same periodic trend as suggested by the other pgms and that its entropy of fusion can be determined by the Chekhovskoi-Kats equation. This would suggest anomalies in the input values selected by Fokin et al., especially in the selection of Z = 2 for osmium since the value for the analogue ruthenium is only 1.5 whilst the value for the neighbouring element iridium is only 1.2 where the selection of such values would lead to higher enthalpies of fusion for osmium. It is suggested that in view of the lack of any real correlation for Z that the value for osmium may well be independent and could even be 1.0 leading to an enthalpy of fusion similar to that obtained from the Chekhovskoi-Kats equation. Therefore until the actual enthalpy of fusion of osmium is determined it is assumed that it behaves as a normal Groups 8 to 10 element.

Conclusions

Estimated entropy and enthalpy values of fusion of osmium have been revised leading to corrections of the thermodynamic properties of the liquid phase and therefore to the vapour pressure curve above the melting point. The revisions are based on the assumption that osmium behaves as a normal Group 8 to 10 element and contradicts recent suggestions that its behaviour could be abnormal.