Introduction

Previous reviews on electrical resistivity were given in Part I for palladium and platinum (1) and in Part II for rhodium and iridium (2).

The elements ruthenium and osmium are both superconducting with transition temperatures of 0.49 ± 0.015 K for ruthenium and 0.66 ± 0.03 K for osmium (3). Both have hexagonal close-packed structures and resistivity values are therefore selected along directions both perpendicular to the c axis (ρ⊥) and parallel to the c axis (ρ‖). The average resistivity is then given by ρ_avr = (2 ρ⊥ + ρ‖)/ 3.The melting point of ruthenium is a secondary fixed point on the International Temperature Scale of 1990 (ITS-90) at 2606 ± 10 K (4) whilst the melting point of osmium is estimated as being 3400 ± 50 K (5).

Ruthenium

Selected resistivity values at 273.15 K are given in Table I. Because of the possibility of preferred orientation in polycrystalline samples only results for single crystals are considered in the selection. On this basis the selected values are an average of the measurements of Powell et al. (11), Azhazha et al. (12) and Volkenshteyn et al. (13).

At 30 K and below selected intrinsic anisotropic and average values are given by the equations of Volkenshteyn et al. (10) as Equations (i) to (iii).

Anistropic measurements of Azhazha et al. (12) to 25 K lead to identical values at 20 K whilst the average value at 20 K of 0.0019 μΩ cm is in excellent agreement with the value of 0.0017 μΩ cm calculated from the equation of Schriempf and Macinnes (15) (4–20 K).

Between 30 K and 273.15 K for Volkenshteyn et al. (10) and below 273.15 K for Azhazha et al. (12) and Volkenshteyn et al. (13) the anisotropic resistivity measurements were only shown graphically with actual values estimated from these graphs. Average resistivity values of White and Woods (6, 7) (25–295 K) when normalised to the selected value at 273.15 K using the ratio 6.16/6.69 show excellent agreement with average values of Volkenshteyn et al. (13) estimated at 80 K and above with the average bias being only 0.01 μΩ cm low at 120 K and above. The measurements of Volkenshteyn et al. (13) were therefore selected to 260 K, combined with the selected values at 273.15 K and fitted to Equations (iv) to (vi) to represent the range from 100 K to 273.15 K. The overall accuracies as standard deviations of ±0.03 μΩ cm and ±0.02 μΩ cm respectively indicate a satisfactory degree of correlation considering that the values were only estimated.

Below 100 K the measurements of White and Woods (6, 7) over the range 40 to 60 K were converted from average to anisotropic values using ratios of ρ_i ‖/ρ_i ⊥ determined from the measurements of Volkenshteyn et al. (10) after correction for ρ₀ whilst values of ρ_i ⊥ and ρ_i ‖ at 70 K and 90 K were estimated by interpolation.

In comparison with Equations (iii) and (iv) the estimated measurements of Azhazha et al. (12) show a maximum deviation of 0.19 μΩ cm low at 180 K along both axes whilst after correction for residual resistivity the measurements of Volkenshteyn et al. (10) trend to values at 273.15 K of 0.48 μΩ cm high perpendicular to the c axis but only 0.12 μΩ cm high parallel to the c axis.

In the high temperature region anisotropic resistivity measurements of Savitskil et al. (16) (300–1600 K) were only shown graphically with actual data points given by Savitskil et al. (17). These can be made to show satisfactory agreement with the selected values at 273.15 K only when considered over the range 600 K to 1600 K while the values at 300 K and 400 K showed marked deviations and were therefore rejected. After correction for thermal expansion using length values selected by the present author (18) the electrical resistivity values over the range 273.15 K to 1600 K were represented by Equations (vii) to (ix) with derived values given in Table II. Along the axes overall accuracies as standard deviations are ±0.27 μΩ cm and ±0.10 μΩ cm respectively.

Average electrical resistivity measurements of Binkele and Brunen (19) (273–1421 K) trend from initially 4.9% high to 0.5% high at 1100 K and then increases to 1.4% high at 1421 K whilst average measurements of Milošević and Nikolić (20) (250–2500 K) trend from initially 7.3% high to 0.7% low at 1600 K. These two sets of measurements differ sharply above 1100 K with the difference reaching 1.7% at 1421 K, the experimental limit of Binkele and Brunen. Since the measurements of Milošević and Nikolić were fitted to a quadratic equation it was found that the values at 2300 K and above showed a reasonable degree of correlation with an extrapolation of Equation (ix) and therefore the selected average value at 1600 K was combined with the high temperature measurements of Milošević and Nikolić at 2300 K, 2400 K and 2500 K and fitted to Equation (x) to give a fairly satisfactory representation of the average electrical resistivity in the range from 1600 K up to the melting point. Values derived from Equation (x) are given in Table III.

Percentage deviations from the selected values of the average measurements of Savitskil et al., Binkele and Brunen and Milošević up to 2500 K are shown in Figure 1.

Osmium

Selected resistivity values at 273.15 K are given in Table IV. As with ruthenium, because of the possibility of preferred orientation in polycrystalline samples only results for single crystals are considered in this selection. Values given by Powell et al. (11) were corrected for residual resistivity based on the ratio ρ_{273 K} / ρ_{4.2 K} = 33.3 given as a private communication to Ho et al. (21). The selected values in Table IV are based on the values of Volkenshtein (22) since they were precision determinations on high purity material at 273.15 K.

Schriempf (23) (2–20 K) determined the anisotropic resistivities at 60º and 16º to the c axis but did not give values of ρ_i ⊥ and ρ_i ‖. The average values of White and Woods (6, 7) (25–295 K) were corrected to conform to the selected value at 273.15 K using the ratio 8.07/8.35 and at 80 K and above fitted to Equation (xi) with an overall accuracy as a standard deviation of ±0.02 μΩ cm. Values were only given at 30 K and above because of the possibility of unaccounted for residual resistivity.

In the high temperature region anisotropic resistivity measurements of Savitskii et al. (24) (300–1600 K) were only shown graphically with actual data points given by Savitskii et al. (17). These only show satisfactory agreement with the selected values at 600 K and above for the axis perpendicular to the c axis and 1000 K and above for the axis parallel to the c axis and therefore lower temperature measurements were rejected in each case. The values were corrected for thermal expansion using the length values selected by the present author (25). However these extended only to 1300 K and values above this temperature were obtained by extrapolation. The corrected values were then fitted to Equations (xii) to (xiv) which were used to represent the thermal expansion from 273.15 K to 1600 K with overall accuracies as standard deviations of ±0.40 μΩ cm and ±0.51 μΩ cm respectively. Percentage deviations of the measurements of Savitskii et al. from the selected values are shown in Figure 2 whilst selected values of intrinsic electrical resistivity for osmium are given in Table V.

Anisotropic measurements of Schriempf (23) at 297 K differs significantly from the selected value perpendicular to the c axis being 0.98 μΩ cm low whilst the value along the c axis is 0.15 μΩ cm high. The corrected average value of Powell et al. (11) at 500 K is 15% low whilst average values of L’vov et al. (26) (100–1700 K) over the mutual high temperature range 500 K to 1300 K average 22% low. Average measurements of Gugnin et al. (27) (373–1973 K) were only shown in the form of small graphs.