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Johnson Matthey Technol. Rev., 2016, 60, (3), 179

doi:10.1595/205651316x691618

Selected Electrical Resistivity Values for the Platinum Group of Metals Part III: Ruthenium and Osmium

Improved values obtained for ruthenium and osmium

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Article Synopsis

Anisotropic and average intrinsic electrical resistivity measurements of ruthenium were evaluated from 10 K to 1600 K and average values above this temperature up to the melting point. For osmium average values were evaluated from 30 K to 273.15 K and anisotropic and average values above this temperature and up to 1600 K.

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 ρavr = (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).

Table I

Electrical Resistivity of Ruthenium at 273.15 K

AuthorsRef.ρi ⊥, μΩ cmρi ‖, μΩ cmρi avr, μΩ cmTemperature of data
White and Woods 6, 7 6.69 At 273.15 K
Powell et al. 8 6.54 At 273.15 K. Corrected ρ0 0.57 μΩ cm
Tainsh and White 9 6.72 At 273.15 K. Corrected ρ0 0.02 μΩ cm
Volkenshteyn et al. 10 7.15 5.26 6.52 At 273.15 K. Corrected ρ0 ⊥ 0.10 μΩ cm; ρ0 || 0.09 μΩ cm
Powell et al. 11 6.75 5.12 6.21 Interpolated 200–400 K. Corrected for both axes by ρ0 0.07 μΩ cm
Azhazha et al. 12 6.61 5.14 6.12 At 273.15 K
Volkenshtein et al. 13 6.65 5.15 6.15 At 273.15 K. Estimated by Bass (14) from a graphical representation


Selected 6.67±0.08 5.14±0.02 6.16±0.05 At 273.15 K

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 ρi ‖/ρi ⊥ determined from the measurements of Volkenshteyn et al. (10) after correction for ρ0 whilst values of ρi ⊥ and ρi ‖ 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.

Table II

Intrinsic Electrical Resistivity of Ruthenium (10 K to 1600 K)

Temperature, Kρi ⊥, μΩ cmρi ‖, μΩ cmρi avr, μΩ cmTemperature, Kρi ⊥, μΩ cmρi ‖, μΩ cmρi avr, μΩ cm
10 0.0003 0.0003 0.0003 230 5.30 4.12 4.91
20 0.0020 0.0017 0.0019 240 5.62 4.36 5.20
30 0.0093 0.0079 0.0088 250 5.94 4.60 5.49
40 0.038 0.030 0.035 260 6.25 4.83 5.78
50 0.11 0.08 0.10 270 6.57 5.07 6.07
60 0.25 0.17 0.22 273.15 6.67 5.14 6.16
70 0.42 0.33 0.39 280 6.91 5.28 6.37
80 0.63 0.52 0.59 290 7.26 5.48 6.67
90 0.89 0.73 0.84 300 7.61 5.68 6.96
100 1.20 0.96 1.12 400 11.1 7.74 9.97
110 1.51 1.21 1.41 500 14.6 9.89 13.0
120 1.83 1.46 1.71 600 18.0 12.1 16.1
130 2.14 1.71 2.00 700 21.5 14.4 19.2
140 2.46 1.95 2.29 800 25.0 16.8 22.3
150 2.77 2.20 2.58 900 28.5 19.3 25.4
160 3.09 2.44 2.87 1000 32.0 21.9 28.6
170 3.40 2.88 3.16 1100 35.4 24.5 31.8
180 3.72 2.93 3.46 1200 38.9 27.3 35.0
190 4.04 3.17 3.75 1300 42.4 30.1 38.3
200 4.35 3.41 4.04 1400 45.9 33.0 41.6
210 4.67 3.65 4.33 1500 49.3 36.0 44.9
220 4.99 3.89 4.62 1600 52.8 39.1 48.2

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.

Table III

Average Intrinsic Electrical Resistivity of Ruthenium (1600 K to 2606 K)

Temperature, Kρi avr, μΩ cmTemperature, Kρi avr, μΩ cm
1600 48.2 2200 67.5
1700 51.4 2300 70.8
1800 54.5 2400 74.1
1900 57.7 2500 77.5
2000 61.0 2600 80.9
2100 64.2 2606 81.1

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.

Fig. 1.

Solid ruthenium – percentage deviations from selected curve

Solid ruthenium – percentage deviations from selected curve

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 ρ273 K / ρ4.2 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 ρi ⊥ and ρi ‖. 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.

Table IV

Electrical Resistivity of Osmium at 273.15 K

AuthorsRef.ρi ⊥, μΩ cm ρi ‖, μΩ cmρi avr, μΩ cmTemperature of data
White and Woods 6, 7 8.35 At 273.15 K
Powell et al. 8 8.26 At 273.15 K. As received sample corrected for ρ0 0.27 μΩ cm
7.88 At 273.15 K. Sample annealed at 1813 K corrected for ρ0 0.24 μΩ cm
Powell et al. 11 7.85 Interpolated 200–400 K. Corrected for ρ0 0.24 μΩ cm
Volkenshteyn 22 9.346 5.532 8.075 At 273.15 K


Selected 9.35 5.53 8.07 At 273.15 K

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.

Fig. 2.

Solid osmium – percentage deviations from selected curve

Solid osmium – percentage deviations from selected curve

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.

Table V

Intrinsic Electrical Resistivity of Osmium

Temperature, Kρi avr, μΩ cmTemperature, Kρi ⊥, μΩ cmρi ‖, μΩ cmρi avr, μΩ cm
30 0.027 240 6.92
40 0.11 250 7.26
50 0.25 260 7.61
60 0.48 270 7.76
70 0.76 273.15 9.35 5.53 8.07
80 1.05 280 9.70 5.73 8.38
90 1.45 290 10.2 6.03 8.82
100 1.85 300 10.7 6.32 9.25
110 2.23 400 15.7 9.27 13.6
120 2.62 500 20.6 12.2 17.8
130 2.99 600 25.4 15.1 22.0
140 3.36 700 30.0 18.1 26.0
150 3.73 800 34.5 21.0 30.0
160 4.10 900 39.0 23.9 33.9
170 4.46 1000 43.2 26.8 37.8
180 4.81 1100 47.4 29.7 41.5
190 5.17 1200 51.5 32.6 45.2
200 5.52 1300 55.4 35.5 48.8
210 5.87 1400 59.2 38.4 52.3
220 6.22 1500 62.9 41.3 55.7
230 6.57 1600 66.5 44.2 59.1

Low Temperature Intrinsic Resistivity of Ruthenium Below 30 K

ρi ⊥ (μΩ cm) = 2.8 × 10–6 T 2 + 2.8 × 10–10 T 5 μΩ cm (i)

ρi ‖ (μΩ cm) = 2.3 × 10–6 T 2 + 2.4 × 10–10 T 5 μΩ cm (ii)

ρi avr (μΩ cm) = 2.6 × 10–6 T 2 + 2.7 × 10–10 T 5 μΩ cm (iii)

Low Temperature Intrinsic Resistivity of Ruthenium (100 to 273.15 K)

ρi ⊥ (μΩ cm) = 3.13425 × 10–2 T + 7.13667 × 10–7 T 2 – 1.94445 (iv)

ρi ‖ (μΩ cm) = 2.57537 × 10–2 T – 4.37527 × 10–6 T 2 – 1.56817 (v)

ρi avr (μΩ cm) = 2.94796 × 10–2 T – 9.82645 × 10–7 T 2 – 1.81902 (vi)

High Temperature Intrinsic Resistivity of Ruthenium (273.15 to 1600 K)

ρi ⊥ (μΩ cm) = 3.48448 × 10–2 T – 3.42085 × 10–8 T 2 – 2.84530 (vii)

ρi ‖ (μΩ cm) = 1.77020 × 10–2 T + 4.20211 × 10–6 T 2 – 8.82460 × 10–3 (viii)

ρi avr (μΩ cm) = 2.91305 × 10–2 T + 1.37790 × 10–6 T 2 – 1.89981 (ix)

High Temperature Intrinsic Resistivity of Ruthenium (1600 to 2606 K)

ρi avr (μΩ cm) = 2.68820 × 10–2 T + 1.37576 × 10–6 T 2 + 1.70317 (x)

Low Temperature Intrinsic Resistivity of Osmium (80 to 273.15 K)

ρi avr (μΩ cm) = 4.68970 × 10–2 T – 4.94870 × 10–5 T 2 + 6.71192 × 10–5 T 3– 2.41554 (xi)

High Temperature Intrinsic Resistivity of Osmium (273.15 to 1600 K)

ρi ⊥ (μΩ cm) = 5.41521 × 10–2 T – 5.90401 × 10–6 T 2 – 5.00114 (xii)

ρi ‖ (μΩ cm) = 2.96326 × 10–2 T – 2.67298 × 10–7 T 2 – 2.54420 (xiii)

ρi avr (μΩ cm) = 4.59789 × 10–2 T – 4.02511 × 10–6 T 2 – 4.18216 (xiv)

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The Author

 John W. Arblaster John W. Arblaster is interested in the history of science and the evaluation of the thermodynamic and crystallographic properties of the elements. Now retired, he previously worked as a metallurgical chemist in a number of commercial laboratories and was involved in the analysis of a wide range of ferrous and non-ferrous alloys.

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