Journal Archive

Johnson Matthey Technol. Rev., 2016, 60, (1), 4
doi: 10.1595/205651316X689855

Selected Electrical Resistivity Values for the Platinum Group of Metals Part II: Rhodium and Iridium

Improved values obtained for liquid phases of rhodium and iridium

Article Synopsis

Electrical resistivity values for both the solid and liquid phases of the platinum group metals (pgms) rhodium and iridium are evaluated. In particular improved values are obtained for the liquid phases of these metals.

1. Introduction

A previous review on electrical resistivity was given in Part I for palladium and platinum (1).

The elements rhodium and iridium are both superconducting with transition temperatures of 325 μK for rhodium (2) and 0.1125 ± 0.001 K for iridium (3). Both metals have a face-centred cubic structure and their melting point are secondary fixed points on the International Temperature Scale of 1990 (ITS-90) at 2236 ± 3 K and 2719 ± 6 K respectively (4).

2. Rhodium

2.1 Solid

As given in Table I the measurement of Powell and Tye (5) is assumed to be superseded by the later measurements of Powell et al. (8, 9) and the measurement of White and Woods (6) by the later measurement of White and Woods (7). The measurement of Powell et al. (8) is not considered to be superseded by the later measurements of Powell et al. (9) since it is at a specific temperature whereas the later measurements are obtained from an interpolation. The selected value is an average of the last four determinations.

Table I

Electrical Resistivity of Rhodium at 273.15 K

Authors Ref. ρi, μΩ cm Temperature of Data
Powell and Tye 5 4.34 Interpolated 213.8–281.6 K
White and Woods 6 4.38 At 273.15 K
White and Woods 7 4.36 At 273.15 K
Powell et al. 8 4.31 At 273.15 K. Corrected for ρ0 0.024 μΩ cm
Powell et al. 9 4.33 First sample. Interpolated 200–400 K. Corrected for ρ0 0.024 μΩ cm
4.38 Second sample. Interpolated 200–400 K. Corrected for ρ0 0.019 μΩ cm
Selected 4.35 ± 0.04 At 273.15 K

Values up to 273.15 K are based on the measurements of White and Woods (7) (20–295 K) after correction to the selected value at 273.15 K using the ratio 4.35/4.36. At 100 K and above the data was fitted to Equation (i) which has an overall accuracy as a standard deviation of ±0.02 μΩ cm.

The measurements of White and Woods (7) are considered to exceed their earlier measurements (6) (15–295 K). Measurements of Powell and Tye (5) (86–282 K) vary from initially 2.5% high to 4.3% high at 97 K and 1.3% low at 214 K then converge towards the selected values whilst those of Kemp et al. (10) (4.2–292 K) above 50 K can be considered as trending from 2.6% high to 7.1% high. After correction for residual resistivity the value of Natarajan and Chari (11) at 4 K and 0.014 μΩ cm is notably higher than the value obtained by White and Woods (7) at 0.0018 μΩ cm at 20 K.

In the high temperature region the combined measurements of Sorokin et al. (12) (1250–2050 K) and of Filippov and Yurchak (13, 14) (1300–2000 K) showed a distinct change in slope at 1750 K allowing a linear extrapolation to the melting point of 53.8 μΩ cm which is notably lower than the value of 60.7 μΩ cm determined by Hüpf et al. (15) (1950–2236 K in the solid region). The measurements of Milošević (16) (300–2200 K) are intermediate extrapolating to a value of 57.4 μΩ cm at the melting point. The values of Milošević compared to those of Sorokin et al. and Filippov and Yurchak trend from initially 5.3% low at 1250 K to 4.0% low at 1700 K and then to 5.5% low at 2050 K. The measurements of Hüpf et al. trend from 3.6% high to 5.6% high. Measurements of Jain et al. (17) (1180–1573 K) trend from 0.9% lower to 8.9% higher than the measurements of Milošević.

Because of these large discrepancies and in order to obtain a consistent set of values for solid rhodium it is noted for the cubic pgms that at the melting points the ratio of the resistivities of the liquid phase (ρL) and of the solid phase (ρS) can be considered in terms of the entropy of fusion (ΔSM) by using a modified version of the Mott equation (18): ln (ρL/ρS) = A ΔSM + B where A and B are constants. Using selected values of ρL/ρS of 1.738 for palladium (1), 1.610 for platinum (1) and 1.391 for iridium (see below) and values of ΔSM of 8.80 J mol–1 K–1 for palladium (19), 10.83 J mol–1 K–1 for platinum (20) and 15.20 J mol–1 K–1 for iridium (21) leads to the equation ln (ρL/ρS) = 0.85387 – 3.4535 × 10–2ΔSM with the degree of correlation indicated by the fact that the standard deviation was only ±0.008. Substituting in the entropy value of ΔSM = 12.21 J mol–1 K–1 for rhodium (22) then ρL/ρS = 1.541 and based on the selected value of ρL = 89.2 μΩ cm then ρS = 57.9 μΩ cm which is very close to the extrapolated experimental value of Milošević which is therefore selected after taking into account possible systematic errors in the entropies of fusion and the liquid electrical resistivity measurements. However although the measurements of Milošević were given preference it is noted that the equation given by Milošević extrapolates to a value at 273.15 K which is 13% higher than the selected value and in order to achieve compatibility only the measurements of Milošević at 1000 K and above could be considered. However these were used to produce Equation (ii) which is assumed to represent the electrical resistivity from 273.15 K to the melting point. The measurements of Binkele and Brunen (23) (273–1373 K) gave a value at 273.15 K which was 6.0% higher than the selected value and therefore these measurements could not be considered below 700 K but above this temperature bias only 0.5% low which, based on very large differences between the various sets of other measurements, is considered as confirming the selection procedure. Therefore above 100 K Equations (i) and (ii) were used to generate the selected values for the solid in Table II where values at 600 K and above were given to four significant figures only for interpolation purposes.

Table II

Intrinsic Electrical Resistivity of Rhodium

Temperature, K ρi, μΩ cm Temperature, K ρi, μΩ cm Temperature, K ρi, μΩ cm
Solid
20 0.0018 180 2.52 700 13.74
25 0.0049 190 2.72 800 16.22
30 0.011 200 2.92 900 18.77
40 0.043 210 3.12 1000 21.39
50 0.10 220 3.32 1100 24.08
60 0.20 230 3.51 1200 26.81
70 0.34 240 3.71 1300 29.59
80 0 .51 250 3.90 1400 32.41
90 0.69 261 4.10 1500 35.27
100 0.88 270 4.29 1600 38.17
110 1.09 273.15 4.35 1700 41.10
120 1.30 280 4.48 1800 44.07
130 1.51 290 4.68 1900 47.07
140 1.71 300 4.87 2000 50.10
150 1.92 400 6.91 2100 53.18
160 2.12 500 9.08 2200 56.30
170 2.32 600 11.36 2236 57.44
Liquid
2236 89.2 2500 93.6 2900 100.3
2250 89.4 2600 95.3 3000 102.0
2300 90.2 2700 97.0 3100 103.7
2400 91.9 2800 98.6 3150 104.5

Three sets of measurements of resistivity ratios were corrected for thermal expansion using values selected by the present author (24) and then values above 273.15 K were compared with the selected curve (Figure 1). The measurements of Holborn (25) (81–773 K) were given as RT/R273.15 K and on this basis trended to 4.0% low at 773 K. Mimeault and Hansen (26) (100–700 K) gave measurements as the ratio RT/R295 and after correcting to RT/R273.15 K trended to 12.5% low whilst the measurements of García and Löffler (27) (295–1000 K) which were also corrected from RT/R295 to RT/R273.15 K trended to 13.5% low. For comparison purposes as given in Figure 2 the resistivity ratios are reconsidered as being electrical resistivity values. At the melting point the measurement of Savvatimskii (28) is 6.2% high and that of Martynyuk and Tsapkov (29) is 2.7% high. The electrical resistivity measurements of Glazkov (30) (800–2000 K) are given only as a temperature coefficient of electrical resistivity which over the given temperature range decreases from 0.021 to 0.019 μΩ cm K–1, differing from the present evaluation which suggests a rise from 0.025 to 0.031 μΩ cm K–1 over the same temperature range.

Fig. 1.

Solid rhodium – percentage deviations from selected curve

Fig. 2.

Solid rhodium – percentage deviations from selected curve

2.2 Liquid

Measured electrical resistivity values for rhodium at the melting point are given in Table III. In the liquid region electrical resistivity measurements of Hüpf et al. (15) (2236–3150 K) were accepted and are given by Equation (iii) and are also included in Table II.

Table III

Differences Between the Solid and Liquid Electrical Resistivity of Rhodium at the Melting Point

Authors Reference ρS, μΩ cm ρL, μΩ cm ρL/ρS
Savvatimskii 28 61.0 85.5 1.402
Martynyuk and Tsapkov 29 59.0 92.5 1.568
Hüpf et al. 15 60.7 89.2 1.470
Present assessment – 57.44 89.2 1.553

3. Iridium

3.1 Solid

As given in Table IV the measurement of Powell and Tye (5) is assumed to be superseded by the later measurements of Powell et al. (8, 9) and the measurements of White and Woods (6) by the later measurement of White and Woods (7). The measurement of Powell et al. (8) is not considered to be superseded by the later measurements of Powell et al. (9) since it is at a specific temperature whereas the later measurements are obtained from an interpolation. The selected value is an average of the last three determinations.

Table IV

Electrical Resistivity of Iridium at 273.15 K

Authors Reference ρi μΩ cm Temperature of Data
Powell and Tye 5 4.75 Extrapolated 277.5–289.3 K
Wimber and Halvorson 31 5.29 Extrapolated from equation 295–2275 K
García and Löffler 27 8.47 Extrapolated from 295–850 K
White and Woods 6 4.63 At 273.15 K
White and Woods 7 4.65 At 273.15 K
Powell et al. 8 4.65 At 273.15 K. Corrected for ρ0 0.055 μΩ cm
Powell et al. 9 4.72 Interpolated 200–400 K. Corrected for ρ0 0.056 μΩ cm
Selected 4.67 ± 0.05 At 273.15 K

Values up to 273.15 K are based on the measurements of White and Woods (7) (20–295 K) after correction to the selected value at 273.15 K using the ratio 4.67/4.65. At 100 K and above, but less than 220 K, the data was fitted to Equation (iv) which has an overall accuracy as a standard deviation of ±0.01 μΩ cm.

The measurements of White and Woods (7) are considered as superseding their earlier measurements (6) (15–295 K). Measurements of Volkenshtein et al. (32) (0.4–70 K) are only shown graphically whilst measurements of Volkenshtein et al. (33) (4.2–300 K) are also shown graphically except at 25 K and below. These are given in the form of an equation which appears to lead to electrical resistivity values about half those of White and Woods (7). Measurements of Powell and Tye (5) (83–289 K) are initially 2.8% high drifting to 5.6% high at 90 K to 0.6% high at 191 K and then to an average of 1.6% high at 278 K and above.

In the high-temperature region measurements of Trukhanova and Filippov (34) (1300–2500 K) and of Filippov and Yurchak (13, 14) (1500–2500 K) over the full range at 100 K intervals, Pottlacher (35) (2000–2719 K in the solid range) at 50 K intervals from 2000 to 2700 K and Wimber and Halvorson (31) (293–2300 K) at 100 K intervals from 700 to 1900 K, after correcting the latter for thermal expansion using values selected by the present author (36), were combined with the selected value at 273.15 K and fitted to Equation (v) with an overall accuracy as a standard deviation of ±0.33 μΩ cm. Therefore above 100 K Equations (iv) and (v) were used to generate a selected value for the solid in Table V where values at 600 K and above were given to four significant figures only for interpolation purposes. Deviations of the input values from this equation are shown in Figure 3 except for the measurements of Wimber and Halvorson at 300 K and 400 K which are respectively 10.2% and 7.3% higher than the selected values.

Table V

Intrinsic Electrical Resistivity of Iridium

Temperature, K ρi, μΩ cm Temperature, K ρi, μΩ cm Temperature, K ρi, μΩ cm
Solid
15 0.0013 190 3.01 1000 21.19
20 0.0050 200 3.22 1100 23.76
25 0.015 210 3.42 1200 26.38
30 0.032 220 3.62 1300 29.06
40 0.10 230 3.82 1400 31.77
50 0.20 240 4.02 1500 34.53
60 0.35 250 4.21 1600 37.32
70 0.53 260 4.41 1700 40.14
80 0.72 270 4.61 1800 42.98
90 0.90 273.15 4.67 1900 45.84
100 1.11 280 4.80 2000 48.71
110 1.33 290 5.00 2100 51.59
120 1.55 300 5.20 2200 54.46
130 1.76 400 7.23 2300 57.33
140 1.97 500 9.36 2400 60.20
150 2.18 600 11.57 2500 63.05
160 2.39 700 13.87 2600 65.88
170 2.60 800 16.24 2700 68.69
180 2.81 900 18.68 2719 69.22
Liquid
2719 96.3 3000 100.0 3400 105.2
2750 96.7 3100 101.3 3500 106.6
2800 97.3 3200 102.6 3550 107.2
2900 98.7 3300 103.9 – –
Fig. 3.

Solid iridium – percentage deviations from selected curve

Measurements of Binkele and Brunen (23) (273–1373 K) combined from four runs trend from initially 16% high to 1.4% high whilst measurements of Gathers et al. (37) (2000–2720 K in the solid range) trend from 2.7% high to 6.4% high and those of Lʼvov et al. (38) (100–1700 K) above 273.15 K scatter 5.8% low to 4.6% high. At the melting point the value of electrical resistivity determined by Lebedev et al. (39) is 1.6% high whilst that determined by Martynyuk and Tsapkov (29) is 4.8% low.

Values determined as resistivity ratios were corrected for thermal expansion (36) and from RT/R295 K to RT/R273.15 K. Measurements of Mimeault and Hansen (26) (100–700 K) on this basis trend to 18% low above 273.15 K whilst the measurements of García and Löffler (27) (295–1100 K) trend to 30% low. Measurements of Gugnin et al. (40) (473–1973 K) were only shown in the form of a small graph. Deviations of these measurements from Equation (v) above 300 K are shown in Figure 4 where values of Mimeault and Hansen and of García and Löffler were reconsidered as electrical resistivity values based on the selected value at 273.15 K.

Fig. 4.

Solid iridium – percentage deviations from selected curve

3.2 Liquid

Electrical resistivity values for iridium at the melting point are given in Table VI. The variation of electrical resistivity with temperature as given by Pottlacher (35) (2719–3550 K) are accepted and are given as Equation (vi) and included in Table V. Over the common temperature range of 2719 to 3550 K the measurements of Gathers et al. (37) (2719–4250 K in the liquid range) trend from 3.8% high to 1.3% high.

Table VI

Differences Between the Solid and Liquid Electrical Resistivity of Iridium at the Melting Point

Authors Reference ρS, μΩ cm ρL, μΩ cm ρL/ρS
Lebedev et al. 38 70.3 92.0 1.309
Martynuk and Tsapkov 28 65.9 85.5 1.297
Gathers et al. 36 73.7 100.0 1.357
Pottlacher 34 69.1 96.3 1.394
Present assessment – 69.22 96.3 1.391

Low Temperature Intrinsic Resistivity of Solid Rhodium (100 to 273.15 K)


(i)

High Temperature Intrinsic Resistivity of Solid Rhodium (273.15 to 2236 K)


(ii)

Intrinsic Resistivity of Liquid Rhodium (2236 to 3150 K)


(iii)

Low Temperature Intrinsic Resistivity of Solid Iridium (100 to 273.15 K)


(iv)

High Temperature Intrinsic Resistivity of Solid Iridium (273.15 to 2719 K)


(v)

Intrinsic Resistivity of Liquid Iridium (2719 to 3550 K)


(vi)

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Notice of Correction - Online Version

Please note that the web version of this article originally contained a mistake in Table II in which the resistivity value for rhodium at 80 K had been altered from 0.51 to 1.51. The PDF version of the article contains the correct values.

The error has been corrected on 11th Feb 2016.

The Author

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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