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As given in **Table I** the measurement of Powell and Tye (5) is assumed to be superseded by the later measurements of Powell *et al.* (8, 9) and the measurement of White and Woods (6) by the later measurement of White and Woods (7). The measurement of Powell *et al.* (8) is not considered to be superseded by the later measurements of Powell *et al.* (9) since it is at a specific temperature whereas the later measurements are obtained from an interpolation.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

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 ρ_{0} 0.024 μΩ cm |

Powell et al. | 9 | 4.33 | First sample. Interpolated 200–400 K. Corrected for ρ_{0} 0.024 μΩ cm |

4.38 | Second sample. Interpolated 200–400 K. Corrected for ρ_{0} 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 (ρ_{L}) and of the solid phase (ρ_{S}) can be considered in terms of the entropy of fusion (ΔS_{M}) by using a modified version of the Mott equation (18): ln (ρ_{L}/ρ_{S}) = *A* ΔS_{M} + *B* where *A* and *B* are constants. Using selected values of ρ_{L}/ρ_{S} of 1.738 for palladium (1), 1.610 for platinum (1) and 1.391 for iridium (see below) and values of ΔS_{M} 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 (ρ_{L}/ρ_{S}) = 0.85387 – 3.4535 × 10^{–2}ΔS_{M} with the degree of correlation indicated by the fact that the standard deviation was only ±0.008. Substituting in the entropy value of ΔS_{M} = 12.21 J mol^{–1} K^{–1} for rhodium (22) then ρ_{L}/ρ_{S} = 1.541 and based on the selected value of ρ_{L} = 89.2 μΩ cm then ρ_{S} = 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

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 R_{T}/R_{273.15 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 R_{T}/R_{295} and after correcting to R_{T}/R_{273.15 K} trended to 12.5% low whilst the measurements of García and Löffler (27) (295–1000 K) which were also corrected from R_{T}/R_{295} to R_{T}/R_{273.15 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.

#### Fig. 2.

### 2.2 Liquid

## 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

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 ρ_{0} 0.055 μΩ cm |

Powell et al. | 9 | 4.72 | Interpolated 200–400 K. Corrected for ρ_{0} 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

#### Fig. 3.

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 R_{T}/R_{295 K} to R_{T}/R_{273.15 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.

### 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

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)**

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

**Intrinsic Resistivity of Liquid Rhodium (2236 to 3150 K)**

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

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

**Intrinsic Resistivity of Liquid Iridium (2719 to 3550 K)**

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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.