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Platinum Metals Rev., 1997, 41, (4), 184

Crystallographic Properties of Rhodium

  • By J. W. Arblaster
  • Rotech Laboratories, Wednesbury, West Midlands, England
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Article Synopsis

The crystallographic properties of rhodium at temperatures from absolute zero to its melting point are assessed following a review of the literature published during the period 1915 to date. Selected values of thermal expansion coefficients and length change measurements have been used to calculate the variations with temperature of lattice parameters, interatomic distances, atomic and molar volumes and density. Literature values are compared graphically with the selected values.

Rhodium exists in a face-centred cubic structure (Pearson symbol cF4) at temperatures up to its melting point, which is a proposed secondary fixed point on the International Temperature Scale, ITS-90, at 2236 K (1). In the low temperature region high precision thermal expansion data are only available up to 85 K and at 283 K. Interpolation in the region 85 to 283 K is estimated from a relationship between thermal expansion and specific heat, as explained in a previous review on platinum (2).

The adoption of this procedure for rhodium is justified on the grounds that the equation leads to a close agreement with the length change measurements of Erfling (3) in this region (see the section entitled “Comparison with Other Data”, below). In the high temperature region crystallographic properties are based entirely on lattice parameter measurements.


Low Temperature Thermal Expansion Data

(i)

(ii)
Low Temperature Thermal Expansion Data (Spline-Fitted Equations above 28 K)

(iii)

(iv)

(v)

(vi)

vii)
High Temperature Thermal Expansion Data

(viii)

(ix)

Thermal Expansion


Low Temperature Region


In the low temperature region the thermodynamic thermal expansion coefficient, α, is based on the measurements made by White and Pawlowicz (4) at 3–85 K and 283 K, except for the value at 283 K which was revised by White (5) to (8.40 ± 0.10) × 10−6K−1. The thermal expansion coefficients were represented by Equations (i) and (ii) where the second equation is derived as described in the review on platinum (2) using specific heat measurements tabulated by Furukawa, Reilly and Gallagher (6), which were incorporated into an assessment of the thermodynamic properties of rhodium by the present author (7).

Equation (i) is accurate to 4 × 10−10 K−1, while Equation (ii) is accurate to 2 × 10−8 K−1 below 85 K but decreasing to 1 × 10−7 K−1 at 283 K. Equation (ii) was extrapolated to the reference temperature 293.15 K. Because the use of this Equation would require a knowledge of the specific heat values, it can also be represented by a series of spline-fitted polynomials, Equations (iii) to (vii), which agree with Equation (ii) to within 1 × 10−9 K−1.

High Temperature Region


In the high temperature region selected values are based on a close agreement between the lattice parameter measurements of Ross and Hume-Rothery (8) at 296 to 2223 K (but specifically the high precision measurements 296 to 1168 K) and those of Schröder, Schmitz-Pranghe and Kohlhaas (9) at 87 to 1942 K which were joined with the low temperature data and fitted to Equation (viii) with its derivative, the thermal expansion coefficient relative to 293.15 K, α*, being represented by Equation (ix). These equations representing the crystallographic data were extrapolated to the melting point of rhodium. A comparison between experimental and calculated values shows that Equation (viii) has an overall accuracy of 0.002 when considered in terms of the relationship:

Lattice Parameter at 293.15 K


In Table I are shown a combination of the values selected by Donohue (10) as well as more recent determinations both of which were corrected from kX and ångström units to nm using conversion factors recommended in the 1986 revision of the fundamental constants (11). Lattice parameter values were corrected to 293.15 K using thermal expansion coefficients selected in this review.


Table I

Values of Lattice Constants from the Literature

AuthorsReferenceLattice constant, nm at 293.15 KOriginal temperature, K
Owen and Iball 12 0.38034 289.7
Owen and Yates 13 0.38036 291
Swanson, Fuyat and Ugrinic 14 0.38032 298
Anderson and Hume-Rothery 15 0.38033 293
Černohorsky 16 0.38038 294.7
Ross and Hume-Rothery 8 0.38033 295.8
Pawar 17 0.38034 301
Singh 18 0.38033 303
Schröder et al 9 0.38030 299
Selected     0.38034 ± 0.00002

The values of molar volume and density in Table II were calculated using an atomic weight of 102.90550 (19) and an Avogadro’s Constant of 6.0221367 × 1023 mol−1 (11).


Table II

Crystallographic Properties

Temperature, KThermal expansion, 106 × α, K1Length change, δa/a × 100Lattice parameter, nmInteratomic distance, nmAtomic volume, 103 × nm3Molar volume, 106 × m3 mol−1Density, kg m−3
0 0 -0.1603 0.37973 0.26851 13.689 8.244 12483
10 0.023 -0.1603 0.37973 0.26851 13.689 8.244 12483
20 0.091 -0.1603 0.37973 0.26851 13.689 8.244 12483
30 0.34 -0.1601 0.37973 0.26851 13.689 8.244 12483
40 0.86 -0.1595 0.37973 0.26851 13.689 8.244 12483
50 1.61 -0.1583 0.37974 0.26852 13.690 8.244 12482
60 2.41 -0.1563 0.37975 0.26852 13.690 8.245 12482
70 3.16 -0.1535 0.37976 0.26853 13.692 8.245 12481
80 3.85 -0.1500 0.37977 0.26854 13.693 8.246 12479
90 4.45 -0.1458 0.37979 0.26855 13.695 8.247 12478
100 4.98 -0.1411 0.37980 0.26856 13.697 8.248 12476
110 5.43 -0.1359 0.37982 0.26858 13.699 8.250 12474
120 5.83 -0.1303 0.37984 0.26859 13.701 8.251 12472
130 6.16 -0.1243 0.37987 0.26861 13.704 8.253 12470
140 6.46 -0.1180 0.37989 0.26862 13.706 8.254 12467
150 6.71 -0.1114 0.37992 0.26864 13.709 8.256 12465
160 6.94 -0.1046 0.37994 0.26866 13.712 8.257 12462
180 7.32 -0.0903 0.38000 0.26870 13.718 8.261 12457
200 7.61 -0.0754 0.38005 0.26874 13.724 8.265 12451
220 7.86 -0.0599 0.38011 0.26878 13.730 8.268 12446
240 8.07 -0.0440 0.38017 0.26882 13.737 8.272 12440
260 8.24 -0.0277 0.38023 0.26887 13.743 8.276 12433
280 8.38 -0.0111 0.38030 0.26891 13.750 8.281 12427
293.15 8.46 0 0.38034 0.26894 13.755 8.283 12423
300 8.48 0.006 0.38036 0.26896 13.757 8.285 12421
400 8.87 0.093 0.38069 0.26919 13.793 8.306 12389
500 9.25 0.183 0.38104 0.26943 13.831 8.329 12355
600 9.64 0.278 0.38140 0.26969 13.870 8.353 12320
700 10.03 0.377 0.38177 0.26995 13.911 8.377 12284
800 10.43 0.479 0.38216 0.27023 13.954 8.403 12246
900 10.86 0.586 0.38257 0.27052 13.998 8.430 12207
1000 11.31 0.698 0.38299 0.27082 14.045 8.458 12167
1100 11.79 0.814 0.38344 0.27113 14.094 8.487 12125
1200 12.31 0.936 0.38390 0.27146 14.145 8.518 12081
1300 12.87 1.063 0.38438 0.27180 14.198 8.550 12035
1400 13.48 1.196 0.38489 0.27216 14.254 8.584 11988
1500 14.14 1.336 0.38542 0.27253 14.314 8.620 11938
1600 14.86 1.483 0.38598 0.27293 14.376 8.657 11886
1700 15.64 1.638 0.38657 0.27335 14.442 8.697 11832
1800 16.50 1.801 0.38719 0.27379 14.512 8.739 11775
1900 17.42 1.974 0.38785 0.27425 14.586 8.784 11716
2000 18.43 2.157 0.38854 0.27474 14.664 8.831 11653
2100 19.52 2.351 0.38928 0.27526 14.748 8.881 11587
2200 20.69 2.557 0.39006 0.27582 14.837 8.935 11517
2236 21.14 2.634 0.39036 0.27602 14.871 8.955 11491

Comparison with Other Data


On the basis of the relationship:

Figure 1 shows the deviation of the low temperature length change measurements made by Laquer (20) at 0–300 K and the measurements below 300 K of Schröder, Schmitz-Pranghe and Kohlhaas (9) taken at 87–1942 K. Not shown are the measurements of Erfling (3) at 58–273 K which agree with the selected values to within 0.001. On the same basis, Figure 2 shows the deviations of the dilatometric measurements made by Swanger (21) at 293–773 K, Holzmann (22) 293–1269 K and Ebert (23) 373–1773 K, and the lattice parameter measurements of Pawar (17) 301–860 K and Singh (18) 303–1138K.

Fig. 1

Deviation of low temperature experimental length change measurements compared to those derived from Equations (i) to (vii)

Deviation of low temperature experimental length change measurements compared to those derived from Equations (i) to (vii)

Fig. 2

Deviation of high temperature experimental length change measurements compared to Equation (viii)

Deviation of high temperature experimental length change measurements compared to Equation (viii)

Figure 3, which is a coarser version of Figure 2, shows the deviation of the lattice parameter measurements of Raub, Beeskow and Menzel (24) 293–1473 K (results shown graphically only), the higher temperature measurements of Ross and Hume-Rothery (8) in the range 1323–2223 K (results shown graphically only) and the extraordinary deviant measurements of Bale (25) at 298–1819 K, shown only graphically with actual values being given by Touloukian and colleagues (26) – the expanded lattice found in these measurements may be due to severe oxygen contamination (27). Figure 4 shows the percentage deviation of the thermal expansion coefficients of Valentiner and Wallot (28) 96–287 K, which are 5 per cent lower to 6 per cent higher than the selected values, and the high temperature measurements of Glazov (29) 1200–2000 K which are 4 per cent lower to 1 per cent higher. Since selected values of the thermal expansion coefficient in the high temperature region are derived from the length change measurements then the agreement with the values of Glazov must be considered to be reasonable.

Fig. 3

Deviation of high temperature experimental length change measurements compared to Equation (viii)

Deviation of high temperature experimental length change measurements compared to Equation (viii)

Fig. 4

Percentage deviation of experimental thermal expansion data

Percentage deviation of experimental thermal expansion data

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