Crystallographic Properties of Rhodium
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Crystallographic Properties of Rhodium
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 |
| Low Temperature Thermal Expansion Data (Spline-Fitted Equations above 28 K) |
| High Temperature Thermal Expansion Data |
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
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
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)
Fig. 2
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)
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