Introduction

Reviews by Crabtree (1) and the present author (2–5) established that at 293.15 K (20°C) osmium is the densest metal at 22,589 ± 5 kg m^–3 compared to 22,562 ± 11 kg m^–3 for iridium, the difference of 27 ± 12 kg m^–3 considered as confirming this. The question then arises as to whether osmium is always the densest metal. Although it would have been desirable to consider this in terms of a full pressure-temperature-volume evaluation, limited high pressure data for iridium confines the evaluation to just two aspects – the effect of temperature at ambient pressure and the effect of pressure at room temperature.

The Effect of Temperature at Ambient Pressure

The thermal expansion of iridium is known with precision below room temperature, satisfactory up to 2000 K and estimated above this temperature (4) whilst the thermal expansion of osmium is known only between room temperature and 1300 K and is estimated below room temperature (5). Because the room temperature thermal expansion coefficient of iridium at 6.47 × 10^–6 K^–1 is higher than the average value for osmium at 4.99 × 10^–6 K^–1, it would be expected that with the greater contraction below room temperature iridium would be the densest metal at low temperatures. However this proves not to be the case with the density of osmium at 0 K being 22,661 ± 11 kg m^–3 compared to a value of 22,652 ± 11 kg m^–3 for iridium. The difference of 9 ± 16 kg m^–3 indicates an ambiguity and the possibility that iridium could be the densest metal statistically. Assuming that the assigned accuracy for osmium increases linearly from ±5 kg m^–3 at 293.15 K to ±11 kg m^–3 at 0 K then the density ambiguity exists below 150 K where the density difference becomes equal at 14 ± 14 kg m^–3. The variation of the density of both elements over the range from 0 to 300 K is shown in Figure 1. In the high temperature region there is no ambiguity with the density difference increasing to 147 ± 12 kg m^–3 at 1300 K, the experimental limit for osmium, whilst comparison with neighbouring elements rhodium (6) and ruthenium (7) suggests that the average thermal expansion coefficient for osmium will continue to be lower than that of iridium so that osmium will remain the densest metal in the high temperature region.

The Effect of Pressure at Room Temperature

The effect of pressure (P) on volume (V) is given in terms of a third order Birch–Murnaghan equation of state:

P = 1.5 B₀ (Y^7/3 – Y^5/3) [1 + 0.75 (Bʹ₀ – 4)(Y^2/3 – 1)] (i)

where Y = V₀/V and V₀ is the volume at zero pressure, B₀ is the bulk modulus and Bʹ₀ is the pressure derivative of the bulk modulus. When Bʹ₀ = 4 the equation is said to be second order.

The equation indicates that the higher the value of B₀ then the less compressible would be the material and therefore it was a complete surprise when Cynn et al. (8) determined the value of B₀ for osmium to be 462 GPa compared to 443 GPa for diamond which appeared to overturn a long held belief that diamond was the least compressible element. This resulted in further measurements for osmium as indicated in Table I which suggest that the value determined by Cynn et al. appears to have been too high and subject to a systematic error which Liang and Fang (9) suggested was due to different quasi-hydrostatic conditions which were better determined in the later experiments. Distinction is made between determining the bulk modulus by elastic constant measurements (EC) and volume compression (VC).

The selected values are simple averages with the assigned accuracies encompassing all of the accepted values. The selected value of B₀ for osmium is now less than that of diamond and therefore the latter regains its status as the least compressible element. Pantea et al. (14) showed that low temperature had little effect on the value of B₀ for osmium with the value at 0 K being only 5 GPa greater than that at 300 K. However at high temperature Voronin et al. (13) showed a decrease of 58 GPa between 300 K and 1273 K.

Room temperature volume compression values for iridium are given in Table II with the cross-over pressures calculated from Equation (i) using selected values of V₀ as 8.5195 ± 0.0042 cm³ mol^–1 for iridium (4) and 8.4214 ± 0.0013 cm³ mol^–1 for osmium (5).

Since the measurements of Cynn et al. (8) for osmium appear to be subject to a systematic error it is considered that the same error may apply to their measurements on iridium and that these values should not be considered further. The third order and second order equations determined from the measurements of Cerenius and Dubrovinsky (18) lead to pressure values which do not agree with each other or with the selected curve in the graphical representation. However values of B₀ calculated from elastic constants measurements at 355 GPa for MacFarlane and Rayne (19) and 361 GPa for Adamesku et al. (20) show excellent agreement with the second order value of Cerenius and Dubrovinsky and it is considered possible that systematic errors in measurements which may have influenced the third order fit were restrained by the second order fit. The third order fit is therefore rejected. However the calculated cross-over pressure for the second order fit is well below the experimental limit of measurements at 10 GPa and therefore must initially be considered with some suspicion. The selected compressibility curve is therefore the interpretation by Gschneidner Jr. (21) of the pressure measurements of Bridgman (22) which up to 3 GPa can be represented by the equation:

V/V₀ = 1 – 2.775 × 10^–3 P – 2.64 × 10^–10 P² (ii)

where P is the pressure in GPa.

The cross-over pressure using Equations (i) and (ii) is 2.98 GPa at a density of 22,750 kg m^–3 in excellent agreement with the second order value of Cerenius and Dubrovinsky. In fact the agreement of the extrapolated values of the latter agree so closely with Equation (ii) at 3 GPa that they can be considered as being representative of the volume compression values for iridium from this pressure up to the experimental limit at 65 GPa.

The average value of B₀ from Equation (ii) at 355 GPa (21) is in such excellent agreement with the values obtained from the elastic constant measurements of MacFarlane and Rayne (19) and Adamesku et al. (20) and the second order value of Cerenius and Dubrovinsky (18) that 355 ± 10 GPa can be considered as representing the value of B₀ for iridium in the room temperature region. A further room temperature value of 371 GPa (actually 37,800 kgf mm^–2) selected by Darling (23) is almost certainly due to a different interpretation of the measurements of Bridgman.

Taking into account the assigned accuracies of the selected B₀ value for osmium and iridium the cross-over pressure is considered to be accurate to 5% (±0.15 GPa). Based on this value and the density values for the individual elements then the density at the cross-over point can be considered to be accurate to ±20 kg m^–3. The behaviour of the density values with pressure in the relevant region 2.5 GPa to 3.5 GPa are shown in Figure 2 where the value for iridium at 3.5 GPa is the second order value of Cerenius and Dubrovinsky.

Conclusions

At ambient pressure it is shown that osmium appears to be the densest metal at all temperatures although there is an ambiguity below 150 K which will not be resolved until new measurements are carried out on the low temperature thermal expansion of osmium. At room temperature iridium appears to become the densest metal above a pressure of 2.98 ± 0.15 GPa and a density of 22,750 ± 20 kg m^–3, although it is considered that further experimental determinations are definitely required. With the presently available data it is considered that representative room temperature B₀ values are 413 ± 25 GPa for osmium and 355 ± 10 GPa for iridium.