Crystallographic Properties

Previous reviews by the present author on the crystallographic properties of ruthenium (1), rhodium (2), palladium (3), iridium (4) and platinum (5, 6) in each case gave values from absolute zero up to their melting points. The exception was osmium (7) where the limited experimental lattice parameter measurements of Owen and Roberts (8, 9) (323 K to 873 K) and Schröder et al. (10) (289 K to 1287 K) only allowed the values to be given up to a rounded temperature of 1300 K. Based on the previous review equations for length values from 293.15 K to 1300 K are given in Table I and actual property values covering the range 293.15 K to 1300 K are given in Tables II and III. Estimated crystallographic properties below 293.15 K were given in the original paper (7). Fixed values at 293.15 K are:

Table I

Thermal Expansion Equations for Osmium 293.15 K to 3400 K

293.15 K to 1300 K

Equation (i):

Equation (ii):

Equation (iii):

1300 K to 2000 K

Equation (iv):

2000 K to 3400 K

Equation (v):

Bulk Properties

Onufriev (11) determined the mean thermal expansion over the range 1631 K to 2572 K. Multiplying these values by (T – 293 K) leads to length change values which can be represented analytically by Table IV, Equation (vi). At 1600 K this leads to a length change value of 7.12 × 10^–3 whilst extrapolation of the average crystallographic equation to this temperature leads to a value of 7.88 × 10^–3, or a difference of 7.6 × 10^–4. Since crystallographic measurements give separate values for the a and c thermal expansion then they can be considered to be anisotropically correct. However for dilatometric measurements samples may show preferential orientation leading to values which are not representative of the true average values. It is proposed that the samples used to measure the thermal expansion of osmium may be so affected and in order to overcome this problem it was assumed that in the high temperature region the derived thermal expansion coefficients are independent of the orientation. Therefore crystallographic thermal expansion coefficients at 1300 K and below were combined with dilatometric thermal expansion coefficients at 2000 K and above and fitted to a perfect equation (four coefficients and four thermal expansion values). This equation was then integrated in order to obtain length change values over the range 1300 K to 2000 K as Table IV Equation (vii). Above 2000 K and up to 2600 K initially thermal expansion values are related back to the original equation of Onufriev but corrected for the revised length change values as Table IV Equation (viii). However this equation cannot be satisfactorily extrapolated above 2600 K since it leads to a thermal expansion coefficient which varies only linearly with temperature and does not take in to account an increase above the linear relationship caused, for example, by the onset of thermal vacancy effects. In order to try and obtain realistic thermal expansion coefficients it was assumed that length change values from 2000 K to 2600 K behaved in a similar manner to thermodynamic properties, specifically absolute enthalpy values, H°_T – H°₀, through the relationship, Equation (xii):

(xii)

where the length change values are given by Equation (xiii):

(xiii)

Table IV

Secondary Equations for Osmium

1631 K to 2572 K

Equation (vi):

1300 K to 2000 K

Equation (vii):

2000 K to 2600 K

Equation (viii):

298.15 K to 3400 K

Equation (ix):

2000 K to 3400 K

Equation (x):

Equation (xi):

Values of absolute enthalpy selected by the present author (12) are given in Table IV, Equation (ix) and coefficients corresponding to the correlation between length change values and absolute enthalpy are given as Table IV, Equation (x). This equation was extrapolated to the melting point at 3400 K. However this equation is clearly cumbersome and it was found that from 2000 K to 3400 K the values could also be represented with a high degree of correlation by use of the cubic equation given as Table IV, Equation (xi). Therefore in order to represent the length properties from 1300 K to 3400 K Equations (vii) and (xi) were transferred to Table I. Bulk properties based on these equations are given in Table V. Above 2000 K the measurements of Onufriev (11) have an average uncertainty of 0.23₅ %. If this value is applied to the melting point values then the density is 21,031 ± 49 kg m^–3 and the molar volume (9.045 ± 0.021) × 10^–6 m³ mol^–1.

Kulyamina et al. (13) used an independent approach in which the volumetric thermal expansion value (β) was calculated from Equation (xiv):

(xiv)

where values of the specific heat (C°_p) and absolute enthalpy (H°_T – H°₀) were given by Cherkhovskoi and Ramanauskas (14) and the value of the enthalpy of sublimation (ΔH°_sub) was from a previous review on osmium by the present author (15). The value of the enthalpy constant Q₀ was determined as 1606 kJ mol^–1 based on values of β corresponding to the crystallographic values from 800 K to 1300 K. The equation was extrapolated to the selected melting point of 3320 K where the derived molar volume of 9.022 × 10^–6 m³ mol^–1 is in exact agreement with the value derived in the present review giving some confidence as to the use of both methods.

Properties in the Melting Point Region

Ishikawa et al. (16) measured the density of liquid osmium mainly in the undercooled region 2800 K to 3450 K and the results can be expressed as Equation (xv):

(xv)

leading to a density of 19,295 ± 162 kg m^–3 and a molar volume of (9.859 ± 0.083) × 10^–6 m³ mol^–1 at the selected melting point of 3400 K which compares to the molar volume of the solid as (9.045 ± 0.021) × 10^–6 m³ mol^–1. The increase in molar volume on melting is therefore ΔV = (8.14 ± 0.86) × 10^–7 m³ mol^–1 and this value can be used in the Clausius-Clapeyron equation to determine the initial slope of the melting curve of osmium as Equation (xvi):

(xvi)

where the melting point (T_M) at 3400 ± 50 K and the enthalpy of fusion (ΔH_M) at 68,005 ± 1653 J mol^–1 were selected by the present author (12). The derived value of dT/dP = 40.7 ± 4.5 K GPa^–1 is in agreement with the value of 40.4 K GPa^–1 given by Kulyamina et al. (13) but is notably lower than the estimate of 49.5 K GPa^–1 by Burakovsky et al. (17) and the experimental value determined as 58 K GPa^–1 by Patel and Sunder (18). The discrepancy from the experimental value is almost certainly due to the difficulty in carrying out measurements in the region of the melting point of osmium, for example, the large extrapolation of the thermal expansion values for the solid, the estimates of the melting point and enthalpy of fusion and possible systematic errors in the measurement of the density of the liquid and the initial slope of the melting curve. Clearly far more measurements are required in order to account for the difference.

Is Osmium Always the Densest Metal?

The present author (19) compared the effect of temperature on the densities of osmium and iridium to evaluate which was the densest metal. Above room temperature the density difference in favour of osmium increased from 27 kg m^–3 at room temperature to 147 kg m^–3 at 1300 K, the then limit for osmium, and it was speculated that this difference would continue in to the high temperature region. With the values published in Table V the speculation is resolved and the difference increases to 575 kg m^–3 at the melting point of iridium (2719 K) and thus proving that solid osmium is the densest metal at all temperatures. A comparison of the effect of temperatures on the densities is given in Figure 1 and on their difference in Figure 2 where the density values for iridium are those selected by the present author (4) with bulk values above 2000 K to be comparable with the bulk values for osmium.

New Equation for the Density of Liquid Osmium

In the review of the densities of the liquid platinum group metals (20) the values for osmium were based on the measurements of Paradis et al. (21). These have now been superseded by the measurements of Ishikawa et al. (16) over the range 2800 K to 3450 K which are given by Equation (xvii):

(xvii)

At the selected melting point of 3400 K the calculated density is 19,295 ± 162 kg m^–3 and the derived molar volume is (9.859 ± 0.083) × 10^–6 m³ mol^–1 leading to the density equation corresponding to the selected melting as Equation (xviii):

(xviii)

applicable over the temperature range 2800 K to 3400 K. Corrected values of density and molar volume are given in Table VI.