Crystallographic Properties of Osmium
Crystallographic Properties of Osmium
Assessment of properties from absolute zero to 1300 K
The crystallographic properties of osmium at temperatures from absolute zero to the experimental limit at 1300 K are assessed following a review of the literature published between 1935 and to date. Selected values of the thermal expansion coefficients and measurements of length changes due to thermal expansion have been used to calculate the variation with temperature of the lattice parameters, interatomic distances, atomic and molar volumes and densities. The data is presented in the form of Equations and Tables. The density of osmium at 293.15 K is 22,589 kg m−3.
This is the seventh in a series of papers in this Journal on the crystallographic properties of the platinum group metals (pgms), following two papers on platinum (1, 2) and one each on rhodium (3), iridium (4), palladium (5) and ruthenium (6). Like ruthenium, osmium exists in a hexagonal close-packed (hcp) structure (Pearson symbol hP2) up to the melting point estimated by the present author to be 3400 ± 50 K (7) for the pure metal. The actual published values of 3318 ± 30 K by Knapton et al. (8) were for metal of only about 99.7% purity and of 3283 ± 10 K by Douglass and Adams (9) for metal of 99.5% purity.
The thermal expansion is represented by three sets of lattice parameter measurements: those of Owen and Roberts (10, 11) (from 293 K to 873 K) and Schröder et al. (12) (from 289 K to 1287 K) in the high-temperature region and those of Finkel’ et al. (13) (from 79 K to 300 K) in the low-temperature region. The latter measurements were only shown graphically and by incorrect equations with the actual data points as length change values being given by Touloukian et al. (14). As shown below the latter measurements are incompatible with the high-temperature data so the high- and low-temperature data were initially treated separately.
Length change values derived from the lattice parameter measurements of Owen and Roberts (10, 11) and Schröder et al. (12) agree satisfactorily and are represented by Equations (i) and (ii) for the a-axis and c-axis respectively. On the basis ± 100δL/L293.15 this leads to standard deviations of ± 0.004 and ± 0.002 respectively. The selected values were extended to a rounded temperature of 1300 K.
The measurements of Finkel’ et al. (13) as given by Touloukian et al. (14) (Figure 1) were fitted to smooth Equations (iii) and (iv). The incompatibility of these measurements with the high-temperature data can be shown by deriving thermal expansion coefficients from these equations at 293.15 K as αa = 5.8 × 10−6 K−1 and αc = 8.8 × 10−6 K−1. These values are notably higher than those calculated from Equations (i) and (ii) and as given in Tables I and II. In spite of the high purity claimed for the metal used in the experiments of Finkel’ et al., the c-axis lattice parameter value of 0.43174 nm at 293.15 K is notably lower than all other values given in Table III suggesting that these measurements must be treated with a certain degree of suspicion. Because it does not appear to be possible to reconcile the high- and low-temperature data the measurements of Finkel’ et al. were rejected.
|Temperature, K||Thermal expansion coefficient, αa, 10−6 K−1||Thermal expansion coefficient, αc, 10−6 K−1||Thermal expansion coefficient, αavr, 10−6 K−1 a||Length change, δa/a293.15 K× 100, %||Length change, δc/c293.15 K × 100, %||Length change, δavr/avr293.15 K × 100, %|
|Temperature, K||Lattice parameter, a, nma||Lattice parameter, c, nm||c/a ratio||Interatomic distance, d1, nm||Atomic volume, 10−3 nm3||Molar volume, 10−6 m3 mol−1||Density, kg m−3|
|Authors (Year)||Reference||Original temperature, K||Original units||Lattice parameters, a, corrected to 293.15 K, nm||Lattice parameters, c, corrected to 293.15 K, nm||Notes|
|Owen et al. (1935)||(20)||291||kX||0.27361||0.43189||(a)|
|Owen and Roberts (1936)||(10)||291||kX||0.27357||0.43191||(a)|
|Owen and Roberts (1937)||(11)||293||kX||0.27355||0.43194||(a)|
|Finkel’ et al. (1971)||(13)||293||Å||0.27346||0.43174||(a), (b)|
|Swanson et al. (1955)||(22)||299||Å||0.27342||0.43198|
|Mueller and Heaton (1961)||(23)||rt||Å||0.27345||0.43200|
|Taylor et al. (1961, 1962)||(24, 25)||296||Å||0.27342||0.43201|
|Schröder et al. (1972)||(12)||289||Å||0.27340||0.43198|
In order to extrapolate below room temperature the procedure given in Appendix A was adopted. This utilises specific heat values selected by the present author (15) as expanded in Appendix C, leading to Equations (vii) and (viii) which were extrapolated in order to represent thermal expansion from 0 K to 293.15 K. Because there are two axes, the values of low-temperature specific heat as given in Appendix C can be substituted into the Equations, removing the need to develop a relatively large number of complimentary spline-fitted polynomial equations to correspond to Equations (vii) and (viii). On the basis of the expression:
100 × (δL/L293.15 K (experimental) − δL/L293.15 K (calculated))
where δL/L293.15 K (experimental) are the experimental length change values relative to 293.15 K as calculated from Equations (iii) and (iv) and δL/L293.15 K (calculated) are the relative length change values as given in Table I, the measurements of Finkel’ et al. for the a-axis over the range 80 K to 240 K show a bias of 0.005 to 0.006 lower than the selected values. For the c-axis at 80 K the difference is 0.029 lower with a trend to agree with the selected values with increasing temperature.
The Lattice Parameter at 293.15 K
The values of the lattice parameters, a and c, given in Table III represent a combination of those values selected by Donohue (16) and more recent measurements. Values originally given in kX units were converted to nanometres using the 2010 International Council for Science: Committee on Data for Science and Technology (CODATA) Fundamental Constants (17, 18) conversion factor for CuKα1, which is 0.100207697 ± 0.000000028. Values given in angstroms (Å) were converted using the default ratio 0.100207697/1.00202 where the latter value represents the old conversion factor from kX units to Å. Lattice parameter values were corrected to 293.15 K using the values of the thermal expansion coefficient selected in the present review. Density values given in Tables I and II were calculated using the currently accepted atomic weight of 190.23 ± 0.03 (19) and an Avogadro constant (NA) of (6.02214129 ± 0.00000027) × 1023 mol−1 (17, 18). From the lattice parameter values at 293.15 K selected in Table III as: a = 0.27342 ± 0.00002 nm and c = 0.43199 ± 0.00002 nm, the derived selected density is 22,589 ± 5 kg m−3 and the molar volume is (8.4214 ± 0.0013) × 10−6 m3 mol−1. The difference from the density value for iridium, 22,562 ± 11 kg m−3 (4), at 27 ± 12 kg m−3 is considered to be the proof that osmium is the densest metal at room temperature and pressure.
In Tables I and II the interatomic distance d1 = (a2/3 + c2/4)½ and d2 = a. The atomic volume is (√3 a2 c)/4 and the molar volume is calculated as NA (√3 a2 c)/4, equivalent to atomic weight divided by density. Thermal expansion αavr = (2 αa + αc)/3 and length change δavr/avr293.15 K = (2 δa/a293.15 K + δc/c293.15 K)/3 (avr = average).
High-Temperature Thermal Expansion Equations for Osmium (293.15 K to 1300 K)
δa/a293.15 = −1.32379 × 10−3 + 4.46595 × 10−6 T + 1.69909 × 10−10 T 2 (i)
δc/c293.15 = −1.53749 × 10−3 + 4.64427 × 10−6 T + 2.04826 × 10−9 T 2 (ii)
Equations Representing the Thermal Expansion Data of Finkel’ et al. (13) (79 K to 300 K)
δa/a293.15 = −1.22081 × 10−3 + 3.13600 × 10−6 T + 1.37670 × 10−9 T 2 + 7.27143 × 10−12 T 3 (iii)
δc/c293.15 = −1.71224 × 10−3 + 3.88446 × 10−6 T + 3.26721 × 10−9 T 2 + 1.16202 × 10−11 T 3 (iv)
αa (K−1) = Cp (−3.14503 × 10−8 + 6.95814 × 10−10 T + 1.86500 × 10−5 / T) (v)
αc (K−1) = Cp (−7.35814 × 10−8 + 1.16358 × 10−9 T + 2.62261 × 10−5 / T) (vi)
Low-Temperature Thermal Expansion Equations for Osmium (0 K to 293.15 K)
αa (K−1) = Cp (1.58546 × 10−7 + 1.09521 × 10−11 T + 6.88982 × 10−6 / T) (vii)
αc (K−1) = Cp (1.71988 × 10−7 + 1.41412 × 10−10 T + 6.95413 × 10−6 / T) (viii)
The number of measurements of the thermal expansion data for osmium is very limited and although the two high-temperature sets of lattice parameter measurements show satisfactory agreement, their usefulness only applies from room temperature to about 1300 K. The low-temperature lattice parameter measurements appear to be completely incompatible with the high-temperature data and were therefore rejected. Instead a novel approach was used to obtain values in the low-temperature region that agreed with the high-temperature data. Clearly the thermal expansion situation for osmium is unsatisfactory and new measurements are required at both low- and high-temperatures.
Representative Equations for Extrapolation Below 293.15 K
Equations (i) and (ii) are considered to be confined within the experimental limits of 289 K to 1287 K except for an extrapolation to a rounded maximum of 1300 K. Therefore in order to extrapolate beyond these limits a thermodynamic relationship is required such as that proposed by the present author to represent a correlation and interpolation of low-temperature thermal expansion data (1). In this case the relationship was evaluated in the high-temperature region and extrapolated to the low-temperature region. Equations (i) and (ii) were differentiated in order to obtain values of α*, the thermal expansion coefficient relative to 293.15 K, with thermodynamic thermal expansion coefficients calculated as α = α*/(1 + δL/L293.15 K). Selected values of α at 293.15 K and in the range 300 K to 700 K at 50 K intervals were then combined with high-temperature specific heat values calculated from Equation (ix) to derive Equations (vii) and (viii). These were then extrapolated to the low-temperature region using the specific heat values given in Appendix C. The range 293.15 K to 700 K was selected since this gave a satisfactory agreement between the derived experimental and calculated values. Length change values corresponding to Equations (vii) and (viii) were obtained by three-point integration.
The Quality of the Density Value for Osmium at 0 K
In view of the novel approach used to estimate the low-temperature properties and the relatively large extrapolation used, an independent estimate of the density at 0 K would be considered as a test of the quality of the procedure used. Such a value can be obtained from the rejected measurements of Finkel’ et al. (13) as given by Touloukian et al. (14). Equations (iii) and (iv) are considered as being confined within their experimental limits of 80 K to 293.15 K and therefore in order to extrapolate beyond these limits a similar approach to that used in Appendix A was applied. This approach led to Equations (v) and (vi) which are applicable between the limits 80 K to 293.15 K and these were extrapolated to 0 K using the specific heat values given in Appendix C. Three-point integration was used to derive values at 0 K of 100 δa/a293.15 = −0.107 and 100 δc/c293.15 = −0.153 so that the derived density value is thus 22,672 kg m−3 which is surprisingly only 11 kg m−3 (0.05%) greater than the selected value. It is possible therefore that the true density could lie between these two values although based on the selected value it is considered that the density at 0 K can best be represented as 22,661 ± 11 kg m−3.
Specific Heat Values for Osmium
Because of the large number of spline fitted equations that would be required to conform to both Equations (vii) and (viii), a different approach has been used for the non-cubic metals in that specific heat values are directly applied to these equations. However this would require that the table of low-temperature specific heat values originally given by the present author (15) has to be more comprehensive and the revised table is given as Table IV. In the high-temperature region Equation (ix) represents the specific heat essentially from 240 K to the melting point and is obtained by differentiating the selected enthalpy equation given by the present author (15). Selected values derived from Equation (ix) are given in Table V.
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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.