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Johnson Matthey Technol. Rev., 2017, 61, (2), 80

doi:10.1595/205651317x694461

Selected Values for the Densities and Molar Volumes of the Liquid Platinum Group Metals and of the Initial Melting Curves of Iridium, Rhodium and Ruthenium

Assessing different determinations of the density of the liquid platinum group metals

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Definitive equations are suggested to represent the variation with temperature of the densities and molar volumes of the liquid platinum group metals whilst the previously unknown initial slopes of the melting curves for iridium, rhodium and ruthenium are estimated.

1. Introduction

Paradis et al. (1) summarised determinations of the densities of the liquid platinum group metals but a number of important determinations were not included. These are given in Table I in which values are presented as a b (TTm) where a is the liquid density at the melting point Tm and b represents the density thermal expansion. Unfortunately, in the case of the measurements of Pottlacher (2) volume ratios were considered to vary linearly with temperature so that derived density values could only be fitted to quadratic equations (Equations (i)(iv)), whereas a very large number of determinations of the densities of medium and high melting point metals and alloys clearly indicate that liquid density values vary linearly with temperature and this would therefore limit the usefulness of the values of Pottlacher (2). Paradis et al. (1) did not suggest definitive values for the densities of the metals but would undoubtedly have given preference to their own electrostatic levitation determinations which are considered to be accurate to about 2%. The problem with the selection was that the differences between various determinations were significant to a certain extent making an objective evaluation difficult. One alternative approach is to indirectly obtain the liquid density at the melting point from the value for the solid density by use of the Clausius-Clapeyron equation (Equation (v)):

Table I

Additional Determinations of the Densities of Liquid Platinum Group Metals

AuthorsRef.Tm, Ka b
Iridium
Pottlacher 2 2719 19,722 2.049*
Palladium
Pottlacher 2 1828 10,690 0.733*
Stankus and Tyagel’skii 3 1827 10,631 0.734
Popel et al. 4 1828 10,605 1.056
Platinum
Pottlacher 2 2042 18,968 1.170*
Stankus and Khairulin 5 2042 18,932 1.168
Rhodium
Pottlacher 2 2236 11,004 1.022*

*Initial slope dD/dT at the melting point from the quadratic fits to the density values (Equations (i) to (iv)):

 

(i)

 

(ii)

 

(iii)

 

(iv)

 

(v)

 

where ΔV is the difference between the molar volumes of the solid and the liquid, ΔH is the enthalpy of fusion in J mol–1 at melting point Tm, K, and dP/dT is the initial slope of the melting curve in MPa K–1. In the case of iridium, rhodium and ruthenium dP/dT is unknown so that Equation (v) can be reversed to estimate these values. In applying Equation (v) the densities of the solids at the melting point were all assumed to have an accuracy of ±20 kg m–3 which is roughly twice the room temperature uncertainty and therefore equivalent to a 95% confidence level.

2. Platinum

Selected values for the fit to Equation (v) are melting point 2041.3 ± 0.4 K (6), enthalpy of fusion 22,113 ± 940 J mol–1 (7) and slope of the melting curve dP/dT 22.5 ± 1.3 MPa K–1 taken from an average of the dT/dP values of 42 K GPa–1 as determined by Mitra et al. (8) and 47 K GPa–1 as determined by Errandonea (9). The resultant value is ΔV = 0.482 ± 0.034 cm3 mol–1 which when combined with the bulk density of the solid as 20,173 ± 20 kg m–3 (10, 11) leads to a density of the liquid at the melting point of 19,215 ± 67 kg m–3. This is in extraordinary agreement with the value of 19,200 ± 380 kg m–3 determined by Ishikawa et al. (12). Other density determinations such as that of Stankus and Khairulin (5) at 18,932 ± 90 kg m–3 and that of Pottlacher (2) at 18,968 kg m–3 are notably lower but agree with other determinations summarised by Paradis et al. (1) suggesting that a possible value for the density could be 18.9 ± 0.1 kg m–3 and that the determination of Ishikawa et al. (12) would then be an outlying value. However, the indirect density value obtained from the Clausius-Clapeyron equation (Equation (v)) clearly confirms the determination of Ishikawa et al. (12) as being the most likely value. The significant difference resulting in the lower density values can be traced to much larger values determined for ΔV at 0.582 cm3 mol–1 by Stankus and Khairulin (5) and 0.696 cm3 mol–1 by Pottlacher (2). The density thermal expansion at b = –0.96 cm3 mol–1 K–1 as determined by Ishikawa et al. (12) is much lower than previous values but is in reasonable agreement with the value of –1.168 ± 0.062 cm3 mol–1 K–1 as determined by Stankus and Khairulin (5). Therefore, a suggested equation (Equation (vi)) to represent the density of liquid platinum over the range from 1700 K to 2200 K with an accuracy of about 0.5% would be:

(vi)

3. Palladium

Selected values for the fit to Equation (v) are melting point 1828.0 ± 0.1 K (6), enthalpy of fusion 16,080 ± 740 J mol–1 (13) and slope of the melting curve dP/dT 21.7 ± 2.2 MPa K–1, equivalent to the dT/dP value of 46 K GPa–1 as determined by Errandonea (9) and assuming an accuracy of 10%. The resultant value is ΔV = 0.405 ± 0.045 cm3 mol–1 and when combined with the density of the solid of 11,179 ± 20 kg m–3 (14) leads to a density of the liquid of 10,723 ± 50 kg m–3 which is higher than any of the experimental values but is encompassed within the accuracy of the determination of Paradis et al. (15) at 10,660 ± 210 kg m–3 and the value of Pottlacher (2) at 10,690 kg m–3. Two further recent determinations are notably lower with Popel et al. (4) obtaining the value 10,605 kg m–3 and Stankus and Tyagel’skii (3) obtaining 10,631 ± 45 kg m–3, although in the case of the latter the value of ΔV at 0.506 cm3 mol–1 is again much larger than the value obtained using Equation (v). It is known that the values of the enthalpy of fusion and the density of the solid at the melting point are tentative so that the value obtained from Equation (v) may not be fully representative. It is also noted that the average of the four sets of measurements considered above is very close to the value of Paradis et al. (15) and therefore this value is selected since it does include the Equation (v) value in its uncertainty. The density thermal expansion coefficient of b = –0.77 cm3 mol–1 K–1 as determined by Paradis et al. (15) is confirmed by the value of –0.734 cm3 mol–1 K–1 obtained by Stankus and Tyagel’skii (3) and by the value –0.733 cm3 mol–1 K–1 at the melting point calculated from the quadratic fit to the measurements of Pottlacher (2). Therefore, the equation (Equation (vii)) given by Paradis et al. (15) is considered as being representative for palladium over the temperature range 1600 to 1900 K when consideration is given to its 2% accuracy:

(vii)

4. Rhodium

Strong and Bundy (16) determined an initial slope of the melting curve of 62 K GPa–1 but the value determined for platinum at the same time, 72 K GPa–1, far exceeds the more recent determinations given above. Therefore, it is assumed that the slope dP/dT is poorly known and can be calculated by reversing Equation (v) with a melting point of 2236 ± 3 K (6), an enthalpy of fusion of 27,295 ± 850 J mol–1 (17) and a value of ΔV = 0.555 ± 0.191 cm3 mol–1 based on the density of the solid at the melting point at 11,491 ± 20 kg m–3 (18) and for the liquid at 10,820 ± 220 kg m–3 (19). The derived melting curve pressure is 22.0 ± 7.6 MPa K–1 or the equivalent dT/dP value of 45 ± 16 K GPa–1 which agrees closely with the values obtained for both platinum and palladium. The relatively poor accuracy assigned to dT/dP is due almost entirely to the 2% accuracy assigned to the liquid density value and its effect on ΔV . The density equation given by Paradis et al. (19) over the range 1820 to 2250 K has been repeated as Equation (viii) to remove the ambiguity created by Paradis et al. (1) who included two different melting point values. The quadratic fit to the density values of Pottlacher (2) (2236 to 3500 K) leads to a value of 11,004 kg m–3 at the melting point which is encompassed within the accuracy assigned to the measurements of Paradis et al. (19). Perhaps coincidentally the volume ratios of Pottlacher (2) also lead to ΔV = 0.555 cm3 mol–1 at the melting point although the value obtained of b = –1.022 kg m–3 K–1 is notably higher than the value given by Paradis et al. (19) in Equation (viii) below:

(viii)

5. Iridium

The melting point slope is unknown and was also derived by reversing Equation (v). Initially Ishikawa et al. (20) reported that their group (21) obtained a liquid density value of 19,870 kg m–3 at the melting point although the actual published value had been reduced to 19,500 kg m–3. For the reverse of Equation (v) input values are melting point 2719 ± 4 K (6), enthalpy of fusion 41,335 ± 1128 J mol–1 (22) and ΔV = 0.666 ± 0.197 cm3 mol–1 based on the density of the solid at the melting point at 20,913 ± 20 kg m–3 (23) and for the liquid at the melting point 19,500 ± 390 kg m–3 (21). The derived melting curve pressure is 22.8 ± 6.8 MPa K–1 or the equivalent dT/dP value of 44 ± 13 K GPa–1 which again agrees closely with the values obtained for both platinum and palladium. The relatively poor accuracy assigned to dT /dP is due almost entirely to the 2% accuracy assigned to the liquid density value and its effect on ΔV. The density equation of Ishikawa et al. (21) which covers the range 2300 to 3000 K is reproduced as Equation (ix):

(ix)

Measurements given by Pottlacher (2) were ambiguous since the baseline solid density was given as a value for commercial purity iridium at 22,420 kg m–3 rather than the X-ray value of 22,560 kg m–3 (23). Using the assigned commercial value, the liquid density value derived from the quadratic fit at 19,722 kg m–3 is encompassed by the accuracy assigned to the measurement of Ishikawa et al. (20). However, the derived value at the initial slope of the melting curve derived from the quadratic fit at b = –2.049 kg m–3 K–1 differs considerably from the value given in Equation (ix).

6. Ruthenium

The only precision liquid density measurements are those of Paradis et al. (24) over the range 2225 to 2775 K. Again the slope of the melting curve was unknown and was derived by reversing Equation (v) using values of melting point 2606 ± 10 K (6), enthalpy of fusion 39,038 ± 1400 J mol–1 (25) and ΔV = 0.532 ± 0.189 cm3 mol–1 based on the density of the solid at the melting point 11,396 ± 20 kg m–3 (26) and for the liquid 10,751 ± 210 kg m–3 (24). The derived melting curve pressure dP/dT is 28.2 ± 10.1 MPa K–1 or the equivalent dT/dP value of 36 ± 13 K GPa–1 which is lower, but still within the accuracy limits, measured or derived for the face-centred cubic platinum group metals. For comparison theoretical dT/dP values for osmium vary between 40.4 K GPa–1 (27) and 49.5 K GPa–1 (28) in agreement with the face-centred cubic values. Paradis et al. (24) assumed a melting point of 2607 K for ruthenium rather than the International Temperature Scale (ITS-90) value of 2606 K. The published density equation has therefore been adjusted to correspond to the corrected melting point (Equation (x)):

(x)

7. Osmium

Actual density measurements of solid osmium extend only to 1300 K (29) and therefore estimating possible values above this temperature is speculative. Paradis and Ishikawa (30) measured the liquid density over the range 2670 to 3380 K and assumed that measurements were both undercooled and in equilibrium by taking the melting point to be 3306 K. However, this literature value was obtained on osmium metal of only commercial purity and is considered to be far too low. Arblaster (31) suggested that the true melting point of pure osmium was likely to be in the order of 3400 ± 50 K and the published equation was revised to correspond to this estimated melting point. However, this correction is only formal so that all melting points conform to selected values and the actual derived density values correspond to the experimentally determined values (Equation (xi)):

(xi)

8. Conclusions

An evaluation of different determinations of the density of the liquid platinum group metals concludes that the determinations using the electrostatic levitation method are possibly the most reliable and derived equations from this method are given in Table II, with slight modifications for the density of liquid platinum and the melting points of ruthenium and osmium. Derived molar volume equations are given in Table III whilst Table IV gives the values of density and molar volume at the melting points. Derived densities and molar volumes at other temperatures are given in Table V.

The initial slopes of the melting curves for ruthenium, rhodium and iridium were at first considered to be unknown and were derived using the Clausius-Clapeyron equation (Equation (v)). This showed that the initial slopes derived for rhodium and iridium were very close to the actual experimental values of palladium and platinum suggesting a common value for dT/dP of about 45 K GPa–1 for the face-centred cubic platinum group metals. The value of 36 K GPa–1 obtained for ruthenium and estimates of 40 to 50 K GPa–1 for osmium suggest that a possible common value for the hexagonal close-packed platinum group metals is less certain.

Table II

Density Equations for the Liquid Platinum Group Metalsa

ElementTm, Ka b Temperature range, K
Ruthenium 2606 10,751 0.85 2200–2800
Rhodium 2236 10,820 0.76 1800–2300
Palladium 1828.0 10,660 0.77 1600–1900
Osmium 3400 19,047 1.16 2600–3400
Iridium 2719 19,500 0.85 2300–3000
Platinum 2041.3 19,215 0.96 1700–2200

aLiquid density values are fitted to the equation: D (kg m–3) = a b (TTm) where a is the density at the melting point Tm, K, and b is the density thermal expansion. The temperature range approximates to the actual experimental range and therefore the density values mainly correspond to the undercooled region

Table III

Molar Volume Equations for the Liquid Platinum Group Metalsa

ElementAtomic weightc d e
Ruthenium 101.07 7.8532 4.445 × 10–4 5.734 × 10–8
Rhodium 102.90550 8.2430 4.660 × 10–4 5.734 × 10–8
Palladium 106.42 8.8362 5.338 × 10–4 5.122 × 10–8
Osmium 190.23 8.3206 3.730 × 10–4 3.448 × 10–8
Iridium 192.217 8.8261 3.288 × 10–4 1.856 × 10–8
Platinum 195.084 9.2214 4.052 × 10–4 2.500 × 10–8

aBecause liquid density values vary linearly with temperature then the reciprocal, molar volumes, can only be accurately represented by fitting to quadratic equations. The molar volume is given by Vm (cm3 mol–1) = Ar/D = c + d T + e T 2 where Ar is the atomic weight and these equations are considered to be valid over the same temperature ranges as adopted for the liquid metals. The 2015 atomic weights were adopted (32)

Table IV

Densities and Molar Volumes of the Liquid Platinum Group Metals at their Melting Pointsa

ElementTm, KLiquid density, kg m–3Molar volume, cm3 mol–1
Ruthenium 2606 10,751 ± 210 9.401 ± 0.19
Rhodium 2236 10,820 ± 220 9.511 ± 0.19
Palladium 1828.0 10,660 ± 210 9.983 ± 0.20
Osmium 3400 19,047 ± 380 9.987 ± 0.20
Iridium 2719 19,500 ± 390 9.857 ± 0.20
Platinum 2041.3 19,215 ± 100 10.153 ± 0.05

aValues are based on the equations given in Tables III and IV. A conservative value for the accuracy of the density of platinum is assumed to be ±100 kg m–3 whilst all other density values are assumed to be accurate to 2%. Molar volumes are extended to three decimal places for interpolation purposes

Table V

The Variation with Temperature of the Densities and Molar Volumes of the Liquid Platinum Group Metalsa

Ruthenium
T, K 2200 2300 2400 2500 2600 2700 2800
D 11,100 11,010 10,930 10,840 10,760 10,670 10,590
Vm 9.109 9.179 9.250 9.323 9.397 9.471 9.547
Rhodium
T, K 1800 1900 2000 2100 2200 2300
D 11,520 11,360 11,200 11,040 10,880 10,720
Vm 9.228 9.291 9.356 9.421 9.487 9.554
Palladium
T, K 1600 1650 1700 1750 1800 1850 1900
D 10,840 10,800 10,760 10,720 10,680 10,640 10,600
Vm 9.821 9.856 9.892 9.927 9.963 9.999 10.035
Osmium
T, K 2600 2700 2800 2900 3000 3100 3200 3300 3400
D 19,980 19,860 19,740 19,630 19,510 19,400 19,280 19,160 19,050
Vm 9.523 9.579 9.635 9.692 9.750 9.808 9.867 9.927 9.987
Iridium
T, K 2300 2400 2500 2600 2700 2800 2900 3000
D 19,860 19,770 19,690 19,600 19,520 19,430 19,350 19,260
Vm 9.681 9.722 9.764 9.806 9.849 9.892 9.936 9.980
Platinum
T, K 1700 1800 1900 2000 2100 2200
D 19,540 19,450 19,350 19,250 19,160 19,060
Vm 9.982 10.032 10.082 10.132 10.183 10.234

aLiquid density (D) is in units of kg m–3 and molar volume (Vm) in units of cm3 mol–1. The accuracy of these values can be considered to be the same as those determined at the melting point. Molar volumes are extended to three decimal places for interpolation purposes

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The Author


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.

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