Journal Archive

Platinum Metals Rev., 1994, 38, (3), 119

The Thermodynamic Properties of Platinum on ITS-90

  • By J. W. Arblaster
  • Brookside Metal Company Limited, Willenhall, West Midlands, England

Platinum exists in a face–centred cubic structure with a lattice parameter at 20°C of 0.39235 nm and a density of 21.45 g/cm3 (1,2). The freezing point is a proposed secondary fixed point on the International Temperature Scale ITS–90 at 1768.1°C (3). Wherever possible values have been corrected to the currently accepted atomic weight of 195.08 (4) and to the ITS–90 temperature scale (5–9), including the further correction to this scale between 630.615 and 1064.18°C (10–12). Previous assessments for platinum were performed by Hultgren and co–workers (13) and by Furukawa, Reilly and Gallagher (14).

Solid

Selected specific heat measurements below 30 K lead to the following values of the electronic specific heat coefficient (γ) and the Debye temperature (θD), as shown in Table I.

Table I

Electronic Specific Heat Coefficients and Debye Temperatures

  γ, mJ/mol K2 θD, K
Dixon et al(15) 1.242 K 6.507 ± 0.006 234.9 ± 0.4
Dixon, Hoare and Holden (16) 1.24.2 K 6.517 ± 0.012 235.5 ± 1.6
Shoemake and Rayne (17) 1.2-100 K 6.56 ± 0.03 234.4 ± 2.5
Berg (18) 2.6-20.3 K 6.59 ± 0.03 240.1 ± 2.3
Boerstoel, Zwart and Hansen (19) 1.2-30 K 6.54 ± 0.02 237.0 ± 0.5
Recommended 6.54 ± 0.03 236 ± 2

On average the measurements of Berg, and Boerstoel, Zwart and Hansen agree with the selected curve to 0.6 per cent while earlier measurements of Clusius, Losa and Franzosini (20) 11–274 K are from 7 per cent high to 3 per cent low in this region. Other measurements were rejected in the previous assessments.

Between 30 and 300 K selected values are based on the specific heat measurements of Clusius, Losa and Franzosini (20) 11–274 K and Yokokawa and Takahashi (21) 81–983 K with preference being given to the latter above 80 K and which on average agree with the selected curve to 0.3 per cent, while the former measurements are up to 1.6 per cent too high at the highest temperatures measured. The derived value of the enthalpy H°298.15 – H°0 is in exact agreement with that selected by Yokokawa and Takahashi, but the entropy S°298.15 is slightly higher due mainly to the adoption of a different value of entropy at 80 K, see Table II and Figure 1.

Table II

Low Temperature Specific Heat Data

T, K C°p, J/mol K T, K C°p, J/mol K T, K C°p, J/mol K
1 0.00669 16 0.828 90 18.425
2 0.0143 18 1.155 100 19.559
3 0.0237 20 1.550 120 21.245
4 0.0359 25 2.793 140 22.376
5 0.0518 30 4.323 160 23.185
6 0.0727 35 5.994 180 23.803
7 0.100 40 7.632 200 24.278
8 0.134 45 9.210 220 24.623
9 0.177 50 10.699 240 24.920
10 0.230 60 13.326 260 25.210
12 0.371 70 15.437 280 25.469
14 0.568 80 17.078 298.15 25.648
Overall accuracy above 30 K is ± 0.06 J/mol K
  Solid Gas
H°298.15-H°0 J/mol 5694 6576.6
S°298.15 J/mol K 41.53 192.409
Corrected to one bar standard state pressure
Fig. 1

Low temperature specific heats of platinum from 0 to 300 K

(1) Present Beleoted values

(2)Furukawa, Reilly and Gallagher (14)

Percentage deviation = 100 x (C°p selected - C°p calculated)/C°p, calculated

In the high temperature region values are based on the enthalpy measurements of Kendall, Orr and Hultgren (22) taken between 339 and 1436 K and Macleod (23) 401–1633 K, and the specific heat measurements of Yokokawa and Takahashi (21) 81–983 K, and Righini and Rosso (24) 1000–2000 K. These two different measuring techniques were reconciled by first separately fitting the enthalpy data to the Maier–Kelley equation (25) and then differentiating at sufficient intervals in order to give approximately equal weight to the four sets of data. However derived values of Kendall, Orr and Hultgren above 1200 Kwere not used since they deviate by up to 1.4 per cent low above this temperature, while similar values for Macleod above 1400 K were not used since they deviate by up to 1.6 per cent low. The selected values were fitted to the following recommended equation, which has an overall accuracy of 0.3 per cent (± 0.09 J/mol K):


Specific heat measurements of Yeh and Brooks (26) taken between 350 and 1200 K are on average 2 per cent higher than the selected curve, while those of Wheeler (27) 938–1368 K are 4 per cent higher and those of Vollmer and Kohlhaas (28) 298–1900 K are 2 per cent lower. Specific heat measurements using the modulation technique tend to give values rising sharply above 1600 K, with those of Kraftmakher and Lanina (29, 30), taken between 1000 and 2000 K, being up to 12 per cent high, those of Seville (31) 1280–1860 K (read from graph) up to 6 per cent high and those of Zinov'ev, Korshunov and Gel'd (32) 1100–1900 K (read from graph) up to 14 per cent high. Smoothed true specific heat values, calculated from older mean specific heat measurements, agree closely with the recommended values up to 1300 K, but above this temperature the values of White (33) 373–1573 K are up to 1 per cent low and the values of Jaeger and Rosenbohm (34) 484–1877 K and Jaeger, Rosenbohm and Bottema (35) 681–1664 K are up to 3 per cent low, see Table III and also Figure 2.

Table III

High Temperature Data

Condensed Phases Pt(s, l) Gas Phase Pt (g, bar)
T, K C°p, J/mol K H°T-H°298.15 J/mol K S° J/mol K -G°T-H°298.15 J/mol K / T C°p, J/mol K H°T-H°298.15 J/mol K S° J/mol K -G°T-H°298.15 J/mol K / T
298.15 25.648 0 41.533 41.533 25.531 0 192.409 192.409
300 25.663 47 41.692 41.533 25.577 47 192.567 192.41
320 25.82 562 43.353 41.596 26.031 563 194.233 192.472
340 25.969 1080 44.923 41.746 26.399 1088 195.823 192.623
360 26.112 1601 46.411 41.964 26.684 1619 197.34 192.843
380 26.248 2125 47.827 42.236 26.889 2155 198.789 193.118
400 26.38 2651 49.176 42.549 27.023 2694 200.172 193.437
420 26.508 3180 50.467 42.896 27.095 3235 201.492 193.789
440 26.632 3711 51.703 43.268 27.112 3777 202.753 194.168
460 26.753 4245 52.889 43.661 27.084 4319 203.958 194.568
480 26.87 4781 54.03 44.069 27.108 4860 205.109 194.983
500 26.986 5320 55.13 44.49 26.923 5400 206.21 195.41
600 27.534 8046 60.099 46.688 26.191 8058 211.059 197.628
700 28.049 10826 64.382 48.917 25.349 10635 215.032 199.84
800 28.545 13655 68.16 51.091 24.591 13131 218.366 201.953
900 29.036 16535 71.551 53.179 23.965 15557 221.225 203.939
1000 29.531 19463 74.635 55.173 23.468 17928 223.723 205.795
1100 30.04 22441 77.474 57.073 23.083 20255 225.941 207.528
1200 30.575 25472 80.11 58.884 22.791 22548 227.937 209.147
1300 31.144 28557 82.58 60.613 22.574 24815 229.752 210.663
1400 31.757 31702 84.91 62.266 22.418 27065 231.419 212.087
1500 32.422 34911 87.123 63.85 22.313 29301 232.962 213.428
1600 33.15 38189 89.239 65.371 22.249 31529 234.399 214.694
1700 33.949 41543 91.272 66.835 22.22 33752 235.747 215.893
1000 34.829 44981 93.237 68.248 22.219 35973 237.017 217.032
1900 35.799 48512 95.146 69.613 22.241 38196 238.219 218.116
2000 36.869 52144 97.009 70.937 22.283 40422 239.361 219.15
2041.3(s) 37.314 53677 97.767 71.472 22.305 41343 239.816 219.563
2041.3(l) 36.432 75006 108.216 71.472
2200 36.432 80788 110.944 74.222 22.412 44891 241.49 221.085
2400 36.432 88075 114.114 77.416 22.584 49390 243.447 222.868
2600 36.432 95361 117.03 80.353 22.784 53926 245.263 224.522
2800 36.432 102647 119.73 83.07 23.001 58505 246.959 226.065
3000 36.432 109934 122.243 85.599 23.226 63127 248.554 227.511
3200 36.432 117220 124.595 87.963 23.453 67795 250.06 228.874
3400 36.432 124507 126.803 90.184 23.678 72508 251.489 230.162
3600 36.432 131793 128.886 92.277 23.898 77266 252.848 231.385
3800 36.432 139079 130.856 94.256 24.111 82067 254.146 232.549
4000 36.432 146366 132.724 96.133 24.318 86910 255.388 233.66
4200 36.432 153652 134.502 97.918 24.517 91794 256.579 234.724
Fig. 2

High temperature specific heats of platinum from 300 K to the melting point

(1)Present selected values

(2)Hultgren and others (13) and references therein

(3)Vollmer and Kohlhaas (28)

(4)Yeh and Brooks (26)

(5)Krhakher and Lanina (29,30)

(6)Seville (31)

(7)Zinov'ev, Kurahunov and Gel'd (32)

(8)Wheeler (27)

Percentage deviation = 100 x (C°p selected - C°p calculated)/C°p, calculated

Liquid

The liquid enthalpy measurements of Chaudhuri and co–workers (36) 2204–2649 K were fitted to the following equation which is relative to the solid at 298.15 K and which has an overall accuracy of 1.2 per cent (± 1180 J/mol):


This leads to a constant specific heat value of 36.4 ± 2.2 J/mol K, a value for the heat of fusion of 21.33 ± 1.19 kJ/mol and an entropy of fusion of 10.45 ± 0.58 J/mol K, see Table III. Rapid pulse heating measurements by Gathers, Shaner and Hodgson (37) 2041–8000 K lead to a higher specific heat of 49 J/mol K and an approximate heat of fusion of 27 ± 6 kJ/mol; while using a similar technique Lebedev, Sawatimskii and Smirnov (38) obtained a heat of fusion of 25 kJ/mol. Improvements in the rapid pulse heating method are eliminating the discrepancies obtained between this technique and drop calorimetry.

Gas

Thermodynamic properties of the monatomic gas were calculated from the 201 energy levels listed by Blaise and colleagues (39) using the method outlined by Kolsky, Gilmer and Gilles (40) together with the 1986 fundamental constants (41) except for the Gas Constant and the Boltzmann Constant which are from the later measurements of Moldover and coworkers (42). Values were corrected to the recommended standard state pressure of one bar (43).

Vapour Pressure

Third Law heats of sublimation were calculated from the following Langmuir determinations, see Tables IV and V.

Table IV

Third Law Heats of Sublimation

    ΔH°298.15 KJ/mol
Jones, Langmuir and Mackay (44) 1697-2034 K 564.8 ± 1.7
aDreger and Margrave (45) 1573-1785 K 566.5 ± 1.4
bHarnpson and Walker (46) 918-2049 K 565.7 ± 0.5
cKoch and co-workers (47) 2032-2445 K 559.5 ± 1.1
dPlante, Sessoms and Fitch (48) 1675-1977 K 564.4 ± 0.2
Recommended   565 ± 2

Two data points rejected by the authors

Eight data points rejected by the authors

Weighted average of two data sets

Weighted average of eight data sets

Table V

Vapour Pressure Data Pt(s, 1) = Pt (g, bar)

T, K P, bar ΔG°, J/mol ΔH°, J/mol P, bar T, K
298.15 7.89 × 10-92 520016 565000 10-12 1489
400 1.26 × 10-66 504645 565043 10-11 1569
500 7.23 × 10-52 489540 565080 10-10 1659
600 4.98 × 10-42 474436 565012 10-9 2759
700 5.29 × 1035 459354 564809 10-8 1872
800 9.77 × 10-30 444310 564776 10-7 2002
900 1.21 × 10-25 429316 564022 10-6 2156
1000 2.27 × 10-22 414378 563465 10-5 2339
1100 1.07 × 10-19 399500 562814 10-4 2556
1200 1.80 × 10-17 384684 562076 10-3 2821
1300 1.37 × 10-15 369935 561258 10-2 3149
1400 5.57 × 10-14 355251 560363 10-1 3567
1500 1.38 × 10-12 340633 559390 1 4122
1600 2.26 × 10-11 326083 558340 NBP 4125
1700 2.67 × 10-10 311601 557209 NBP: normal boiling point at one atmosphere (1.01325b ar)
1800 2.38 × 10-9 297189 555992
1900 1.68 × 10-8 282844 554684
2000 9.68 × 10-8 268574 553278
2041.3(s) 1.90 × 10-7 262702 552666
2041.3(1) 1.90 × 10-7 262702 531337 ΔH°0 = 564.117 ± 2.000 kJ/mol ΔvapS°4122= 122.29 ± 0.29 J/mol K
2200 1.81 × 10-6 241901 529103
2400 2.00 × 10-5 215915 526315
2600 1.51 × 10-4 190161 523565
2800 8.49 × 10-4 164614 520858
3000 3.76 × 10-3 139264 518193
3200 1.37 × 10-2 114085 515575
3400 4.28 × 10-2 89075 513001
3600 0.117 64211 510473
3800 0.287 39489 507988
4000 0.639 14892 505544
4200 1.316 -9585 503142

The recommended value gives most weight to the measurements of Hampson and Walker and Plante, Sessoms and Fitch. Torsion measurements of Peleg and Alcock (49) 1800–2300 K were unfortunately shown only in the form of a graph but lead to a heat of sublimation about 5 kJ/mol higher than the recommended value. However Plante, Sessoms and Fitch have criticised the temperature measuring technique used in these experiments. Mass spectrometric measurements of Norman, Staley and Bell (50) 1752–2045 K lead to a second law heat of sublimation of 538 ± 17 kJ/mol.

Fundamental Constants

  • Avogadro’s number = 6.0221367 (36) x 1023/mol (41)

  • Velocity of light = 299,792,458 m/s (41)

  • Planck’s constant = 6.66260755 (40) x 10-34 Js (41)

  • Gas constant = 8.314471 (14) J/mol K (42)

  • Boltzmann constant = 1.3806513 (25) x 10-23 J/K (42)

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