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A Re-assessment of the Thermodynamic Properties of Palladium Improved values for the enthalpy of fusion

John W Arblaster Droitwich Worcestershire UK

Email jwarblasteryahoocouk

The thermodynamic properties were reviewed by the author in 1995 A new assessment of the enthalpy of fusion has led to a revision of the thermodynamic properties of the liquid phase and although the enthalpy of sublimation at 29815 K is retained as 377 plusmn 4 kJ molndash1 the normal boiling point is revised to 3272 K at one atmosphere pressure

Introduction

The thermodynamic properties of palladium were reviewed by the author in 1995 (1) At that time the value for the enthalpy of fusion was considered to be tentative since it differed significantly from the only known experimental value Newly considered enthalpy of fusion values now indicate that the original selected value was almost certainly incorrect and a more likely value has been suggested which leads to a major alteration to the selected values for the liquid phase Additional measurements of the vapour pressure do not alter the selected enthalpy of sublimation value of 377 kJ molndash1 but the accuracy can now be refined to give a 95 confidence value of plusmn4 kJ molndash1

Solid

Selected values in the low-temperature region as given in the previous review (1) were based mainly on the specific heat values of Boerstoel

et al (2) Clusius and Schachinger (3) and Mitacek and Aston (4) and continue to be considered satisfactory However only limited information was given in the original review which above 50 K consisted of specific heat values at 10 K intervals from 50 to 100 K and at 20 K intervals from 100 to 280 K and with the value at 29815 K also included This is now considered to be far too little information and instead a comprehensive review of the low-temperature thermodynamic properties is given in Table I In the high-temperature solid region closely

agreeing specific heat values derived from the enthalpy measurements of Cordfunke and Konings (5) (528 to 848 K) and the direct specific heat measurements of Miiller and Cezairliyan (6) (1400 to 1800 K) were selected since they were in excellent agreement with an extrapolation of the selected low-temperature values and allowed a single smooth specific heat curve to represent both the low- and high-temperature regions More recent high-temperature specific heat values by Milošević and Babić (7) (248 to 1773 K) differ significantly from the selected values showing a trend from 13 lower at 323 K to 39 lower at 723 K to 23 lower at 1223 K to 59 lower at 1773 K However at the low-temperature change over point at 270 K the measurements of Milošević and Babić show a sharp change in the slope of the specific heat curve compared to the selected low-temperature values indicating that these high-temperature measurements are incompatible with those obtained at low temperatures On these grounds the original high-temperature values were retained and can be represented by Equation (i) to cover the range from 29815 K to the accepted melting point at 18280 K

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5

Table I Low Temperature Thermodynamic Data

Cdegp HdegT ndash Hdeg0 K SdegT ndashGdegT ndash Hdeg0 K ndash(GdegT ndash Hdeg0 K)TT K J molndash1 Kndash1J molndash1 Kndash1 J molndash1 J molndash1 Kndash1 J molndash1

00594 0133 00512 0123 00246

10 0196 0722 0128 0554 00554

15 0490 2355 0256 1485 00990

20 0999 5978 0461 3241 0162

25 1768 1278 0761 6253 0250

30 2794 2413 1172 1104 0368

35 3998 4097 1689 1815 0519

40 5388 6440 2313 2811 0703

45 6809 9490 3030 4143 0921

50 8190 1324 3819 5853 1171

60 10724 2273 5541 1052 1753

70 12921 3458 7364 1697 2424

80 14803 4846 9215 2526 3157

90 16411 6409 11054 3539 3933

100 17784 8121 12856 4735 4735

110 18949 9959 14607 6109 5554

120 19926 1190 16299 7655 6379

130 20746 1394 17927 9367 7205

140 21443 1605 19491 1124 8027

150 22043 1822 20991 1326 8842

160 22561 2046 22431 1543 9646

170 23012 2273 23813 1775 10439

180 23406 2506 25139 2020 11219

190 23752 2741 26414 2277 11986

200 24059 2980 27641 2548 12738

210 24334 3222 28821 2830 13476

220 24582 3467 29959 3124 14200

230 24806 3714 31057 3429 14909

240 25007 3963 32117 3745 15604

250 25189 4214 33141 4071 16285

260 25352 4467 34133 4408 16952

270 25499 4721 35092 4754 17607

280 25629 4977 36022 5109 18248

290 25751 5234 36923 5474 18876

29815 25845 5444 37638 5778 19379

Notes to Table I CdegP is specific heat HdegT ndash H0 K is enthalpy SdegT is entropy ndashGdegT ndash Hdeg0 K and ndash(GdegT ndash Hdeg0 K)T are free energy functions

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Cdegp (J molndash1 Kndash1) = 240658 + 954408 times 10ndash3 T ndash 531329 times 10ndash6 T 2 + 202516 times 10ndash9 T 3

ndash 578356 T 2 (i)

Equivalent enthalpy and entropy equations are given in Table II and derived thermodynamic values are given in Table III In comparison with the selected equations the

specific heat values of Vollmer and Kohlhaas (8)

(300 to 1825 K) trend from 26 lower at 300 K to 53 lower at 800 K to an average of 15 higher above 1600 K (Figure 1) Enthalpy measurements of Holzmann (9) (575 to 1177 K) trend from 04 higher to 17 higher whilst those of Jaeger and Veenstra (10) (573 to 1772 K) scatter from 07 lower to 14 lower with an average of 11 lower (Figure 2) More recent enthalpy measurements of Cagran and Pottlacher (11) (1550 to 1828 K)

Table II Thermodynamic Equations Above 29815 K

Solid 29815 to 18280 K

Cdegp (J molndash1 Kndash1) = 240658 + 955408 times 10ndash3 T ndash 531329 times 10ndash6 T 2 + 202516 times 10ndash9 T 3 ndash 578356T 2

HdegT ndash Hdeg29815 K (J molndash1) = 240658 T + 477704 times 10ndash3 T 2 ndash 177109667 times 10ndash6 T 3 + 506290 times 10ndash10 T 4 + 578356T ndash 775091

SdegT (J molndash1 Kndash1) = 240658 ln (T) + 955408 times 10ndash3 T ndash 2656645 times 10ndash6 T 2 + 675053333 times 10ndash10 T 3 + 289178 T 2 ndash 1024348

Liquid 18280 to 3300 K

Cdegp (J molndash1 Kndash1) = 412000

HdegT ndash H29815 K (J molndash1) = 412000 ndash 109030

SdegT (J molndash1 Kndash1) = 412000 ln (T) ndash 2089240

Notes to Table II

CdegP is specific heat

HdegT ndash H29815 K is enthalpy

SdegT is entropy

Table III High Temperature Thermodynamic Data

Cdegp HdegT ndash Hdeg29815 K SdegT ndash(GdegTndashHdeg29815K)TT K J molndash1 Kndash1 J molndash1 J molndash1 Kndash1 J molndash1 Kndash1

29815 25845 0 37638 37638

300 25866 48 37798 37639

400 26805 2684 45375 38665

500 27536 5402 51438 40633

600 28162 8188 56515 42868

700 28727 11033 60899 45138

800 29255 13932 64770 47355

900 29766 16883 68245 49486

1000 30274 19885 71407 51522

1100 30794 22938 74317 53464

1200 31339 26045 77019 55316

1300 31922 29207 79551 57084

1400 32555 32431 81939 58774

(Continued)

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Cdegp (J molndash1 Kndash1) = 240658 + 954408 times 10ndash3 T ndash 531329 times 10ndash6 T 2 + 202516 times 10ndash9 T 3

ndash 578356 T 2 (i)

Equivalent enthalpy and entropy equations are given in Table II and derived thermodynamic values are given in Table III In comparison with the selected equations the

specific heat values of Vollmer and Kohlhaas (8)

(300 to 1825 K) trend from 26 lower at 300 K to 53 lower at 800 K to an average of 15 higher above 1600 K (Figure 1) Enthalpy measurements of Holzmann (9) (575 to 1177 K) trend from 04 higher to 17 higher whilst those of Jaeger and Veenstra (10) (573 to 1772 K) scatter from 07 lower to 14 lower with an average of 11 lower (Figure 2) More recent enthalpy measurements of Cagran and Pottlacher (11) (1550 to 1828 K)

Table II Thermodynamic Equations Above 29815 K

Solid 29815 to 18280 K

Cdegp (J molndash1 Kndash1) = 240658 + 955408 times 10ndash3 T ndash 531329 times 10ndash6 T 2 + 202516 times 10ndash9 T 3 ndash 578356T 2

HdegT ndash Hdeg29815 K (J molndash1) = 240658 T + 477704 times 10ndash3 T 2 ndash 177109667 times 10ndash6 T 3 + 506290 times 10ndash10 T 4 + 578356T ndash 775091

SdegT (J molndash1 Kndash1) = 240658 ln (T) + 955408 times 10ndash3 T ndash 2656645 times 10ndash6 T 2 + 675053333 times 10ndash10 T 3 + 289178 T 2 ndash 1024348

Liquid 18280 to 3300 K

Cdegp (J molndash1 Kndash1) = 412000

HdegT ndash H29815 K (J molndash1) = 412000 ndash 109030

SdegT (J molndash1 Kndash1) = 412000 ln (T) ndash 2089240

Notes to Table II

CdegP is specific heat

HdegT ndash H29815 K is enthalpy

SdegT is entropy

Table III High Temperature Thermodynamic Data

Cdegp HdegT ndash Hdeg29815 K SdegT ndash(GdegTndashHdeg29815K)TT K J molndash1 Kndash1 J molndash1 J molndash1 Kndash1 J molndash1 Kndash1

29815 25845 0 37638 37638

300 25866 48 37798 37639

400 26805 2684 45375 38665

500 27536 5402 51438 40633

600 28162 8188 56515 42868

700 28727 11033 60899 45138

800 29255 13932 64770 47355

900 29766 16883 68245 49486

1000 30274 19885 71407 51522

1100 30794 22938 74317 53464

1200 31339 26045 77019 55316

1300 31922 29207 79551 57084

1400 32555 32431 81939 58774

(Continued)

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Cdegp HdegT ndash Hdeg29815 K SdegT ndash(GdegTndashHdeg29815K)TT K J molndash1 Kndash1 J molndash1 J molndash1 Kndash1 J molndash1 Kndash1

1500 33251 35720 84209 60395

1600 34023 39083 86379 61952

1700 34882 42528 88467 63450

1800 35841 46063 90487 64896

1828 (s) 36129 47071 91043 65293

1828 (l) 41200 64411 100528 65293

1900 41200 67377 102120 66658

2000 41200 71497 104232 68485

2100 41200 75617 106243 70235

2200 41200 79737 108160 71916

2300 41200 83857 109991 73532

2400 41200 87977 111745 75088

2500 41200 92097 113427 76588

2600 41200 96217 115043 78036

2700 41200 100337 116597 79436

2800 41200 104457 118096 80790

2900 41200 108577 119542 82101

3000 41200 112697 120938 83373

3100 41200 116817 122289 84606

3200 41200 120937 123597 85805

3300 41200 125057 124865 86969

Notes to Table III

CdegP is specific heat

HdegT ndash H29815 K is enthalpy

SdegT is entropy

ndash(GdegT ndash Hdeg29515 K)T is the free energy function

300 500 700 900 1100 1300 1500 1700 1900 Temperature K

2

0

ndash2

ndash4

ndash6

Ref (7) Ref (8)

Fig 1 Percentage deviations of specific heat in the high-temperature region

Dev

iatio

n

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determined using the rapid pulse heating technique trend from 14 to 37 lower in the solid range (Figure 3)

Liquid

Drop calorimetry enthalpy measurements by Treverton and Margrave (12) were initially determined over the range 1846 to 2334 K on the International Practical Temperature Scale of 1948 (IPTS-48) but a short note added in the proof indicated further corrections for radiation losses and a conversion to the temperature scale IPTS-68 However only the amended liquid specific heat value and the liquid enthalpy at the melting point (given as 1827 K) were given After correction

for atomic weight to the melting point of 18280 K and to the International Temperature Scale of 1990 (ITS-90) the liquid enthalpy at the melting point is HdegT ndash Hdeg29815 K = 63151 J molndash1 which in combination with the enthalpy of the solid at the melting point leads to an enthalpy of fusion of 1608 plusmn 074 kJ molndash1 This is notably lower than actual experimental values of 1764 kJ molndash1

determined by Nedumov (13) using differential thermal analysis and rapid pulse heating values of 174 plusmn 20 kJ molndash1 determined by Seydel et al (14 15) and 1698 kJ molndash1 determined by Cagran and Pottlacher (11) The reason why the indirect determination of the enthalpy of fusion was low is not known but may be due to either an overestimation of the enthalpy values for the solid or more likely

Dev

iatio

n

2 Fig 2 Percentage deviations of

1 enthalpy in the high-temperature region

0 500 700 900 1100 1300 1500 1700 1900

Temperature K

ndash1

ndash2

Ref (9) Ref (10)

Fig 3 Percentage deviations of enthalpy in the high-temperature region

Ref (11) Melting point

Temperature K 1500 1700 1900 2100 2300 2500 2700 2900 0

ndash1

ndash2

ndash3

ndash4

ndash5

ndash6

Dev

iatio

n

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to the fact that even the revised values of Treverton and Margrave had still not accounted for all of the systematic errors that may have been present in their measurements Not including the measurement of Seydel et al because of the large uncertainty the two other enthalpy values were equivalent to entropy of fusion values of 965 J molndash1 Kndash1 and 929 J molndash1 Kndash1 respectively Kats and Chekhovskoi (16) noted that for a particular structure type the entropies of fusion (ΔSM) could be linearly related to the melting points (Tm) by means of the equation ΔSM = a Tm + b where a and b are constants For the face-centred cubic platinum group metals rhodium iridium and platinum selected entropy

molndash1 Kndash1of fusion values of 1221 plusmn 038 J at a melting point of 2236 K for rhodium (17) 1520 plusmn 041 J molndash1 Kndash1 at a melting point of 2719 K for iridium (18) and 1083 plusmn 046 J molndash1 Kndash1

at a melting point of 20413 K for platinum (19) when fitted to the above equation extrapolated to 952 J molndash1 Kndash1 for palladium in excellent agreement with the above experimental entropy values The two experimental entropy values for palladium were therefore combined with the values for rhodium iridium and platinum and were fitted to the equation ΔSM = 64574 times 10ndash3 Tm

ndash 23211 with the derived value for palladium as 9483 plusmn 040 J molndash1 Kndash1 where the error is assigned to match those obtained for the other elements The derived enthalpy of fusion value is rounded to 1734 plusmn 073 kJ molndash1 and leads to an enthalpy for the liquid at the melting point of 64411 J molndash1 suggesting that even with corrections applied the enthalpy measurements of Treverton and Margrave were 20 too low This confirms the suggestion that other liquid enthalpy measurements obtained by Treverton and Margrave also appear to be systematically low with for example the values obtained for vanadium (20) being on average 24 lower than the preferred values of Berezin et al (21) and Lin and Frohberg (22) The liquid specific heat determined by Treverton

and Margrave (12) on IPTS-68 corrected to the value 4120 plusmn 138 J molndash1 Kndash1 on ITS-90 which is notably higher than the value for the liquid of 373 J molndash1 Kndash1 determined by Cagran and Pottlacher (11) (1828 to 2900 K) using rapid pulse heating However it is noted that Cagran and Pottlacher obtained a specific heat value for the solid which is some 10 to 16 lower than the selected values Therefore the value of Treverton and Margrave was selected on the assumption that the apparently lower enthalpy values obtained

are due to a constant systematic error Over the range 1828 to 3300 K the actual enthalpy can be expressed as (Equation (ii))

HdegT ndash Hdeg29815 K (J molndash1) = 412000 T ndash 109030 (ii)

Equivalent specific heat and entropy equations are also given in Table II whilst derived thermodynamic properties are given in Table III The more recent liquid enthalpy measurements of Cagran and Pottlacher (11) trend from 33 lower at 1828 K to 58 lower at 2900 K

Gas

Selected values are based on the 143 energy levels selected by Engleman et al (23) The thermodynamic properties were calculated using the method of Kolsky et al (24) and the 2014 Fundamental Constants selected by Mohr et al (25 26) Derived thermodynamic values based on a one bar standard state pressure are given in Table IV

Enthalpy of Sublimation at 29815 K

Because of a general lack of detail as to what temperature scales were used and problems associated with the exact measurement of temperature no attempt was made to correct vapour pressure measurements to ITS-90 from what would have been contemporary scales For results given in the form of the Clausius-Clapeyron equation log(p) = A + BT (where p is pressure and T is temperature) the enthalpy of sublimation was calculated at the two temperature extremes and averaged For the measurements of Walker et al (27) Lindscheid and Lange (28) and Chegodaev et al (29) no temperature ranges were given and therefore these measurements were not included From Table V in view of possible systematic errors in the earlier measurements only the twelve determinations from Taberko et al (42 43) to Ferguson et al (51) were considered The unweighted average value of 377 kJ molndash1

is assigned an accuracy of plusmn4 kJ molndash1 which is equivalent to a 95 confidence level (two standard deviations)

Vapour Pressure Equations

The vapour pressure equations as given in Table VI were evaluated for the solid from free energy

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Table IV Thermodynamic Properties of the Gaseous Phase

Cdegp HdegT ndash Hdeg29815 K SdegT ndash(GdegT ndash Hdeg29815 K)TT K J molndash1 Kndash1 J molndash1 J molndash1 Kndash1 J molndash1 Kndash1

29815 20786 0 167066 167066

300 20786 38 167194 167066

400 20786 2117 173174 167881

500 20786 4196 177812 169421

600 20788 6274 181602 171145

700 20802 8354 184807 172874

800 20854 10436 187588 174543

900 20991 12527 190051 176132

1000 21273 14639 192276 177637

1100 21763 16789 194324 179062

1200 22508 19000 196248 180414

1300 23537 21300 198088 181704

1400 24850 23717 199878 182938

1500 26424 26279 201646 184126

1600 28213 29009 203407 185276

1700 30152 31926 205175 186395

1800 32167 35042 206955 187488

1828 32734 35951 207456 187790

1900 34179 38360 208749 188559

2000 36115 41875 210551 189614

2100 37908 45578 212358 190654

2200 39505 49450 214159 191681

2300 40869 53471 215946 192698

2400 41977 57615 217709 193703

2500 42823 61858 219441 194698

2600 43411 66171 221133 195682

2700 43757 70532 222779 196656

2800 43883 74916 224373 197617

2900 43815 79302 225912 198567

3000 43582 83673 227394 199503

3100 43213 88014 228817 200426

3200 42734 92312 230182 201334

3300 42172 96558 231489 202229

Notes to Table IV

CdegP is specific heat

HdegT ndash H29815 K is enthalpy

SdegT is entropy

ndash(GdegT ndash Hdeg29515 K)T is the free energy function

Hdeg29815 K ndash Hdeg0 K = 61974 J molndash1

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Table V Enthalpies of Sublimation at 29815 K

ΔHdeg29815 K ΔHdeg29815 K TemperatureAuthors Ref Method (II) (III) Notes range K kJ molndash1 kJ molndash1

Babeliowsky (30) MS 1250ndash1730 385 plusmn 4 ndash (a)

Trulson and Schissel (31) MS 1370ndash1785 382 plusmn 5 ndash

Haefling and Daane (32) KE 1388ndash1675 332 plusmn 7 3529 plusmn 05

Alcock and Hooper (33) Trans 1673ndash1773 459 3761 plusmn 24

Zanitsanov (34) KE 1537ndash1841 368 plusmn 22 3759 plusmn 12 (b)

Dreger and Margrave (35) L 1220ndash1640 362 plusmn 11 3806 plusmn 10

Hampson and Walker (36) L 1294ndash1488 365 plusmn 4 3734 plusmn 02

Norman et al (37) KEMS 1485ndash1710 381 3805 plusmn 01 (c)

Strassmair and Stark (38) L 1361ndash1603 372 plusmn 14 3733 plusmn 06

Myles (39) TE 1515ndash1605 372 3720 plusmn 01 (c)

Darby and Myles (40) TE 1517ndash1608 372 3718 plusmn 01 (c)

Novosolov et al (41) TE 1730ndash1938 363 3700 plusmn 04 (c)

(42Taberko et al Evap 1828ndash2023 381 plusmn10 3769 plusmn 0343)

Zaitsev et al (44) KE 1267ndash1598 377 plusmn 1 3773 plusmn 01

1511ndash1678 (s) 389 plusmn 4 3766 plusmn 02Bodrov et al (45) AA 1842ndash2046 (l) 394 plusmn12 3731 plusmn 05

Naito et al (46) KEMS 1567ndash1758 386 3755 plusmn 05 (c)

Chandrasekharaiah (47) KEMS 1439ndash1724 373 plusmn 5 3779 plusmn 02 (d)et al

Stoslashlen et al (48) KEMS 1523ndash1743 389 3755 plusmn 05 (c)

1627ndash1818 (s) 378 plusmn 7 3777 plusmn 02 (d)Bharadwaj et al (49) KEMS 1833ndash2041 (l) 380 plusmn 8 3767 plusmn 02 (d)

Kulkarni et al (50) KEMS 1237ndash1826 375 plusmn 2 3817 plusmn 03 (e)

1473ndash1825 (s) 373 plusmn 7 3778 plusmn 04Ferguson et al (51) KE 1840ndash1973 (l) 385 plusmn 7 3774 plusmn 02

Selected 377 plusmn 4

Notes to Table V

ΔHdeg29815 K (II) and ΔHdeg29815 K (III) are the Second Law and Third Law enthalpies of sublimation at 29815 K

(a) Value given only at 29815 K

(b) Two runs combined since individual Second Law values were 433 kJ molndash1 and 312 kJ molndash1 respectively

(c) Values given only in terms of the Clausius-Clapeyron equation

(d) Average of two runs

(e) Average of five runs

Methods

AA atomic absorption

Evap evaporation

KE Knudsen effusion

KEMS Knudsen effusion mass spectrometry

L Langmuir free evaporation

MS mass spectrometry

TE torsion effusion

Trans transpiration

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Table VI Vapour Pressure Equations

TemperaturePhase A B C D E range K

ndash126392 times 203201 timesSolid 900ndash1828 1471536 0220029 ndash4534916 10ndash3 10ndash7

394374Liquid 1828ndash3300 9257304 ndash1078530 ndash5130562 10ndash3 times ndash233142

times 10ndash7

Table VII Free Energy Equations Above 29815 K

Solid 29815 to 18280 K

GdegT ndash Hdeg29815 K (J molndash1) = 1265006 T ndash 477704 times 10ndash3 T 2 + 885548333 times 10ndash7 T 3

ndash 168763333 times 10ndash10 T 4 + 289178 T ndash 240658 T ln (T) ndash 775091

Liquid 18280 to 3300 K

GdegT ndash Hdeg29815 K (J molndash1) = 2501240 T ndash 412000 T ln (T) ndash 109030

Note to Table VII

GdegT ndash Hdeg29815 K is the free energy function

Table VIII Transition Values Involved with the Free Energy Equations

ΔHM J molndash1Transition Temperature K ΔSM J molndash1 Kndash1

Fusion 18280 1734000 94858

Table IX Vapour Pressure

T K p bar ΔGdegT J molndash1 ΔHdegT J molndash1 p bar T K

10ndash1529815 516 times 10ndash60 338411 377000 911

10ndash14300 132 times 10ndash59 338172 376991 956

10ndash13400 331 times 10ndash43 325314 376433 1005

500 220 times 10ndash33 312606 375794 1012 1060

10ndash11600 759 times 10ndash27 300034 375087 1122

10ndash10700 347 times 10ndash22 287585 374321 1191

1269800 107 times 10ndash18 275250 373504 10ndash9

900 543 times 10ndash16 263019 372644 10ndash8 1359

1000 786 times 10ndash14 250886 371754 10ndash7 1462

1100 456 times 10ndash12 238843 370851 10ndash6 1582

17251200 133 times 10ndash10 226882 369956 10ndash5

18991300 230 times 10ndash9 214994 369093 10ndash4

1400 263 times 10ndash8 203171 368286 10ndash3 2121

1500 216 times 10ndash7 191403 367558 10ndash2 2403

27701600 136 times 10ndash6 179680 366926 10ndash1

(Continued)

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T K p bar ΔGdegT J molndash1 ΔHdegT J molndash1 p bar T K

1700 689 times 10ndash6 167994 366399 1 326852

1800 291 times 10ndash5 156336 365979 NBP 327188

1828 (s) 423 times 10ndash5 153076 365880

1828 (l) 423 times 10ndash5 153076 348540

1900 101 times 10ndash4 145388 347983

2000 303 times 10ndash4 134742 347378

2100 817 times 10ndash4 124121 346961

2200 202 times 10ndash3 113516 346713

2300 460 times 10ndash3 102919 346614

2400 979 times 10ndash3 92323 346638

2500 196 times 10ndash2 81725 346761

2600 373 times 10ndash2 71120 346954

2700 675 times 10ndash2 60506 347195

2800 0117 49883 347459

2900 0196 39251 347745

3000 0318 28609 347976

3100 0498 17960 348197

3200 0760 7304 348375

326852 1000 0 348467

3300 1130 ndash3356 348501

Notes to Table IX

ΔGdegT is the free energy of formation at one bar standard state pressure and temperature T and ΔHdegT is the enthalpy of sublimation at temperature T

Enthalpy of sublimation at 0 K ΔHdeg0 = 376247 plusmn 4000 kJ molndash1

NBP is the normal boiling point at one atmosphere pressure (101325 bar)

functions for the solid and the gas at 50 K intervals from 900 K to 1800 K and the melting point and for the liquid at the melting point and at 50 K intervals from 1850 to 3300 K and were fitted to the following equation (Equation (iii))

ln (p bar) = A + B ln (T) + CT + D T + E T 2

(iii)

Acknowledgement

The author is indebted to Venkatarama Venugopal Bhabha Atomic Research Centre India for supplying the vapour pressure data corresponding to the measurements of Kulkarni et al (50)

References

1 J W Arblaster Calphad 1995 19 (3) 327

2 B M Boerstoel J J Zwart and J Hansen Physica 1971 54 (3) 442

3 K Clusius and L Schachinger Z Naturforsch A 1947 2a (2) 90

4 P Mitacek and J G Aston J Am Chem Soc 1963 85 (2) 137

5 E H P Cordfunke and R J M Konings Thermochim Acta 1989 139 99

6 A P Miiller and A Cezairliyan Int J Thermophys 1980 1 (2) 217

7 N Milošević and M Babić Int J Mater Res 2013 104 (5) 462

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httpdxdoiorg101595205651318X696648 Johnson Matthey Technol Rev 2018 62 (1)

8 O Vollmer and R Kohlhaas Z Naturforsch A 1969 24 (10) 1669

9 H Holzmann lsquoSieberts Festschrift zum 50 Jahr Bestehen der Platinschmelzersquo 1931 p 149

10 F M Jaeger and W A Veenstra Proc R Acad Amsterdam 1934 37 (5) 280

11 C Cagran and G Pottlacher Platinum Metals Rev 2006 50 (3) 144

12 J A Treverton and J L Margrave J Phys Chem 1971 75 (24) 3737

13 N A Nedumov ldquoDifferential Thermal Analysis Fundamental Aspectsrdquo ed R C Mackenzie Vol 1 Academic Press London UK 1970 p 161

14 U Seydel and U Fischer J Phys F Met Phys 1978 8 (7) 1397

15 U Seydel H Bauhof W Fucke and H Wadle High Temp-High Press 1979 11 (6) 635

16 S A Kats and V Y Chekhovskoi High Temp-High Press 1979 11 (6) 629

17 J W Arblaster Calphad 1995 19 (3) 357

18 J W Arblaster Calphad 1995 19 (3) 365

19 J W Arblaster Platinum Metals Rev 2005 49 (3) 141

20 J A Treverton and J L Margrave J Chem Thermodyn 1971 3 (4) 473

21 B Ya Berezin V Ya Chekhovskoy and A E Sheindlin High Temp Sci 1972 4 (6) 478

22 R Lin and M G Frohberg Z Metallkd 1991 82 (1) 48

23 R Engleman U Litzeacuten H Lundberg and J-F Wyart Phys Scr 1998 57 (3) 345

24 H G Kolsky R M Gilmer and P W Gilles ldquoThe Thermodynamic Properties of 54 Elements Considered as Ideal Monatomic Gasesrdquo Los Alamos Scientific Laboratory Report No LAndash2110 New Mexico USA 20th December 1956

25 P J Mohr D B Newell and B N Taylor Rev Mod Phys 2016 88 (3) 035009

26 P J Mohr D B Newell and B N Taylor J Phys Chem Ref Data 2016 45 (4) 043102

27 R F Walker J Efimenko and N L Lofgren Planet Space Sci 1961 3 24

28 H Lindscheid and K W Lange Z Metallkd 1975 66 (9) 546

29 A I Chegodaev E L Dubinin A I Timofeev N A Vatolin and V I Kapitanov Zh Fiz Khim 1978 52 (8) 2124 Transl Russ J Phys Chem 1978 52 (8) 1229

30 T P J H Babeliowsky Physica 1962 28 (11) 1160

31 O C Trulson and P O Schissel J Less Common Metals 1965 8 (4) 262

32 J F Haefling and A H Daane Trans Met Soc AIME 1958 212 (1) 115

33 C B Alcock and G W Hooper Proc R Soc A 1960 254 (1279) 551

34 P D Zavitsanos J Phys Chem 1964 68 (10) 2899

35 L H Dreger and J L Margrave J Phys Chem 1960 64 (9) 1323

36 R F Hampson and R F Walker J Res Nat Bur Stand A Phys Chem 1962 66A (2) 177

37 J H Norman H G Staley and W E Bell J Phys Chem 1965 69 (4) 1373

38 H Strassmair and D Stark Z Angew Phys 1967 23 (1) 40

39 K M Myles Trans Met Soc AIME 1968 242 (8) 1523

40 J B Darby and K M Myles Met Trans 1972 3 (3) 653

41 B M Novoselov E L Dubinin and A I Timofeev Izv Vyssh Uchebn Zaved Tsvetn Metall 1978 (6) 41

42 A V Taberko S E Vaisburd and L Sh Tsemekhman Zh Fiz Khim 1977 51 (1) 273 Transl Russ J Phys Chem 1977 51 (1) 164

43 S E Vaisburd L Sh Tsemekhman A V Taberko

and Yu A Karasev in ldquoProtsessy Tsvetn Metall Nizk Davleniyakhrdquo ed A I Manokhin Izd Nauka Moscow Russia 1983 p 120

44 A I Zaitsev Yu A Priselkov and A N Nesmeyanov Teplofiz Vys Temp 1982 20 (3) 589

45 N V Bodrov G I Nikolaev and A M Nemets Zh Prikl Spektrosk 1985 43 (4) 535 Transl J Appl Spectrosc 1985 43 (4) 1063

46 K Naito T Tsuji T Matsui and A Date J Nucl Mater 1988 154 (1) 3

47 M S Chandrasekharaiah M J Stickney and K A Gingerich J Less Common Metals 1988 142 329

48 S Stoslashlen T Matsui and K Naito J Nucl Mater 1990 173 (1) 48

49 S R Bharadwaj A S Kerkar S N Tripathi and

R Kameswaran J Chem Thermodyn 1990 22 (5) 453

50 S G Kulkarni C S Subbanna V Venugopal D D Sood and S Venkateswaran J Less Common Metals 1990 160 (1) 133

51 F T Ferguson K G Gardner and J A Nuth III J Chem Eng Data 2006 51 (5) 1509

59 copy 2018 Johnson Matthey

httpdxdoiorg101595205651318X696648 Johnson Matthey Technol Rev 2018 62 (1)

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

58 copy 2018 Johnson Matthey

httpdxdoiorg101595205651318X696648 Johnson Matthey Technol Rev 2018 62 (1)

8 O Vollmer and R Kohlhaas Z Naturforsch A 1969 24 (10) 1669

9 H Holzmann lsquoSieberts Festschrift zum 50 Jahr Bestehen der Platinschmelzersquo 1931 p 149

10 F M Jaeger and W A Veenstra Proc R Acad Amsterdam 1934 37 (5) 280

11 C Cagran and G Pottlacher Platinum Metals Rev 2006 50 (3) 144

12 J A Treverton and J L Margrave J Phys Chem 1971 75 (24) 3737

13 N A Nedumov ldquoDifferential Thermal Analysis Fundamental Aspectsrdquo ed R C Mackenzie Vol 1 Academic Press London UK 1970 p 161

14 U Seydel and U Fischer J Phys F Met Phys 1978 8 (7) 1397

15 U Seydel H Bauhof W Fucke and H Wadle High Temp-High Press 1979 11 (6) 635

16 S A Kats and V Y Chekhovskoi High Temp-High Press 1979 11 (6) 629

17 J W Arblaster Calphad 1995 19 (3) 357

18 J W Arblaster Calphad 1995 19 (3) 365

19 J W Arblaster Platinum Metals Rev 2005 49 (3) 141

20 J A Treverton and J L Margrave J Chem Thermodyn 1971 3 (4) 473

21 B Ya Berezin V Ya Chekhovskoy and A E Sheindlin High Temp Sci 1972 4 (6) 478

22 R Lin and M G Frohberg Z Metallkd 1991 82 (1) 48

23 R Engleman U Litzeacuten H Lundberg and J-F Wyart Phys Scr 1998 57 (3) 345

24 H G Kolsky R M Gilmer and P W Gilles ldquoThe Thermodynamic Properties of 54 Elements Considered as Ideal Monatomic Gasesrdquo Los Alamos Scientific Laboratory Report No LAndash2110 New Mexico USA 20th December 1956

25 P J Mohr D B Newell and B N Taylor Rev Mod Phys 2016 88 (3) 035009

26 P J Mohr D B Newell and B N Taylor J Phys Chem Ref Data 2016 45 (4) 043102

27 R F Walker J Efimenko and N L Lofgren Planet Space Sci 1961 3 24

28 H Lindscheid and K W Lange Z Metallkd 1975 66 (9) 546

29 A I Chegodaev E L Dubinin A I Timofeev N A Vatolin and V I Kapitanov Zh Fiz Khim 1978 52 (8) 2124 Transl Russ J Phys Chem 1978 52 (8) 1229

30 T P J H Babeliowsky Physica 1962 28 (11) 1160

31 O C Trulson and P O Schissel J Less Common Metals 1965 8 (4) 262

32 J F Haefling and A H Daane Trans Met Soc AIME 1958 212 (1) 115

33 C B Alcock and G W Hooper Proc R Soc A 1960 254 (1279) 551

34 P D Zavitsanos J Phys Chem 1964 68 (10) 2899

35 L H Dreger and J L Margrave J Phys Chem 1960 64 (9) 1323

36 R F Hampson and R F Walker J Res Nat Bur Stand A Phys Chem 1962 66A (2) 177

37 J H Norman H G Staley and W E Bell J Phys Chem 1965 69 (4) 1373

38 H Strassmair and D Stark Z Angew Phys 1967 23 (1) 40

39 K M Myles Trans Met Soc AIME 1968 242 (8) 1523

40 J B Darby and K M Myles Met Trans 1972 3 (3) 653

41 B M Novoselov E L Dubinin and A I Timofeev Izv Vyssh Uchebn Zaved Tsvetn Metall 1978 (6) 41

42 A V Taberko S E Vaisburd and L Sh Tsemekhman Zh Fiz Khim 1977 51 (1) 273 Transl Russ J Phys Chem 1977 51 (1) 164

43 S E Vaisburd L Sh Tsemekhman A V Taberko

and Yu A Karasev in ldquoProtsessy Tsvetn Metall Nizk Davleniyakhrdquo ed A I Manokhin Izd Nauka Moscow Russia 1983 p 120

44 A I Zaitsev Yu A Priselkov and A N Nesmeyanov Teplofiz Vys Temp 1982 20 (3) 589

45 N V Bodrov G I Nikolaev and A M Nemets Zh Prikl Spektrosk 1985 43 (4) 535 Transl J Appl Spectrosc 1985 43 (4) 1063

46 K Naito T Tsuji T Matsui and A Date J Nucl Mater 1988 154 (1) 3

47 M S Chandrasekharaiah M J Stickney and K A Gingerich J Less Common Metals 1988 142 329

48 S Stoslashlen T Matsui and K Naito J Nucl Mater 1990 173 (1) 48

49 S R Bharadwaj A S Kerkar S N Tripathi and

R Kameswaran J Chem Thermodyn 1990 22 (5) 453

50 S G Kulkarni C S Subbanna V Venugopal D D Sood and S Venkateswaran J Less Common Metals 1990 160 (1) 133

51 F T Ferguson K G Gardner and J A Nuth III J Chem Eng Data 2006 51 (5) 1509

59 copy 2018 Johnson Matthey

httpdxdoiorg101595205651318X696648 Johnson Matthey Technol Rev 2018 62 (1)

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

59 copy 2018 Johnson Matthey

httpdxdoiorg101595205651318X696648 Johnson Matthey Technol Rev 2018 62 (1)

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