JPEDAV (2015) 36:422–444 DOI: 10.1007/s11669-015-0399-x 1547-7037 ASM International

Thermodynamic Properties of Copper J.W. Arblaster

(Submitted March 19, 2015; in revised form July 13, 2015; published online August 20, 2015) The thermodynamic properties of copper have been evaluated to 2900 K. Selected values include an enthalpy of sublimation of 337.2 ± 1.7 kJ/mol for the monatomic gas at 298.15 K, a dissociation enthalpy D0 of 192.0 ± 2.0 kJ/mol for the diatomic gas species at absolute zero and a derived equilibrium boiling point of 2843 K at one atmosphere pressure.

Keywords

copper, gas, liquid, solid, thermodynamic properties

1. Introduction The freezing point is a primary fixed point on ITS-90 at 1357.77 K (Preston-Thomas[1]). The equivalent thermodynamic temperature is currently considered to be about 0.05 K higher (Fischer et al.[2]). Wherever possible, values have been corrected to the currently accepted atomic weight of 63.546 ± 0.003 (Wieser et al.[3]) and to the ITS-90 temperature scale using correction factors of Douglas,[4] Rusby,[5] Rusby et al.[6] and Weir and Goldberg.[7] Previous reviews on copper have been given by Furukawa et al.,[8] Hultgren et al.,[9] White and Collocott,[10] Head and Sabbah,[11] CODATA (Cox et al.[12]), White and Minges[13] and JANAF (Chase[14]). Even commercially, copper is available with purity of 99.999 %, and therefore the metal has been used extensively in evaluating new instruments for measuring specific heat, enthalpy and vapor pressures, leading to a large number of measurements, many of which are of high precision; For example, from 30 K to the freezing point, the specific heat of the solid is known to accuracy of 0.1 %. In the present review, the properties of the diatomic gas have also been fully evaluated, since its effect becomes significant in the region of the boiling point.

is usually represented in terms of a limited Debye temperature, hD, where h3D = (12/5)p4R/A = 1943.770/A, where R is the gas constant and A is given in units of J/(mol K4). Most values in this temperature range are given only in terms of the 1958 helium-4 temperature scale (Brickwedde et al.[15]), but a comparison with the ITS-90 helium-4 temperature scale (Preston-Thomas[1]) indicates that there is no straightforward relationship between the two scales, and therefore it would not be possible to preserve the simple two-term representation if such a conversion were used. Therefore, the values are as given on their original temperature scales. The average values selected in Table 1 for c and hD differ little from those selected by both Furukawa et al.[8] and Phillips[16] at c of 0.695 ± 0.005 mJ/ (mol K2) and hD of 344.5 ± 1.5 K. Alers[17,18] obtained a closely agreeing value of hel of 345.2 ± 0.9 K from elastic constant measurements. Other measurements in this region on lower-purity material not included in the evaluation were given by Furukawa et al.[8] except for the additional measurements of Tsumura et al.[19] (0.1 to 0.9 K). 2.2 Range 4.2 to 30 K In this region the specific heat measurements of Ahlers[38] (1.3 to 20 K), Osborne et al.[40] (1.0 to 22.6 K), Holste et al.[55] (1 to 30 K), Martin et al.[56] (3 to 30 K), Martin[58] (2.5 to 30 K) and Hurley and Gerstein[59] (0.6 to 27.9 K) were given equal weight and combined with the selected values of c and hD to give Eq 1, which has an overall accuracy as a standard deviation of ±0.0006 J/mol K (0.20 %). Cop ðJ/mol KÞ ¼ 6:94000  104 T þ 4:76249

2. Solid Phase

 105 T 3 þ 1:05866  109 T 5 þ 1:02870 2.1 Range 0 to 4.2 K

 1010 T 7  1:68191  1013 T 9

Low-temperature specific P heat is generally given in terms of the Debye equation Cp ¼ n¼0 a2nþ1 T 2nþ1 , where below 4.2 K only the first two terms are considered so that Cp ¼ cT þ AT 3 , where c is the electronic coefficient and A

þ 9:01270  1017 T 11  1:13003

Electronic supplementary material: The online version of this article (doi:10.1007/s11669-015-0399-x) contains supplementary material, which is available to authorized users. J.W. Arblaster, Wolverhampton, West Midlands WV5 8JU, England, UK. Contact e-mail: [email protected].

422

 1020 T 13 : ðEq 1Þ In order to give equal weight, the values of Osborne et al.[40] were calculated from the equation fitted to the original data by Hurley and Gerstein.[59] Because of difficulties in correcting the values from their original temperature scales to ITS-90, the measurements were

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 1

Electronic coefficient and Debye temperature values for copper Ref.

Temperature range (K)

c (mJ/mol K2)

hD (K)

Corak et al. Rayne Manchester Franck et al. Du Chatenier and De Nobel Veal and Rayne O’Neal Kneip et al. Phillips Ahlers Isaacs Isaacs and Massalski Dixon et al.

[20] [21] [22] [23] [24,25] [26] [27] [28] [29] [30,31] [32] [33] [34]

1 to 5 1.5 to 4.2 1.2 to 4.2 0.4 to 1.5 1 to 30 1 to 4.2 0.1 to 1.1 1.2 to 4.5 0.1 to 4.2 2.3 to 20 1.6 to 4.2 1.6 to 4.2 1.2 to 4.2

Senozan Martin Clune and Green

[35] [36] [37]

0.2 to 25 3 to 30 2 to 4

Ahlers Sargent et al. Osborne et al. Isaacs Gmelin and Gobrecht Boerstoel et al.

[38] [39] [40] [41] [42] [43]

1.3 to 21 1.6 to 4.2 1.0 to 23 1.6 to 4.2 0.4 to 30 1 to 30

Martin Dixon et al. Cetas et al. Sato et al. Martin

[44] [45] [46] [47,48] [49]

0 to 4.0 0.2 to 4.2 1.6 to 4.2 1.5 to 4.2 0 to 3

Waterhouse Bloom et al.

[50] [51]

0.4 to 3.0 1.5 to 20

Leadbetter and Wycherley Clune and Green

[52] [53]

1.4 to 20 1 to 2.3

Zrudsky et al. Holste et al. Martin et al. Novotny and Meincke Martin Hurley and Gernstein Aleksandrov et al. Park and Vaidya

[54] [55] [56] [57] [58] [59] [60] [61]

1 to 14 1 to 4.2 0.4 to 30 1.5 to 15 2.5 to 30 0.6 to 28 2.3 to 5 2 to 6

0.688 0.686 0.697 0.682 0.721 0.692 0.702 0.697 0.695 0.704 0.698 0.698 I 0.695 II 0.698 0.698 0.696 I 0.702 II 0.696 0.696 0.698 0.694 0.698 0.696 I 0.693 II 0.697 0.6915 0.697 0.6932 0.697 I 0.6888 II 0.6896 0.6920 I 0.6903 II 0.6843 0.696 I 0.698 II 0.696 0.696 0.6945 0.691 0.695 0.691 0.691 0.695 0.6961

343.8 345.1 344 327 338.9 342.7 342.9 345.1 343.4 344 342.3 342.3 I 343.2 II 343.2 342 345.6 I 344.9 II 344.1 343.8 342.3 345.2 342.2 344.4 I 343.7 II 344.4 345.8 343.4 343.7 342.0 I 347.7 II 346.6 347.0 I 345.4 II 345.3 346.6 I 345.6 II 346.3 343.3 343.7 344.4 344.5 344.3 343.9 345.1 344.4

Authors

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Notes

a, b c, b c, b b

d, b e, b e, b f, b f, b c, b g, b g, b h e, b h, i

h h

j

h h h h h

423

Table 1

continued

Authors

Ref.

Temperature range (K)

c (mJ/mol K2)

hD (K)

Notes

Gmelin and Ro¨dhammer Collocott Selected

[62] [63]

1.5 to 30 2 to 20

0.6956 0.6916 0.694 ± 0.004

343.6 344.5 344.3 ± 1.5

h

I and II refer to the first and second samples, respectively (a) Superseded by Veal and Rayne[26] (b) Not included in the evaluation (c) Superseded by Martin[44,49] (d) Superseded by Ahlers[38] (e) Superseded by Isaacs[41] (f) Superseded by Dixon et al.[45] (g) Superseded by Clune and Green[53] (h) First two terms of a polynomial equation (i) Calculated by Hurley and Gernstein[59] (j) Superseded by Holste et al.[55]

Fig. 1 Low-temperature specific heat for solid copper, calculated from Eq 1 and expressions in Table 10

accepted as given. The 1965 Calorimetry Copper Standard (Osborne et al.[40,64]) (1 to 25 K), which was based mainly on the measurements of Ahlers,[38] Martin[36] and Osborne et al.,[40,64] trends to 0.2 % low at 15 K, before increasing to 0.7 % high at 25 K. Measurements of Buravoi et al.[65] (5 to 30 K) were only shown in the form of a small graph and were not considered further. Derived thermodynamic values are included in Table 18, whilst deviations from the selected values in this region are given in Table 14. 2.3 Range 30 to 400 K High-precision specific heat measurements on pure copper by Robie et al.[66] (15.4 to 379 K), Martin[67] (20 to 320 K), Stevens and Boerio-Goates[68] (6.6 to 398 K),

424

Bissengaliyeva et al.[69] (4.2 to 320 K) and Bronson et al.[70] (267 to 380 K) were combined. The temperature values of Robie et al.[66] were directly converted from IPTS68 to ITS-90, whilst the measurements of Martin[67] were given in the form of an equation, which was converted from IPTS-68 to ITS-90 by Archer.[71] The measurements of both Stevens and Boerio-Goates[68] and Bissengaliyeva et al.[69] were already given on ITS-90, with the latter given in the form of a series of equations, which were used for the evaluation. The measurements of Bronson et al.[70] were not corrected for temperature scale but were given only onethird weight in order to give approximately equal weights to all values in the different evaluation regions. The measurements were fitted to the five equations as given in Table 10,

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Fig. 2 Specific heat for copper for 300 K < T < 1500 K, calculated from expressions in Table 11

Fig. 3 High-temperature thermodynamic properties of copper for 300 K < T < 2900 K, taken from Table 19

Table 2

Selected values for the solid at 298.15 K

Authors

Ref.

Cpo (J/mol K)

o o H298:15 K  H0 (J/mol)

o S298:15 K (J/mol K)

Furukawa et al. Hultgren et al. CODATA (Cox et al.) JANAF (Chase) This work

[8] [9] [12] [14] —

24.44 24.44 24.44 24.44 24.44

5005 5004 5004 5007 4999

33.15 33.15 33.15 33.16 33.13

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

425

Table 3

Enthalpy of fusion values for copper Ref.

Methods

DHM (J/mol)

[84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101,102] [103]

DC DC DC DC DC DC DC DC AC DTA RPH DSC PD PD DC Mod RPH DC RPH

11,517 11,072 13,557 13,285 13,538 12,682 12,891 13,770 13,000 12,722 12,900 13,100 12,803 12,301 12,895 14,091 13,154 13,594 14,685

Authors Richards Glaser Wu¨st et al. Umino Esser et al. Oelsen et al. Schu¨rmann and Kaune Dokken and Elliott Volmer and Kohlhaas Nedumov Pottlacher et al. Baricco et al. Kelley Nathan and Leider Novikov et al. Orlik and Petrunin Kanaev et al. Chekhovskoi et al. Cagran et al. Weighted average

% Uncertainty 10 15 15 10 7.5 3 3 7.5 1.5 5 5 4 10 10 5 15 5 5 15 12,961 ± 128

Notes

a

b

(a) As corrected by Esser et al.[88] (b) In conjunction with enthalpy measurements on the solid by Chekhovskoi and Tarasov[104] Methods: DC drop calorimetry, AC adiabatic calorimetry, DTA differential thermal analysis, DSC differential scanning calorimetry, RPH rapid pulse heating, PD phase diagrams, Mod modulation method

Table 4

Enthalpy and specific heat values for liquid copper

Authors Wu¨st et al. Umino Esser et al. Chaudhuri et al. Bonnell Stevens Stretz and Bautista Kuntz and Bautista Novikov et al. Dokko and Bautista Chekhovskoi et al. Cagran et al. Unweighted average

Ref. [86] [87] [88] [109] [110] [111] [105] [106] [98] [112] [101,102] [103]

Temperature range (K) 1373 1373 1373 1386 1387 1428 1358 1700 1372 1415 1451 1357

to to to to to to to to to to to to

1573 1773 1473 1887 1889 2007 2061 2000 1520 2048 1986 2000

A

B

Cpo (J/mol K)

Notes

30.788 32.366 29.406 32.991 34.569 33.439 32.448 34.061 33.289 30.189 36.333 33.775

+680.1 +1171.5 +3259.8 1980.5 3825.5 1977.9 1241.6 3870.9 2858.9 +1137.2 5763.5 2952.9

30.79 ± 0.85 32.37 ± 0.13 29.41 32.99 ± 1.72 34.57 ± 1.80 33.44 ± 3.28 33.45 ± 0.75 34.06 ± 0.84 33.29 ± 0.43 30.19 ± 0.39 36.33 ± 0.74 33.77 33.52 ± 1.90

a a a a, b a

(a) Not included in the evaluation (b) Superseded by Bonnell[107]

which have an overall accuracy as a standard deviation of ±0.008 J/(mol K) (0.06 %). Derived low-temperature thermodynamic data are given in Table 18, whilst the deviations of other specific heat values in the low-temperature region are given in Table 14.

426

However, not included are the measurements of Berge and Blanc[72] (80 to 273 K) and Chapman et al.[73] (78 to 105 K), which were shown only in the form of small graphs. Selected specific heat values of Furukawa et al.[8] (1 to 300 K) were generally only based on commercial-purity materials above

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 5

Second Law enthalpies of sublimation of the monatomic gas at 298.15 K

Authors

Ref.

Method

Range (K)

o H298:15 K (II) (kJ/mol)

Notes

Ackermann and Rauh Babeliowski Avery et al. Moore et al. Golonka et al. Katsov et al. Vrestal and Tomiska

[125] [126] [127] [128] [129] [130] [131]

MS MS MS MS MS AA KEMS

1360 to 1450 1217 to 1314 1474 to 1851 1250 1298 to 1502 1375 to 1423 1134 to 1344

341 ± 5 320 ± 16 352 ± 5 337 ± 5 354 ± 3 339 324 ± 7

a b c a

Acronyms and notes as in Table 7

Table 6

Enthalpies of sublimation of the monatomic gas at 298.15 K (not included in the evaluation) Ref.

Method

Range (K)

o H298:15 K (II) (kJ/mol)

o H298:15 K (III) (kJ/mol)

Notes

Greenwood Greenwood Rosenhain and Ewen Ruff and Bergdahl Ruff and Mugdan Mack et al. Ruff and Konschak Jones et al. Harteck Baur and Brunner Marshall et al. Daane Edwards and Downing Knacke and Schmolke Nesmeyanov et al. McLellan and Shuttleworth Grieveson et al. Kirshenbaum and Cahill Kirshenbaum and Cahill Matern Kasarev et al. Nemets and Nikolaev

[132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146,147] [148] [149] [150] [151] [152] [153] [154] [155]

Muradov et al. Novoselov et al. Vaisburd et al. Panday and Ganguly Severin et al.

[156] [157] [158] [159] [160]

Starovoitov Severin et al.

[161] [124]

Subbotina et al. Duan et al.

[162] [163]

2583 2253 to 2453 1288 2378 to 2573 2148 to 2531 1083 2138 to 2643 1186 to 1298 1419 to 1463 1768 to 2116 1268 to 1466 1383 to 1478 1383 to 1603 1215 to 1338 1192 to 1360 987 to 1357 1429 to 1846 2820 2811 1251 to 1393 1473 to 1673 (s) 1140 to 1348 (l) 1375 to 1580 (s) 1140 to 1348 (l) 1375 to 1580 1113 to 1283 1488 to 1695 1373 to 1773 1080 to 1250 (s) 1160 to 1345 (l) 1362 to 1511 1400 to 1664 (s) 1219 to 1306 (l) 1375 to 1468 (s) 1206 to 1269 (l) 1372 to 1482 2143 to 2341 1609 to 1892

… 249 … 501 ± 35 426 ± 32 … 391 ± 18 318 264 ± 49 278 ± 11 399 ± 12 323 ± 22 … 334 ± 26 338 ± 17 337 330 … … 355 322 ± 7 321 ± 13 333 ± 16 327 ± 11 332 ± 16 307 ± 5 358 327 ± 7 336 328 ± 3 328 ± 4 356 ± 2 286 ± 11 318 ± 10 328 ± 3 330 ± 4 339 ± 18 351 ± 13

309.2 314.7 ± 2.8 355.3 ± 2.9 317.3 ± 2.6 320.7 ± 3.6 330.7 322.2 ± 3.1 349.3 ± 1.4 342.2 ± 0.6 306.9 ± 1.0 338.2 ± 1.0 343.5 ± 0.5 337.6 330.8 ± 0.8 339.4 ± 0.7 343.5 ± 1.0 336.3 ± 0.8 334.7 333.7 338.1 ± 0.9 331.4 ± 0.4 330.7 ± 0.7 333.5 ± 0.7 332.6 ± 0.6 335.9 ± 0.7 339.3 ± 0.3 333.6 ± 1.6 339.1 ± 0.7 335.4 ± 0.1 327.9 ± 0.1 328.2 ± 0.1 336.3 ± 0.4 331.4 ± 0.4 336.3 ± 0.2 327.8 ± 0.1 327.8 ± 0.1 329.6 ± 0.5 341.2 ± 0.7

d d

Nemets et al.

BP BP Evap BP BP Flow BP Evap KE BP L KE Eff Evap KE KE KE + Trans BP BP KE Evap AA AA AA AA AA TE Eff AA KE KE L KE KE KE KE BP CG

Authors

d d d

d

e

f f d d f

f f

g g h h d

Acronyms and notes as in Table 7

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

427

Table 7

Enthalpies of sublimation of the monatomic gas at 298.15 K (included in the evaluation)

Authors

Ref.

Method

Range (K)

o H298:15 K (II) (kJ/mol)

o H298:15 K (III) (kJ/mol)

Hersh

[164]

Edwards et al. Morris and Zellars Krupowski and Golonka McCormack et al. Ponslet and Bariaux Myles and Darby Pomerantsev

[165] [166] [167] [168] [169] [170] [171]

Geiger et al. Selected

[172]

KE KE KE Trans L KE L TE KE KE BP

(s) 1242 to 1340 (l) 1370 to 1563 1143 to 1292 1600 to 1879 1367 to 1523 1475 to 1707 1253 to 1382 1265 to 1356 (s) 1186 to 1344 (l) 1376 to 1492 2470 to 2787

338 ± 1 344 ± 5 338 ± 4 333 ± 3 334 ± 7 349 ± 5 330 ± 8 334 ± 6 338 ± 4 339 ± 2 335 ± 2

340.4 ± 0.4 340.3 ± 0.2 337.2 ± 0.2 336.6 ± 0.1 335.4 ± 0.2 338.9 ± 0.3 336.4 ± 0.2 336.4 ± 0.1 336.2 ± 0.2 336.1 ± 0.1 336.8 ± 0.1 337.2 ± 1.7

Notes

a

d, i

o o H298:15 K (II) and H298:15 K (III) are the Second Law and Third Law enthalpies of sublimation at 298.15 K (a) Unweighted average of two runs (b) Value given only at 298.15 K (c) Weighted average of two runs (d) Corrected for the presence of the diatomic gas (e) Value given only at 0 K (f) Given only in the form of the Clausius–Clapeyron equation (g) Tantalum cells (h) Graphite cells (i) One data point rejected Methods: AA atomic absorption, BP boiling point, CG carrier gas method, Eff effusion, Evap evaporation, Flow dynamic flow, KE Knudsen effusion, KEMS Knudsen effusion mass spectrometry, L Langmuir technique, MS mass spectrometry, TE torsion effusion, Trans transport

Table 8

Enthalpy of dissociation of the diatomic gas at 0 K

Authors Drowart and Honig Schissel Ackerman et al. Hilpert Hilpert and Gingerich Wilhite Selected

Ref. [177,178] [175] [176] [181] [180] [177]

Range (K) 1530 1575 1549 1238 1801 1480

to to to to to

1730 1709 1569 1897 1673

Do0 K (II) (kJ/mol)

Do0 K (III) (kJ/mol)

— 206 ± 16 195 ± 11 191 ± 3 211 ± 33 211 ± 18

196.9 193.7 ± 0.4 192.5 ± 0.3 189.0 ± 0.9 180.4 ± 0.6 189.8 ± 0.5 192.0 ± 2.0

Notes a b a, c a, b

Do0 K (II) and Do0 K (III) are the Second Law and Third Law enthalpies of dissociation at 0 K (a) Not included in the average (b) One data point rejected (c) The actual selected value is 190.2 ± 5.4 kJ/mol as an average of Do0 K (II) and Do0 K (III) Methods: Drowart and Honig[177,178] used mass spectrometry (MS). All other experiments used Knudsen effusion mass spectrometry (KEMS)

30 K and show a sinusoidal behaviour when compared with the selected values, trending from 0.3 % high at 30 K to 0.5 % low at 60 K, then increasing to 0.3 % high at 210 K before converging to the selected values at 300 K. The lowtemperature equation of Head and Sabbah,[11] known as the IUPAC equation, was based on the measurements of Martin,[74] Robie et al.[66] and Downie and Martin,[75]

428

although the latter measurements were only shown graphically and are not readily available. This equation also showed sinusoidal behaviour when compared with selected values, trending to 0.2 % low at 70 K, increasing to 0.1 % high at 180 K and then converging to the selected value at 230 K before increasing to 0.2 % high at 270 K and then decreasing to 0.1 % low at 300 K (Fig. 1, 2, 3).

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 9

vapor pressure equations

Phase Solid + Cu1 Solid + Cu2 Liquid + Cu1 Liquid + Cu2 Liquid + Cu1 + Cu2

Table 10

Range (K)

A

B

C

D

E

750 to 1357.77 750 to 1357.77 1357.77 to 2900 1357.77 to 2900 1357.77 to 2900

19.46614 30.09721 22.99791 40.82706 27.49394

0.492555 1.43018 1.05184 2.98759 1.67598

40,737.3 58,193.6 39,893.5 56,666.0 40,324.0

1.240229104 2.728839104 3.225689104 2.904659104 7.598799105

4.490659108 7.821489108 +3.690309108 +3.218709108 +3.076339108

Low-temperature specific heat equations: 30 to 298.15 K

Range 30 to 50 K Cpo ðJ/mol KÞ ¼ 4:137880:457798T þ 1:73771  102 T 2  1:81035  104 T 3 þ 6:57663  107 T 4 Range 50 to 70 K Cpo ðJ/mol KÞ ¼ 3:44481 þ 2:71874  102 T þ 5:82694  103 T 2  5:92990  105 T 3 þ 1:76354  107 T 4 Range 70 to 100 K Cpo ðJ/mol KÞ ¼ 11:52550 þ 0:418850T  1:13549  103 T 2  5:92034  106 T 3 þ 2:93875  108 T 4 Range 100 to 200 K Cpo ðJ/mol KÞ ¼ 15:14608 þ 0:577212T  3:639869  103 T 2 þ 1:12101  105 T 3  1:363615  108 T 4 Range 200 to 298.15 K Cpo ðJ/mol KÞ ¼ 6:33481 þ 0:162424T  5:78862  104 T 2 þ 9:95052  107 T 3  6:62868  1010 T 4

Table 11

High-temperature representative equations

Solid: 298.15 to 1357.77 K Cpo ðJ/mol KÞ ¼ 23:55055 þ 6:89498  103 T  2:95229  106 T 2 þ 1:78088  109 T 3  84616:4=T 2 o 3 2 7 3 10 4 HTo  H298:15 T þ 84616:4=T  7589:27 K ¼ 23:55055T þ 3:44749  10 T  9:85097  10 T þ 4:45220  10 o 3 6 2 ST ðJ/mol KÞ ¼ 23:55055 lnðT Þþ6:89498  10 T  1:477645  10 T þ 5:93627  1010 T 3 þ 42308:2=T 2  103:4651 Liquid: 1357.77 to 2900 K Cpo ðJ/mol KÞ ¼ 33:52 o HTo  H298:15 K ðJ=molÞ ¼ 33:52T  2699:24 o ST ðJ/mol KÞ ¼ 33:52 lnðT Þ  157:6884

Table 12

Free energy equations above 298.15 K

Solid: 298.15 to 1357.77 K o 3 2 7 3 10 4 GoT  H298:15 T þ 42308:2=T  23:55055T lnðT Þ  7589:27 K ðJ/molÞ ¼ 127:01565T  3:44749  10 T þ 4:925483  10 T  1:484066  10 Liquid: 1357.77 to 2900 K o GoT  H298:15 K ðJ/molÞ ¼ 191:2084T  33:52T lnðT Þ  2699:24

Table 13 Transition Fusion

Transition values involved with the free energy equations T (K)

o DHM (J/mol)

o DSM (J/mol K)

1357.77

12,961.000

9.5458

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

429

Table 14

Deviations of low-temperature specific heat measurements

Authors

Ref.

Schmitz Nerst Keesom and Kammerlingh Onnes Griffiths and Griffiths Keesom and Kammerlingh Onnes Denizot Eucken and Werth Dockerty Maier and Anderson

[182] [183] [184]

Temperature range (K)

% Deviations from the selected values

188 and 333 23.5 to 88 15.2 to 21.5

7.3 high and 0.3 high, respectively Initially 19.0 high then scatters 3.3 low to 2.6 high Trends 6.4 high to 1.8 low at 20.9 K and 0.8 high at 21.5 K

[181,186,187] 138 to 371 [188] 14.5 to 89

Trends 4.8 high to 0.2 high at 337 K then increases to 0.6 high at 371 K Scatters 3.9 low to 2.2 high

[189] [190] [191] [192]

170 to 370 84 to 215 201 to 299 53 to 294

Kok and Keesom Dockerty

[193] [194]

1.2 to 19.6 29 to 194

Aoyama and Kanda Giauque and Meads Eder Sandenaw

[195] [196] [197] [198]

82 to 273 14.7 to 300 90 and 300 5 to 298

Martin

[74]

20 to 300

Franck et al. Martin Martin Du Chatenier and De Nobel Gmelin and Gobrecht Boerstoel et al. Cetas et al. Zrudsky et al. Novotny and Meinke Alexandrov et al.

[23] [199] [36] [25]

0.4 to 30 16 to 90 3 to 30 1 to 30

Scatters 0.3 high to 1.9 high First run: trends 0.3 low to 1.1 high; Second run: scatters 1.7 low to 0.7 high Average 0.1 low First run: scatters 1.3 low to 1.9 high; Second run: initially 3.4 high then scatters 1.5 low to 1.4 high First run: above 2.3 K scatters 1.1 low to 9.7 high; Second run: scatters 0.6 low to 7.3 high Initially 1.1 low increasing to 2.4 high at 43 K then decreasing to 0.2 low at 103 K then averaging 0.2 high above 144 K Initially trends 0.6 high to 2.0 low at 105 K then increases to average 2.0 high above 145 K Initially trends 6.5 low to 1.9 high at 33.5 K then decreases to average 0.4 high above 75 K First run: 24.3 low and exact, respectively; Second run: 24.9 low and 3.8 high, respectively Initially 33.0 high then scatters 4.4 low to 5.3 high to 80 K then averages 0.7 high above 80 K First run: trending initially 2.5 high to 0.6 low at 70 K then averaging 0.1 high above 90 K; Second run: trending initially 1.3 high to 0.3 low at 70 K then averaging 0.2 high above 90 K; Third run: trending initially 2.1 high to 0.4 low at 75 K then averaging 0.2 high above 90 K Above 3 K scatters 0.3 low to 0.7 high Trends 1.6 high to 1.1 low at 60 K increasing to 0.4 high at 90 K Trends from initially 0.7 low to 0.9 high at 27 K decreasing to 0.2 low at 30 K Averages 4.0 high

[42] [43] [46] [54] [57] [60]

2 to 30 1 to 30 1.0 to 33 1 to 14 1.5 to 15 2.3 to 331

Collocott

[63]

2 to 20

Trends from initially 0.3 high to 0.1 low at 14 K increasing to 1.2 high at 30 K Trends from initially 0.2 high to 0.1 low at 13 K increasing to 0.9 high at 30 K Scatters 0.7 low to 0.3 high; average 0.1 low above 4 K Average 0.4 high Trends 0.1 high to 0.6 low Trends from initially 0.2 high at 2.3 K to 2.4 low at 11 K increasing to 1.1 high at 29 K then decreasing to 0.8 low at 54 K before increasing to 0.7 high at 184 K then decreasing to 0.7 low at 331 K Initially 0.3 low but increases to average of 0.3 high above 5 K

2.4 Range 298.15 to 1357.77 K The precision low-temperature specific heat measurements extending to 400 K dictate the behaviour of the specific heat curve in the high-temperature region. The measurements above 298.15 K of Bronson et al.[70] (267 to 380 K), Robie et al.[66] (15.4 to 379 K) and Stevens and Boerio-Goates[68] (6.6 to 398 K) were combined with selected values from the specific heat measurements of Pawel and Stansbury[76] (363 to 883 K), Yeh and Brooks[77] (370 to 1073 K) and Dobrosavljevic´ and Maglic´[78] (300 to 1300 K), leading to a specific heat equation which has an overall accuracy as a standard deviation of ± 0.028 J/mol K (0.10 %). The equivalent enthalpy equation is given as

430

HoT  Ho298:15 K ðJ/molÞ ¼ 23:55055T þ 3:44749  103 T 2  9:85097  107 T 3 þ 4:45220  1010 T 4

ðEq 2Þ

þ 84616:4=T  7589:27: On a specific heat basis, the selected values of Hultgren et al[9] differ from the present selected values by trending to 1.8 % low at 1000 K and then increasing sharply to 4.6 % high at the freezing point, whilst also on the same basis the selected values of CODATA (Cox et al.[12]) trend to 1.9 % low at 900 K and increase to 3.0 % high at the freezing

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 15

Deviations of high-temperature solid specific heat measurements

Authors

Ref.

Temperature range (K)

Tilden and Perry Jaeger and Diesselhorst Kahlbaum et al. Gaede Nerst et al. Harper Klinkhardt Bronson and Chisholm Seekamp Dockerty Sykes Honda and Tokunaga Quinney and Taylor Thomas and Davis Avramescu Fo¨rster and Tschentke Persoz Trice et al. Picklesimer Lucks and Deem Butler and Inn Bell Lyusternik Lehman Howse et al. Jenkins and Parker Masudaa

[200] [201] [202] [203] [204] [205,206] [207] [208] [209] [191] [210] [211] [212] [213] [214] [215] [216] [217] [218] [219,220] [221] [222] [223] [224] [225] [226] [227]

291 291 273 290 276 288 373 293 291 299 369 298 373 293 373 293 287 603 373 273 337 288 323 421 366 295 473

Kraftmakher Brooks et al. Vollmer and Kohlhaas Chekhovskoi and Gerasinab Chernenko and Ivon

[228] [229] [92] [230] [231]

500 313 300 295 415

and 373 to 293 to 365 to 295 to 323 to 1073 to 553 to 973 to 389 to 834 to 713 to to to to to to to to to

1273 1173 640 794 1183 1339 946 701 1273

to 544 to 973 to to to to

1250 1193 1357 903

% Deviations from the selected values 1.3 high 0.6 low and 2.9 low, respectively 1.9 high at average temperature 283 K Average 0.5 low 0.1 low at average temperature 285 K Average 0.2 low Average 0.3 high Scatters 0.4 low to 0.7 high Trends 1.0 low to 0.3 low above 373 K Average 0.1 low Trends 5.1 high to 0.9 low 1.5 low Scatters 7.5 low to 1.3 high 0.1 low Trends 0.5 low to 7.9 high Scatters 0.2 high to 1.4 high Scatters 0.8 low to 1.1 high Trends 4.4 low to 13.3 high Above 403 K trends 8.7 low to 3.6 low Trends 3.8 high to 1.8 low at 700 K to 8.2 high at 1339 K Scatters 1.6 low to 2.7 high Scatters 2.4 low to 3.0 high Trends 1.0 low to 1.4 high at 773 K to average 2.2 high above 873 K 4.9 low Trends 1.2 low to 6.0 low 5.7 high First run: trends 19.0 high initially to 1.0 high at 613 K then increasing to average 17.2 high above 753 K; Second run: average 17.8 high Trends 1.4 low to 2.5 high Trends 0.5 low to 3.9 high Trends 0.7 low to 0.6 high at 1050 K to then converge to selected values Scatters up to 2.4 low 3.0 low

(a) Data shown graphically—actual data points given by Touloukian and Buyco[232] (b) Actual data points given by Chekhovskoi and Tarasov[104]

point. Other reviews such as those of White and Collocott,[10] White and Minges[13] and JANAF (Chase[14]) accepted the high-temperature values of Hultgren et al.[9] Derived high-temperature thermodynamic data are included in Table 19. The deviations of other specific heat measurements not included in the evaluation for the solid are considered in Table 15, whilst the deviations of enthalpy values are considered in Table 16 except for the lowtemperature mean specific heat measurements of Richards and Jackson[79] (85 to 293 K), Koref[80] (83 to 190 K and 197 to 275 K), Dewar[81] (20 to 177 K) and Boosz[82] (83 to 298 K). 2.5 Comparison of Selected Values at 298.15 K The comparison is given in Table 2. The selected values of Hultgren et al.[9] and JANAF (Chase[14]) at 298.15 K were basically the values of Furukawa et al.,[8] whilst

CODATA (Cox et al.[12]) also considered the measurements of Robie et al.[66] The present evaluation is based on newer specific heat measurements, leading to distinctly lower values of both enthalpy and entropy.

3. Liquid Phase 3.1 Enthalpy of Fusion The procedure adopted by Stølen and Grønvold[83] is accepted in that no values are rejected but are given a percentage uncertainty (P) which is combined with the enthalpy of fusion (DHM) to give a weight W1 = DHMP/ 100. The contribution of each data point to the total is then 2 of these are given by W2 = DH P PM/W1, and the summations given by XA = W2 and XB = 1/W21. The weighted

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

431

Table 16

Deviations of solid enthalpy measurements

Authors

Ref.

Tilden Glaser Magnus Schimpff Schu¨bel

[233] [85] [234] [235] [236]

288 to 373 296 to 1278 288 to 611 83 to 373 291 to 904

Wu¨st et al. Doerinckel and Werner Umino Roth and Bartram Ruer and Kremers Jaeger et al. Bronson et al.

[86] [237] [87] [238] [239] [240] [70]

273 291 273 293 293 273 255

Esser et al. Fieldhouse et al. Neel et al. Booker et al. Novikov et al. Chekhovskoi and Tarasov Cagran et al.

[88] [241] [242] [243] [98] [104] [103]

273 to 1273 811 to 1311 545 to 1123 690 to 1213 273 to 1355 1262 to 1308 1100 to 1357

Table 17

Temperature range (K)

to to to to to to to

% Deviations from the selected values Mean Cp: 1.1 low at 373 K 8.6 high at 1165 K and 3.7 high at 1278 K 0.4 low at 511 K and 1.1 low at 611 K Mean Cp: 290 to 373 K: 0.9 low at 373 K Trends 1.3 low initially to 0.3 low at 477 K to 1.9 low at 679 K to 0.1 high at 904 K Trends 6.7 high initially at 373 K to 1.6 low at 1273 K to 0.4 low at 1343 K Trends average 2.0 low initially at 505 K to average 0.8 low above 601 K Trends to 6.2 high at 1323 K Scatters 0.1 low to 1.1 low; average 0.7 low Scatters 0.1 to 1.7 low; average 1.1 low Trends 0.4 low to 1.5 low First run: Trends 0.4 low to 0.8 low; Second run: 0.1 low to average 0.4 low above 508 K Trends 2.0 high to 0.4 low Trends 4.2 low to 0.6 low Scatters 3.8 low to 1.4 high Trends 3.4 low to 1.2 low Trends 3.2 low at 320 K to 1.2 high at 579 K then averages 1.1 low above 674 K Three data points 0.2 low, 1.2 high and 1.7 low Trends 6.9 low to 5.3 low

1343 K 1086 1323 973 1123 1232 774

Deviations of liquid enthalpy measurements

Authors Glaser (1904) Wu¨st et al. (1918) Umino (1926) Esser et al. (1933) Chaudhuri et al. (1970) Bonnell (1972) Stevens (1974) Stretz and Bautista (1974) Kuntz and Bautista (1976) Novikov et al. (1976) Dokko and Bautista (1980) Gathers (1983) Pottlacher et al. (1993) Chekhovskoi et al. (2000) Cagran et al. (2006)

Ref.

Temperature range (K)

[85] [86] [87] [88] [109] [110] [111] [105] [106] [98] [112] [244] [94] [101,102] [103]

average value is then DHM = XA/XB, and the standard deviation of the fit is r = 1/XB. In Table 3 the first 12 values, which were also given by Stølen and Grønvold,[83] have been independently assessed, but the assigned percentage uncertainties are those selected by the latter. For the remaining values the percentage uncertainties were assigned in the present evaluation. Based on more limited data sets, Hultgren et al.[9] selected an enthalpy of fusion of 13.05 ± 0.4 kJ/mol, CODATA (Cox et al.[12]) 13.14 kJ/mol

432

1354 1373 1373 1373 1386 1387 1428 1358 1700 1372 1415 2000 1657 1451 1357

and 1359 to 1573 to 1773 and 1473 to 1887 to 1889 to 2007 to 2061 to 2000 to 1520 to 2048 to 4500 to 2000 to 1986 to 2000

% Deviations from the selected values 4.4 high and 0.2 high, respectively Averages 1.3 low Trends 5.2 high to 3.2 high 0.7 high and 0.2 low, respectively Scatters 3.1 low to 1.3 high Scatters 1.5 low to 3.3 high Scatters 4.7 low to 6.7 high Trends to 1.1 low Averages 0.3 low Averages 1.1 low Averages 3.4 low Trends to 5.5 low Averages 0.9 low Shows scatter but averages 3.2 high Averages 0.3 high

and JANAF (Chase[14]) 13.14 ± 0.4 kJ/mol, which compare favourably with the selected value of 12.961 ± 0.128 kJ/mol. 3.2 Enthalpy and Specific Heat Values for the Liquid The enthalpy of the solid at the freezing point combined with the selected enthalpy of fusion leads to a fixed value of o 42,813 ± 131 J/mol for the enthalpy HTo  H298:15 K of the

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 18

Low-temperature thermodynamic properties

Temperature (K) 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15

Cpo (J/mol K)

HTo  H0oK (J/mol)

STo (J/mol K)

ðGTo  H0oK Þ (J/mol)

ðGTo  H0oK Þ=T (J/mol K)

0.00943 0.0555 0.184 0.461 0.956 1.688 2.627 3.727 4.926 6.172 8.640 10.905 12.888 14.586 16.023 17.229 18.249 19.111 19.844 20.470 21.007 21.474 21.883 22.245 22.565 22.842 23.094 23.322 23.53 23.72 23.894 24.053 24.101 24.2 24.335 24.439

0.0161 0.155 0.707 2.241 5.687 12.20 22.90 38.73 60.33 88.07 162.3 260.2 379.4 517.0 670.2 836.7 1014 1201 1396 1598 1805 2018 2234 2455 2679 2906 3136 3368 3602 3839 4077 4316 4392 4558 4800 4999

0.00546 0.0230 0.0660 0.152 0.304 0.539 0.868 1.289 1.796 2.380 3.725 5.230 6.819 8.438 10.051 11.637 13.181 14.676 16.120 17.511 18.850 20.138 21.377 22.570 23.720 24.827 25.896 26.927 27.925 28.889 29.823 30.728 31.007 31.605 32.457 33.133

0.0112 0.0746 0.283 0.807 1.916 3.988 7.466 12.82 20.50 30.91 61.26 105.9 166.1 242.4 334.9 444.4 567.5 706.8 860.9 1029 1211 1406 1613 1833 2065 2308 2561 2825 3100 3384 3677 3980 4077 4292 4612 4879

0.00223 0.00746 0.0189 0.0403 0.0766 0.133 0.213 0.320 0.456 0.618 1.021 1.513 2.077 2.694 3.349 4.031 4.729 5.437 6.149 6.860 7.568 8.270 8.964 9.649 10.324 10.988 11.642 12.284 12.915 13.535 14.143 14.741 14.927 15.328 15.904 16.365

liquid at the freezing point. A value for the specific heat of the liquid is then derived from measurements of the enthalpy, where values were fitted to the equation o HTo  H298:15 K = AT + B, with the specific heat value derived as the constant A. Apart from the measurements of Stretz and Bautista[105] and Kuntz and Bautista,[106] which were given only in the form of equations, all other values in Table 4 were recalculated to derive the constants A and B. Because of the equations, no attempt was made to correct other selected values to ITS-90 from the likely temperature scale IPTS-68, since such correction would amount to less than 1 K up to 2650 K (Rusby et al.[6]). The combination of the selected specific heat value with the selected value of the enthalpy at the freezing point leads to the enthalpy equation HoT  Ho298:15 K ðJ/molÞ ¼ 33:52T  2699:24:

ðEq 3Þ

Derived thermodynamic properties to 2900 K are given in Table 19. The derived specific heat value of 33.52 ± 1.90 J/(mol K) can be compared with other, directly determined values. Vollmer and Kohlhaas[92] (1357 to 1500 K) obtained 32.2 J/(mol K), whilst Akhmatova[107] (1463 to 1638 K) reported the results only as thermal capacity in J/cm3C, which can be interpreted as a variable specific heat of 26.0 to 29.7 J/mol K. Graphical values of Mardykin and Filippov[108] (1390 to 1730 K) also show a trend but can be averaged to 28.0 J/(mol K). Lower values of liquid specific heat compared with Eq 3 were selected in other reviews, with Hultgren et al.[9] selecting 32.64 J/(mol K), JANAF (Chase[14]) 32.84 J/(mol K) and CODATA (Cox et al.[12]) 32.80 J/(mol K), where in the latter two cases most weight was given to the obsolete measurements of Chaudhuri et al.,[109] which were superseded by the later measurements of Bonnell.[110] The

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

433

Table 19

High-temperature thermodynamic properties

Temperature (K) 298.15 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1357.77 1357.77 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

Cpo (J/mol K)

o HTo  H298:15 K (J/mol)

STo (J/mol K)

o ðGTo  H298:15 K Þ=T (J/mol K)

24.439 24.462 24.987 25.421 25.799 26.143 26.465 26.773 27.072 27.367 27.660 27.955 28.253 28.556 28.867 29.187 29.517 29.860 30.216 30.588 30.976 31.382 31.808 31.876 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520 33.520

0 45.2 1282 2542 3823 5122 6437 7768 9114 10,475 11,851 13,241 14,646 16,067 17,502 18,954 20,421 21,905 23,407 24,927 26,466 28,025 29,605 29,852 42,813 44,229 47,581 50,933 54,285 57,637 60,989 64,341 67,693 71,045 74,397 77,749 81,101 84,453 87,805 91,157 94,509

33.133 33.284 37.096 40.461 43.478 46.214 48.721 51.037 53.192 55.209 57.107 58.902 60.605 62.229 63.781 65.270 66.702 68.083 69.418 70.711 71.968 73.191 74.383 74.566 84.111 85.138 87.451 89.614 91.646 93.562 95.374 97.094 98.729 100.287 101.779 103.205 104.574 105.888 107.153 108.372 109.549

33.133 33.133 33.433 34.105 34.982 35.970 37.017 38.090 39.170 40.244 41.306 42.350 43.374 44.377 45.357 46.316 47.253 48.169 49.064 49.939 50.795 51.633 52.453 52.579 52.579 53.546 55.730 57.781 59.714 61.542 63.275 64.923 66.495 67.996 69.432 70.810 72.133 73.406 74.633 75.816 76.959

deviations of liquid enthalpy values from the selected equation are given in Table 16.

et al.[114,115] The thermodynamic properties were calculated using the method of Kolsky et al.[116] and the 2010 Fundamental Constants (Mohr et al.[117,118]), and derived thermodynamic values are listed in Table 20.

4. Gas Phase

4.2 Thermodynamic Properties of the Diatomic Gas

4.1 Thermodynamic Properties of the Monatomic Gas Selected values are based on 59 energy levels below 60,000 cm1, which consist of 53 levels selected by Sugar and Musgrove,[113] of which 18 levels were revised by Civis et al.,[114,115] plus a further six levels measured by Civis

434

The thermodynamic properties were calculated by Rand[119] from six energy levels, which include the five energy levels, X1R+g , A1R+u , B1R+u , CPu and J, for which full spectroscopic constants are available (Morse,[120] Page and Gudeman[121] and Ram et al.[122]), and a sixth level, a 3R+u , for which the constants xexe, Be, ae and De were estimated

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 20

Thermodynamic properties of the monatomic gas

Temperature (K) 298.15 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1357.77 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

Cpo (J/mol K)

o HTo  H298:15 K (J/mol)

STo (J/mol K)

o ðGTo  H298:15 K Þ=T (J/mol K)

20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.786 20.787 20.787 20.789 20.790 20.793 20.797 20.804 20.812 20.813 20.823 20.856 20.909 20.985 21.091 21.231 21.407 21.622 21.878 22.173 22.508 22.878 23.282 23.716 24.174 24.653

0 38.5 1078 2117 3156 4196 5235 6274 7314 8353 9392 10,432 11,471 12,510 13,549 14,589 15,628 16,668 17,707 18,747 19,786 20,826 21,867 22,028 22,908 24,991 27,080 29,174 31,278 33,393 35,525 37,676 39,851 42,053 44,287 46,556 48,863 51,213 53,607 56,049

166.398 166.527 169.731 172.506 174.955 177.145 179.126 180.934 182.598 184.139 185.572 186.914 188.174 189.362 190.486 191.553 192.567 193.534 194.458 195.343 196.192 197.008 197.793 197.912 198.550 199.988 201.335 202.605 203.807 204.951 206.044 207.094 208.106 209.084 210.035 210.961 211.866 212.753 213.624 214.480

166.398 166.398 166.651 167.214 167.940 168.753 169.608 170.477 171.346 172.206 173.050 173.875 174.679 175.462 176.224 176.964 177.683 178.381 179.061 179.721 180.363 180.987 181.595 181.688 182.187 183.327 184.410 185.444 186.431 187.376 188.282 189.153 189.992 190.801 191.582 192.339 193.073 193.785 194.478 195.153

o o H298:15 K  H0 K 6197:4 J/mol

by Rand.[119] Derived thermodynamic data are given in Table 21. 4.3 Enthalpy of Sublimation of the Monatomic Gas For values given in the form of the Clausius–Clapeyron equation a ‘‘pseudo’’ Third Law value was calculated by evaluating the enthalpy of sublimation at the temperature extremes and then averaging. Because of a general lack of detail as to which temperature scales were used, no attempt was made to correct vapor pressure measurements to ITS-90

from what would have been contemporary scales. Only high-temperature boiling point determinations were corrected for the presence of the diatomic gas. Values are summarised in Tables 5, 6, and 7. The measurements in the liquid range by Chegodaev et al.[123] were not included since no specific temperature range was given. The selected value is an average of values given in Table 7. The first eight values were also selected by CODATA (Cox et al.[12]) to give an average of 337.4 ± 1.2 kJ/mol. Attention should be paid to the measurements of Severin et al.[122] using graphite crucibles,

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

435

Table 21

Thermodynamic properties of the diatomic gas

Temperature (K) 298.15 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1357.77 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

Cpo (J/mol K)

o HTo  H298:15 K (J/mol)

STo (J/mol K)

o ðGTo  H298:15 K Þ=T (J/mol K)

36.578 35.591 36.888 37.099 37.259 37.384 37.488 37.575 37.652 37.721 37.783 37.841 37.895 37.946 37.995 38.043 38.088 38.133 38.176 38.219 38.261 38.303 38.344 38.350 38.385 38.468 38.553 38.644 38.743 38.855 38.985 39.140 39.325 39.548 39.815 40.133 40.508 40.947 41.454 42.035

0 67 1905 3755 5614 7480 9352 11,228 13,109 14,993 16,881 18,772 20,665 22,561 24,460 26,361 28,264 30,169 32,077 33,987 35,899 37,813 39,729 40,027 41,648 45,490 49,341 53,201 57,070 60,950 64,842 68,748 72,671 76,614 80,582 84,579 88,611 92,683 96,802 100,976

241.619 241.845 247.510 252.450 256.829 260.761 264.329 267.595 270.606 273.399 276.003 278.444 280.739 282.907 284.960 286.910 288.767 290.540 292.236 293.862 295.423 296.424 298.371 298.591 299.766 302.417 304.902 307.242 309.454 311.552 313.548 315.453 317.278 319.031 320.720 322.351 323.933 325.469 326.968 328.432

241.619 241.620 242.066 243.062 244.353 245.801 247.325 248.880 250.437 251.979 253.495 254.979 256.427 257.838 259.212 260.549 261.849 263.113 264.343 265.539 266.703 267.837 268.941 269.111 270.017 272.090 274.064 275.947 277.748 279.472 281.127 282.716 284.246 285.721 287.144 288.520 289.851 291.142 292.395 293.613

o o H298:15 K  H0 K 9926 J/mol

which gave extremely close agreement for Second Law and Third Law values for both the solid and liquid phases, but the derived enthalpy of sublimation value is 9.4 kJ/mol lower than the agreement obtained for the selected values. 4.4 Enthalpy of Dissociation of the Diatomic Gas For silver, Franzreb et al.[173] showed that there was a variation of the ionization cross section ratio rAg2/rAg1 with the experimental ionizing energies. However, it is uncertain

436

whether the same ratios can be applied to copper, and therefore a default ratio rCu2/rCu1 = 1.5 (Drowart and Goldfinger[174]) was adopted for all measurements. Values are summarised in Table 8, where the selected value is based on the measurements of Schissel,[175] Ackerman et al.[176] and Wilhite.[177] However, because the number of data points (N) determined by Wilhite[177] (N = 31) overwhelms the number determined by Schissel[175] (N = 10) and Ackerman et al.[176] (n = 6), it is considered that weighting as N would introduce a bias into the selected

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

Table 22

Vapor pressure Monatomic gas

T (K)

p (bar)

298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1357.77 1357.77 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

7.6991053 1.7891052 8.3191038 5.1291029 3.6391023 5.3891019 7.1491016 1.8991013 1.6391011 6.1691010 1.269108 1.619107 5.919107 5.919107 1.389106 8.379106 4.049105 1.619104 5.479104 1.639103 4.339103 1.059102 2.329102 4.809102 9.329102 0.171 0.299 0.502 0.809 1.260

Diatomic gas

DGTo (J/mol)

DHTo (J/mol)

p (bar)

DGTo (J/mol)

DHTo (J/mol)

297,466 297,220 283,957 270,809 257,768 244,827 231,980 219,223 206,552 193,966 181,462 169,039 161,900 161,900 157,102 145,805 134,593 123,460 112,400 101,409 90,483 79,618 68,809 58,053 47,346 36,686 26,068 15,489 4946 5562

337,200 337,193 336,775 336,274 335,706 335,078 334,390 333,644 332,835 331,962 331,019 330,001 329,376 316,415 315,879 314,611 313,347 312,089 310,841 309,605 308,384 307,183 306,006 304,856 303,738 302,655 301,611 300,608 299,651 298,740

1.2091075 3.9691075 2.9091054 8.7991042 1.7491033 1.4091027 3.6291023 9.5091020 5.0491017 8.3591015 5.7991013 2.0591011 1.2691010 1.2691010 4.0291010 4.769109 4.099108 2.699107 1.429106 6.229106 2.339105 7.649105 2.239104 5.919104 1.439103 3.229103 6.769103 1.349102 2.519102 4.499102

427,650 427,326 409,991 393,002 376,312 359,889 343,709 327,756 312,015 296,478 281,138 265,989 257,323 257,323 251,837 238,988 226,329 213,850 201,536 189,381 177,372 165,506 153,771 142,162 130,674 119,299 108,033 96,867 85,798 74,819

479,932 479,909 479,602 477,168 475,624 473,974 472,221 470,362 468,422 466,290 464,064 461,695 460,255 434,322 433,122 430,260 427,407 424,563 421,728 418,904 416,092 413,294 410,513 407,752 405,016 402,309 399,637 397,005 394,420 391,890

DH0o (Cu1) 336.002 kJ/mol; DH0o (Cu2) 480.004 kJ/mol

value, and therefore a simple average is selected. The mass spectrometric measurements of Drowart and Honig[178,179] were considered to be preliminary and not included in the evaluation, whilst the measurements of Hilpert and Gingerich[180] are clearly discrepant. Although the values of Hilpert[181] are probably of higher quality, they are based on free energy functions which trend from 0.9 to 1.1 kJ/mol too low, and because of a lack of reported experimental data the measurements could not be corrected.

equilibrium values for liquid and Cu1(g) + Cu2(g) were obtained by combining the two individual equations for the liquid. Values were fitted to the following equation with constants given in Table 9:

4.5 Vapor Pressure Equations

5. Summary of Representative Equations

Values for the solid and Cu1(g) were evaluated at 25-K intervals from 750 to 1350 K and the freezing point. Values for the solid and Cu2(g) were evaluated at 50-K intervals from 750 to 1350 K and the freezing point. Values for the liquid and Cu1(g) and the liquid and Cu2(g) at 50-K intervals from 1400 to 2900 K and the freezing point and

Low-temperature specific heat equations are given in Table 10, and high-temperature representative equations in Table 11. Free energy equations are given in Table 12, and transition values involved with the free energy equations in Table 13.

lnðp; barÞ ¼ A þ B lnðT Þ þ C=T þ DT þ ET 2 :

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

437

Table 23

Equilibrium vapor pressure

Total p (bar)

Cu1 p (bar)

Cu2 p (bar)

T (K)

1015 1014 1013 1012 1011 1010 109 108 107 106 105 104 103 102 101 1 NBP

1.0091015 1.0091014 1.0091013 1.0091012 1.0091011 1.0091010 1.009109 1.009108 1.009107 1.009106 9.999106 9.999105 9.979104 9.939103 9.859102 0.9682 0.9809

5.8291023 1.5191021 3.8691020 9.9891019 2.5491017 6.5091016 1.6591014 4.1791013 1.0591011 2.5991010 6.079109 1.409107 3.209106 7.129105 1.549103 3.189102 3.239102

805 844 887 935 988 1048 1115 1192 1280 1384 1511 1664 1854 2094 2409 2839.77 2842.70

3.

4.

5. 6. 7.

8.

NBP normal boiling point at one atmosphere pressure (1.01325 bar)

9.

6. Deviations from the Selected Values 10.

Deviations of low-temperature specific heat values are given in Table 14, and of the high-temperature specific heat values in Table 15. Deviations of enthalpy measurements for the solid are given in Table 16, and for the liquid in Table 17.

11. 12. 13.

7. Thermodynamic Tables Low-temperature thermodynamic properties of the solid are given in Table 18, and the high-temperature thermodynamic properties of the condensed phases in Table 19. Thermodynamic properties of the monatomic gas are given in Table 20, and of the diatomic gas in Table 21. The vapor pressure summary is given in Table 22, and equilibrium vapor pressure data in Table 23.

14. 15. 16. 17.

Acknowledgments The author is indebted to Malcolm Rand for calculating the thermodynamic properties of the diatomic gas.

18. 19.

References

20.

1. H. Preston-Thomas, The International Temperature Scale of 1990 (ITS-90), Metrologia, 1990, 27, p 3–10 and 107 2. J. Fischer, M. de Podesta, K.D. Hill, M. Moldover, L. Pitre, R. Rusby, P. Steur, O. Tamura, R. White, and L. Wolber, Present Estimates of the Differences Between Thermody-

438

21. 22.

namic Temperatures and the ITS-90, Int. J. Thermophys., 2011, 32, p 12-25 M.E. Wieser, N. Holden, T.B. Coplen, J.K. Bo¨hike, M. Berglund, W.A. Brand, P. De Bie`vre, M. Gro¨ning, R.D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, and X.-K. Zhu, Atomic Weights of the Elements 2011, Pure Appl. Chem., 2013, 85, p 10471078 T.B. Douglas, Conversion of Existing Calorimetrically Determined Thermodynamic Properties to the Basis of the International Practical Temperature Scale of 1968, J. Res. Natl. Bur. Stand., 1969, 73A, p 451-470 R.L. Rusby, The Conversion of Thermal Reference Values to the ITS-90, J. Chem. Thermodyn., 1991, 23, p 1153-1161 R.L. Rusby, R.P. Hudson, and M. Durieux, Revised Values for (t90–t68) from 630C to 1064C, Metrologia, 1994, 31, p 149-153 R.D. Weir and R.N. Goldberg, On the Conversion of Thermodynamic Properties to the Basis of the International Temperature Scale of 1990, J. Chem. Thermodyn., 1996, 28, p 261-276 G.T. Furukawa, W.G. Saba, and M.L. Reilly, Critical Analysis of the Heat-Capacity Data of the Literature and Evaluation of Thermodynamic Properties of Copper, Silver and Gold from 0 to 300 K, Natl. Stand. Ref. Data Ser. Natl. Bur. Stand. NSRDS-NBS 18, 1968 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley, and D.D. Wagman, Selected Values of the Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, 1973 G.K. White and S.J. Collocott, Heat Capacity of Reference Materials: Cu and W, J. Phys. Chem. Ref. Data, 1984, 13, p 1251-1257 A.J. Head and R. Sabbah, Recommended Reference Materials for the Realization of Physiochemical Properties, K.N. Marsh, Ed., Blackwell Scientific, Oxford, 1987, p 219-319 J.D. Cox, D.D. Wagman, and V.A. Medvedev, CODATA Key Values for Thermodynamics, Hemisphere, New York, 1989 G.K. White and M.L. Minges, Thermophysical Properties of Some Key Solids: An Update, Int. J. Thermophys., 1997, 18, p 1269-1327 M.W. Chase Jr., NIST-JANAF Thermochemical Tables, Fourth Edition, J. Phys. Chem. Ref. Data, Monogr. No. 9, 1998 F.G. Brickwedde, H. van Dijk, M. Durieux, J.R. Clement, and J.K. Logan, The 1958 He4 Scale of Temperatures, J. Res. Natl. Bur. Stand, 1960, 64A, p 1-17 N.E. Phillips, Low Temperature Heat Capacity of Metals, CRC Crit. Rev. Solid State Sci., 1972, 2, p 467-553 G.A. Alers, Use of Sound Velocity Measurements in Determining the Debye Temperature of Solids, Physical Acoustics—Principles and Methods, Vol 3, Part B: Lattice Dynamics , W.P. Mason, Ed., Academic, New York, 1965, p 1-42 G.A. Alers, Priv. Commun. to Martin [44] R. Tsumura, M. Chavez, A. Ravex, and J.P. Faure, Specific Heat Measurements of Pure Copper Below One Kelvin, Rev. Mex. Fis., 1986, 32, p 197-209 W.S. Corak, M.P. Garfunkel, C.B. Satterthwaite, and A. Wexler, Atomic Heats of Copper, Silver and Gold From 1K to 5K, Phys. Rev., 1955, 98, p 1699-1707 J.A. Rayne, The Heat Capacity of Cooper Below 4.2K, Aust. J. Phys., 1956, 9, p 189-197 F.D. Manchester, A Cryostat for Measuring Specific Heats Between 1 and 4.2K, Can. J. Phys., 1959, 37, p 989-1001

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

23. J.P. Franck, F.D. Manchester, and D.L. Martin, The Specific Heat of Pure Copper and of Some Copper + Iron Alloys Showing a Minimum in the Electrical Resistance at Low Temperatures, Proc. R. Soc. Lond. A, 1961, 263, p 494-507 24. F.J. Du Chatenier and J. De Nobel, Heat Capacities of Some Dilute Alloys, Physica, 1962, 28, p 181-183 25. F.J. Du Chatenier and J. De Nobel, Heat Capacities of Pure Copper and Silver and of Dilute Alloys of Cu, Ag, Zn, Mg and Al with Transition Metals of the First Row at Low Temperatures, Physica, 1966, 32, p 1097-1109 26. B.W. Veal and J.A. Rayne, Heat Capacity of b-CuZn Below 4.2K, Phys. Rev., 1962, 128, p 551-555 27. H.R. O’Neal, The Low Temperature Heat Capacity of Tin and Indium, Thesis, University of California, Lawrence Radiation Laboratory, U.S. Atomic Energy Commission, Rep. UCRL-10426, 1963 28. G.D. Kneip, J.O. Betterton, Jr., and J.O. Scarbrough, Low Temperature Specific Heats of Titanium, Zirconium and Hafnium, Phys. Rev., 1963, 130, p 1687-1692 29. N.E. Phillips, Low Temperature Heat Capacities of Gallium, Cadmium and Copper, Phys. Rev., 1964, 134, p A385-A391 30. G. Ahlers, Some Properties of Solid Hydrogen at Small Volumes, Thesis, University of California, Lawrence Radiation Laboratory, U.S. Atomic Energy Commission, Rep. UCRL-10757, 1963 31. G. Ahlers, Lattice Heat Capacity of Solid Hydrogen, J. Chem. Phys., 1964, 41, p 86-94 32. L.L. Isaacs, Low Temperature Specific Heat of Gold, Silver and Copper, J. Chem. Phys., 1965, 43, p 307-308 33. L.L. Isaacs and T.B. Massalski, Low Temperature Specific Heats of Alloys Based on the Noble Metals, Cu, Ag, and Au, a-Phase Cu-Zn Alloys, Phys. Rev., 1965, 138, p A134-A138 34. M. Dixon, F.E. Hoare, T.M. Holden, and D.E. Moody, The Low Temperature Specific Heats of Some Pure Metals (Cu, Ag, Pt, Al, Ni, Fe, Co), Proc. R. Soc. Lond. A, 1965, 285, p 561-580 35. N.M. Senozan, Similarity Principle and Isotope Effect in Superconducting Indium. II. Low-Temperature Heat Capacity of Niobium, Thesis, University of California, Lawrence Radiation Laboratory, U.S. Atomic Energy Commission, Rep. UCRL-11901, 1965 36. D.L. Martin, Specific Heats of Copper, Silver and Gold Below 30K, Phys. Rev., 1966, 141, p 576-582 37. L.C. Clune and B.A. Green, Jr., Low-Temperature Specific Heats of a-CuSn and a-CuZn Alloys, Phys. Rev., 1966, 144, p 525-528 38. G. Ahlers, Heat Capacity of Copper, Rev. Sci. Instrum., 1966, 37, p 477-480 39. G.A. Sargent, L.L. Isaacs, and T.B. Massalski, Low Temperature Specific Heats of a-Phase Copper-Silver Alloys, Phys. Rev., 1966, 143, p 420-422 40. D.W. Osborne, H.E. Flotow, and F. Schreiner, Calibration and Use of Germanium Resistance Thermometers for Precise Heat Capacity Measurements From 1 to 25K. High Purity Copper for Interlaboratory Heat Capacity Comparisons, Rev. Sci. Instrum., 1967, 78, p 159-168 41. L.L. Isaacs, Priv. Commun. 1967 to Furukawa et al. [8] 42. E. Gmelin and K.H. Gobrecht, Die Prazisionsmessung der Atomware von Reinstkupfer fur Kalorimetrie bei Tiefen Temperaruren, Z. Angew. Phys., 1967, 24, p 21-24 43. B.M. Boerstoel, W.J.J. Van Dissell, and M.B.M. Jacobs, A Cryostat for Heat Capacity Measurements Between 1K and 30K; Specific Heat of Copper, Physica, 1968, 38, p 287-299 44. D.L. Martin, Specific Heats Below 3K of Pure Copper, Silver and Gold, and of Extremely Dilute Gold-TransitionMetal Alloys, Phys. Rev., 1968, 170, p 650-655

45. M. Dixon, F.E. Hoare, and T.M. Holden, The Low-Temperature Specific Heat of Some Nickel-Based Iron and Copper Alloys, Proc. R. Soc. Lond. A, 1968, 303, p 339-354 46. T.C. Cetas, C.R. Tilford, and C.A. Swenson, Specific Heats of Cu, GaAs, GaSb, InAs, and InSb From 1 to 30K, Phys. Rev., 1968, 174, p 835-844 47. Y. Sato, J.M. Sivertsen, and L.E. Toth, Changes in LowTemperature Specific Heats of Cu-Pd Alloys Resulting From Changes in Short-Range Order, Phys. Lett. A, 1968, 28, p 118-119 48. Y. Sato, J.M. Sivertsen, and L.E. Toth, Low-Temperature Specific-Heat Study of Cu-Pd Alloys, Phys. Rev. B, 1970, 1, p 1402-1410 49. D.L. Martin, Specific Heat of Pure Single-Crystal and Polycrystalline Copper Below 3K, Can. J. Phys., 1969, 47, p 1253-1255 50. N. Waterhouse, An Anomaly in the Specific Heat Below 3K of Copper Containing Hydrogen, Can. J. Phys., 1969, 47, p 1485-1491 51. D.W. Bloom, D.H. Lowndes, Jr., and L. Finegold, Low Temperature Specific Heat of Copper: Comparison of Two Samples of High Purity, Rev. Sci. Instrum., 1970, 41, p 690695 52. A.J. Leadbetter and K.E. Wycherley, A Calorimeter for the Range 1 to 30 K the Heat Capacity of Copper and Glycerol Glass, J. Chem. Thermodyn., 1970, 2, p 855-866 53. L.C. Clune and B.A. Green, Jr., Rigid-Band Behaviour in the Specific Heats of PbTl and PbBi Alloys: Electron-Phonon Enhancement Effects, Phys. Rev. B, 1970, 1, p 1459-1467 54. D.R. Zrudsky, W.G. Delinger, W.R. Savage, and J.W. Schweitzer, Specific Heats of a-Phase Cu-Al and Dilute Magnetic Cu-Al(Fe) Alloys, Phys. Rev. B., 1971, 3, p 30253032 55. J.C. Holste, T.C. Cetas, and C.A. Swenson, Effects of Temperature Scale Differences on the Analysis of Heat Capacity Data: The Specific Heat of Copper From 1 to 30 K, Rev. Sci. Instrum., 1972, 43, p 670-676 56. D.L. Martin, L.L.T. Bradley, W.J. Cazemier, and R.L. Snowden, Automatic Calorimetry in the 3-30 K Range. The Specific Heat of Copper, Rev. Sci. Instrum., 1973, 44, p 675-684 57. V. Novotny and P.P.M. Meincke, Calorimetry of Small Samples with Low Thermal Diffusivity, Rev. Sci. Instrum., 1973, 44, p 817-820 58. D.L. Martin, Specific Heats of Copper, Silver and Gold Below 30 K, Phys. Rev. B, 1973, 8, p 5357-5360 59. M. Hurley and B.C. Gerstein, The Low-Temperature Heat Capacity of 1965 Calorimetry- Conference Copper: A Comparison With Previous Results, J. Chem. Thermodyn., 1965, 1974(6), p 787-793 60. V.V. Aleksandrov, A.N. Borzyak and I.I. Novikov, Specific Heat of Copper in the 2.3 to 330 K Temperature Range, V. Sb. Fiz.-Mekh. i Teplofiz. Svoistva Metallov., 1976, 22-31 61. J.G. Park and A.W. Vaidya, Resistive SQUID Calorimetry at Low Temperatures, J. Low Temp. Phys., 1980, 40, p 247-274 62. E. Gmelin and P. Ro¨dhammer, Automatic Low Temperature Calorimetry for the Range 0.3–320 K, J. Phys. E: Sci. Instrum., 1981, 14, p 223-228 63. S.J. Collocott, A Simple Microcomputer-Controlled Calorimeter: The Heat Capacity of Copper, Invar and RbNiCl3, Aust. J. Phys., 1983, 36, p 573-581 64. D.W. Osborne, H.E. Flotow, and F. Schreiner, Precise Low Temperature Calorimetry with Germanium Resistance Thermometers, Ann. Acad. Sci. Fenn. Ser. A. VI, 1966, 210, p 3539

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

439

65. S.E. Buravoi, E.A. Bogomazov, and V.A. Samoletov, Measurement of the Heat Capacities of Materials at Cryogenic Temperatures During Heating and Cooling, Izv. Vyssh. Uchebn. Zaved. Priborostr., 1988, 31(12), p 74-78 66. R.A. Robie, B.S. Hemingway, and W.H. Wilson, The Heat Capacities of Calorimetry Conference Copper and of Muscovite, Pyrophyllite and Illite between 15 and 375 K and Their Standard Entropies at 298.15 K, J. Res. U.S. Geol. Surv., 1976, 4, p 631-644 67. D.L. Martin, ‘‘Tray’’ Type Calorimeter for the 15-300 K Temperature Range: Copper as a Specific Heat Standard in This Range, Rev. Sci. Instrum., 1987, 58, p 639-646 68. R. Stevens and J. Boerio-Goates, Heat Capacity of Copper on the ITS-90 Temperature Scale Using Adiabatic Calorimetry, J. Chem. Thermodyn., 2004, 36, p 857-863 69. M.R. Bissengaliyeva, D.B. Gogol, S.T. Taymasova, and N.S. Bekturganov, Measurement of Heat Capacity by Adiabatic Calorimetry and Calculation of Thermodynamic Functions of Standard Substances: Copper, Benzoic Acid and Heptane (For Calibration of an Adiabatic Calorimeter), J. Chem. Eng. Data, 2011, 56, p 195-204 70. H.L. Bronson, H.M. Chisholm, and S.M. Dockerty, On the Specific Heats of Tungsten, Molybdenum and Copper, Can. J. Res., 1933, 8, p 282-303 71. D.G. Archer, Enthalpy Increment Measurements for NaCl (cr) and KBr (cr) from 4.5 K to 350 K. Thermodynamic Properties of the NaCl + H2O System, J. Chem. Eng. Data, 1997, 42, p 281-292 72. P. Berge and G. Blanc, Calorime`tre adiabatique, J. Phys. Radium, 1969, 21(7), p 129A-133A 73. I.V. Chapman, J.G. Pronko, T.T. Bardin, T.R. Fisher, J.D. Perez, and L. Senbetu, Specific-Heat Measurements on HighTc Superconductors Using Accelerated Ions as the Heat Pulse, Nucl. Instrum. Methods Phys. Res. B, 1989, 40(41), p 1088-1092 74. D.L. Martin, The Specific Heat of Copper From 20 to 300K, Can. J. Phys., 1960, 38, p 17-24 75. D.B. Downie and J.F. Martin, An Adiabatic Calorimeter for Heat-Capacity Measurements Between 6 and 300 K. The Molar Heat Capacity of Aluminium, J. Chem. Thermodyn., 1980, 12, p 779-786 76. R.E. Pawal and E.E. Stansbury, The Specific Heat of Copper, Nickel and Copper-Nickel Alloys, J. Phys. Chem. Solids, 1965, 26, p 607-613 77. C.C. Yeh and C.R. Brooks, The Heat Capacity of Platinum From 350 to 1200 K: Experimental Data and an Analysis of Contributions, High Temp. Sci., 1973, 5, p 403-413 78. A.S. Dobrosavljevic´ and K.D. Maglic´, Heat Capacity and Electrical Resistivity of Copper Research Material for Calorimetry, High Temp. High Pressures, 1991, 23, p 129133 79. T.W. Richards and F.G. Jackson, The Specific Heat of the Elements at Low Temperatures, Z. Physik. Chem., 1910, 70, p 414-451 80. F. Koref, Messungen der Spezifischen Wa¨rme bei tiefen Temperaturen mit dem Kupferkalorimeter, Ann. Phys., 1911, 341, p 49-73 81. J. Dewar, Atomic Specific Heats Between the Boiling Points of Nitrogen and Hydrogen. I. The Mean Atomic Specific Heats at 50º Absolute of the Elements a Periodic Function of the Atomic Weights, Proc. R. Soc. Lond. A, 1913, 89, p 158169 82. H.J. Boosz, Die Mittleren Spezifischen Wa¨rmen von Hartmetallen zwischen Zimmertemperaturen und - 190C, Metallics, 1957, 11, p 22-23

440

83. S. Stølen and F. Grønvold, Critical Assessment of the Enthalpy of Fusion of Metals Used as Enthalpy Standards at Moderate to High Temperatures, Thermochim. Acta, 1999, 327, p 1-32 84. J.W. Richards, The Specific Heats of the Metals, J. Franklin Inst., 1893, 136, p 37-53 85. F. Glaser, Schmelzwa¨rmen—und Spezifische Wa¨rmebestimmungen von Metallen bei Ho¨heren Temperaturen, Metallurgie, 1904, 1, p 121-128 86. F. Wu¨st, A. Meuthen, and R. Durrer, Die TemperaturWa¨rmeinhaltskurven der Technisch Wichtigen Metalle, Forsch. Gebiete Ingenieurw., 1918, 204, p 1-63 87. S. Umino, On the Latent Heat of Fusion of Several Metals and Their Specific Heats at High Temperatures, Sci. Rep. Toˆhuku Univ., 1926, 15, p 597-617 88. H. Esser, R. Averdieck, and W. Grass, Wa¨rmeinhalt einiger Metalle, Legierungen und Schlackenbildner bei Temperaturen bis 1200º, Arch. Eisenhuttenw., 1933, 6, p 289-292 89. W. Oelsen, E. Schu¨rmann, and D. Buchholz, Kalorimetrie und Thermodynamik der Kupfer- Wismut-Legierungen, Arch. Eisenhuttenw., 1961, 32, p 39-46 90. E. Schu¨rmann and A. Kaune, Kalorimetrie und Thermodynamik der Kupfer-Blei- Legierungen, Z. Metallkde, 1965, 56, p 453-461 91. R.N. Dokken and J.F. Elliott, Calorimetry at 1100º to 1200C: The Copper-Nickel, Copper-Silver, Copper-Cobalt Systems, Trans. Met. Soc. AIME, 1965, 233, p 1351-1358 92. O. Vollmer and R. Kohlhaas, Die Atom- und Schmelzwa¨rme von Kupfer, Silber und Gold, Z. Metallkde, 1968, 59, p 273277 93. N.A. Nedumov, Metals and Alloys, Differential Thermal Analysis, R.C. Mackenzie, Ed., Academic, New York, London, 1970, p 161-191 94. G. Pottlacher, E. Kaschnitz, and H. Ja¨ger, Investigations of Thermophysical Properties of Liquid Metals With a Rapid Resistive Heating Technique, J. Non-Cryst. Solids, 1993, 156-158, p 374-378 95. M. Baricco, L. Battezzati, and P. Rizzi, Calorimetric Measurements on Some Undercooled Metals and Alloys, J. Alloys Compd., 1995, 220, p 212-216 96. K.K. Kelley, Contributions to the Data on Theoretical Metallurgy. V. Heats of Fusion of Inorganic Substances, U.S. Bur. Mines Bull. 393, 1936 97. M.W. Nathan and M. Leider, Studies of Bismuth Alloys. I. Liquidus Curves of the Bismuth-Copper, Bismuth-Silver and Bismuth-Gold Systems, J. Phys. Chem., 1962, 66, p 20122015 98. I.I. Novikov, V.V. Roshchupkin, and L.K. Fordeeva, The Enthalpy and Heat Capacity of Copper in Melting, FizikoMekhanicheskie i Teplofizicheskie Svoistva Metallov (The Physicochemical and Thermal Properties of Metals), I.I. Novikova, N.N. Rykalin, and I.I. Novikov, Ed., Nauka, Moscow, 1976, p 90-96 99. E.V. Orlik and G.I. Petrunin, Apparatus for the Determination of the Enthalpy of Fusion and Thermal Parameters of Compounds in the Temperature Range 800–2000 K, Vest. Mosk. Univ. Ser. 3 Fiz. Astron., 1981, 22(4), p 69-71 100. N.A. Kanaev, S.V. Lebedev, A.I. Savvatimskii, N.V. Stepanova, and B.A. Fochenkov, Electrical Resistivity and Enthalpy of Solid and Molten Copper, Brasses and Bronzes, Izv. Akad. Nauk SSSR Metally, 1989, 3, p 48-55, Russian Metallurgy—Metally, 1989 (3), 45-52 101. V.Y. Chekhovskoi, V.D. Tarasov, and YuV Gusev, Calorific Properties of Liquid Copper, Teplofiz. Vys. Temp., 2000, 38, p 418-423, High Temp., 2000, 38, 394-399

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

102. V.Y. Chekhovskoi, Y.V. Gusev, and V.D. Tarasov, Experimental Study of the Specific Heat and Enthalpy of Copper in the Range 300–2000 K, High Temp. High Pressures, 2002, 34, p 291-298 103. C. Cagran, B. Wilthan, and G. Pottlacher, Enthalpy, Heat of Fusion and Specific Electrical Resistivity of Pure Silver, Pure Copper and the Binary Ag-28Cu Alloy, Thermochim. Acta, 2006, 445, p 104-110 104. V.Y. Chekhovskoi and V.D. Tarasov, The Caloric Properties of Copper: Thermal Vacancies, Zh. Fiz. Khim., 2000, 74, p 208-212, Russ. J. Phys. Chem. 74, 150–154 105. L.A. Stretz and R.G. Bautista, The High Temperature Heat Content of Liquid Yttrium by Levitation Calorimetry, Metall. Trans., 1974, 5, p 921-928 106. L.K. Kuntz and R.G. Bautista, The Heat Capacities and Heat Content of Molten Cerium by Levitation Calorimetry, Metall. Trans. B, 1976, 7, p 107-113 107. A.I. Akhmatova, Thermal Capacity of Fused Gallium and Copper at High Temperature, Izmer. Tekh., 1967, 8, p 14-17, Meas. Tech. 1967, 909–912 108. I.P. Mardykin and L.P. Filippov, Thermal Properties of Liquid Metals. I, Copper, Antimony, Fiz. Khim. Obrab. Mater., 1968, 1, p 110-112 109. A.K. Chaudhuri, D.W. Bonnell, L.A. Ford, and J.L. Margrave, Thermodynamic Properties by Levitation Calorimetry. I. Enthalpy Increments and Heats of Fusion for Copper and Platinum, High Temp. Sci., 1970, 2, p 203212 110. D.W. Bonnell, Property Measurements at High Temperatures—Levitation Calorimetry Studies of Liquid Metals, Ph.D. Thesis, Rice University, Houston, Texas, 1972 111. H.P. Stevens, Determination of the Enthalpy of Liquid Copper and Uranium with a Liquid Argon Calorimeter, High Temp. Sci., 1974, 6, p 156-166 112. W. Dokko and R.G. Bautista, The High Temperature Heat Content and Heat Capacity of Liquid Cerium-Copper Alloys by Levitation Calorimetry, Metall. Trans. B, 1980, 11, p 511518 113. J. Sugar and A. Musgrove, Energy Levels of Copper, Cu I, Through Cu XXIX, J. Phys. Chem. Ref. Data, 1990, 19, p 527-616 114. S. Civisˇ, I. Matulkova´, J. Cihelka, P. Kubelı´k, K. Kawaguchi, and V.E. Chernov, Time-Resolved FTIR Emission Spectroscopy of Cu in the 1800-3800 cm1 Region: Transitions Involving f and g States and Oscillator Strengths, J. Phys. B: At. Mol. Opt. Phys., 2011, 44, p 025002-1-025002-7 115. S. Civisˇ, I. Matulkova´, J. Cihelka, P. Kubelı´k, K. Kawaguchi, and V.E. Chernov, Low-Excited f-, g- and h-States in Au, Ag and Cu Observed by Fourier-Transform Infrared Spectroscopy in the 1000-7500 cm1 Region, J. Phys. B: At. Mol. Opt. Phys., 2011, 44, p 105002-105002-10 116. H.G. Kolsky, R.M. Gilmer P.W. Gilles, The Thermodynamic Properties of 54 Elements Considered as Ideal Monatomic Gases. U.S. Atomic Energy Commission Rep. LA 2110, 1957 117. P.J. Mohr, B.N. Taylor, and D.B. Newell, CODATA Recommendations of the Fundamental Physical Constants: 2010, Rev. Mod. Phys., 2012, 84, p 1527-1605 118. P.J. Mohr, B.N. Taylor, and D.B. Newell, CODATA Recommendations of the Fundamental Physical Constants, J. Phys. Chem. Ref. Data, 2012, 41, p 043109-1-043109-84 119. M.H. Rand, Priv. Commun., 2009 120. M.D. Morse, Clusters of Transition-Metal Atoms, Chem. Rev., 1986, 86, p 1049-1109

121. R.D. Page and C.S. Gudeman, Rotationally Resolved Dicopper (Cu2) Laser-Induced Fluorescence Spectra, J. Chem. Phys., 1991, 94, p 39-51 122. R.S. Ram, C.N. Jarman, and P.F. Bernath, Fourier-Transform Emission Spectroscopy of the Copper Dimer, J. Mol. Spectrosc., 1992, 156, p 468-486 123. A.I. Chegodaev, E.L. Dubinin, A.I. Timofeev, N.A. Vatolin, and V.I. Kapitanov, The Vapour Pressures of Liquid Metals at High Temperature, Zh. Fiz. Khim., 1978, 52, p 2124, Russ.J.Phys.Chem., 1978, 52, 1229 124. V.I. Severin, YuA Priselkov, A.V. Tseplyaeva, N.E. Khandamirova, N.A. Chernova, and I.V. Golubtsov, Study of the Vaporization of Copper, Teplofiz. Vys. Temp., 1998, 36, p 577-582, High Temp., 1998, 36, 553-558 125. R.J. Ackermann and E.G. Rauh, Vapor Pressures of Scandium, Yttrium and Lanthanum, J. Chem. Phys., 1962, 36, p 448-452 126. T.P.J.H. Babeliowski, Mass Spectrometric Determination of the Heat of Vaporization of Some Solid Elements, Physica, 1962, 28, p 1160-1169 127. D.F. Avery, J. Cuthbert, N.J.D. Prosser, and C. Silk, High Temperature Vaporization Studies by Mass Spectrometry I: The Coinage Metals—a Discussion of the Method and Errors, J. Sci. Instrum., 1966, 43, p 436-442 128. D.E. Moore, D. Robinson, and B.B. Argent, The Use of High Resolution Mass Spectrometry in the Measurement of Thermodynamic Properties of Metallic Systems, J. Phys. E: Sci. Instrum., 1975, 8, p 641-648 129. J. Golonka, J. Botor, and M. Dulat, Study of Cu-Ag Liquid Solutions by Combined Effusion Vaporization and Mass Spectrometry Sensing, Met. Technol., 1979, 6, p 267-272 130. D.A. Katsov, B.V. Lvov, L.K. Polzik, and YuA Semenov, Investigation of the Process of the Formation of an Absorbing Layer of Atoms in Graphite Furnaces in Atomic Absorption Analysis, Zh. Prikl. Spektrosk., 1977, 26, p 598605, J.Appl.Spectrosc., 1977, 26, 430-436 131. J. Vrestal and J. Tomiska, Ein Knudsenzellen-Monopolmassenspektrometer fu¨r den Einsatz in der Hochtemperaturthermodynamik, Monatsch. Chem., 1993, 124, p 1099-1106 132. H.E. Greenwood, An Approximate Determination of the Boiling Point of Metals, Proc. R. Soc. Lond. A, 1909, 82, p 396-408 133. H.E. Greenwood, The Influence of Pressure on the Boiling Points of Metals, Proc. R. Soc. Lond. A, 1910, 83, p 483-491 134. W. Rosenhain and D. Ewen, Intercrystalline Cohesion in Metals, J. Inst. Met., 1912, 8, p 149-185 135. O. Ruff and B. Bergdahl, Arbeiten im Gebiet Hoher Temperaturen-Die Messung von Dampfspannungen bei Sehr ¨ ber die Hohen Temperatuen Nebst Einigen Beobachtungen U Lo¨slichkeit von Kohlenstoff in Metallen, Z. Anorg. Allgem. Chem., 1919, 106, p 76-94 136. O. Ruff and S. Mugdan, Die Messung von Dampfdrucken bei Hohen Temperaturen und die Dampfdrucke der Alkalihalogenide, Z. Anorg. Allgem. Chem., 1921, 117, p 147-171 137. E. Mack, G.G. Osterhof, and H.M. Kraner, Vapor Pressure of Copper Oxide and of Copper, J. Am. Chem. Soc., 1923, 45, p 617-623 138. O. Ruff and M. Konschak, Dampfdruckmessungen am Cu, Au, Al2O3, SiO2, Si and SiC.Des Letzteren Bildung und Zersetzung, Z. Elektrochem., 1926, 32, p 515-525 139. H.A. Jones, I. Langmuir, and G.M.J. Mackay, The Rates of Evaporation and the Vapor Pressures of Tungsten, Molybdenum, Platinum, Nickel, Iron, Copper and Silver, Phys. Rev., 1927, 30, p 201-214

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

441

140. P. Harteck, Dampfdruckmessungen von Ag, Au, Cu, Pb, Ga, Sn und Berechnung der Chemischen Konstanten, Z. Physik. Chem., 1928, 134, p 1-20 141. E. Baur and R. Brunner, Dampfdruckmessungen an Hochsiedenden Metallen, Helv. Chim. Acta, 1934, 17, p 958-969 142. A.L. Marshall, R.W. Dornte, and F.J. Norton, The Vapor Pressure of Copper and Iron, J. Am. Chem. Soc., 1937, 59, p 1161-1166 143. A.H. Daane, The Vapor Pressures of Lanthanum and Praseodymium, U.S. Atomic Energy Commission, Rep. AECD-3209 (ISC-121), 1950 144. R.K. Edwards and J.H. Downing, Mechanisms of Permeation of Silver, Copper and Mercury Gases of Solid Graphite Walls, J. Phys. Chem., 1955, 59, p 1079-1083 ¨ ber die Verdampfung sehr 145. O. Knacke and R. Schmolke, U Du¨nner Kupfer- und Silberschichten, Z. Metallkde, 1956, 47, p 22-24 146. A.N. Nesmeyanov, L.A. Smakhtin, and V.I. Lebedev, The Measurement of the Vapor Pressures of the Solid Solutions Au-Ag and Ag-Cu, Dokl. Akad. Nauk SSSR, 1957, 112, p 700-702, Proc.Acad.Sci.USSR—Phys. Chem. Section, 1957, 112, 101-104 147. A.N. Nesmeyanov, L.A. Smakhtin, DYa Choporov, and V.I. Lebedev, Investigation into the Thermodynamics of Solid Solutions of Gold, Silver and Copper. I, Zh. Fiz. Khim., 1959, 33, p 342-348 148. R.B. McLellan and R. Shuttleworth, The Vapor Pressure of Solid Copper, Z. Metallkd. 1960, 51, p 143-144 149. P. Grieveson, G.W. Hooper, and C.B. Alcock, The Vapor Pressures of the Liquid Metals Copper, Silver and Gold, The Physical Chemistry of Process Metallurgy—Part 1, G.R. Pierre, Ed., Interscience, New York, 1961, p 341-352 150. A. Kirshenbaum and J.A. Cahill, The Density of Liquid Tin From Its Melting Point to Its Normal Boiling Point and an Estimate of Its Critical Constants, Trans. Q. ASM, 1962, 55, p 844-847 151. A. Kirshenbaum and J.A. Cahill, The Direct Determination of the Boiling Point of Tin, J. Inorg. Nucl. Chem., 1963, 25, p 232-234 152. H.Matern H, Investigation of the Evaporation of Some Metals and Alloys, Cand. Sci. (Chem.), Diss., Moscow State University. 1968 153. YuA Karasev, LSh Tsemekhman, and S.E. Vaisburd, Vapor Pressure of Iron, Cobalt and Copper Above the Melting Point, Zh. Fiz. Khim., 1971, 45, p 2068-2070 (Russ.J.Phys.Chem., 1971, 45, 1172-1173) 154. A.M. Nemets and G.I. Nikolaev, Determination of the Saturated Vapor Pressure of Copper, Titanium and Vanadium by Atomic Absorption, Zh. Prikl. Spektrosk., 1973, 18, p 571-578 (J.Appl.Spectrosc., 1973, 18, 418-423) 155. A.M. Nemets, G.I. Nikolaev, V.G. Flisyuk, and N.V. Bodrov, Distribution of Metal Vapor Concentration in an Open Cuvette with a Graphite Heater During Evaporation in an Inert Medium, Zh. Prikl. Spektrosk., 1974, 21, p 795-798 (J.Appl.Spectrosc., 1974, 21, 1442-1445) 156. V.G. Muradov, EYu Yablochkov, and V.S. Rogatskin, Use of an Atomic Absorption Method for Determination of the Saturated Vapor Pressure of Solid Copper, Uch. Zap. Ul’yanovsk. Gos. Ped. Inst., 1974, 27, p 22-26 157. B.M. Novoselov, E.L. Dubinin, and A.I. Timofeev, Measurements of Vapor Pressure of Pure Metals at High Temperatures using the Effusion-Torsion Method, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall., 1978, 6, p 41-47 158. S.E. Vaisburd, I.Sh. Tsemekhman, A.V. Taberko and Yu.A. Karasev, Vapor Pressure Over Molten Metals: Iron, Cobalt,

442

159.

160.

161. 162.

163. 164. 165.

166.

167. 168. 169. 170. 171.

172. 173. 174. 175. 176.

177.

Nickel, Palladium, Copper, Silver, Gold, Tin and Lead, Protsessy Tsvetn. Metall. Nizk. Davleniyakh, A.I. Manokhin (Ed.), Izd. Nauka, Moscow, 1983, p 120-128 V.K. Panday and A.K. Ganguly, Measurement of Monatomic Vapor Concentrations of Some Elements by Atomic Absorption: Cu, Ag, Au, Mn and Al, Appl. Spectrosc., 1985, 39, p 526-531 V.I. Severin, A.V. Tseplyaeva, YuA Priselkov, and L.P. Ryabtseva, Vapor Pressure and Heat of Sublimation of Copper, Tepolfiz. Vys. Temp., 1986, 24, p 487-492 (High Temp. 1986, 24, 363-368) E.M. Starovoitov, Determination of the Vapor Pressure and Heat of Sublimation of Copper, Teplofiz. Vys. Temp., 1987, 25, p 1022-1024 OYu Subbotina, N.V. Kishkoparov, and I.V. Frishberg, The Vapor Pressure of Copper, Tin and Cu-Sn Alloys in the HighTemperature Region, Teplofiz. Vys. Temp., 1999, 37, p 220225 (High Temp., 1999, 37, 198-203) Y.J. Duan, B. Chen, Y.C. Ma, M. Gao, and K. Liu, Determination of Vapor Pressure of Liquid Copper by Carrier Gas Method, J. Mater. Sci. Technol., 2013, 29, p 1209-1213 H.N. Hersh, The Vapor Pressure of Copper, J. Am. Chem. Soc., 1953, 75, p 1529-1531 J.W. Edwards, H.L. Johnston, and W.E. Ditmars, Vapor Pressures of Inorganic Substances. XI. Titanium between 1587 and 1764K and Copper between 1143 and 1292K, J. Am. Chem. Soc., 1953, 75, p 2467-2470 J.P. Morris and G.R. Zellars, Vapor Pressure of Liquid Copper and Activities in Liquid Fe-Cu Alloys, Trans. AIME 1956, 206, 1086-1090 (J. Metals, 1956, 8, 1086-1090) A. Krupkowski and J. Golonka, Vapour Pressures of Liquid Copper and Silver, Bull. Acad. Pol. Sci. Ser. Sci. Tech., 1964, 12, p 69-74 J.M. McCormack, J.R. Myers, and R.K. Saxer, Vapor Pressure of Liquid Copper, J. Chem. Eng. Data, 1965, 10, p 319-320 A. Ponslet and D. Bariaux, Vitesse d’Evaporation et Pression de Vapeur du Cuivre, Bull. Classe. Sci. Acad. R. Belg., 1966, 52, p 248-260 K.M. Myles and J.B. Darby, Thermodynamic Properties of Solid Palladium-Copper and Platinum-Copper Alloys, Acta Met., 1968, 16, p 485-492 A.P. Pomerantsev, Investigation of Evaporation of Binary Alloys on the Basis Copper, Silver and Manganese Using Radionuclides, Cand. Sci. (Chem.) Diss., Moscow State University, 1980 F. Geiger, C.A. Busse, and R.I. Loehrke, The Vapor Pressure of Indium, Silver, Gallium, Copper, Tin and Gold Between 0.1 and 3.0 Bar, Int. J. Thermophys., 1987, 8, p 425-436 K. Franzreb, A. Wucher, and H. Oechsner, Absolute Cross Sections for Electron Impact Ionization of Ag2, Z. Phys. D, 1991, 19, p 77-79 J. Drowart and P. Goldfinger, Investigation of Inorganic Systems at High Temperature by Mass Spectrometry, Angew. Chem. Int. Ed., 1967, 6, p 581-596 P. Schissel, Dissociation Energies of Cu2 Ag2 and Au2, J. Chem. Phys., 1957, 26, p 1276-1280 M. Ackerman, F.E. Stafford, and J. Drowart, Mass Spectrometric Determination of the Dissociation Energies of the Molecules AgAu, AgCu and AuCu, J. Chem. Phys., 1960, 33, p 1784-1789 D.W. Wilhite, Investigation of High Temperature Gaseous Species by Knudsen Cell Mass Spectrometry above the Condensed Systems – Cu-Y-Ru-C, Ag-Y-Ru-C and Au-Y-

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

178. 179. 180. 181. 182. 183. 184.

185. 186.

187. 188.

189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199.

Ru-C, Masters Thesis, Texas A & M University, College Station, Texas, 1988 J. Drowart and R.E. Honig, Mass Spectrometric Study of Copper, Silver and Gold, J. Chem. Phys., 1956, 25, p 581-582 J. Drowart and R.E. Honig, a Mass Spectrometric Method for the Determination of Dissociation Energies of Diatomic Molecules, J. Phys. Chem., 1957, 61, p 980-985 K. Hilpert and K.A. Gingerich, Atomization Enthalpies of the Molecules Cu3, Ag3 and Au3, Ber. Bunsengen. Phys. Chem., 1980, 84, p 739-745 K. Hilpert, Mass Spectrometric Determination of the Dissociation Energies of CuTb (g), CuDy (g) and CuHo (g), Ber. Bunsengen. Phys. Chem., 1979, 83, p 161-167 H.E. Schmitz, On the Determination of Specific Heats, Especially at Low Temperatures, Proc. R. Soc. Lond., 1903, 72, p 177-192 W. Nerst, Der Energieinhalt Fester Stoffe, Ann. Phys., 1911, 341, p 395-439 W.H. Keesom and H. Kammerlingh Onnes, The Specific Heat at Low Temperatures. I. Measurements of the Specific Heats of Lead Between 14 and 80K and Copper Between 15 and 22K, Comm. Phys. Lab. Univ. Leiden, No. 143, 1914 E.H. Griffith and E. Griffiths, The Capacity for Heat of Metals at Different Temperatures, Proc. R. Soc. Lond. A, 1913, 88, p 549-560 E.H. Griffith and E. Griffiths, IV, The Capacity for Heats of Metals at Different Temperatures, Being an Account of Experiments Performed in the Research Laboratory of the University College of South Wales and Monmouthshire, Phil. Trans. R. Soc. A, 1913, 213, p 119-185 E.H. Griffith and E. Griffiths, The Capacity for Heat of Metals at Low Temperatures, Phil. Trans. R. Soc. A, 1914, 214, p 319-357 W.H. Keesom and H. Kammerlingh Onnes, The Specific Heat at Low Temperatures. II. Measurement on the Specific Heat of Copper Between 14 and 90 K, Comm. Phys. Lab. Univ. Leiden, No.147a, 1915 A. Denizot, Sur le Rapport de la Chaleur Spe´cifique a` la Tempe´rature, Bl. Soc. Amis. Sci. Poznan B, 1926, 1-3 A. Eucken and W. Werth, Die Spezifische Wa¨rme einiger Metalle und Metallegierungen bei tiefen Temperaruren, Z. Anorg. Allgem. Chem., 1930, 188, p 152-172 S.M. Dockerty, On the Specific Heat of Copper From –78º to 0C, Can. J. Res., 1933, 9, p 84-93 C.G. Maier and C.T. Anderson, The Disposition of Work Energy Applied to Crystals, J. Chem. Phys., 1934, 4, p 513-527 J.A. Kok and W.H. Keesom, Measurement of the Atomic Heats of Platinum and of Copper From 1.2 to 20K, Physica, 1936, 3, p 1035-1045 S.M. Dockerty, The Specific Heat of Copper From 30º to 200º, Can. J. Res. A., 1937, 15, p 59-66 S. Aoyama and E. Kanda, Specific Heat of Nickel and Cobalt at Low Temperature, J. Chem. Soc. Japan, 1941, 62, p 312-315 W.F. Giauque and P.F. Meads, The Heat Capacities and Entropies of Aluminium and Copper From 15 to 300K, J. Am. Chem. Soc., 1941, 63, p 1897-1901 F.X. Eder, Internal Energy of Deformed Metals at Low Temperatures, Annexe 1955-2 au Bulletin de l’Institut International du Froid, 1955, p 137-141 T.A. Sandenaw, Heat Capacity of Copper Below 300K. A Test of Two Calorimeter Designs, U.S. Atomic Energy Commission Rep. LA 2307, 1959 D.L. Martin, A Modified Continuous-Heating Calorimeter for the Temperature Range 15º to 300K, Can. J. Phys., 1962, 40, p 1166-1173

200. W.A. Tilden and J. Perry, The Specific Heats of Metals and the Relation of Specific Heat to Atomic Weight, Phil. Trans. R. Soc. A, 1900, 194, p 233-255 201. W. Jaeger and H. Diesselhorst, Wa¨rmeleitung, Elektricita¨tsleitung, Wa¨rmecapacacita¨t und Thermokraft einiger Metalle, Abh. Phys. Tech. Reichanstalt., 1900, 3, p 269-424 ¨ ber Metalldes202. G.W.A. Kahlbaum, K. Roth, and P. Siedler, U tillation und U¨ber Destillierte Metalle, Z. Anorg. Chem., 1902, 29, p 177-294 ¨ ber die A ¨ nderung der Spezifischen Wa¨rme der 203. W. Gaede, U Metalle mit der Temperature, Phys. Z., 1903, 4, p 105-106 204. W. Nerst, F. Koref, and F.A. Lindemann, Untersuchungen U¨ber die Spezifische Wa¨rme bei Tiefen Temperaturen, Ber. Berl. Acad., 1910, 1, p 247-261 205. D.R. Harper, III, Specific Heat of Copper in the Interval 0º to 50º, with a Note on Vacuum-Jacketed Calorimeters, J. Wash. Acad., 1914, 4, p 489-490 206. D.R. Harper, III, Specific Heat of Copper in the Interval 0º to 50º, with a Note on Vacuum-Jacketed Calorimeters, Natl. Bur. Stand. Tech. News Bull., 1915, 11, p 259-329 207. H. Klinkhardt, Messung von Wahren Spezifischen Wa¨rmen bei Hohen Temperaturen Durch Heizung mit Glu¨helektronen, Ann. Phys., 1927, 389, p 167-200 208. H.L. Bronson and H.M. Chisholm, On the Specific Heat of Tungsten, Molybdenum and Copper, Proc. Nova Scotian Inst. Sci., 1929, 17, p 44-45 209. H. Seekamp, U¨ber die Messung Wahrer Spezifischer Wa¨rmen Fester und Flussiger Metalle bei Hohen Temperaturen, Z. Anorg. Allgem. Chem., 1931, 195, p 345-365 210. C. Sykes, Methods for Investigating Thermal Changes Occurring During Transformations in a Solid Solution, Proc. R. Soc. Lond. A, 1935, 148, p 422-446 211. K.Honda and M.Tokunaga M., On the True Specific Heat of Some Metals and Alloys, Sci. Rep. Toˆhuka Univ. 1935, 23, 816-834 212. H. Quinney and G.I. Taylor, The Emission of the Latent Energy due to Previous Cold Working When a Metal is Heated, Proc. R. Soc. Lond. A, 1937, 163, p 157-181 213. W.J. Thomas and R.M. Davis, The Determination of Specific Heats by an Eddy Current Method. Part II. Experimental, Philos. Mag., 1937, 24, p 713-744 214. A. Avramescu, Temperaturabha¨ngigkeit der Wahren Spezifischen Wa¨rme von Leitungskupfer und Leitungsaluminium bis zum Schmelzpunkt, Z. Tech. Phys., 1939, 20, p 213-217 215. F. Fo¨rster and G. Tschentke, Ein Verfahren zur Messung der Temperatur-Abha¨ngigkeit von Elektrischem Widerstand und Spezifischer Wa¨rme Fester und Flu¨ssiger Metalle, Z. Metallkde, 1940, 32, p 191-195 216. B. Persoz, Nouvelles Me´thodes de Mesure de la Chaleur Spe´cifique Vraie des Me´taux a Haute Tempe´rature, Ann. Phys., 1940, 14, p 237-301 217. J.B. Trice, J.J. Neely and C.E. Tetter Jr., The Heat Capacity of Beryllium Carbide Powder, U.S. Atomic Energy Commission, Rep. NEPA 816-SCR-28, 1948 218. M.L. Picklesimer, Calorimetric Measurements on High Purity Iron and Eutectoid Steels, Ph.D. Thesis, University of Tennessee, 1954 219. C.F. Lucks and H.W. Deem, Thermal Conductivities, Heat Capacities and Linear Thermal Expansion of Five Materials, Wright Air Development Center, Air Research and Development Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADC-TR-55-496, 1956 220. C.F. Lucks and H.W. Deem, Thermal Properties of Thirteen Metals, ASTM Spec. Tech. Publ. 227, 1958

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015

443

221. C.P. Butler and E.C.Y. Inn, A Radiometric Method for Determining Specific Heat at Elevated Temperatures, U.S. Naval Radiological Defence Lab., Tech. Rep. USNRDL-TR235, 1958 222. I.P.Bell, Fast Reactor: Physical Properties of Materials of Construction, U.K. Atomic Energy Authority, Industrial Group, R & DB (C), Tech. Note 127, 1959 223. V.E. Lyusternik, Automatic Calorimeter for Quantitative Thermal Analysis of Heat Resistant Steels, Pribory Tekhn. Eksperim., 1959, 4, p 127-129 224. G.W. Lehman, Thermal Properties of Refractory Materials, Aeronautical Systems Division, Air Force Systems Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADD-TR-60-581, 1960 225. P.T. Howse Jr., C.D. Pears and S. Oglesby Jr., The Thermal Properties of Some Plastic Panels, Aeronautical Systems Division, Air Force Systems Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADDTR-60-657, 1961 226. R.J. Jenkins and W.J. Parker, A Flash Method for Determining Thermal Diffusivity Over a Wide Temperature Range, Aeronautical Systems Division, Air Force Systems Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADD-TR-61-95, 1961 227. Y. Masuda, Calorimetric Study on the Sintering of Copper Powder Compact, Sci. Rep. Res. Inst. Toˆhoku Univ., 1962, A14, p 156-164 228. YaA Kraftmakher, Vacancy Formation in Copper, Fiz. Tverd. Tela, 1967, 9, p 1850-1851 (Sov. Phys.- Solid State, 1967, 9, 1458) 229. C.R. Brooks, W.E. Norem, D.E. Hendrix, J.W. Wright, and W.C. Northcutt, The Specific Heat of Copper from 40 to 920C, J. Phys. Chem. Solids, 1968, 29, p 565-574 230. V.Y. Chekhovskoi and G.Z. Gerasina, True Heat Capacity of Copper and of 1Kh18N9T Steel in the 300-900K Temperature Range, Teplofiz. Vys. Temp., 1971, 9, p 938-942 231. I.M. Chernenko and A.I. Ivon, Electrical Method for Heat Capacity Determinations of Materials, Zavod. Lab., 1976, 42, p 825-826 232. Y.S. Touloukian and E.H. Buyco, Specific Heat—Metallic Elements and Alloys, Thermophysical Properties of Matter, Vol 4, Y.S. Touloulian and C.Y. Ho, Ed., IFI/Plenum, New York, 1970,

444

233. W.A. Tilden, The Specific Heat of Metals and the Relation of Specific Heat to Atomic Weight, Proc. R. Soc. Lond., 1900, 66, p 244-247 234. A. Magnus, A., U¨ber die Bestimmung Spezifischer Wa¨rmen, Ann. Phys., 1910, 336, p 597-608 235. H. Schimpff, U¨ber die Wa¨rmekapazita¨t von Metallen und Metallverbindungen, Z. Physik. Chem., 1910, 71, p 257-300 236. P. Schu¨bel, Metallographische Mitteilungen aus dem Institut fu¨r Physikalische Chemie der Universita¨t Go¨ttingen.LXXXVII.U¨ber die Wa¨rmekapazita¨t von Metallen und Metallverbindungen Zwischen 18-600º, Z. Anorg. Chem., 1914, 87, p 81-119 ¨ ber die Spezifische Wa¨rme 237. F. Doerinckel and M. Werner, U Technischer Cu-Zn-Legierungen bei Ho¨heren Temperaturen, Z. Anorg. Allgem. Chem., 1921, 115, p 1-48 238. W.A. Roth and W. Bertram, Messung der Spezifischen Wa¨rmen von Metallurgisch Wichtigen Stoffen in einen Gro¨sseren Temperaturintervall mit Hilfe von Zwei Neun Calorimetertypen, Z. Elektrochem., 1929, 35, p 297-308 239. R. Ruer and K. Kremers, Das System Kupfer-Zink, Z. Anorg. Allg. Chem., 1929, 184, p 193-231 240. F.M. Jaeger, E. Rosenbohm, and J.A. Bottema, The Exact Measurement of the Specific Heats of Solid Substances at High Temperatures: VII. Metals in Stabilized and Nonstabilized Condition—Copper and Gold, Proc. Acad. Sci. Amsterdam, 1932, 35, p 772-779 241. D. Fieldhouse, J.C. Hedge, J.L. Lang, A.N.Takata and T.E.Waterman T.E., Measurements of Thermal Properties, Wright Air Development Center, Air Research and Development Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADC-TR-55-495, Part 1, 1956 242. D.S. Neel, C.D. Pears and S. Oglesby Jr., The Thermal Properties of Thirteen Solid Materials to 5000F for Their Destruction Temperatures, Aeronautical Systems Division, Air Force Systems Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADD-TR-60-924, 1961 243. J. Booker, R.M. Paine and A.J. Stonehouse, Investigation of Intermetallic Compounds for Very High Temperature Applications, Aeronautical Systems Division, Air Force Systems Command, U.S. Air Force, Wright-Patterson Air Force Base, Ohio, Tech. Rep. WADD-TR-60-889, 1961 244. G.R. Gathers, Thermophysical Properties of Liquid Copper and Aluminium, Int. J. Thermophys., 1983, 4, p 209-226

Journal of Phase Equilibria and Diffusion Vol. 36 No. 5 2015