Journal Archive

Platinum Metals Rev., 1997, 41, (1), 12

Crystallographic Properties of Platinum

  • By J. W. Arblaster
  • Rotech Laboratories, Wednesbury, West Midlands, England

Article Synopsis

Crystallographic and bulk properties of platinum from absolute zero to the melting point are assessed from a review of the literature covering the period 1901 to date. Selected values of thermal expansion are used to calculate the variation with temperature of length changes, lattice parameters, inter-atomic distances, atomic and molar volumes, and density. The crystallographic properties are based mainly on the precise dilatometric thermal expansion data, including corrections to account for thermal vacancy effects at the highest temperatures. Literature values are compared graphically with the selected values, and an Appendix is included to explain some of the terms used.

Platinum exists in a face-centred cubic structure (Pearson symbol cF4) up to the melting point, which is a proposed secondary fixed point on the International Temperature Scale, ITS-90, at 2041.3 K (1). High precision thermal expansion data for platinum is available up to 85 K and from 246 to 1900 K which allows the use of this metal as a thermal expansion standard above room temperature. In the temperature interval from 85 to 246 K thermal expansion values are estimated from a relationship between thermal expansion and specific heat developed by the present author from earlier Russian work (see Appendix). The close agreement between experimental length change measurements in this region and those obtained by integrating the estimated thermal expansion values gives validity to this approach to interpolation.

Only the lattice parameter at 293.15 K (20°C) has been used in deriving the crystallographic properties, all other values are based on the precision dilatometric measurements and include the thermal vacancy corrections which apply above 1300 K. The large scatter in the lattice parameter measurements, especially at high temperatures, is surprising for an element which is inert and obtained in very high purity. This scatter precludes comparison with the dilatometric data to obtain an independent estimate of the thermal vacancy parameters.

Thermal Expansion

Of the 22 sets of thermal expansion data tabulated by Touloukian and co-workers (2) in 1975, Kirby (3) considered that only those of: Holborn and Day (4) from 273 to 1273 K, Austin (5) from 273 to 1173 K, White (6) 3 to 85 and 283 K and Hahn and Kirby (7) 293 to 1900 K, as well as the more recent measurements of Edsinger, Reilly and Schooley (8) 246 to 841 K, satisfy the necessary criteria of sensitivity of method and purity of the materials used, and of these only those of Edsinger, Reilly and Schooley were reported in sufficient detail to allow an unambiguous temperature scale correction (from IPTS-68 to ITS-90).

Low Temperature Thermal Expansion Data
0–26 K:
(i)
26–71 K:
(ii)
71–272 K:
(iii)

In the low temperature region the thermodynamic thermal expansion coefficient, α, is based on the measurements of White (6) and Edsinger, Reilly and Schooley (8). The derivation of Equations (ii) and (iii) is explained in the Appendix.

The values of Cp, are taken from the recent review by the present author (9). Equation (i) is accurate to ± 3 × 10−10 K−1 and Equations (ii) and (iii) to ± 2 × 10−8 K−1. Although Kirby (3) used a different approach to interpolate within the range 85 to 245 K, calculated values of α* in this region agree to within 7 × 10−8 K−1. Since Table II is given at relatively wide temperature intervals at low temperature, a knowledge of Cp, is required in order to use Equations (ii) and (iii). For interpolation this requirement has been overcome by fitting smoothed values of α calculated from Equations (ii) and (iii) to a series of spline-fitted polynomials, Equations (iv) to (vii).

Low Temperature Thermal Expansion Data
(Spline-Fitted Equations above 25 K)
(iv)
(v)
(vi)
(vii)
High Temperature Dilatometric Thermal Expansion
(viii)
(ix)
High Temperature Lattice Parameter Thermal Expansion
(x)
(xi)
Table II

Crystallographic Properties

Temp., K Thermal expansion, 106 × α. K−1 Length change, δa/a × 100 Lattice parameter, nm Interatomic distance, nm Atomic volume, 103 × nm3 Molar volume, 106 × m3 mol−1 Density, kg m−3
0 0 −0.1933 0.39160 0.27690 15.013 9.041 21577
10 0.071 −0.1933 0.39160 0.27690 15.013 9.041 21577
20 0.51 −0.1930 0.39160 0.27690 15.013 9.041 21576
30 1.45 −0.1921 0.39161 0.27691 15.014 9.041 25176
40 2.61 −0.1900 0.39161 0.27691 15.015 9.042 21575
50 3.69 −0.1869 0.39163 0.27692 15.016 9.043 21573
60 4.60 −0.1827 0.39164 0.27693 15.018 9.044 21570
70 5.32 −0.1777 0.39166 0.27695 15.020 9.045 21567
80 5.89 −0.1722 0.39168 0.27696 15.023 9.047 21563
90 6.37 −0.1660 0.39171 0.27698 15.026 9.049 21559
100 6.77 −0.1595 0.39173 0.27700 15.028 9.050 21555
110 7.10 −0.1525 0.39176 0.27702 15.032 9.052 21550
120 7.37 −0.1453 0.39179 0.27704 15.035 9.054 21546
130 7.59 −0.1378 0.39182 0.27706 15.038 9.056 21541
140 7.78 −0.1301 0.39185 0.27708 15.042 9.058 21536
150 7.93 −0.1223 0.39188 0.27710 15.045 9.060 21531
160 8.07 −0.1143 0.39191 0.27712 15.049 9.063 21526
180 8.29 −0.0980 0.39198 0.27717 15.056 9.067 21515
200 8.46 −0.0812 0.39204 0.27722 15.064 9.072 21504
220 8.59 −0.0642 0.39211 0.27726 15.072 9.076 21493
240 8.70 −0.0469 0.39218 0.27731 15.079 9.081 21482
260 8.80 −0.0294 0.39224 0.27736 15.087 9.086 21471
280 8.89 −0.0117 0.39231 0.27741 15.095 9.091 21459
293.15 8.93 0 0.39236 0.27744 15.101 9.094 21452
300 8.95 0.006 0.39238 0.27746 15.103 9.095 21448
400 9.25 0.097 0.39274 0.27771 15.145 9.120 21389
500 9.48 0.191 0.39311 0.27797 15.187 9.146 21329
600 9.71 0.287 0.39349 0.27824 15.231 9.172 21268
700 9.94 0.386 0.39387 0.27851 15.276 9.199 21205
800 10.19 0.487 0.39427 0.27879 15.322 9.227 21142
900 10.47 0.591 0.39468 0.27908 15.370 9.256 21076
1000 10.77 0.698 0.39510 0.27938 15.419 9.285 21009
1100 11.10 0.808 0.39553 0.27968 15.469 9.316 20940
1200 11.43 0.921 0.39597 0.28000 15.522 9.347 20870
1300 11.77 1.038 0.39643 0.28032 15.576 9.380 20797
1400 12.11 1.159 0.39691 0.28066 15.632 9.414 20723
1500 12.48 1.284 0.39740 0.28100 15.690 9.448 20647
1600 12.86 1.412 0.39790 0.28136 15.749 9.484 20568
1700 13.31 1.545 0.39842 0.28173 15.811 9.522 20488
1800 13.86 1.683 0.39896 0.28211 15.876 9.561 20404
1900 14.58 1.827 0.39953 0.28251 15.944 9.601 20318
2000 15.57 1.981 0.40013 0.28294 16.016 9.645 20226
2041.3 16.07 2.047 0.40039 0.28312 16.047 9.664 20187

In the high temperature region selected values of α*, defined in the Appendix, are based on the measurements of Holborn and Day (4) (to 1023 K), Austin (5) (to 873 K), Hahn and Kirby (7) and Edsinger, Reilly and Schooley (8), see Equation (viii).

Equation (viii) for α* has an overall accuracy of ± 2 × 10−8 K−1 and agrees with the interpretation of the same data by Kirby (3) to within 5 × 10−8 K−1.

Because of the scatter in the lattice parameter data, Equations (i) to (ix), were used to represent both the crystallographic and bulk properties of platinum up to the melting point, with the crystallographic properties in the high temperature range calculated from the dilatometrie data by taking into account thermal vacancy effects.

Unfortunately, there are no absolute measurements of the thermal vacancy concentration, cv (that is simultaneous measurements of dilatometric and lattice thermal expansion) but such measurements for copper (10), silver (11), gold (12) and aluminium (13) suggest a common value of (7 ± 2) × 10−4 at the melting point. The enthalpy of monovacancy formation in platinum, Hvf, is now well established as 1.51 eV (14–16) and adopting the above value of cv leads to a value for the entropy of monovacancy formation, Svf, of (1.32 ± 0.3)k (k is the Boltzmann Constant), which is in excellent agreement with values of 1.3k, calculated by Schumacher, Seeger and Härlin (17) from a re-analysis of the self-diffusion experiments of Kidson and Ross (18) and Cattaneo, Germagnoli and Grasso (19), and 1.45 k estimated by Heigl and Sizmann (15) from results using a millisecond heat pulse technique. Therefore a value for Cv of 7 × 10−4 at the melting point is adopted for platinum, and the lattice thermal expansion can be related to the dilatometric thermal expansion as in Equations (x) and (xi).

Table 1

Values of Lattice Constants from the Literature

Authors Reference Lattice constant at 293.15 K, nm Original temperature, K
Van Arkel 22 0.39223 rt*
Stenzel and Weerts 23 0.39232 293
Owen and Yates 24 0.39240 291
Owen and Yates 25 0.39244 288
Moeller 26 0.39226 293
Esch and Schneider 27 0.39239 rt*
Goldschmidt and Land 28 0.39242 rt*
Grube, Schneider and Esch 29 0.39238 rt*
Swanson and Tatge 30 0.39232 298
Kidron 31 0.39237 298
Evans and Fischer 32 0.39236 293
Schröder and co-workers 33 0.39234 927
Waseda, Hirata and Ontani 34 0.39241 298
Stankus and Khairulin 35 0.39240** 293
  Selected 0.39236 ± 0.00006

is room temperature – no thermal expansion correction applied

from direct density measurement 21445 kg−3

Lattice Parameter at 293.15 K

A combination of those values selected by Donohue (20) as well as more recent determinations were corrected from kX and ångström units to nm using conversion factors recommended in the 1986 review of the fundamental constants (21). Lattice parameters were corrected to 293.15 K using thermal expansion coefficients selected in this review.

Density values in Table II were calculated using an atomic weight of 195.078 (36) and 6.0221367 × 1023 mol−1 for Avogadro’s Constant (21). Crystallographic and bulk properties, Tables II and III, respectively, would be identical below 1300 K.

Table III

Bulk Properties*

Temperature, K Thermal expansion, 106 × α, K−1 Length change, δL/L × 100 Molar volume, 106 × m3 mol−1 Density, kg m−3
1300 11.79 1.039 9.380 20797
1400 12.16 1.160 9.414 20723
1500 12.56 1.285 9.449 20646
1600 13.01 1.414 9.485 20567
1700 13.56 1.549 9.523 20485
1800 14.26 1.690 9.563 20400
1900 15.17 1.839 9.605 20310
2000 16.40 2.000 9.650 20214
2041.3 17.03 2.070 9.670 20173

This Table would be identical to Table II below 1300 K

Comparison with Other Data

Figure 1 shows those dilatometric measurements which differ notably from the selected values – the measurements of Vertogradskii (37) 356–1589 K and the direct density measurements of Stankus and Khairulin (35) 293–2042 K. The finer scale graph, see Figure 2, shows the dilatometric measurements of Cowder and colleagues (38) 293–1773 K and the AGARD (Advisory Group for Aerospace Research and Development) pooled data, as reported by Weisenburger (39) and 573–1173 K (five participants), Fitzer (40) 573–1273 K (average of ten participants) and Fitzer and Weisenburger (41) 373–1873 K (five participants in all).

Fig. 1

Deviation of high temperature experimental dilatometrie length change measurements compared to Equation (ix) (purple line) (Refs. 35, 37)

Fig. 2

Deviation of high temperature experimental dilatometrie length change measurements compared to Equation (ix), (purple line) (Refs. 38 to 41)

Not shown are the measurements of Dorsey (42) 93–293 K which, on the basis of:

agree with the selected values to within 0.001; and those of Scheel (43) 83–373 K, Scheel and Heuse (44) 90–289 K, Henning (45) 82–289 K, Nix and MacNair (45) 85–368 K, Branchereau, Navez and Perroux (46) 573 K, Amatuni and co-workers (47) 373–1273 K, and the interferometric measurements of participant no. 7 (373–1073 K) noted by Fitzer and Weisenburger (41), which all agree with the selected curve to within 0.002. The measurements of Esser and Eusterbrock (49) 273–1273 K agree to within 0.001 up to 973 K, then deviate up to 0.007 low. The single measurement of Masumoto and Kobayashi (50) at 313 K is 0.006 low.

The comparison of lattice parameters, see Figure 3, includes measurements by: Owen and Yates (25) 288–873 K, Shinoda (51) 288–1373 K, Esser, Eilander and Bungardt (52) 293–1373 K, Eisenstein (53) 1148 K, Edwards, Speiser and Johnston (54) 291–2005 K, Mauer and Bolz (55) 273–1663 K, Brand and Goldschmidt (56) 673–1607 K, Lui, Takahashi and Bassett (57) 286–701 K, Evans and Fischer (32) 293–1783 K, Schroder, Schmitz-Pranghe and Kohlhaas (33) 85–1933 K, and Waseda, Hirata and Ohtani (34) 298–2029 K. The scatter in the data, especially at high temperatures, indicates the difficulties in reaching conclusions concerning thermal vacancy effects by trying to match unrelated lattice and dilatometric measurements.

Fig. 3

Deviation of experimental lattice parameter length change measurements compared to Equation (x) (yellow line) (Refs. 25, 32 to 34, 51 to 57)

Figure 4 shows deviations of the thermal expansion coefficients reported by Valentiner and Wallot (58) 96–284 K, which are up to 3 per cent low, and those of Kraftmakher (59) 1000–1900 K which rise sharply upwards reaching 25 per cent higher than the selected value at 1900 K. The low temperature measurements of Andres (60) 2–13 K are reported in equation form, which gives a value at 10 K of 1.0 × 10−8K−1 (14 per cent) higher than the selected value.

Fig. 4

Percentage deviation of experimental thermal expansion data (Refs. 58, 59)

Appendix

The Definition of Thermal Expansion

The thermodynamic thermal expansion coefficient, α, is the instantaneous change in length per unit length per degree or (1/L)(∂L/∂T). In practice it is determined as a change in length over a very short temperature interval and over this length α is defined as ((L2 – L1)/L1))/(T2 -T1) at the mean temperature (T2 + T1)/2. In the higher temperature region length changes are measured relative to a reference temperature such as 293.15 K (20°C) and are fitted to a polynomial as (LT – Lref)/Lref. Differentiation of this equation leads to the instantaneous thermal expansion coefficient relative to the reference temperature α* = (l/Lref)(∂L/∂T); α and α* are related by the Equation:

The kX Lattice Parameter Unit

The X unit (X.U.) was introduced by Seigbahn (61, 62) to be exactly equal to the milliångström unit (10−13 m) and is defined as being equal to a lattice spacing of a calcite crystal. Throughout the 1930s and early 1940s X-ray wavelengths were defined in terms of this scale, and lattice spacing values were reported in 1000 X.U. (kX units). However when the lattice spacings of different calcite crystals were shown to be variable and it was realised that the kX unit was 0.2 per cent too large because of an error in the fundamental constants used in its original derivation, then by international agreement the kX unit was defined as being exactly equal to 1.00202 ångström units (63). Continual improvement in the determination of this ratio led in the 1986 revision of the fundamental constants (21) to a derivation that the kX unit was equivalent to 0.100207789 ± 0.000000070 nm on the scale in which the primary X-ray wavelength, Cu Kα1, is defined as being exactly 1537.400 X.U. All relevant lattice parameter values reported in the literature as being in kX units have been corrected using this ratio and those reported in conventional ångström units have been corrected using the ratio 0.100207789/1.00202.

Precision Relationship between Thermal Expansion and Specific Heat

In the specific heat at constant pressure (CP) version of the Grüneisen equation:

where α is the linear thermal expansion coefficient, Γ is the Grüneisen parameter, Bs is the adiabatic bulk modulus and V is the molar volume, α and CP increase rapidly below room temperature, whereas Γ, Bs and V vary only slowly and can be lumped together as a weak function of temperature. Mel’nikova and co-workers (64–67) developed this relationship to:

where A and B are constants and T is temperature, in order to represent the sparse thermal expansion coefficient data for the alkali metals lithium to rubidium. However the bulk of the thermal expansion data for these elements is in the form of length change measurements which are poorly represented by the constants chosen by Mel’nikova and colleagues, especially for sodium and potassium below 200 K.

An independent assessment of this equation for certain metals for which high quality thermal expansion and specific heat data is available below room temperature indicates that it gives a reasonable correlation down to about 150 K but is unsatisfactory below this temperature. However it can be shown (68) that the addition of further terms to this basic equation does lead to a precision relationship between α and CP in the form:

which, when n = 2, leads to a fit of the thermal expansion coefficient data for aluminium and tungsten below 300 K to within 1.6 x 10 −8 K −1 and 1.1 ×10−8 K−8 respectively, and for copper using either n = 1 or 2 to within 8 × 10−9 K−1. Therefore the behaviour of this equation suggests that it can be used for interpolation for the surprising number of metals for which high quality thermal expansion data is available only below 90 K and at room temperature. The order of the equation used depends on the quality of the available data and for platinum it is found that the best compromise is to use two equations both with n = 1 rather than a single equation or one of higher order.

The Thermal Vacancy Effect

The generation of thermal vacancies close to the melting point leads to a difference between macroscopic or bulk thermal expansion (dL/dT) and microscopic or lattice thermal expansion (da/dT) and this difference can be exploited in order to obtain an absolute value of the vacancy concentration parameter (cv) as:

where L0 and a0 are referred to a temperature at which Cv is zero but which can be assumed to be the reference temperature 293.15 K without any loss in accuracy. Considered only in terms of monovacancies and neglecting the effects of divacancies or interstitials, Cv can then be related to the entropy (Svf) and enthalpy (Hvf) of vacancy formation as: exp (Svf/k – Hvf/k T) where k is Boltzmann’s Constant, 8.617385 x 10 −5 eV K−1(21) and T is temperature.

Therefore since the above two equations are equal, Svf and Hvf can be determined by a measurement of the thermal expansion difference. Of other techniques which could be used these parameters can also be determined with a fair degree of accuracy from a combination of electrical resistivity measurements on specimens with quenched-in vacancies and diffusion experiments (17). These measurements and a comparison with actual determinations for other metals allow an accurate estimate of the thermal vacancy parameters for platinum even though absolute values have not yet been determined.

References

  1. 1
    R. E. Bedford,, G. Bonnier,, A. Maas and F. Pavese, Metrologia, 1996, 33, 133
  2. 2
    Y. S. Touloukian, R. K. Kirby,, R. E. Taylor, and P. D. Desai,, “ Thermal Expansion – Metallic Elements and Alloys ”, Thermophysical Properties of Matter, Vol. 12, eds. Y. S. Touloukian and C. Y. Ho, IFI/Plenum, New York, 1975
  3. 3
    R. K. Kirby, Int. J. Thermophys ., 1991, 12, 679
  4. 4
    L. Holborn and A. L. Day, Ann. Phys. (Leipzig), 1901, 4, 104 ; Am. J. Sci ., 1901, 32, 374
  5. 5
    J. P. Austin, Physics, 1932, 3, 240
  6. 6
    G. K. White, J. Phys. F: Met. Phys ., 1972, 2, L30
  7. 7
    T. A. Hahn, and R. K. Kirby,, “ Thermal Expansion 1971 ”, American Institute of Physics Conference Proceedings No.3, eds. M. G. Graham and H. E. Hagy, American Institute of Physics, New York, 1972, 87
  8. 8
    R. E. Edsinger,, M. L. Reilly and J. F. Schooley, J. Res. Nat. Bur. Stand ., 1986, 91, 333
  9. 9
    J. W. Arblaster, Platinum Metals Rev ., 1994, 38, (3), 119
  10. 10
    T. Hehenkamp,, W. Berger,, J. E. Kluin,, C. Lüdecke and J. Wolff, Phys. Rev ., 1992, B4S, 1998
  11. 11
    K. Mosig,, J. Wolff,, J. E. Kluin and T. Hehenkamp, J. Phys.: Condens. Matter, 1992, 4, 1447
  12. 12
    R. O. Simmons and R. W. Balluffi, Phys. Rev ., 1962, 125, 862
  13. 13
    R. O. Simmons and R. W. Balluffi, Phys. Rev ., 1960, 117, 52
  14. 14
    J. J. Jackson, in “ Lattice Defects in Quenched Metals ”, eds. R. M. J. Cotterill,, M. Doyama,, J. J. Jackson and M. Meshii, Academic Press, New York, 1965, 467
  15. 15
    F. Heigl and R. Sizmann, Cryst. Lattice Defects, 1972, 3, 13
  16. 16
    M. Senoo,, H. Mii,, I. Fujishiro and T. Takeuchi, Jpn. J. Appl. Phys ., 1973, 12, 1621
  17. 17
    D. Schumacher,, A. Seeger and O. Härlin, Phys. Status Solidi, 1968, 25, 359
  18. 18
    G. V. Kidson and R. Ross, “ Proceedings of the International Conference on Radioisotopes in Science Research ”, Vol. 1, Paris, 1957, 185
  19. 19
    F. Cattaneo,, E. Germagnoli and F. Grasso, Philos. Mag ., 1962, 7, 1373
  20. 20
    J. Donohue, in “ The Structures of the Elements ”, John Wiley and Sons, New York, 1974
  21. 21
    E. R. Cohen and B. N. Taylor, CODATA Bulletin, No. 63, November, 1986
  22. 22
    A. E. Van Arkel, Z. Krist ., 1928, 67, 235
  23. 23
    W. S. Stenzel and J. Weerts, Festschrift der Platinschmelze, G. Siebert, Hanau, 1931, 300
  24. 24
    E. A. Owen and L. Yates, Philos. Mag ., 1933, 15, 472 ; ibid ., 1933, 16, 606
  25. 25
    E. A. Owen and L. Yates, Philos. Mag ., 1934, 17, 113
  26. 26
    K. Moeller, Z. Krist ., 1937, 97, 170
  27. 27
    U. Esch and A. Z. Schneider, Elektrochem ., 1944, 50, 268
  28. 28
    H.J. Goldschmidt and T. Land, J. Iron Steel Inst ., 1947, 155, 221
  29. 29
    G. Grube,, A. Schneider and U. Esch, Heraeus Festschrift, 1951, 20
  30. 30
    H. E. Swanson and E. Tatge, Natl. Bur. Stand. Circ ., 539, Vol. I, June 1953
  31. 31
    A. Kidron, Trans. ASM, 1965, 58, 432
  32. 32
    D. L. Evans, and G. R. Fischer,, “ Thermal Expansion 1971 ”, American Institute of Physics Conference Proceedings No. 3, eds. M. G. Graham and H. E. Hagy, American Institute of Physics, New York, 1972, 97
  33. 33
    R. H. Schroder,, N. Schmitz-Pranghe and R. Kohlhaas, Z. Metattkd ., 1972, 63, 12
  34. 34
    Y. Waseda,, K. Hirata and M. Ohtani, High Temp.-High Pressures, 1975, 7, 221
  35. 35
    S. V. Stankus and R. A. Khairulin, Teplofiz. Vys. Temp ., 1992, 30, 487 ; [ High Temp ., 1992, 30, 386 ]
  36. 36
    Commission on Atomic Weights and Isotopie Abundances, Pure Appl. Chem ., to be published
  37. 37
    V. A. Vertogradskii, Zaved. Lab ., 1969, 35, 515 ; [ Ind. Lab ., 1969, 35, 612 ]
  38. 38
    L. R. Cowder,, R. W. Zocher,, J. F. Kerrick and L. L. Lyon, J. Appl. Phys ., 1970, 41, 5118
  39. 39
    S. Weisenburger, Rev. Int. Hautes Temp. Refract ., 1970, 7, 410
  40. 40
    E. Fitzer, Advisory Group for Aerospace Research and Development Corp., Rept. AGARD-AR-31-71, 1971
  41. 41
    E. Fitzer and S. Weisenburger, High Temp.-High Pressures, 1972, 4, 559
  42. 42
    H. G. Dorsey, Phys. Rev ., 1907, 25, 88
  43. 43
    K. Scheel, Verh.d Deutsch. Physik Ges ., 1907, 9, 3
  44. 44
    K. Scheel and W. Heuse, Verh.d Deutsch. Physik Ges ., 1907, 9, 449
  45. 45
    F. Henning, Ann. Phys. (Leipzig), 1907, 22, 631
  46. 46
    F. C. Nix and D. MacNair, Phys. Rev ., 1942, 61, 74
  47. 47
    M. Branchereau,, M. Navez and M. Perroux, Verres Refract ., 1962, 16, 159
  48. 48
    A. N. Amatuni,, T. I. Malyutina,, V. Ya. Chekhovskoi and V. A. Petukhov, High Temp-High Pressures, 1976, 8, 565
  49. 49
    H. Esser and H. Eusterbrock, Arch. Eisenhüttenwes ., 1941, 14, 341
  50. 50
    H. Masumoto and T. Kobuyashi, Trans. Jpn. Inst. Met ., 1965, 6, 113
  51. 51
    G. Shinoda, Proc. Phys.-Math. Soc. Jpn ., 1934, 16, 436
  52. 52
    H. Esser,, W. Eilander and K. Bungardt, Arch. Eisenhüttenw ., 1938, 12, 157
  53. 53
    A. Eisenstein, J. Appl. Phys ., 1946, 17, 434
  54. 54
    J. W. Edwards,, R. Speiser and H. L. Johnston, J. Appl. Phys ., 1951, 22, 424
  55. 55
    F. A. Mauer and L. H. Bolz, U.S. Air Force Rept. WADC-TR-55-473, 1955 and Suppl. No.l Nat. Bur. Stand. Rept. NBS-5837, 1957
  56. 56
    J. A. Brand and H. J. Goldschmidt, J. Sci Instrum ., 1956, 33, 41
  57. 57
    L. G. Lui,, T. Takahashi and W. A. Bassett, J. Phys. Chem. Solids, 1970, 31, 1345
  58. 58
    S. Valentiner and J. Wallot, Ann. Phys. (Leipzig), 1915, 46, 837
  59. 59
    Yu. A. Kraftmakher, Fiz. Tverd. Tela, 1967, 9, 1528 ; [ Sov. Phys.- Solid State, 1967, 9, 1197 ]
  60. 60
    K. Andres, Phys. Kondens. Mater ., 1964, 2, 294
  61. 61
    M. Seigbahn and A. Leide, Philos. Mag ., 1919, 38, 647
  62. 62
    M. Seigbahn, Ark. Mat. Astron. Fys ., 1920, 14, (9)
  63. 63
    W. L. Bragg, J. Sci. Instrum ., 1947, 24, 27
  64. 64
    T. N. Mel’nikova,, M. S. Trakhtengerts and K. A. Yakimovich, High Temp.-High Pressures, 1987, 19, 407
  65. 65
    T. N. Mel’nikova and A. G. Mozgovoi, Teplofiz. Vys. Temp ., 1988, 26, 1099 ; [ High Temp ., 1988, 26, 848 ]
  66. 66
    T. N. Mel’nikova, Teplofiz. Vys. Temp ., 1989, 27, 185
  67. 67
    T. N. Mel’nikova and A. G. Mozgovoi, Teplofiz. Vys. Temp, 1989, 27, 490 ; [ High Temp ., 1989, 27, 382 ]
  68. 68
    J. W. Arblaster, in preparation
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