Advanced Search
RSS LinkedIn Twitter

Journal Archive

Johnson Matthey Technol. Rev., 2015, 59, (3), 174

doi:10.1595/205651315x688091

Selected Electrical Resistivity Values for the Platinum Group of Metals Part I: Palladium and Platinum

Improved values obtained for liquid phases of palladium and platinum

SHARE THIS PAGE:

Article Synopsis

Electrical resistivity values for both the solid and liquid phases of the platinum group metals (pgms) palladium and platinum are evaluated. In particular improved values are obtained for the liquid phases of these metals. Previous reviews on electrical resistivity which included evaluations for the pgms included those of Meaden (1), Bass (2), Savitskii et al. (3) and Binkele and Brunen (4) as well as individual reviews by Matula (5) on palladium and White (6) on platinum.

1. Introduction

Electrical resistivity (ρ) is defined in terms of the International System of Units (SI units) as:

ρ = R A / l (i)

where

R is the electrical resistance of a uniform specimen of material in ohms (Ω)

A is the cross-sectional area of the specimen in square metres (m2)

l is the length of the specimen in metres (m)

The units of ρ are therefore Ω m although practically the most useful units are μΩ cm.

The measured electrical resistivity (ρ) usually consists of a temperature dependent intrinsic resistivity, ρi, which is due to the pure metal and is caused by the scattering of the charge carriers (electrons or holes) by phonons (quantised vibrations of the lattice) and by their collisions with each other, and a residual resistivity (ρ0) due to impurities which also scatter the carriers and increase the resistivity. The quantity ρ0 is considered to be a summation of the effects of different impurities and is also considered to be temperature independent. The two contributions to the total resistivity are combined according to Matthiessen's Rule: ρ = ρ0 + ρi and because ρ0 may vary from sample to sample then attempts are made to evaluate values of ρi which should be universal for a specific metal.

1.1 Correction for Thermal Expansion Effects

In order to obtain a reference value to which all other measurements are adjusted the electrical resistivity is evaluated at 273.15 K (0ºC).

In the low temperature region below about 30 K the resistivity can be represented by ρ = ρ0 + A T2 + B T5 where the temperature dependent terms represent the intrinsic resistivity, whilst up to room temperature the experimental values are generally given in such a form that interpolation can be achieved by using simple polynomials rather than using the complicated Bloch-Grüneisen formula (79). In the definition of resistivity as ρ = R A / l then A and l are usually measured at room temperature and therefore at different temperatures both A and l have to be corrected for thermal expansion effects. It is found below room temperature that for the level of accuracy given for ρ, thermal expansion corrections are generally negligible but at higher temperature the measurements have to be corrected, especially if they are based entirely on the room temperature values for A and l which are usually measured at 293.15 K, the accepted reference temperature for length change measurements:

ρ (corrected) = ρ (uncorrected) [(AT / A293.15) × (I293.15 / IT)] (ii)

= ρ (uncorrected) [1 + (ITI293.15) / I293.15] (iii)

where Equation (iii) can be considered to be a close approximation of Equation (ii). However since 273.15 K is the actual reference temperature then corrected values of ρ(T) should be further corrected for thermal expansion from 293.15 K to 273.15 K. Since this correction is usually negligible at the level of accuracy given then it is not applied.

In the case of rapid pulse heating to high temperatures, because of inertia l generally is unaltered and it is A that changes. If D is the diameter of the wire then:

ρ (T) = ρ (measured) (DT2 / D293.152) = ρ (measured) (VT / V293.15) (iv)

where VT is the volume of the sample at temperature T and V293.15 is the volume at 293.15 K. These are essentially DT2 and D293.152 respectively since l is assumed to be unaltered.

2. Palladium

Palladium has a face-centred cubic structure and the melting point is a secondary fixed point on the International Temperature Scale of 1990 (ITS-90) at 1828.0 ± 0.1 K (10).

2.1 Solid

Electrical resistivity values for solid palladium at 273.15 K are given in Table I. The selected value is an average of the last three determinations. The ρ0 correction to the measurement of Laubitz and Matsumura (14) was suggested by Matula (5) who also appears to have selected this value as the reference value.

Table I

Electrical Resistivity of Palladium at 273.15 K

AuthorsRef.ρi, μΩ cmTemperature of data
Powell et al. 11 9.79 At 273.15 K. Corrected for ρ0 0.144 μΩ m
Powell et al. 12 9.75 Interpolated 200 – 400 K. Corrected for ρ0 0.143 μΩ m
White and Woods 13 9.70 At 273.15 K. Average of three samples
Laubitz and Matsumura 14 9.760 Interpolated 250–300 K. Corrected for ρ0 0.020 μΩ m
Williams and Weaver 15 9.751 At 273.15 K. Corrected for ρ0 0.007 μΩ m
Khellar and Vuillemin 16 9.765 Calculated. Fit 17–300 K
Selected 9.76 ± 0.01 At 273.15 K

From 71 data sets for solid palladium Matula (5) selected only the measurements of Schriempf (17) (1.6 K–10.6 K), White and Woods (13) (10 K–295 K) and Laubitz and Matsumura (14) (90 K–1300 K). However it is considered that the values of White and Woods have been superseded by the later high precision measurements of Williams and Weaver (15) (0 K–300 K) and Khellar and Vuillemin (16) (17 K–300 K), with the latter given only in the form of an equation which was evaluated at 17 K and then at 10 K intervals from 20 K to 270 K. The measurements of Williams and Weaver were interpolated above 100 K so as to also obtain a full evaluation at 10 K intervals from 20 K to 270 K. The measurements of Schriempf and of Williams and Weaver agree satisfactorily and were averaged to 10 K with the measurements of Williams and Weaver being extended to 16 K. The measurements of the latter and of Khellar and Vuillemin do not agree below 35 K. However the equation of Khellar and Vuillemin showed peculiar behaviour below this temperature with derived values being 6% higher than those of Williams and Weaver at 17 K but 31% lower at 20 K. Therefore the latter measurements were given preference up to 35 K. At this temperature and above values from the two sets of measurements were averaged. Overall agreement is to within 0.5% between 60 K and 180 K and to within 0.1% above 180 K. The selected values of Matula below 273.15 K are based on a combination of the measurements of White and Woods and of Laubitz and Matsumura and on average the intrinsic values show a bias of 0.02 μΩ cm above the more recently selected values. Other measurements in the low temperature region were discussed by Matula.

In the high temperature region Matula (5) selected only the measurements of Laubitz and Matsumura (14) (90 K–1300 K). After correction for ρ0 = 0.020 μΩ cm the values were calculated at 50 K intervals from 350 to 1300 K. In the present evaluation these measurements were combined with the more recent measurements of Khellaf et al. (18) (295 K–1700 K) which were given in the form of an equation which was also evaluated at 50 K intervals but over the range 350 K to 1750 K. After correction of both sets of measurements for thermal expansion using the values selected by the present author (19) they were fitted to Equation (v) which has an overall accuracy as a standard deviation of ± 0.13 μΩ cm. The two sets of measurements show a maximum disagreement of 1.0% at 1300 K. The equation was extrapolated to the melting point and selected values are given in Table II.

Table II

Intrinsic Electrical Resistivity of Palladium

Temperature, Kρi, μΩ cmTemperature, Kρi, μΩ cmTemperature, Kρi, μΩ cm
Solid
5 0.0008 140 4.36 400 14.47
10 0.0038 150 4.79 500 17.92
15 0.011 160 5.21 600 21.14
20 0.028 170 5.63 700 24.15
25 0.061 180 6.04 800 26.96
30 0.113 190 6.45 900 29.59
35 0.189 200 6.86 1000 32.03
40 0.294 210 7.26 1100 34.30
45 0.420 220 7.66 1200 36.42
50 0.566 230 8.06 1300 38.39
60 0.908 240 8.46 1400 40.23
70 1.29 250 8.85 1500 41.95
80 1.71 260 9.25 1600 43.55
90 2.14 270 9.64 1700 45.05
100 2.59 273.15 9.76 1800 46.46
110 3.04 280 10.02 1828 46.84
120 3.48 290 10.41
130 3.92 300 10.79
Liquid
1828 81.4 2200 82.2 2700 83.3
1850 81.5 2300 82.4 2800 83.5
1900 81.6 2400 82.6 2900 83.7
2000 81.8 2500 82.8
2100 82.0 2600 83.1

Measurements of Milošević and Babić (20) (250 K–1800 K) were independently corrected for thermal expansion. Their equation differs from the selected equation sinusoidally by trending from initially 0.3% high to 1.7% high at 400 K to 0.9% low at 1400 K to 0.4% high at 1800 K. Figure 1 shows the deviations of the selected values of Matula (which are considered as incorporating the measurements of Laubitz and Matsumura) and the experimental values of Khellaf et al. and Milošević and Babić from the fitted curve. Measurements of Binkele and Brunen (4) (273–1423 K) which were also independently corrected for thermal expansion, showed systematic biases of 1.3% high for runs 1 and 2 and 1.7% high for run 3.

Fig. 1.

Solid palladium – percentage deviations from selected curve

Solid palladium – percentage deviations from selected curve

Also in the high temperature region there are a number of other measurements which were published after the review of Matula. After correction for thermal expansion (19) the electrical resistivity measurements of Miiller and Cezairliyan (21) (1400 K–1800 K) trend from 4.0% to 6.9% high whilst the measurement of Pottlacher (22) at the melting point is 5.9% high. Resistivity ratio measurements of García and Löffler (23) (295 K–1100 K) were corrected from RT/R295 to RT/R273.15 and were also corrected for thermal expansion. On this basis the differences reached a maximum of 4.1% high at 450 K but then showed some scatter varying between 1.0% low at 800 K and 1.6% high at 1100 K. Figure 2 shows the deviations of these three sets of measurements from the fitted curve where the resistivity ratios of García and Löffler were converted to electrical resistivity values for comparison purposes.

Fig. 2.

Solid palladium – percentage deviations from selected curve

Solid palladium – percentage deviations from selected curve

2.2 Liquid

Electrical resistivity values for palladium at the melting point are given in Table III. In the liquid state neither Dupree et al. (24) (1832 K–1924 K) nor Güntherodt et al. (25) (1864 K–2019 K) obtained evidence for any variation of resistivity with temperature. Although Seydel and Fischer (26) (1825 K–3000 K) did obtain evidence of such a variation, the values of Pottlacher (22) (1828 K–2900 K) were selected and fitted to Equation (vi) with selected values for the electrical resistivity of the liquid and are also given in Table II.

Table III

Differences Between the Solid and Liquid Electrical Resistivity of Palladium at the Melting Point

AuthorsReferenceρS, μΩ cmρL, μΩ cmρLSNotes
Dupree et al. 24 (48.8) 83.0 1.700 (a)
Güntherodt et al. 25 47.3 78.8 1.666
Seydel and Fischer 26 50.2 79.1 1.576
Khellaf et al. 18 (45.2) 77.3 1.710 (b)
Pottlacher 22 49.6 81.4 1.641
Present assessment 46.84 81.4 1.738

Notes to Table III

(a) Solid value based on (ρL – ρS)/ ρS = 0.70 ± 0.05

(b) Solid value based on ρL /ρS = 1.71

3. Platinum

Platinum has a face-centred cubic structure and the melting point is a secondary fixed point on ITS-90 at 2041.3 ± 0.4 K (10).

3.1 Solid

The resistance ratio of platinum, WT = RT/R273.15, forms the basis of the International Temperature Scale which White (6) extended to 1300 K and calculated values of intrinsic resistivity using the fixed reference value of 9.82 ± 0.01 μΩ cm at 273.15 K. Above 1300 K White combined the selected values to this temperature with the electrical resistivity measurements of Righini and Rosso (27) (1000 K–2000 K), Laubitz and van der Meer (28) (300 K–1500 K), and Flynn and O’Hagan (29) (273 K–1373 K) and the resistance ratios of Roeser (30) (73 K–1773 K) and Kraftmakher (31) (1000 K–2000 K) together with resistivity measurements given by Martin et al. (32) (300 K–1200 K). White fitted all selected values from 100 K to 2000 K to Equation (vii) which was extrapolated to the melting point. Differences between values derived from this equation and the tabulated values of White as given in Table IV do not exceed 0.01 μΩ cm. An abridged version of the values for the solid phase as given in Table IV was originally given in Platinum Metals Review by Corti (33).

Table IV

Intrinsic Electrical Resistivity of Platinum

Temperature, Kρi, μΩ cmTemperature, Kρi, μΩ cmTemperature, Kρi, μΩ cm
Solid
10 0.0026 150 4.89 500 18.45
15 0.0119 160 5.30 600 22.07
20 0.0367 170 5.70 700 25.59
25 0.0855 180 6.11 800 29.00
30 0.163 190 6.52 900 32.29
35 0.270 200 6.92 1000 35.47
40 0.403 210 7.32 1100 38.54
45 0.560 220 7.72 1200 41.50
50 0.734 230 8.12 1300 44.35
60 1.12 240 8.51 1400 47.09
70 1.53 250 8.91 1500 49.74
80 1.95 260 9.30 1600 52.34
90 2.38 270 9.70 1700 54.93
100 2.80 273.15 9.82 1800 57.51
110 3.23 280 10.09 1900 60.11
120 3.65 290 10.48 2000 62.76
130 4.06 300 10.87 2041.3 63.87
140 4.48 400 14.71
Liquid
2041.3 102.8 2300 105.3 2700 109.1
2050 102.9 2400 106.2 2800 110.1
2100 103.4 2500 107.2 2900 111.1
2200 104.3 2600 108.2

For comparison between these measurements and the selected values as given in Figure 3, the resistivity ratios of Roeser (30) and Kraftmakher (31) were converted to electrical resistivity values and all measurements except those of Flynn and O’Hagan (29) were corrected for thermal expansion using values selected by the present author (34). In addition the measurements of Martin et al. (32) were corrected to correspond to the selected electrical resistivity value at 273.15 K. Because of their larger deviations values of Righini and Rosso (27) are compared with the selected values in Figure 4.

Fig. 3.

Solid platinum – percentage deviations from selected curve

Solid platinum – percentage deviations from selected curve

Fig. 4.

Solid platinum – percentage deviations from selected curve

Solid platinum – percentage deviations from selected curve

In the case of additional electrical resistivity measurements of Birkele and Brunen (4) (273–1497 K), combined runs 1 and 5 trend from initially 0.8% high to 0.1% high at 1200 K to 0.4% high at 1373 K whilst combined runs 2, 3 and 4 trend to an average of 0.5% low above 1000 K. These trends are also shown in Figure 3.

Electrical resistivity measurements of Pottlacher (22) (473 K–1573 K and 1740 K–2042 K in the solid range) are initially 1% higher then trend to an average of 3% higher between 900 and 1573 K before trending to 1.2% higher and then to 0.5% higher between 1740 K and the melting point. These differences are also shown in Figure 5.

Fig. 5.

Solid platinum – percentage deviations from selected curve

Solid platinum – percentage deviations from selected curve

3.2 Liquid

Electrical resistivity values of platinum at the melting point are given in Table V. In the liquid state electrical resistivity measurements of Pottlacher (22) (2042 K–2900 K) were selected as Equation (viii) since in the overlap region they are closely confirmed by measurements of Gathers et al. (36) (2100 K–7300 K) obtained at a pressure of 0.3 GPa which trend from 0.5% low at 2100 K to 1.0% high at 2900 K. Measurements of Hixson and Winkler (37) (2042 K–5100 K) are initially 7% low at the melting point and trend 1% low to 1% high between 2100 K and 2900 K but above 3000 K, in direct comparison with the measurements of Gathers et al., the trend is to an average of 2% low. Selected values for the electrical resistivity of liquid platinum from the melting point to 2900 K are also given in Table IV.

Table V

Differences Between the Solid and Liquid Electrical Resistivity of Platinum at the Melting Point

AuthorsReferenceρS, μΩ cmρL, μΩ cmρLS
Martynyuk and Tsapkov 35 62.1 92.6 1.491
Pottlacher 22 64.2 102.8 1.601
Present assessment 63.87 102.8 1.610

High Temperature Intrinsic Resistivity of Solid Palladium (273.15 to 1828 K)

ρi (μΩ cm) = 4.58639 × 10–2 T – 1.39098 × 10–5 T 2 + 1.84118 × 10–9 T 3 – 1.76742 (v)

Intrinsic Resistivity of Liquid Palladium (1828 to 2900 K)

ρi (μΩ cm) = 2.058 × 10–3 T + 77.7 (vi)

Intrinsic Resistivity of Solid Platinum (100 to 2041.3 K)

ρi (μΩ cm) = 4.681197 × 10–2 T – 3.258075 × 10–5 T 2 + 8.554023 × 10–8 T 3 – 1.594242 × 10–10 T 4 + 1.837342 × 10–13 T 5 - 1.316886 × 10–16 T 6 + 5.678222 × 10–20 T 7 – 1.340980 × 10–23 T 8 + 1.329896 × 10–27 T 9 – 1.621733 (vii)

Intrinsic Resistivity of Liquid Platinum (2041.3 to 2900 K)

ρi (μΩ cm) = 9.604 × 10–3 T + 83.2 (viii)

BACK TO TOP

References

  1.  G. T. Meadon, “Electrical Resistance of Metals”, Plenum Press, New York, USA, 1965
  2.  J. Bass, ‘Electrical Resistivity of Pure Metals and Dilute Alloys’, in “Electrical Resistivity, Kondo and Spin Fluctuation Systems, Spin Glasses and Thermopower”, eds. K.-H. Hellwege and J. L. Olsen, Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, Vol. 15a, Springer-Verlag, Berlin, Heidelberg, New York, 1982, p. 1
  3.  A. Andryushchenko, Yu. D. Chistyakov, A. P. Dostanko, T. L. Evstigneeva, E. V. Galoshina, A. D. Genkin, N. B. Gorina, V. M. Gryaznov, G. S. Khayak, M. M. Kirillova, E. I. Klabunovskii, A. A. Kuranov, V. L. Lisin, V. M. Malyshev, V. A. Matveev, V. A. Mityushov, L. V. Nomerovannaya, V. P. Polyakova, M. V. Raevskaya, D. V. Rumyantsev, E. I. Rytvin, N. M. Sinitsyn, A. M. Skundin, E. M. Sokolovskaya, I. P. Starchenko, N. I. Timofeyev, N. A. Vatolin, L. I. Voronova and V. E. Zinov’yev, “Blagorodnye Metally, Spravochnik” (“Handbook of Precious Metals”), ed. E. M. Savitskii, Metallurgiya Publishers, Moscow, Russia, 1984 (in Russian); English translation by S. N. Gorin, P. P. Pozdeev, B. A. Nikolaev and Yu. P. Liverov, English Edition, ed. A. Prince, Hemisphere Publishing Corp, New York, USA, 1989
  4.  L. Binkele and M. Brunen, “Thermal Conductivity, Electrical Resistivity and Lorentz Function Data for Metallic Elements in the Range 273 to 1500 K”, Forschungszentrum Jülich, Institut für Werkstoffe der Energietechnik, Zentralbibliothek, Germany, 1994
  5.  R. A. Matula, J. Phys. Chem. Ref. Data, 1979, 8, (4), 1147 LINK http://dx.doi.org/10.1063/1.555614
  6.  G. K. White, ‘Recommended Values of Electrical Resistivity and Thermal Conductivity of Platinum’, in “Thermal Conductivity 17”, Gaithersburg, Maryland, USA, 15th–19th June, 1981, Proceedings of the Seventeenth International Thermal Conductivity Conference, ed. J. G. Hust, Purdue Research Foundation, Plenum Press, New York, USA, 1983, p. 95
  7.  F. Bloch, Z. Physik, 1929, 52, (7–8), 555 LINK http://dx.doi.org/10.1007/BF01339455 
  8.  F. Bloch, Z. Physik, 1930, 59, (3–4), 208 LINK http://dx.doi.org/10.1007/BF01341426 
  9.  E. Grüneisen, Ann. Phys., 1933, 408, (5), 530 LINK http://dx.doi.org/10.1002/andp.19334080504 
  10.  R. E. Bedford, G. Bonnier, H. Maas and F. Pavese, Metrologia, 1996, 33, (2), 133 LINK http://dx.doi.org/10.1088/0026-1394/33/2/3 
  11.  R. W. Powell, R. P. Tye and M. J. Woodman, Platinum Metals Rev., 1962, 6, (4), 138LINK https://www.technology.matthey.com/article/6/4/138-143/#  
  12.  R. W. Powell, R. P. Tye and M. J. Woodman, J. Less Common Met., 1967, 12, (1), 1 LINK http://dx.doi.org/10.1016/0022-5088(67)90062-8 
  13.  G. K. White and S. B. Woods, Phil. Trans. R. Soc. Lond. A, 1959, 251, (995), 273 LINK http://dx.doi.org/10.1098/rsta.1959.0004
  14.  M. J. Laubitz and T. Matsumura, Can. J. Phys., 1972, 50, (3), 196 LINK http://dx.doi.org/10.1139/p72-031 
  15.  R. K. Williams and F. J. Weaver, Phys. Rev. B, 1982, 25, (6), 3663LINK http://dx.doi.org/10.1103/PhysRevB.25.3663  
  16.  A. Khellar and J. J. Vuillemin, J. Phys.: Condens. Matter, 1992, 4, (7), 1757 LINK http://dx.doi.org/10.1088/0953-8984/4/7/013  
  17.  J. T. Schriempf, Phys. Rev. Lett., 1968, 20, (19), 1034 LINK http://dx.doi.org/10.1103/PhysRevLett.20.1034 
  18.  A. Khellaf, R. M. Emrick and J. J. Vuillemin, J. Phys. F: Met. Phys., 1987, 17, (10), 2081 LINK http://dx.doi.org/10.1088/0305-4608/17/10/016 
  19.  J. W. Arblaster, Platinum Metals Rev., 2012, 56, (3), 181 LINK https://www.technology.matthey.com/article/56/3/181-189/#  
  20.  N. Milošević and M. Babić, Int. J. Mater. Res., 2013, 104, (5), 462 LINK http://dx.doi.org/10.3139/146.110889 
  21.  A. P. Miiller and A. Cezairliyan, Int. J. Thermophys., 1980, 1, (2), 217 LINK http://dx.doi.org/10.1007/BF00504522
  22.  G. Pottlacher, “High Temperature Thermophysical Properties of 22 Pure Metals”, Edition Keiper, Graz, Austria, 2010, p. 76
  23.  E. Y. García and D. G. Löffler, J. Chem. Eng. Data, 1985, 30, (3), 304 LINK http://dx.doi.org/10.1021/je00041a020 
  24.  B. C. Dupree, J. B. Van Zytveld and J. E. Enderby, J. Phys. F: Met. Phys., 1975, 5, (11), L200 LINK http://dx.doi.org/10.1088/0305-4608/5/11/007 
  25.  H.-J. Güntherodt, E. Hauser, H. U. Künzi and R. Müller, Phys. Lett. A., 1975, 54, (4), 291
  26.  U. Seydel and U. Fischer, J. Phys. F: Met. Phys., 1978, 8, (7), 1397 LINK http://dx.doi.org/10.1088/0305-4608/8/7/013
  27.  F. Righini and A. Rosso, High Temp.-High Pressures, 1980, 12, (3), 335
  28.  M. J. Laubitz and M. P. Van Der Meer, Can. J. Phys., 1966, 44, (12), 66 LINK http://dx.doi.org/10.1139/p66-259 
  29.  D. R. Flynn and M. E. O’Hagan, J. Res. Natl. Bur. Stand., 1967, C71, (4), 255 LINK http://dx.doi.org/10.6028/jres.071C.021
  30.  W. Roeser, “Temperature: Its Measurement and Control in Science and Industry”, ed. M. S. van Dusen, Vol. I, Reinhold Publishing Corp, New York, USA, 1941, p. 1312
  31.  Ya. A. Kraftmakher, High Temp.-High Pressures, 1973, 5, (4), 433
  32.  J. J. Martin, P. H. Sidles and G. C. Danielson, J. Appl. Phys., 1967, 38, (8), 3075 LINK http://dx.doi.org/10.1063/1.1710065 
  33.  C. W. Corti, Platinum Metals Rev., 1984, 28, (4), 164 LINK https://www.technology.matthey.com/article/28/4/164-165/# 
  34.  J. W. Arblaster, Platinum Metals Rev., 1997, 41, (1), 12 LINK https://www.technology.matthey.com/article/41/1/12-21/#
  35.  M. M. Martynyuk and V. I. Tsapkov, Fiz. Metal. Metalloved., 1974, 37, (1), 49; translated into English in Phys. Met. Metallogr., 1974, 37, (1), 40
  36.  G. R. Gathers, J. W. Shaner and W. M. Hodgson, High Temp.-High Pressures, 1979, 11, (5), 529
  37.  R. S. Hixson and M. A. Winkler, Int. J. Thermophys., 1993, 14, (3), 409 LINK http://dx.doi.org/10.1007/BF00566040
 

The Author

John W. Arblaster is interested in the history of science and the evaluation of the thermodynamic and crystallographic properties of the elements. Now retired, he previously worked as a metallurgical chemist in a number of commercial laboratories and was involved in the analysis of a wide range of ferrous and non-ferrous alloys.

Read more from this issue »

BACK TO TOP

SHARE THIS PAGE: