Ref. p. 31 1.1 General remarks 1 1 Introduction 1.1 General remarks Simple arguments from the kinetic theory of gases indicate that, for a system of mobile carriers or particles in the presence of a temperature gradient, the thermal conductivity 1 has the form where C is the specific heat due to the carriers per unit volume, u is the average speed of the carriers and 1 is their mean free path, a quantity which needs further definition. If the carriers are charged particles, such as electrons, each of charge e, then an electric field causes a net current, and the electrical conductivity a becomes a= Ne2 lfmv (2) where m is the mass of each carrier and N the number of carriers per unit volume. Since the mean free path 1 is limited not only by the thermal vibrations of the underlying solid, but also by the presence of physical defects, impurities and solute atoms, both the thermal and the electrical conductivity of metals and alloys display some variability. These irregularities reduce the mean free path both for electrical and for thermal conduction. If the electrons form the principal carriers of heat, there is a connection between the effect of the irregularities on the thermal and electrical conductivities, and both properties display some variability between different samples. However, these changes can be more confusing in the case of thermal conduction, because the thermal conductivity is additively composed of contributions by the conduction electrons (1,) and by the lattice waves (Q. Each component is affected in a different manner by the solute atoms and defects. Fortunately, the user of this volume does not have to be an expert in transport properties of metals to obtain needed thermal conductivity values, nor does he need to subject his metal specimens to detailed chemical and physical analyses. As in the case of electrical conductivity, the greatest sensitivity to chemical and physical imperfections occurs at low temperatures. Also, the lattice component is important mainly at low temperatures; it reaches a maximum typically between 20 and 40 K, and in well-conducting metals it is overshadowed by the electronic component. The electronic component is depressed by solute atoms, similarly to the electrical conductivity. Around room temperature it requires typically a solute content of around 1% to double the electrical resistivity. Similarly one can expect such a level of impurities to halve the room temperature thermal conductivity. Note that this applies to impurities atomically dissolved within the metal matrix; impurities which are segregated at grain boundaries or form precipitates will have a smaller effect. The sensitivity to solute atoms increases as the temperature is lowered and decreasesa t higher temperatures. The majority of users can therefore stop reading the present introduction at this point and look up the thermal conductivity of the metal in question in Chapter 2, (or the thermal conductivity of an alloy, if that alloy has been measured, in Chapter 3). Those who are concerned with metals containing 0.1% or more of solutes or with metals at low tempera- tures have to be more careful. The electronic component 1, is linked to the electrical resistivity. If the electrical resistivity is known, one can often use the Wiedemann-Franz-Lorenz law to estimate 1,. At low temperatures however one must estimate 1, from the “ideal” and the “residual” thermal resistivities, as discussed below. If the alloy composition is known, but the thermal conductivity of that composition is lacking, one must first estimate the electrical conductivity and then estimate 1,. The electrical resistivity has been treated in Landolt-Bornstein, New Series, Volume III/lSa. For convenience, the increase in resistivity of dilute alloys per atomic percent of solute is reproduced in the present volume (Section 3.1) for some alloy combina- tions. In dilute alloys, particularly at ordinary and high temperatures, one can neglect I, and identify I, with the overall thermal conductivity. But at low temperatures, or for nondilute alloys, the lattice component must be considered. It will depend not only on the solute content but also on the state of plastic deformation. To estimate the thermal conductivity in such cases, one must estimate 1, and 1, separately, 1, from the electrical resistivity, while I, requires knowledge of this separate component in similar alloy systems. The Lorenz ratio Under conditions enumerated below, the electronic thermal conductivity 1, is related to the electrical conductivity CTb y 1, = LaT (3) Land&-Bhstein New Series IIII15c Klemens 2 1.1 General remarks [Ref. p. 3 where T is the absolute temperature, L the Lorenz ratio, calculable from the kinetic theory of the electron gas. In metals one must use Fermi-Dirac statistics for the electron gas, and if T is well below the degeneracy temperature, the value of L as obtained by Sommerfeld is L, = (rr2/3)(k/e)2 (4) where k is the Boltzmann constant, e the electronic charge. The numerical value of L, is L, = 2.443.10-* WQ/K’ (or V2/K2) (44 Use of the Sommerfeld value L, requires three conditions to be satisfied: (1) The electron gas is highly degenerate, that means the density of electron states as function of electron energy is practically constant over an energy interval of several kT about the Fermi energy. (2) The processes which scatter the electrons and limit their mean free path are of such a nature as to make the mean free path independent of whether the electron gas is disturbed by an electric field or by a temperature gradient. (3) The Wiedemann-Franz-Lorenz law applies only to the electronic component I.,, not to the total thermal conductivity ).= ).,+).,, so that a correction for R, is required if 2, is small and does not overwhelm I.,. Condition (1) is satisfied at low and at ordinary temperatures, but L may depart somewhat from L, at high temperatures in transition metals and even more so in actinides. Semimetals depart from high degener- acy at ordinary temperatures and are thus treated separately in Chapter 4. Semimetals also have an appreci- able lattice component. Condition (2) is violated in the interaction of electrons with lattice waves at low temperatures, and in the interaction of electrons with each other. For present purposes these deviations from L, are already accounted for when using the ideal thermal resistivity & defined below. The lattice component is comparable to the thermal conductivity of non-metallic solids of similar elastic properties, and may be neglected in well-conducting metals and their dilute alloys. Estimation for metals and dilute alloys Since the electron mean free path is limited both by lattice vibrations and by solute atoms and other lattice defects.t he electrical resistivity Q= l/a is composed of contributions from these scattering mechanisms: e=eiV)+eo+Ae (9 where ei(T), the “ideal” or intrinsic resistivity due to the lattice vibrations is a function of temperature, while the “residual” resistivity e,,, which is also the value of e at T=O, is due to solutes and defects. The term Ap, the deviation from Matthiessen’s rule, depends on T and also on eo, increasing at tirst and eventually saturating as e. is increased; the saturation value is usually a small fraction of ei(T). The electronic thermal resistivity W= l/I., is similarly composed of a defect-induced “residual” component M’, which varies as l/T, and an “ideal” component q due to lattice vibrations. Again there will be some deviation from the additivity of thermal resistivities, so that l/R,= W= W,+w(T)+AW (6) Except at highest temperatures, where the electron gas may not be completely degenerate, e. and W, are related by the Sommerfeld value of the Lorenz ratio, i.e. W = eo& T (7) since scattering of electrons by defects is simple elastic. The intrinsic component is more complicated, and in general YZdLo T (8) the equality holding approximately at ordinary and high temperatures, while at low temperatures w can exceed ei/L, T by a large factor. Generally at low temperatures WrocT 2, while QJL, TaT”, and at very low temperatures nz4. The departure from additivity is also relatively larger: AW/q can be as large as 0.3, while AQ/ei rarely exceeds0 .1. Values of the intrinsic thermal resistivity w are the reciprocals of the thermal conductivities of pure metals given in Chapter 2. The resistivity component W,, given by (7) in terms of e,,, must be included in the case of alloys, and in all cases at sufficiently low temperatures. The value of e. and thus W, must be determined either by measuring the resistivity - preferably at liquid helium temperatures - or estimated from a knowledge of the composition, using the results of Section 3.1. With Wi and W, thus known, ,I,= l/W can be estimated; however at the temperature where W, and w are comparable, AW is at its most important, and may be as large as 0.3 B{. Klemens 1.1 General remarks (references) 3 In well-conducting metal specimens 1, can be identified with the total thermal conductivity. If e. exceeds about 1. lo- 8 am, the lattice component should be considered below about 70 K. In poorly conducting metals and in concentrated alloys it is significant even at ordinary temperatures. Estimation for non-dilute alloys In these alloys, two modifications must be made: (1) one can no longer take y to be that of the parent metal, but must find it by interpolating between the w values of the major constituents. (2) When W, is large enough and L, correspondingly small, some estimate of the lattice component 1, is needed. Although a linear interpolation of B$ with concentration would often be a natural procedure, there are casesw hen this would not be correct, since the band structure may change its character at some critical composition. For example, in the Ag-Pd system there is a change from monovalent metal to transition metal near 40% Pd. Again, systems without a continuous range of solid solubility do not permit linear interpolation. An estimate of w has then to be based on existing thermal conductivities of some compositions of the alloy. If these are not available, one can be guided by electrical resistivity data. In concentrated alloys the residual thermal resistivity frequently dominates over w, so that but the estimation of the lattice component remains a problem. If the interaction of the lattice waves with the electrons can be neglected, then the lattice conductivity of metals has the same form as that of dielectric crystals, i.e. I,= bT-’ (10) where b is usually larger for lighter atoms. At low temperatures the interaction with the electrons becomes important, and 1, reaches a maximum as T is lowered. Now in concentrated alloys the lattice waves are also scattered by solute atoms, so that 1,=b’T-” where+<n<l. (11) For large solute concentrations c, n tends to the minimum value 3, and b’ccc-*. The fractional reduction of 1, by solute atoms is less than that of the electrical conductivity, because low-frequency lattice waves are significant in heat transport but are not scattered by solute atoms. Thus while 1% solutes typically halve the room temperature electrical conductivity, 1, is reduced at room tempera- ture by only 20% ; 4% solutes reduce 1, by perhaps 40 to 50%. For higher solute concentrations c, b’ccc-* and n= 3. Also, the reductions are smaller if solute atoms have nearly the same mass and size as the solvent atoms. Values of 1, for most metals at ordinary temperatures have been estimated by Klemens and Williams [86Kll]. These estimates are given as a fraction of the total thermal conductivity of the metal at two temperatures (the Debye temperature and the highest temperature of measurement), so that the magnitude of the lattice conductivity can be estimated in conjunction with the data of Section 2.2. Values of 1, for alloys are smaller. Thus for Ti, where 1, at 300 K is about 10 W/m K, various solutes in the concentration range around 1 at% cause reductions which are smaller than the uncertainty in the estimate of 1,. However, in alloys with groups of solutes of total concentration around 7.5 at%, 1, is reduced to between 3 . . .5 W/m K. Some estimates of lattice conductivities of alloys are given in Section 3.1. General references Readable and compact accounts of the thermal conductivities of solids have been given by Berman [76Bel] and by Parrott and Stuckes [75Pal]. A more detailed account of the low temperature theory is found in the Handbuch der Physik [56Kll]. The review by Klemens and Williams referred to above [86Kll] concentrates on temperatures above 100 K. The two volumes “Thermal Conductivity” edited by Tye [69Tyl] contain chapters by different contributors on methods of measurements, summaries of results and theory. 56Kll Klemens, P.G.: Thermal Conductivity of Solids at Low Temperatures, Handbuch der Physik, Band XIV: Kaltephysik I, S. Fliigge (ed.), Berlin: Springer-Verlag, 1956, p. 198. 69Tyl Tye, R.P. (ed.): Thermal Conductivity (2 volumes), London, New York: Academic Press, 1969. 75Pal Parrott, J.E., Stuckes, A.D.: Thermal Conductivity of Solids, London: Pion, 1975. 76Bel Berman, R.: Thermal Conduction in Solids, Oxford University Press, 1976. 86Kll Klemens, P.G., Williams, R.K.: Int. Met. Rev. 31 (1986) 197. Land&-Biirnstein New SeriesI II/15c Klemens 4 1.2 List of symbols and abbreviations 1.2 List of symbols and abbreviations Synhols and wits Symbols Units Definitions a m2/s thermal diffusivity 1 da -- Pa-’ normalised pressure dependenceo f thermal diffusivity a dp B T magnetic field d kg/m3 density do kg/m3 theoretical density d m film thickness; diameter e C electronic charge k J/K Boltzmann constant L V2/K2 Lorenz ratio L= QI./T (Lorenz number) L, V2/K2 Lorenz ratio, electronic contribution Lo VZ/K2 Lorenz ratio; the “ideal” Sommerfeld value Lo= (n2/3)(k/e)‘= 2.443. low8 V2/K2 1 dL -- Pa-’ normalised pressure dependenceo f Lorenz ratio Ldp 1e lf m effective mean-free path of phonons P Pa pressure 4 m-l wave vector of phonons RRR ratio of electrical resistance at 273 K to resistance at 4.2 K RRR* ratio of electrical resistance at 293 K to resistance at 4.2 K RRR** ratio of electrical resistance at 300 K to resistance at 4.2 K SC V/K Seebeckc oefficient of electrons Stl V/K Seebeckc oefficient of holes T K’) (absolute) temperature T, K Curie temperature T, K superconducting transition temperature ‘I K liquidus temperature L K melting temperature TN K Ntel temperature T, K solidus temperature M’ mK,/W total thermal resistivity K mK/W electronic thermal resistivity I+; mK/W ideal thermal resistivity Mb mK,/W impurity thermal resistivity VP thermomagnetic tensor component aij Y Griineisen parameter Qo K Debye temperature (determined by fitting the observed specific heat to the Debye theory in the region where the specific heat is about half of the Dulong-Petit value) R Pa-’ compressibility I. W/m K 2, (total) thermal conductivity 41) W/m K thermal conductivity measured perpendicular to the axis of highest symmetry. In the group V semimetals this means perpendicular to the trigonal axis, in graphite it is perpendicular to the c-axis ‘) T[K]=TC]+273.15. 2, I. p’/mK]= 100 I. [W/cm K]=418.68 1. [cal/scm K]= 1.163L [kcal/h m K]= 1.7311 [Btu/h ft”F]. Landoll-BBmstein Klemens New SerieIlsI/ ISc 1.2 List of symbols and abbreviations 5 Symbols Units Definitions WI) W/m K thermal conductivity parallel to the highest symmetry axis & W/m K total electronic thermal conductivity 1, W/m K thermal conductivity due to the electrons L-h W/m K bipolar thermal conductivity 1, W/m K phonon (lattice) thermal conductivity ah W/m K thermal conductivity due to the holes 1, W/m K solidus thermal conductivity at or near melting point 1 da -- Pa-’ normalised pressure dependence of thermal conductivity a dp d In 1 logarithmic volume dependenceo f thermal conductivity d In V am electrical resistivity am ideal electrical resistivity Rm residual resistivity, contribution by impurities Rm galvanomagnetic tensor component f-)-lm-1 electrical conductivity O-lm-l electrical conductivity, contribution by electrons g--lm-1 electrical conductivity, contribution by holes Abbreviations A Angstrom method balance balance: calculated to 100% from the amount of components given by the author bee body-centered cubic C comparative method cub cubic D diffusivity D= I/Cd, a non steady-state method requiring knowledge of the heat capacity C and density d to obtain 1. Methods include the periodic temperature variation used by Angstrom (A) and modern laser flash (F) methods dhcp double hexagonal close packed E electrical (Joule) heating of the specimen with temperature profile determined by thermocouples (K = Kohlrausch) or optical radiometry (W = Worthing) F laser flash method fee face-centered cubic hcp hexagonal close packed hex hexagonal L longitudinal or axial heat flow along a rod, the steady-state method most commonly used particu- larly at low temperatures w longitudinal heat flow along a rod with a comparison or reference rod in series mono monoclinic ortho orthorhombic PC polycrystal(line) R radial heat flow in steady-state RT room temperature rhomb rhombohedral SC single crystal tetr tetragonal Land&-BBmstein New Series 111/15c Klemens 6 2.1 Thermal conductivity at 273 .ee3 00 K [Ref. p. 118 2 Thermal conductivity of pure metals 2.1 Thermal conductivity at 273 - - - 300 K Table 1 gives selected measured values of (1) R at 273.15 K or neighbouring temperatures, (2) the electrical residual resistance ratio, RRR = R(273 K)/R(4.2 K) or RRR* = R(293 K)/R (4.2 K), (3) referencest o the mea- surements of I., (4) electrical resistivity ~~(273K ) taken from Landolt-Bornstein, Volume III/lSa [82bal] and (5) Lorenz ratio L= @I./T at 273 K or nearby temperature. Each metallic element is denoted by its chemical symbol, the crystal structure and whether the sample was single crystal (SC)o r polycrystalline (PC).T he RRR is a measure of the electrical purity and the extent to which the thermal conductivity is reduced below its ‘ideal’ value. For good conductors the thermal conductivity is primarily electronic and therefore an RRR of 100 indicates that impurity scattering is l/100 or 1% at 293 K. It will be correspondingly less important at higher temperatures. Measurements of I. are usually made at room temperature, rather than at the ice-point, 273.15 K, but for metals I. is relatively constant in this region, unlike Q(T) which varies approximately linearly with T at about 0.4% per Kelvin. Table 1. Metal Structure 1 RRR Ref. L Qi W/m K 10m8R m 1O-8 V2/K2 AC No data found for this metal. Ag pc, fee 436 (273) 1050 70Mal 1.467( 273) 2.34 (273) 435.5 (273) 800 71Lal 434 (300) 1050 70Mal Al PC,f ee 236 (273) 10000 76Col 2.429 (273) 2.10 (273) 237 (273) 520 66Mol 232 (273) ? 65Pol 236.5 (300) 10000 76Col As Seec hapter 4 on semimetals. Au PC,f ee 318 (273) 100 71Lal 2.031 (273) 2.39 (273) 320 (273) 93 76Col 318 (273) 110 71Hul 322 (273) ? 7OPol 316 (300) -150 69Lal Ba pc, bee 23.3 (273) 233 78Col 29.8 (273) 2.55 (273) Be PC,h cp 207 (280) <lO 72Wil 3.7 (273) 196 (300) <lO 72Wi 1 3.9 (280) 2.8 (280) Bi Seec hapter 4 on semimetals. C (graphite) Seec hapter 4 on semimetals. Ca PC,f ee 186 (273) 70 75Col 3.08 (273) 2.13 (273) 184 (291) 70 75Col Cd SC,b (II) 84 (296) >lOO 32Gol 7.81 (273) 2.43 (296) SC,h cp (1) 104 (296) >lOO 32Gol 6.30 (273) 2.43 (296) Ce PC,d b 11.2(291) -10 66Jol 77 (273) 11.2(291) ? 71Wil 83 (273) - 3.5 (273) co PC>h cp 100 (285) -50 69Wi 1 5.2 (273) 99 (300) 130 73Lal 5.99 (300) 1.98( 300) Cr PC,b ee 95.7 (280) 280 68Mol 11.8( 273) 4.11(280) 94.3 (293) 330 71Lal 93.7 (290) 380 77Mol 12.4( 290) 4.01 (290) cs pc, bee 37 (295) ? 64Lel 18.0( 273) 2.5 (295) White Ref. p. 1181 2.1 Thermal conductivity at 273 . . . 300 K 7 Metal Structure 1 RRR Ref. L @i W/m K 10e8 Rm 10-s V2/K2 CU pc, fee 403.5 (275) 900 67Mol 1.55 (273) 2.27 (275) 402 (300) 3000 84Hul 1.73 (300) 2.31(300) 399 (300) 900 67Lal 1.73 (300) 2.30 (300) DY SC>h cp (II) 11.4 (275) 12 68Bol 70 (273) 3.1 (275) SC,h cp (1) 10.1 (275) 22 68Bol 104 (273) 4.0 (275) PC, hcp 10.4 (291) ? 66Jol - 93 (291) 3.75 (291) 9.7 (300) 22 89Bil -96 (300) 3.45 (300) Er SC, hcp (II) 18.5 (275) 8 68Bol 40 (273) 3.05 (275) SC,h cp (1) 12.8 (275) 15 68Bol 77 (273) 3.9 (275) PC, hcp 13.8 (291) ? 66Jol 79 (291) 3.75 (291) 12.5 (300) 22 89Bil 3.05 (300) Eu pc, bee - (273) - 86 (273) - 10.0 (500) 10 76Zil 115 (500) 2.3 (500) Fe pc, bee 80.2 (280) 200 66Mol 8.64 (273) 2.57 (280) 79 (300) 100, 84Hul 10.0 (300) 300 Fr No data found for this metal. Ga SC,o rtho (11c ) 16.0 (273) >lOOO 63Pol 50.3 (273) 2.95 (273) SC,o rtho (11a ) 41.0 (273) >lOOO 63Pol 16.05 (273) 2.41(273) SC,o rtho (11b ) 88.6 (273) >lOOO 63Pol 7.5 (273) 2.43 (273) Gd SCh>c p (II) 10.4 (275) 46 69Nel 118 (273) 4.6 (275) 10.8 (300) 46 69Nel 4.4 (300) SCh, cp (1) 10.4 (275) 29 69Nel 128 (273) 5.0 (275) 10.3 (300) 29 69Nel 4.6 (300) PC, hcp 9.1(291) ? 66Jol 128 (273) 4.2 (291) Hf PC, hcp 22.4 (293) ? 61Cal 31 (295) 2.45 (293) 22.3 (323) -6 53Del Hg SC,r homb (II) 34.1(197) ? 32Rel 14.6 (197) 2.53 (197) SC,r homb (I) 25.9 (196) ? 32Rel 19.3 (196) 2.55 (196) Ho SC,h cp (II) 21.6 (275) 17 69Nel 54 (273) 4.6 (275) 22.0 (300) 17 69Nel 4.5 (300) SC,h cp (4 13.7 (275) 35 69Nel 93 (273) 4.8 (275) 13.9 (300) 35 69Nel 4.7 (300) PC, hcp 10.6 (291) ? 66Jol 3.8 (300) 11.8 (300) 21 89Bil 78 (300) 3.2 (300) In SCf,c t (II) 82.8 (280) -8000 68Bal 8.10 (280) 2.395 (280) SC,f ct (I) 80.4 (280) -8000 68Bal 8.40 (280) 2.43 (280) PC 81.0 (280) 10700 68Bal 8.25 (280) 2.385 (280) 87.5 (273) - 100 62Pol 8.00 (273) 2.56 (273) Ir pc, fee 149 (277) 86 67Po2 4.70 (273) 2.57 (277) 148 (300) 86 67Po2 5.3 (300) 2.6 (300) K pc, bee 98.5 (273) >lOOO 79Col 6.20 (273) 2.235 (273) 6.45 (273) 94.6 (300) >lOOO 79Col 7.09 (300) 2.235 (300) La PC, dhcp 14.0 (291) ? 66Jol 59 (273) 2.9 (291) 15 (273) ? 66Gol Land&Biirnstein New SeriesI II/lSc White 8 2.1 Thermal conductivity at 273 ... 300 K [Ref. p. 118 Metal Structure R RRR Ref. L @i W/m K 10e8 Rm lo-‘V=/K= Li pc, bee 65 (273) - 100 26Bi 1 8.5 (273) 2.05 (273) 70 (273) ? 20Mel 2.2 (273) Lu SC>hc p (II) 23 (275) 40 68Bol 30.5 (273) 2.62 (275) SC,h cp (1) 14 (275) 26 68Bol 68 (273) 3.46 (275) PC,h cp 16.2( 291) ? 66Jol ‘v5 0 (273) 3.3 (291) Mg PC,h cp 150.5( 293) ? 65Tal 4.1 (273) 160(291) ? 32Kil 4.3 (291) 153 (301) >50 25Mal 4.5 (301) 2.29 (301) 154.5( 323) >50 64Po 1 MnW PC,c ub 7.8 (291) -13 66Jol 137 (273) 4.0 (29 1) MO PC,t -cc 143 (273) 7000 74Mol 4.88 (273) 2.56 (273) 139 (277) 27 67Bal 2.56 (277) Na pc, bee 142 (273) -600 72Col 4.29 (273) 2.23 (273) 138 (300) - 600 72Col 4.87 (300) 2.25 (300) Nb PC,b ee 51.8 (280) 291 83Wil 13.3( 273) 2.53 (280) 51.8 (300) 35 80Mo 1 2.55 (300) Nd PC,d hcp 16.5( 291) -10 66Jol 58 (273) 3.7 (291) 13.1( 300) 5 89Bil 3.0 (300) Ni PC,f ee 93 (280) >lOO 69Bal 6.24 (273) 2.19 (280) 84 (323) -100 65Po2 2.16 (323) NP No data found for this metal. OS PC,h cp 87 (323) 33 67Pol 8.3 (273) 2.7 (323) Pa No data found for this metal. Pb PC,b ee 35.5 (273) ? 89Hel 19.2( 273) 2.50 (273) 35.5 (273) ? 66Dal 2.50 (273) 34.9 (280) 105 73Mol 2.46 (280) Pd pc, fee 71.7 (275) 250 72Lal 9.74 (273) 2.57 (275) Pm No data found for this metal. PO No data found for this metal. Pr PC,d hcp 12.8( 280) ? 64Del 65 (273) 3.1 (280) 12.0(291) ? 66Jol 2.7 (29 1) Pt pc, fee 71.9 (280) 426 66Mol 9.82 (273) 2.59 (280) 70.4 (280) 600 66Mol 2.54 (280) 71.0 (300) 1890 66Lal 2.57 (300) 69.5 (273) ? 7OPo1 70.3 (273) ? 64Bol Pu pc, mono 5.2 (298) ? 83Anl - 130 (273) 2.48 (298) 6.5 (300) ? 67Anl Rb PC,b ee 55.8 (273) ‘ideal’ 79Co2 11.25( 273) 2.30 (273) 54.4 (290) ‘ideal’ 79co2 2.29 (290) Re PC>h cp 49 (273) 220 63Po2 16.9( 273) 3.05 (273) 48 (293) 220 63Po2 3.08 (273) Rh pc, fee 153 (280) - 200 67Po2 4.35 (273) 2.46 (280) 150 (300) - 200 67Po2 2.45 (300) Landolt-BBmstein White IllilSc New Serin Ref. p. 1183 2.1 Thermal conductivity at 273 ... 300 K 9 Metal Structure /I RRR Ref. L @i W/m K 10e8~m lo-* V2/K2 Ru SCh, cp (II) 131(280) 77 67Po2 5.15 (273) 2.52 (280) 132 (300) 77 67Po2 2.56 (300) SCh, cp (1) 108 (280) 94 67Po2 6.65 (273) 2.66 (280) 109 (300) 94 67Po2 2.73 (300) PC 110 (280) 388 67Po2 6.7 (273) 2.72 (280) 109 (300) 388 67Po2 2.74 (300) Sb See chapter 4 on semimetals. SC PC, hcp 21.8 (273) -5 65Ar1 44 (273) 4.3 (273) 15.7 (291) ? 66Jol 2.8 (291) Sm pc, hex 13.4 (291) ? 66Jol - 90 (273) 4.3 (291) 10.7 (300) 5 89Bil 3.1(300) Sn pc, bet 62.2 (288) ? 85Hel ll(273) 2.5 (288) 69.4 (291) ? 85Hel 2.8 (291) 67 (273) ? 08Lel 2.7 (273) Sr pc, fee 51.9 (273) 28 78Col 11.0 (273) 2.18 (273) 48.6 (282) 16 78Col 2.20 (282) Ta pc, bee 57.7 (280) 230 82Wil 12.1(273) 2.56 (280) 57.8 (300) 170 82Wil 2.58 (300) Tb SC,h cp (II) 14.8 (300) 54 69Nel 99 (273) 5.0 (300) SC,h cp (1) 9.5 (300) 51 69Nel 118 (273) 3.9 (300) PC 10.4 (291) ? 66Jol 110 (273) 4.25 (291) Tc PC, hcp 51(300) ? 65Bal 16.7 (273) - 3.4 (300) Th pc, fee 49.3 (273) 55 70Anl 13.9 (273) 2.56 (273) 48.8 (300) 55 70Anl 2.57 (300) Ti PC, hcp 22.3 (273) ? 85Pel 40 (273) 3.25 (273) 20.5 (280) 18 69Bal 3.21(280) Tl PC, hcp 50.6 (273) ? 27Eul 15 (273) 2.8 (273) Tm SCh, cp (II) 24.1(280) 11 68Edl 40 (273) 3.8 (280) SCh, cp (1) 14.1(280) 47 68Edl 81(273) 4.2 (280) PC 14.0 (291) ? 66Jol -60 (273) 3.5 (291) U pc, ortho 28 (278) 28 53Tyl 24 (273) 2.8 (278) 25 (293) ? 56Bal V pc, bee 35 (260) 1520 77Jul 18.9 (273) 2.41 (260) W pc, bee 183 (280) 400 66Mol 4.85 (273) 3.27 (280) 176 (300) 300 84Hul 3.20 (300) Y PC, hcp 15.9 (291) ? 66Jol - 52 (273) 2.9 (29 1) 13.1 (300) 8 86Bil 2.8 (300) Yb pc, fee - - - 24 (273) - Zn SC,h cp (II) 127 (275) >1500 87Mul 5.6 (273) 2.60 (275) 122 (293) > 100 32Gol 2.52 (293) SC,h cp (J-J 124 (293) > 100 32Gol 5.4 (273) 2.46 (293) PC 114.5 (283) > 50 69Wil 5.5 (273) 2.31(283) Zr PC, hcp 20.5 (323) ? 53De2 39 (273) - 3.4 (323) 20.9 (323) > 20 51Bil 3.2 (323) Land&Bhstein New SeriesI II/lSc White 10 2.2 Thermal conductivity above 50 K [Ref. p. 118 2.2 Thermal conductivity above 50 K Tables and graphs are presented of measured values of 1 in the temperature region where impurity effects are not dominant. At lower temperatures (see section 2.3) impurity scattering becomes dominant and therefore values of ). vary greatly from sample to sample. At ambient and higher temperatures, ). values are intrinsic to the material provided purity is high, e.g. for RRR values exceeding 100. The metals are given in alphabetical order of their symbols together with crystal structure and melting temperature T,. For many elements we have no experimental data at temperatures approaching T,. Data on single crystals of anisotropic elements are also scarce and are listed where published. The data given in the table for each element are also shown in the accompanying figure. They represent a “subjective” selection from reports of measurements on samples of the highest available purity. Not all reports are included except for elements for which there are few published data. Our selection is confined to sets of values which appear to be internally consistent, do not have large (say 55%) random errors and indicate reliable temperature measurement.T hus many sets are from national laboratories where there is thermometric expertise. As indicated by footnotes we have in some cases averaged the values at neighbouring temperatures, say near to 400 or to 500K; in other cases different sets or runs on the same or similar samples have been averaged. Also in some cases we have had to read values from graphs which limits accuracy. The values of I. are sometimes stated here to fewer significant figures than in the original because the apparent errors made the extra figures meaningless. In other cases an extra figure has been retained to illustrate relative changes rather than absolute accuracy. The author thanks those who kindly provided values which were unpublished or only published in graphical form: N. Backlund, L. Binkele, R. Bogaard, P.G. Klemens, J.F. Kos, R.B. Roberts, J. Rungis, F.A. Schmidt, B. Sundqvist, R.J. Tainsh and R.K. Williams. The method of measurement used to obtain each column of data in these tables is indicated in section 1.2 in list of symbols and abbreviations. AC (actinium) Structure: fee; T,= 1323 K. No data found for this metal. Land&-Bdmstein White New Series III.‘ISc