The thermal and electrical conductivity of copper at low temperatures

1952 ◽  
Vol 211 (1104) ◽  
pp. 122-128 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Temperature Variation ◽  
Electrical Resistance ◽  
Low Temperatures ◽  
Small Deviation ◽  
Thermal Resistivity ◽  
Lorenz Number

Following previous work on sodium, the thermal and electrical conductivity of copper has been measured continuously between 90 and 2° K . The specimen was of spectrographic purity, and had been found to have a pronounced minimum in the electrical resistance at about 10° K . A similar, but smaller, anomaly was observed in the thermal resistivity with a corresponding small deviation from the Wiedemann-Franz law at the lowest temperatures. As in the case of sodium, marked disagreement with theory was found in the temperature variation both of the thermal conductivity and of the Lorenz number.

LOW TEMPERATURE RESISTIVITY OF TRANSITION ELEMENTS: VANADIUM, NIOBIUM, AND HAFNIUM

1957 ◽  
Vol 35 (8) ◽  
pp. 892-900 ◽  
Author(s):  
G. K. White ◽  
S. B. Woods
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Electrical Resistivity ◽  
Electrical Resistance ◽  
Thermal Resistivity ◽  
Superconducting Transition ◽  
Transition Elements ◽  
Pure Niobium ◽  
Temperature Resistivity ◽  
The Ideal

Measurements of the thermal conductivity from 2° to 90 ° K. and electrical conductivity from 2° to 300 ° K. are reported for vanadium, niobium, and hafnium. Although the vanadium and hafnium are not as pure as we might wish, measurements on these metals and on niobium allow a tabulation of the "ideal" electrical resistivity clue to thermal scattering for these elements from 300 ° K. down to about 20 ° K. Ice-point values of the "ideal" electrical resistivity are 18.3 μΩ-cm. for vanadium, 13.5 μΩ-cm. for niobium, and 29.4 μΩ-cm. for hafnium. Values for the "ideal" thermal resistivity of vanadium and niobium are deduced from the experimental results although for vanadium and more particularly for hafnium, higher purity specimens are required before a very reliable study of "ideal" thermal resistivity can be made. For the highly ductile pure niobium, the superconducting transition temperature, as determined from electrical resistance, appears to be close to 9.2 ° K.

The thermal and electrical conductivity of sodium at low temperatures

1951 ◽  
Vol 209 (1098) ◽  
pp. 368-375 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Low Temperatures ◽  
Lorenz Curve ◽  
Theoretical Work ◽  
Lattice Vibrations ◽  
Lorenz Number ◽  
Recent Theoretical Work ◽  
Metallic Conduction

Modem theories of metallic conduction, based on the quantum interaction of electrons with the lattice vibrations, predict a considerable variation of Lorenz number with temperature. We have carried out measurements of the thermal and electrical conductivity of two rather pure specimens of sodium continuously from 90 to ~ 4° K and derived an experimental Lorenz curve. Considerable deviations from theory are found; these may in part be due to departure of the lattice vibrations from the Debye spectrum. The thermal conductivity, in particular, is compared with the most recent theoretical work, and the predicted minimum at ~ 0.25Θ has not been found.

Theoretical study of some electrical parameters of graphene

2016 ◽  
Vol 30 (29) ◽  
pp. 1650366
Author(s):  
D. K. Das ◽  
S. Roy ◽  
S. Sahoo
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Electrical Resistivity ◽  
Electrical Properties ◽  
Sample Size ◽  
Electrical Resistance ◽  
Theoretical Study ◽  
Lorenz Number ◽  
Electrical Parameters ◽  
Temperature Range

Graphene, due to its numerous unique properties, is addressed as miraculous material by Novoselov et al. [Nature 490 (2012) 192]. It has ultrahigh heat and thermal conductivity. Several researchers over the globe are working on electrical properties of graphene like electrical resistance, electrical conductivity etc. In this paper, we estimate electrical resistivity, electrical conductivity and Lorenz number for graphene within the temperature range from 300 K to 500 K. Variation of these parameters with respect to temperature and sample size is also reported.

The thermal conductivity of metals at low temperatures

1955 ◽  
Vol 247 (933) ◽  
pp. 441-497 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Single Crystals ◽  
High Purity ◽  
Electrical Resistance ◽  
Low Temperatures ◽  
Lorenz Number ◽  
Normal States ◽  
Full Temperature ◽  
Limiting Value

The thermal conductivity of high-purity samples of thirty-two metals has been measured. These were Ag, Al, Au, Be, Cb, Cd, Ce, Co, Cu, Fe, Ga, In, Ir, La, Mg, Mn, Mo, Ni, Pb, Pd, Pt, Rh, Sb, Sn, Ta, Ti, Tl, U, V, W, Zn and Zr. For most metals measurements were taken from 2 to 40°K, but where necessary they were extended to 90°K. For superconductors they were taken in both the superconducting and normal states. The conductivity was found to be entirely electronic except for Sb and U. Most of the specimens were polycrystalline, but single crystals of Zn, Cd, Sn, Pb, Ga and Ti were measured. For Zn and Ga, specimens of different orientations with respect to the rod axis were obtained, and in both these metals the thermal conductivity was found to be anisotropic. The thermal resistance, W, at low temperatures of nearly all the metals is of the form W — a T 2 + gjT, and the constants a and /? have been calculated. If is the limiting thermal conductivity at high temperatures and 6 is the Debye temperature, then the value of aK^d2 is the same for the metals in any one chemical group. For some metals the electrical resistance was measured at the same time as the thermal conductivity over the full temperature range and hence the Lorenz number, L, was calculated. The limiting value of L at low temperatures for several metals was found to be considerably higher than the theoretical value, in particular for Ti and Zr. A corresponding effect to the minimum in the electrical resistance of Mg has been found in the thermal resistance. A large increase in the thermal conductivity of Fe after a period of time has been ascribed to the precipitation of impurities in the metal. A method is given for estimating the thermal conductivity of a metal at low temperatures.

The thermal conductivity of Ni 2 + doped KMgF 3 in a magnetic field at low temperatures: the effect of single ions and coupled pairs

1970 ◽  
Vol 315 (1523) ◽  
pp. 551-568 ◽  
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Elastic Constants ◽  
Low Temperatures ◽  
Coupling Constants ◽  
Thermal Resistivity ◽  
Paramagnetic Resonance ◽  
Spin Lattice ◽  
Average Spin ◽  
Lattice Coupling

The thermal conductivity between 0.4 and 4.2 K and in magnetic fields up to 50 kOe of KMgF 3 doped with Ni 2+ has been measured. The results are analysed to give values of the average spin-lattice coupling constants ( x Sl ) for the Ni 2+ ion. These are in agreement with values calculated using the magneto-elastic constants (GX1 and 6r44) derived from acoustic paramagnetic resonance (a.p.r.) experiments. Below IK the thermal resistivity as a function of magnetic field shows a number of anomalies, for which possible causes are discussed; it is concluded that they result from phonon interactions with exchange-coupled pairs of Ni 2+ ions. Such pairs are also observed in a.p.r. experiments.

scholarly journals Термоэлектрические свойства полуметаллических и полупроводниковых фольг и нитей Bi-=SUB=-1-x-=/SUB=-Sb-=SUB=-x-=/SUB=-

2019 ◽  
Vol 53 (5) ◽  
pp. 664
Author(s):  
А. Николаева ◽  
Л. Конопко ◽  
И. Гергишан ◽  
К. Рогацкий ◽  
П. Стачовик ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Low Temperatures ◽  
Phonon Scattering ◽  
Surface States ◽  
Experimental Investigations ◽  
Quantum Size ◽  
Thermoelectric Energy ◽  
Conductive Surface ◽  
Order Of Magnitude

AbstractThe results of experimental investigations into the thermoelectric properties (electrical conductivity, thermoelectric power, and thermal conductivity) of microtextured foils and single-crystal wires based on semimetal and semiconductor Bi_1 –_ x Sb_ x alloys are presented in the temperature range of 4.2–300 K. It is found that the band gap Δ E in Bi–17 at % Sb wires increases with decreasing wire diameter d , which is a manifestation of the quantum-size effect. At low temperatures ( T < 50 K), in the wires with d < 400 nm, the electrical conductivity increases due to the significant contribution of highly conductive surface states characteristic of topological insulators. It is found for the first time that the thermal conductivity of semimetal Bi–3 at % Sb foils at low temperatures is two orders of magnitude lower, and that of semiconductor Bi–16 at % Sb foils one order of magnitude lower, than that in bulk samples of the corresponding composition due to significant phonon scattering at grain boundaries and surfaces. This effect leads to considerable enhancement of the thermoelectric figure-of-merit ZT and can be used in miniature low-temperature thermoelectric energy converters.

The thermal conductivities of some dielectric solids at low temperatures (Experimental)

1951 ◽  
Vol 208 (1092) ◽  
pp. 90-108 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Specific Heat ◽  
Temperature Variation ◽  
Temperature Region ◽  
Low Temperatures ◽  
Quartz Crystal ◽  
Corundum Crystal ◽  
Before And After ◽  
Dielectric Solids

An apparatus is described in which the thermal conductivity of solids can be determined at any temperature between 2 and 90°K. Several glasses and dielectric crystals have been measured. It had previously been found that at high temperatures the conductivity of glasses is proportional to the specific heat, but at low temperatures it falls off more slowly than the specific heat. The present experiments show that there is a temperature region in which the conductivity is nearly independent of temperature. A similar variation of conductivity is found for the thermo-plastic Perspex. The effect of lattice defects in crystals was studied by measuring the thermal conductivity of a quartz crystal before and after successive periods of neutron irradiation. After prolonged irradiation the conductivity approached, in both magnitude and temperature variation, that of quartz glass. Subsequent heating produced a substantial recovery in the conductivity. The results on both glasses and on crystals can be explained by the theory developed by Klemens (1951). Further measurements made on a corundum crystal confirm the importance of the ‘Umklapp’ processes, postulated by Peierls, in causing thermal resistance.

scholarly journals Effect of magnetic field on the charge and thermal transport properties of hot and dense QCD matter

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Shubhalaxmi Rath ◽  
Binoy Krishna Patra
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Transport Properties ◽  
Strong Magnetic Field ◽  
Knudsen Number ◽  
Thermal Transport ◽  
Isotropic Medium ◽  
Chemical Potential ◽  
Lorenz Number

Abstract We have studied the effect of strong magnetic field on the charge and thermal transport properties of hot QCD matter at finite chemical potential. For this purpose, we have calculated the electrical conductivity ($$\sigma _\mathrm{el}$$σel) and the thermal conductivity ($$\kappa $$κ) using kinetic theory in the relaxation time approximation, where the interactions are subsumed through the distribution functions within the quasiparticle model at finite temperature, strong magnetic field and finite chemical potential. This study helps to understand the impacts of strong magnetic field and chemical potential on the local equilibrium by the Knudsen number ($$\Omega $$Ω) through $$\kappa $$κ and on the relative behavior between thermal conductivity and electrical conductivity through the Lorenz number (L) in the Wiedemann–Franz law. We have observed that, both $$\sigma _\mathrm{el}$$σel and $$\kappa $$κ get increased in the presence of strong magnetic field, and the additional presence of chemical potential further increases their magnitudes, where $$\sigma _\mathrm{el}$$σel shows decreasing trend with the temperature, opposite to its increasing behavior in the isotropic medium, whereas $$\kappa $$κ increases slowly with the temperature, contrary to its fast increase in the isotropic medium. The variation in $$\kappa $$κ explains the decrease of the Knudsen number with the increase of the temperature. However, in the presence of strong magnetic field and finite chemical potential, $$\Omega $$Ω gets enhanced and approaches unity, thus, the system may move slightly away from the equilibrium state. The Lorenz number ($$\kappa /(\sigma _\mathrm{el} T))$$κ/(σelT)) in the abovementioned regime of strong magnetic field and finite chemical potential shows linear enhancement with the temperature and has smaller magnitude than the isotropic one, thus, it describes the violation of the Wiedemann–Franz law for the hot and dense QCD matter in the presence of a strong magnetic field.

The thermal conductivity of metals

1938 ◽  
Vol 34 (3) ◽  
pp. 474-497 ◽  
Author(s):  
R. E. B. Makinson
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Low Temperatures ◽  
Thermal Equilibrium ◽  
Major Part ◽  
Lattice Energy ◽  
Conduction Electrons ◽  
Electronic Heat ◽  
Lattice Waves ◽  
Lattice Heat

The methods used to measure separately the electronic and lattice heat conductivities κeand κgin a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κeand for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratioLe= κe/σTas a function ofT, both for the monovalent metals and for a model metal with 1·8 × 10−2conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κeand κgas functions ofTare given in both cases, and these, together with a comparison of the observed Lorentz ratio andLe, show that in the monovalent metals κgis unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.

scholarly journals The thermal and the electrical conductivity of a copper crystal at various temperatures

1928 ◽  
Vol 121 (788) ◽  
pp. 640-653 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Low Temperatures ◽  
Thermal Method ◽  
Copper Crystal

The thermal conductivity of a number of regular and non-regular single metallic crystals has been studied by previous workers. There appear to be no marked differences between the conductivity of single and polycrystal specimens of the regular metals, except at low temperatures, but further confirmation of this statement by additional accurate investigations seems necessary, more particularly at low temperatures, where different observers do not agree. The methods which have been used to determine the thermal conductivity of metals are briefly discussed; the thermal method appears to be the simplest, but the electrical or Kohlrausch's method is better adapted for very low temperatures, i.e ., near 20° K.

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