The thermal conductivity of lead at low temperatures

1958 ◽  
Vol 244 (1236) ◽  
pp. 85-100 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Plastic Deformation ◽  
Single Crystals ◽  
Superconducting State ◽  
Low Temperatures ◽  
Conductivity Measurements ◽  
Conduction Electrons ◽  
Lattice Waves ◽  
Normal States ◽  
Theory Of Superconductivity

Thermal conductivity measurements have been made upon a series of lead specimens between 1 and 4° K, in the superconducting and in the normal states. Both single crystals and polycrystals were studied, and also specimens containing various added impurities. The results in the superconducting state confirm the hypothesis that below about 1·4° K the thermal current is carried entirely by lattice waves, and that these are not scattered by conduction electrons. This conclusion is based upon three pieces of evidence: (1) the thermal conductivity K s is insensitive to the amount and species of impurity; (2) it depends upon the geometry of the specimen for sufficiently thin specimens; (3) it is sensitive to plastic deformation, which can be explained if the lattice waves are scattered by dislocations. A brief discussion is given of the possible significance of these results in the theory of superconductivity.

The thermal conductivity of some superconductors

1960 ◽  
Vol 254 (1279) ◽  
pp. 542-550 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Plastic Deformation ◽  
Superconducting State ◽  
Conduction Mechanism ◽  
Lead Alloy ◽  
Conductivity Measurements ◽  
Pure Lead ◽  
Lattice Waves ◽  
Bismuth Alloy ◽  
Temperature Dependance

The thermal conductivities of single crystals of lead, niobium and a lead-bismuth alloy have been measured between 1 and 4°K in the superconducting state. At temperatures near 1 °K the conduction is mostly by lattice waves and the effect of plastic deformation on this conduction mechanism has been investigated. This has shown that deformation greatly reduces the magnitude of the conductivity and that its temperature dependance changes from T 3 to values nearer T 2 for niobium and the lead alloy but remains unchanged for pure lead. It is suggested that these changes in conductivity are due to the scattering of lattice waves by isolated dislocations, and an attempt has been made to correlate the densities of dislocations obtained from thermal conductivity measurements with those obtained from a knowledge of the amount by which the specimen was deformed.

The thermal conductivity of tin at low temperatures

1955 ◽  
Vol 229 (1179) ◽  
pp. 473-492 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Low Temperatures ◽  
Fluid Model ◽  
Accurate Method ◽  
Resistance Thermometers ◽  
Lattice Waves ◽  
Normal States ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Good Agreement

An account is given of an accurate method of measuring the thermal conductivity of metals between 0·2 and 4°K using carbon aquadag resistance thermometers. Experimental curves are shown for tin specimens of different crystal structure and of varying impurity contents in both superconducting and normal states, and they are analyzed on the basis of the two-fluid model of superconductivity. It appears that at low temperatures the conductivity is mainly due to the lattice, since the observed temperature variation for all specimens is consistent with a T 3 law at sufficiently low temperatures. Good agreement is obtained between the effective mean free paths of the lattice waves and the values expected from the rod dimensions and crystal sizes. The electronic contribution to the thermal conduction in the superconducting state falls very rapidly below T c , and, to a first approximation, the ratio of this contribution to that in the normal state is a function of temperature and not of impurity. The effects of magnetic fields on measurements of thermal conductivity are also briefly discussed and it is shown that the results may be complicated by frozen-in flux.

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 Lattice Component of the Thermal Conductivity of Metals and Alloys

1954 ◽  
Vol 7 (1) ◽  
pp. 57 ◽  
Author(s):  
PG Klemens
Keyword(s):  
Thermal Conductivity ◽  
High Temperatures ◽  
Low Temperatures ◽  
Metals And Alloys ◽  
Transverse Lattice ◽  
Conduction Electrons ◽  
Electronic Thermal Conductivity ◽  
Lattice Waves ◽  
Lattice Component

Makinson's (1938) theory of the lattice component of the thermal conductivity of metals and alloys, when limited at low temperatures by interaction with the conduction electrons, is re-examined, and the magnitude of the lattice conductivity is related to the electronic thermal conductivity at low temperatures, thus avoiding uncertainties in the theory at high temperatures. The result depends on whether transverse lattice waves can interact with the electrons.

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.

Thermal Conductivity of Manganese Ferrite Single Crystals at Low Temperatures

1966 ◽  
Vol 5 (5) ◽  
pp. 455-455 ◽  
Author(s):  
Yasutaka Suemune
Keyword(s):  
Thermal Conductivity ◽  
Single Crystals ◽  
Low Temperatures ◽  
Manganese Ferrite

Thermal Conductivity of Single-Crystal and Sintered RBa2Cu3O7 at low Temperatures

1987 ◽  
Vol 99 ◽  
Author(s):  
J. E. Graebner ◽  
L. F. Schneemeyer ◽  
R. J. Cava ◽  
J. V. Waszczak ◽  
E. A. Rietman
Keyword(s):  
Thermal Conductivity ◽  
Particle Size ◽  
Single Crystals ◽  
Free Path ◽  
Low Temperatures ◽  
Rayleigh Scattering ◽  
Resonant Scattering ◽  
Sintered Sample ◽  
Mean Free Path ◽  
Strong Scattering

ABSTRACTThe thermal conductivity k of micro-twinned single crystals of YBa2Cu3O7 and HoBa2Cu3O7 and a sintered sample of YBa2Cu3O7 has been measured for temperatures 0.03<T<5K. For the single crystals, k is small and varies as T1.8-1.9 This behavior resembles k for glassy insulators except for the lack of a plateau above IK. It is concluded that the thermal carriers are phonons with their mean free path limited by resonant scattering from tunneling entities, as in glasses. Suggestions for the location of tunneling systems are given. For the sinter, k is still smaller but does not follow a power law T-dependence. It is similar to other sintered ceramics with the same particle size, where the phonon mean free path is dominated by Rayleigh scattering from the particles. This strong scattering from the microstructure presumably masks the scattering from TS within each particle.

Plastic deformation of nickel single crystals at low temperatures

1958 ◽  
Vol 3 (28) ◽  
pp. 384-418 ◽  
Author(s):  
Peter Haasen
Keyword(s):  
Plastic Deformation ◽  
Single Crystals ◽  
Low Temperatures
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