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

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.

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 specific heat of metals and alloys at low temperatures

1957 ◽  
Vol 240 (1222) ◽  
pp. 321-332 ◽  
Keyword(s):  
Fermi Surface ◽  
Specific Heat ◽  
Liquid Helium ◽  
Brillouin Zone ◽  
Low Temperatures ◽  
Metals And Alloys ◽  
Thermal Excitation ◽  
Electronic Specific Heat ◽  
Conduction Electrons ◽  
Elastic Shear

The effect of thermal excitation of the conduction electrons on the elastic shear constants is investigated in a metal in which the Fermi surface lies close to the Brillouin-zone boundaries. It is shown that in these circumstances electron-lattice interaction leads to an addi­tional term in the specific heat, linear in the temperature in the liquid-helium range, which, therefore, augments the pure electronic specific heat. The variation in magnitude of this linear term is considered in the α-brasses. It is suggested that this is the physical effect underlying the peculiarities of the ‘electronic’ specific heat of these alloys.

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.

Thermal Conductivity of Waste Forms and Geologic Media

1982 ◽  
Vol 15 ◽  
Author(s):  
R. O. Pohl ◽  
J. W. Vandersande
Keyword(s):  
Thermal Conductivity ◽  
Grain Boundaries ◽  
High Temperatures ◽  
Low Temperatures ◽  
Phonon Scattering ◽  
Lamellar Structures ◽  
Waste Forms ◽  
Thermal Conductivities ◽  
Geologic Media

ABSTRACTIn order to predict the range of thermal conductivities to be expected in waste forms and in geologic media, an understanding of the pertinent phonon scattering processes is required. It has been shown that grain boundaries in polycrystalline media are unimportant at low temperatures relative to lamellae which arise from twinning, exsolution, or foreign inclusions within the grains. The possible role of lamellar structures on the conductivity at high temperatures will be discussed.

scholarly journals Deviation from Matthiessen's Rule and Lattice Thermal Conductivity of Alloys

1959 ◽  
Vol 12 (2) ◽  
pp. 199 ◽  
Author(s):  
PG Klemens
Keyword(s):  
Thermal Conductivity ◽  
Electrical Resistivity ◽  
Lattice Thermal Conductivity ◽  
Pure Metal ◽  
Liquid Oxygen ◽  
Electronic Thermal Conductivity ◽  
The Difference ◽  
Matthiessen's Rule ◽  
Lattice Component ◽  
The Ideal

The purpose of this note is to point out that the difference in the ideal -electronic thermal conductivity between an alloy and a pure metal can be estimated from the corresponding difference in the ideal electrical resistivity, using the Wiedemann-Franz law. This allows the separation of the thermal conductivity into an electronic and a lattice component to be made with greater confidence, particularly at liquid oxygen temperatures.

Electrical Resistivity, Thermal Conductivity and Magnetic Susceptibility of Polycrystalline Samarium at Low Temperatures

1966 ◽  
Vol 21 (11) ◽  
pp. 1856-1859 ◽  
Author(s):  
Sigurds Arajs ◽  
G. R. Dunmyre
Keyword(s):  
Thermal Conductivity ◽  
Electrical Resistivity ◽  
Magnetic Susceptibility ◽  
Magnetic Moment ◽  
Low Temperatures ◽  
Fair Agreement ◽  
Magnetic Transformation ◽  
Electronic Thermal Conductivity ◽  
Theoretical Considerations

Electrical resistivity, thermal conductivity, and magnetic susceptibility have been measured, using the same sample of samarium, from 4 to 300 °K, from 5 to 200 °K, and from 4 to 300 °K, respectively. Two anomalies, one at 12 ± 1 °K and another at 106 ± 1 °K, are observed, resulting from an order-order magnetic transformation and an antiferromagnetic-paramagnetic transition, respectively. The Lorenz function is found to be larger at any temperature than that expected for pure electronic thermal conductivity. This implies that there is some phonon and possibly also some magnon thermal conductivity in samarium at low temperatures. The magnetic moment disorder electrical resistivity of samarium is determined to be 39.0 ± 0.5 μΩ cm, in fair agreement with the value to be expected from theoretical considerations.

The thermal and electrical conductivity of silver-palladium and silver-cadmium alloys at low temperatures

1956 ◽  
Vol 233 (1195) ◽  
pp. 480-493 ◽  
Keyword(s):  
Electrical Resistance ◽  
Low Temperatures ◽  
Free Electrons ◽  
Burgers Vector ◽  
Conduction Electrons ◽  
Wide Range ◽  
Electrical Conductivities ◽  
Lattice Waves ◽  
Silver Palladium ◽  
Palladium Content

Measurements have been made from 2 to 300° K of the thermal and electrical conductivities of a wide range of silver-palladium and silver-cadmium alloys. The thermal conductivity is resolved into its electronic and lattice components. It is shown that in annealed alloys below 10°K the lattice waves are scattered mainly by free electrons, that the conduction electrons interact with waves of all polarizations, and that this scattering is particularly strong for alloys of high palladium content, where one expects holes in the d -band. Above 40 % palladium , s - d scattering increases the electrical resistance and serious departures from Matthiessen’s rule are observed. The lattice conductivity of strained specimens is much lower, and the additional thermal resistance varies as T -2 , as does the resistance due to interactions with conduction electrons. It is suggested that the additional scattering is due to dislocations of large Burgers vector.

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