The electrical conductivity of thin wires

1950 ◽  
Vol 201 (1067) ◽  
pp. 545-560 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Free Path ◽  
Mean Free Path ◽  
Fermi Velocity ◽  
Approximate Methods ◽  
Conduction Electrons ◽  
The Third ◽  
Thin Wires ◽  
Velocity Surface ◽  
The Mean

In the first part of this paper, simple approximate methods have been developed for evaluating the electrical conductivity of films and wires of a size comparable with the mean free path of the conduction electrons. In the second part, a rigorous theory has been given of the electrical conductivity of a thin wire, on the assumptions that the Fermi velocity surface is spherical and that the collisions of the electrons at the surface of the wire are inelastic. In the third part of the paper, this theory has been generalized to cover the case where the scattering is no longer inelastic. In the final part, Andrew’s recent experimental results for a thin mercury wire have been fitted to the theoretical curves obtained, and the mean free path evaluated.

The conductivity of thin wires in a magnetic field

1950 ◽  
Vol 202 (1070) ◽  
pp. 378-394 ◽  
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Bulk Material ◽  
Mean Free Path ◽  
Electron Theory ◽  
Conduction Electrons ◽  
Thin Wires ◽  
The Mean ◽  
The Magnetic Field ◽  
Theory And Experiment

A thin film or wire of metal has a lower electrical conductivity than the bulk material if the thickness is comparable with or smaller than the electronic mean free path. Previous workers have obtained expressions for the magnitude of the effect by integrating the Boltzmann equation and imposing the appropriate boundary conditions. The problem is re-examined from a kinetic theory standpoint, and it is shown that the same expressions are obtained by this method, usually rather more simply, while the physical picture is considerably clarified. The method is applied to an evaluation of the conductivity of a thin wire with a magnetic field along the axis, and it is found that the resistivity should decrease as the magnetic field is increased; it should be possible to derive the mean free path and velocity of the conduction electrons by comparison of theory and experiment. The theory has been confirmed by experimental measurements on sodium; estimates of electronic velocity and mean free path are obtained which are in fair agreement with the values given by the free-electron theory.

scholarly journals III. Alkali films with the properties of the normal metal

1938 ◽  
Vol 166 (925) ◽  
pp. 270-277 ◽  
Keyword(s):  
Free Path ◽  
Alkali Metals ◽  
Lattice Strain ◽  
Mean Free Path ◽  
Film Material ◽  
Residual Resistance ◽  
Bulk Metal ◽  
Conduction Electrons ◽  
Considerable Excess ◽  
The Mean

In the present work the measurements of the resistivity of evaporated films of the alkali metals (Lovell 1936 a, b ; Appleyard and Lovell 1937) have been extended to a thickness of several thousand angstroms. The previous results were limited to films of less than a few hundred angstroms in thick­ness; and it appeared that thin creased resistivity of these thin films com­pared with that of the bulk metal was due merely to the shortening of the mean free path of the conduction electrons by collision with the boundaries of the film. It was therefore to be expected that at thicknesses much in excess of the mean free path the resistivity of the film material should closely approximate to that of the bulk metal. The present results confirm this expectation only in the case of caesium, where the resistivity approaches within a few per cent that of the bulk metal. Potassium and rubidium films, on the other hand, show a considerable excess of resistivity above that of the bulk metal, but it is shown that this excess is a residual resistance due to lattice strain, and that it may be partially removed by suitable annealing.

scholarly journals The electrical conductivity of transition metals

1936 ◽  
Vol 153 (880) ◽  
pp. 699-717 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Transition Metals ◽  
Temperature Coefficient ◽  
Noble Metals ◽  
Formal Theory ◽  
Mean Free Path ◽  
Point Of View ◽  
Transition Elements ◽  
Conduction Electrons ◽  
The Mean

1— In a recent paper certain property of the transition metals Ni, Pd, and Pt and of their alloys with Cu, Ag, and Au have been discussed from the point of view of the electron theory of metals based on quantum mechanics. In particular, a qualitative explanation was given of the relatively high electrical resistance of the transition metals. It was shown from an examination of the experimental evidence that the conduction electrons in these metals have wave functions derived mainly from s states just as in Cu, Ag, and Au, and that the effective number of conduction electrons is not much less than in the noble metals. On the other hand, the mean free path is much smaller, because under the influence other the lattice vibrations the conduction electrons may make transitions to the unoccupied d states, and the probability of these transitions is several times greater than the probability of ordinary scattering. Since the unoccupied d states are responsible for the ferromagnetism or high paramagnetism of the transition elements, there is a direct connexion between the magnetic properties and the electrical conductivity. The purpose of this paper is as follows: in 2, 3, and 4 we develop a formal theory of conductivity for metals, such as the tradition metals, where two Brillouin zone are of importance for the conductivity; in 5 we apply the theory to show why, at high temperatures, the temperature coefficient of the paramagnetic metals Pd and Pt falls below the normal value; and in 6 we discuss the resistance of ferromagnetic metals, and show in 7 qualitatively why constantan (Cu-Ni) has zero temperature coefficient at room temperature.

Determination of the Mean Free Path of Conduction Electrons

1961 ◽  
Vol 464 (1-2) ◽  
pp. 62-64
Author(s):  
R. Kleinberg ◽  
F. J. Blatt
Keyword(s):  
Free Path ◽  
Mean Free Path ◽  
Conduction Electrons ◽  
The Mean

scholarly journals Ballistic Heat Transport in Nanocomposite: The Role of the Shape and Interconnection of Nanoinclusions

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1982
Author(s):  
Paul Desmarchelier ◽  
Alice Carré ◽  
Konstantinos Termentzidis ◽  
Anne Tanguy
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Free Path ◽  
Mean Free Path ◽  
Strong Increase ◽  
Moderate Increase ◽  
Energy Propagation ◽  
The Mean ◽  
Dynamics Simulations

In this article, the effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using molecular dynamics simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then used to estimate the thermal conductivity, showing an enhancement of the effective thermal conductivity due to the existence of crystalline structural interconnections. This enhancement is dominated by the ballistic transport of phonons. Equilibrium molecular dynamics simulations confirm the tendency, although less markedly. This leads to the observation that coherent energy propagation with a moderate increase of the thermal conductivity is possible. These findings could be useful for energy harvesting applications, thermal management or for mechanical information processing.

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