No abstract

The body-centered and face-centered cubic monatomic metals are represented by a model consisting of an ion point lattice embedded in an electron gas. The Born-von Kármán lattice dynamics are modified to include the role which the conduction electrons play in acoustical wave motion. This leads to relations connecting the dynamic parameters with the elastic constants, and yields the Fuchs relations in an elementary manner. The discrepancy in the Cauchy relation is shown to be just the bulk modulus of the electron gas. In studying the contribution of the conduction electrons to the thermal motion, two extreme cases are treated: 1.—the electron gas does not partake of the thermal motion appreciably; 2.—the electron gas follows the ion motion almost exactly. The secular equations are given for both cases. The Debye characteristic temperature in the T3 region of atomic heat is computed analytically for both cases when the departure of the elastic constants from the isotropy condition is not too large.

A plot of the superconducting threshold temperatures as a function of the Debye characteristic temperatures of the known superconducting elements discloses .a number of interesting relationships. These relationships, in conjunction with previously known empirical rules, are used to discuss the occurrence of superconduction among other elements. It is concluded that Sc, Y, and Sm are not likely to be found superconducting, but that Ce, Pr, Nd, and Ac (should its atomic volume prove to be of the order of 22 cm 3 /mole) are expected to be superconducting. Data on Pa is very sketchy. The best that can be inferred is that Pa should be superconducting with a threshold temperature in excess of 2 °K.

A superconducing torus was subjected to a magnetic field normal to the plane of the torus and the field distribution across the plane of the superconducting torus was determined experimentally. The magnetic field near the axis of the torus was found to have the same direction as the applied field, but near the inner surface of the torus the field reversed direction in such a manner that the total flux enclosed by the torus was zero. It is concluded that the magnetic field distribution about a superconducting torus in weak magnetic fields can be adequately described by classical electrodynamics and the assumption of perfect diamagnetism.

A numerical table is presented which permits the easy calculation of the Debye characteristic temperature of any cubic metallic element at 0°K. The use of the table presupposes a knowledge of the elastic constants, atomic volume, and density of the element at 0°K. The characteristic temperature can be evaluated for either of the theoretical cases described in an earlier paper by the author.