Lattice Dynamics of Body-Centered and Face-Centered Cubic Metallic Elements

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.