Amplitudes of Thermal Vibration at Fusion

Abstract

On the basis of theoretical results from the Debye-Waller theory of the thermal dependence of x-ray reflection intensity, relatively accurate values of the Lindemann constant are determined for ten metals by use of rigidity moduli at fusion with previously determined bulk moduli. Agreement of the derived value $\rho$ of the critical ratio of root-mean-square amplitude of thermal vibration to nearest-neighbor distance at fusion, with the corresponding value from x-ray intensity data, is improved for the one case (Al) favorable for comparison. The average $\rho$ over the body-centered cubic, face-centered cubic, and hexagonal lattice types is ${0.11}_1$, in excellent agreement with the value ${0.10}_5$ given by Grüneisen. Relatively accurate values of the Lindemann constant for Pb and Al imply that this quantity cannot be a strict constant over a lattice type; however, the assumption of an average over the lattice type yields an excellent approximation for the face-centered cubic elements.