Theory of Temperature-Dependent Surface Force Constant Changes in Body-Centered Cubic Crystals.

摘要

A theoretical calculation has been made of the temperature dependence of the force-constant changes at the (001) free surface of body-centered cubic crystals. The changes arise from anharmonic effects. The procedure consists of first calculating the dynamical displacements by evaluating the Helmholtz free energy including anharmonic terms with the aid of many-body theoretical techniques and then calculating the change in force constants in the vicinity of a crystal surface produced by the cubic anharmonic terms in the crystal potential energy. Numerical estimates of the force-constant changes have been made for alpha-iron using a model consisting of Lennard-Jones 6-12 type central interactions up to second neighbors. The influence of surface force-constant changes on such effects as the surface-mode frequencies, the temperature dependent surface mean-square displacements and the stability of a crystal surface are discussed.