Inelastic Excitation of Crystals in Thermal Equilibrium with the Environment

Abstract

Theories presented in Chapters 6–14 regarding inelastic electron scattering in crystals were based on the assumption that the incident electron-crystal system is isolated from the environment, since the time-independent Schrödinger equation, which is usually employed, is only valid for an isolated system of constant energy and momentum. In practice, the incoming electron crystal system is in contact with the environment, so that the total energy of the system fluctuates due to the exchange of energy with the environment. This fluctuation eventually affects the scattering behavior of the electron. This question was considered by Fanidis et al. (1992, 1993), who proposed a rigorous theory to solve the problem. An alternative approach was proposed by Dudarev et al. (1993a) based on the one-particle density matrix theory. Statistical mechanics calculations predicted that the magnitude of the energy fluctuation due to the thermal equilibrium of a copper crystal of volume 10⁶ nm³ at room temperature is on the order of 400 eV (Mandl, 1971).