Thermal and Elastic Material Response

In chap. 4 we argued that much can be learned by comparing the energetics of different competing states of a crystalline solid. One set of material parameters that can be understood on the basis of total energy methods like those presented in the previous chapter in conjunction with the methods of statistical mechanics are those related to the thermal response of materials. Indeed, one of the workhorses 

In addition to the consideration of equilibrium problems, the treatment of thermal excitations is also important to the investigation of kinetics. An intriguing insight into kinetics is that in many cases, the tools for treating thermal excitations to be described in this chapter can be used to consider driven processes such as diffusion. As will be noted in chap. 7, models of kinetics are tied to the idea that as a result of the random excursion of atoms from their equilibrium positions, a system may occasionally pass from one well in the multi-dimensional potential energy surface to another. Indeed, this eventuality has already been rendered pictorially in fig. 3.22 where we saw an adatom hopping from one energy well to the next in its 

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