The theory of diffusionless phase transitions in elemental solids : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry at Massey University, Albany, New Zealand

Abstract

Although phase transitions in the solid state have been described with the aid of phenomenological theories and molecular dynamics or Monte Carlo simulations, a microscopic framework that treats both crystallography and the energy landscape on equal grounds is still missing. This thesis aims to establish the basis of the theory of diffusionless phase transitions by relating different crystal structures, lattices and non-lattices, described by few parameters through the use of accurate density functional approximations and exact lattice sums. The methods described here, together with the use of fast converging series of modified Bessel functions of the second kind, allow to treat general lattice sums for cubical and hexagonal lattices equivalently during the transformation, as well as to calculate the lattice parameters, cohesive and zero-point vibrational energies, bulk moduli, and entropy to computer precision for systems obeying inverse-power potentials. Furthermore, the relative stability of the infinitely many Barlow packings is assessed, showing that a linear relation between the free energies of the packings explains why only a few of these structures are actually observed in nature.