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This thesis develops a nested sampling algorithm into a black box
tool for directly calculating the partition function, and thus the
complete phase diagram of a material, from the interatomic
potential energy function. It represents a significant step forward
in our ability to accurately describe the finite temperature
properties of materials. In principle, the macroscopic phases of
matter are related to the microscopic interactions of atoms by
statistical mechanics and the partition function. In practice,
direct calculation of the partition function has proved infeasible
for realistic models of atomic interactions, even with modern
atomistic simulation methods. The thesis also shows how the output
of nested sampling calculations can be processed to calculate the
complete PVT (pressure-volume-temperature) equation of state for a
material, and applies the nested sampling algorithm to calculate
the pressure-temperature phase diagrams of aluminium and a model
binary alloy.
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