Numerical modelling of amorphous solids: A classical density functional theory based approach

In this thesis, the Phase-Field Crystal (PFC) model is used to describe amorphous solid materials. These stationary states are metastable minima of the free energy, that are characterised by a non-uniform density distribution displaying no long-range order. In the introductory part of the thesis, first we give a summary of the thermodynamics and kinetics of phase transitions, which is followed by an introduction to the Classical Density Functional Theory (DFT) and its dynamical extension (DDFT), in which the physical state of the matter is characterised by a spatiotemporal scalar field, the density distribution. This part of the thesis ends with the derivation of the PFC model from the DDFT, which is then used to investigate the bulk thermodynamic and microscopic structural properties of amorphous solids. In the next part of the thesis, we present and analyse the results of extensive numerical simulations. First, we determine the distribution of the free energy density in the amorphous state for various system sizes, and show that the amorphous state can be modelled as a collection of uncorrelated finite-sized domains. We calculate the typical size (correlation length) of these correlated regions.