Two important thermodynamic quantities are bulk solid and liquid
free-energy as a function of composition G(x) and the solid-liquid
interfacial free-energy γsl. For both, an accurate determination is
required for modelling crystallisation and melting processes. In this
thesis, I combine statistical mechanics and atomistic simulations to
develop new approaches to calculate G(x) and γsl.
In the case of G(x), a method based on a Free Energy Perturbation
(FEP) technique is proposed, which allows to achieve ab initio accuracy
at a fraction of the cost of previously proposed techniques. A
proof-of-principle of this approach is given using simple many-body
potentials. The case of the melting point calculation for a pure element
and that of the free-energy for a binary Ni-Al alloy are discussed.
Based on simplified theoretical models, the reasons for the success of
this approach and its limitations are explained and guidelines for future,
full ab initio calculations are given.
For the case of γsl, it is proposed to use the Metadynamics (MTD)
technique to reconstruct the Free Energy Surface (FES) for the solidification/
melting process, from which γsl can be extracted. This approach
is first presented and discussed using a model Lennard-Jones
potential. The robustness of this method is demonstrated and its
advantages over other techniques are discussed, together with its limitations
and possible ways to extend its use to more complex energy
descriptions. The method is then applied to the case of Pb as described
with a more realistic Embedded Atom Model (EAM) potential,
and the results are used to assess experimental data.
Given the promising results shown by these novel techniques, their use
to build the foundations of a multi-scale approach to solidification
and their application with more realistic calculations and complex
problems can be envisaged in the future.