Structural Phase Behaviour

ii There are few reliable computational techniques applicable to the problem of structural phase behaviour. This is starkly emphasised by the fact that there are still a number of unanswered questions concerning the solid state of some of the simplest models of matter. To determine the phase behaviour of a given sys-tem we invoke the machinery of statistical physics, which identifies the equilibrium phase as that which minimises the free-energy. This type of problem can only be dealt with fully via numerical simulation, as any less direct approach will involve making some uncontrolled approximation. In particular, a numer-ical simulation can be used to evaluate the free-energy difference between two phases if the simulation is free to visit them both. However, it has proven very difficult to find an algorithm which is capable of efficiently exploring two different phases, particularly when one or both of them is a crystalline solid. This thesis builds on previous work [1] (Physical Review Letters 79 p.3002), exploring a new Monte Carlo approach to this class of problem. This new simulation technique uses a global coordinate trans-formation to switch between two different crystalline structures. Generally, this ‘lattice switch ’ is found to be extremely unlikely to succeed in a normal Monte Carlo simulation. To overcome this, extended