  Lattice-switch Monte Carlo is an efficient method for calculating the free
energy difference between two solid phases, or a solid and a fluid phase. Here,
we provide a brief introduction to the method, and list its applications since
its inception. We then describe a lattice switch for the fcc and bcc phases
based on the Bain orientation relationship. Finally, we present preliminary
results regarding our application of the method to the fcc and bcc phases in
the Lennard-Jones system. Our initial calculations reveal that the bcc phase is
unstable, quickly degenerating into some as yet undetermined metastable solid
phase. This renders conventional lattice-switch Monte Carlo intractable for
this phase. Possible solutions to this problem are discussed.
