  We extend the nested sampling algorithm to simulate materials under periodic
boundary and constant pressure conditions, and show how it can be used to
determine the complete equilibrium phase diagram, for a given potential energy
function, efficiently and in a highly automated fashion. The only inputs
required are the composition and the desired pressure and temperature ranges,
in particular, solid-solid phase transitions are recovered without any a priori
knowledge about the structure of solid phases. We benchmark and showcase the
algorithm on the periodic Lennard-Jones system, aluminium and NiTi.
