Computer simulation on the atomistic level became a powerful tool in modern chemistry in the past decades. Computational techniques are widely used to augment experiments and make initial predictions, thus saving time and money by reducing the amount of experimental work. This is especially useful when designing new drugs or materials or modelling matter at difficult conditions. One of the major fields where computer simulations became widely used is materials science, studying phase transitions and phase diagrams. In recent years a new computational technique has been developed, called nested sampling, which automatically generates all relevant atomic configurations, and determines their stability relative to each other. It has been used successfully to calculate the phase diagram of atomistic systems, such as aluminium and shape memory alloys, but many more challenges lay ahead, such as studying metals at extreme high pressure, charged or molecular systems, or materials in confined space. The aim of a PhD project would be to use the nested sampling technique to study a combination of these problems and further develop and adapt the computational methodology.