Understanding the behavior of different materials not only furthers general knowledge, but can also often be used for practical purposes in e.g. engineering. Computer Simulations, where these materials are simulated as small atoms, that exert forces on each other, play an important role in this field and there are already many applications for many different materials. Since these simulations cannot describe the behavior of the materials without approximations and simplifications, it is always important to assess their error and compare results with experiments, where this is possible. One of the properties, that can be compared, are phase transitions, which are changes in the structure of the material, that happen at certain temperatures, pressures and compositions of the material. In this project one of the methods for calculating transition points (Nested Sampling) was investigated on its strengths and weaknesses. There was a strong focus in the improvement in the usage of this method especially for curbing the errors that appeared. For this many test calculations were necessary. In the end a systematic search for the transition temperatures at different pressures for iron with one specific potential, from which the forces are calculated (Müller-Albe bond-order potential), was done, that was more accurate than calculations that were done, before the improvements were made. Since such calculations are quiet costly, it was necessary to use a High Performance Computer. Furthermore for a variety of other materials (Ga, As, GaAs and GaN) the method was further assessed in its ability to predict the best arrangement the atoms can take in space using potentials specific to these materials. Finally another method (USPEX), that can be used for these purposes, was started to be investigated on for comparison.