The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with N, the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of N, and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination.
On discretely entropy conservative and entropy stable discontinuous Galerkin methods