Unavoidable disorder and entropy in multi-component systems

The need for improved functionalities is driving the search for more complicated multi-component materials. Despite the factorially increasing composition space, ordered compounds with four or more species are rare. Here, we unveil the competition between the gain in enthalpy and entropy with increasing number of species by statistical analysis of the AFLOW data repositories. A threshold in the number of species is found where entropy gain exceeds enthalpy gain. Beyond that, enthalpy can be neglected, and disorder-complete or partial-is unavoidable.