Origins of nonstoichiometry and vacancy ordering in Sc1-x squarexS

Whereas nearly all compounds A(n)B(m) obey Dalton's rule of integer stoichiometry (n: m, both integer), there is a class of systems, exemplified by the rocksalt structure Sc1-x squarexS, that exhibits large deviations from stoichiometry via vacancies, even at low temperatures. By combining first-principles total energy calculations with lattice statistical mechanics, we scan an astronomical number of possible structures, identifying the stable ground states. Surprisingly, all have the same motifs: (111) planes with (112) vacancy rows arranged in (110) columns. Electronic structure calculations of the ground states (identified out of approximately 3x10(6) structures) reveal the remarkable origins of nonstoichiometry.