Spontaneous non-stoichiometry and ordering of metal vacancies in degenerate insulators

We point to a class of materials representing an exception to the Daltonian view that compounds maintain integer stoichiometry at low temperatures, because forming stoichiometry-violating defects cost energy. We show that carriers in the conduction band (CB) of degenerate insulators in Ca-Al-O, Ag-Al-O, or Ba-Nb-O systems can cause a self-regulating instability, whereby cation vacancies form exothermically because a fraction of the free carriers in the CB decay into the hole states formed by such vacancies, and this negative electron-hole recombination energy offsets the positive energy associated with vacancy bond breaking. This Fermi level-induced spontaneous non-stoichiometry can lead to the formation of crystallographically ordered vacancy compounds (OVCs), explaining the previously peculiar occurrence of unusual atomic sequences such as BalNbmOn with l:m:n ratios of 1:2:6, 3:5:15, or 9:10:30. This work has general ramifications as the degenerate insulators have found growing interests in many fields ranging from transparent conductors to electrides that are electron donating promotors for catalyst.