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

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