the interior of crystals: the surfaces of crystals often do not follow the stoichiometry of the bulk. The complex structures on surfaces are described by the term "surface reconstruction". Ion conduction The migration of atoms within a solid is strongly influenced by the defects associated with non-stoichiometry. These defect sites provide pathways for atoms and ions to migrate through the otherwise dense ensemble of atoms that form the crystals. Oxygen sensors and solid state batteries are two applications that rely on oxide vacancies. One example is the CeO2-based sensor in automotive exhaust systems. At low partial pressures of O2, the sensor allows the introduction of increased air to effect more thorough combustion. Superconductivity Many superconductors are non-stoichiometric. For example, yttrium barium copper oxide, arguably the most notable high-temperature superconductor, is a non-stoichiometric solid with the formula YxBa2Cu3O7−x. The critical temperature of the superconductor depends on the exact value of x. The stoichiometric species has x = 0, but this value can be as great as 1. History It was mainly through the work of Nikolai Semenovich Kurnakov and his students that Berthollet's opposition to Proust's law was shown to have merit for many solid compounds. Kurnakov divided non-stoichiometric compounds into berthollides and daltonides depending on whether their properties showed monotonic behavior with respect to composition or not. The term berthollide was accepted by IUPAC in 1960. The names come from Claude Louis Berthollet and John Dalton, respectively, who in the 19th century advocated rival theories of the composition of substances. Although Dalton "won" for the most part, it was later recognized that the law of definite proportions had important exceptions. See also F-Center Vacancy defect References Further reading F. Albert Cotton, Geoffrey Wilkinson, Carlos A. Murillo & Manfred Bochmann, 1999, Advanced Inorganic Chemistry, 6th Edn., pp. 202, 271, 316, 777, 888. 897, and 1145, New York, NY, USA:Wiley-Interscience, , see , accessed 8 July 2015. Roland Ward, 1963, Nonstoichiometric Compounds, Advances in Chemistry series, Vol. 39, Washington, DC, USA: American Chemical Society, , DOI 10.1021/ba-1964-0039, see , accessed 8 July 2015. J. S. Anderson, 1963, "Current problems in nonstoichiometry (Ch. 1)," in Nonstoichiometric Compounds (Roland Ward, Ed.), pp. 1–22, Advances in Chemistry series, Vol. 39, Washington, DC, USA: American Chemical Society, , DOI 10.1021/ba-1964-0039.ch001, see , accessed 8 July 2015. Solid-state chemistry Inorganic chemistry Non-stoichiometric compounds General chemistry