Crystallographic defects can cause solids to be non-stoichiometric

Nonstoichiometry is pervasive for transition metal oxides, especially when the metal is not in its highest oxidation state.^[2] For example, although wüstite (ferrous oxide) has an ideal (stoichiometric) formula FeO, the actual stoichiometry is closer to Fe_0.95O. For each "missing" Fe²⁺ ion, the crystal contains two Fe³⁺ ions to balance the charge. The composition of a non-stoichiometric compound usually varies in a continuous manner over a narrow range. Thus the formula for wüstite is written as Fe_1-xO, where x is a small number (0.05 in the previous example) representing the deviation from the "ideal" formula.^[3] Nonstoichiometry is especially important in solids, which are three-dimensional polymers and which tolerate mistakes. To some extent, entropy drives all solids to be non-stoichiometric. But for practical purposes, the term describes materials where the non-stoichiometry is measurable, usually at least 1% of the ideal composition.

Non-stoichiometric compounds are also known as berthollides (as opposed to the stoichiometric compounds or daltonides). 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 did have important exceptions.^[4]

Examples

Cuprates

A magnet levitating above a high-temperature superconductor

Tungsten oxides

It is sometimes difficult to determine if a material is non-stoichiometric or if the formula is best represented by large numbers. The oxides of tungsten illustrate this situation. Starting from the idealized material tungsten trioxide, one can generate a series of related materials that are slightly deficient in oxygen. These oxygen-deficient species can be described as WO_3-x but in fact they are stoichiometric species with large unit cells with the formulas W_nO_(3n-2) where n = 20, 24, 25, 40. Thus, the last species can be described with the stoichiometric formula W₄₀O₁₁₈, whereas the description non-stoichiometric WO_2.95 implies a more random distribution of oxide vacancies.^[5]

Other cases

• Palladium hydride is a nonstoichiometric material of the approximate composition PdH_x (0.02 < x < 0.58). This solid conducts hydrogen by virtue of the mobility of the hydrogen atoms within the solid.
  • The coordination polymer Prussian Blue, nominally Fe₇(CN)₁₈ is well known to form non-stoichiometrically. In fact the non-stoichiometric phases exhibit more useful properties associated with the ability of the solid to absorb caesium and thallium ions.

Defects vs non-stoichiometry

The cuprate superconductors highlight the concept of a "defect" structures, which is related to non-stoichiometry. YBa₂Cu₃O_7?x can be viewed as a variant of the perovskite family of materials, which have idealized stoichiometry ABO₃. For the cuprates, Y + Ba occupy "A sites" whereas Cu occupies the "B sites". The non-defect material would have the stoichiometry YBa₂Cu₃O₉. Using this way of describing a structure, W₄₀O₁₁₈ is said to be a defect variant of WO₃.

Oxidation catalysis

Many useful chemicals are produced by the reactions of hydrocarbons with oxygen, a conversion that is catalyzed by metal oxides. The process operates via the transfer of "lattice" oxygen to the hydrocarbon substrate, a step that generates temporarily a vacancy. In a subsequent step, the oxygen vacancy is replenished by the O₂. Such catalysts rely on the ability of the metal oxide to form phases that are not stoichiometric. An analogous sequence of events describes other kinds of atom-transfer reactions including hydrogenation and hydrodesulfurization catalysed by solid catalysts. These considerations also highlight the fact that stoichiometry is determined by the interior of crystals: the surfaces of crystals often do not follow the stoichiometry of the bulk. The complex structures on surfaces is described by the term "surface reconstruction."

Ion conduction

The migration of atoms within a solid is strongly influenced by the defects associated 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.

See also

F-center

References

1. ↑ J. Gopalakrishnan, Chintamani Nagesa Ramachandra Rao. New Directions in Solid State Chemistry. Cambridge University Press, 1997, p. 230.
2. ↑ . pp. 642-644
3. ↑ Lesley E. Smart. Solid State Chemistry: An Introduction, 3rd edition. CRC Press, 2005, p. 214.
4. ↑ Henry Marshall Leicester. The Historical Background of Chemistry. Courier Dover Publications, 1971, p. 153.
5. ↑ Shriver, D. F.; Atkins, P. W.; Overton, T. L.; Rourke, J. P.; Weller, M. T.; Armstrong, F. A. ?Inorganic Chemistry? W. H. Freeman, New York, 2006. ISBN: 0-7167-4878-9.