Non-stoichiometric compound

These crystallographic defects cause solids to be non-stoichiometric.

Non-stoichiometric compounds are chemical compounds with an elemental composition that cannot be represented by usual integral numbers. They are almost always inorganic compounds and almost invariably solids. In such materials some small percentage of atoms are missing or too many atoms are packed into an otherwise perfect lattice work. They exhibit special electrical or chemical properties because of these flaws or defects. For example, when atoms are missing, the other atoms can move through the solid more rapidly. Non-stoichiometry is represented by many metal oxides and sulfides. For example, stoichiometric iron(II) oxide, which is rare, has the formula FeO, whereas the more common nonstoichiometric material has the formula Fe_0.95O. Nonstoichiometric compounds are homogenous, they are not mixtures. Batteries often rely on materials that can exist in a range of non-stoichiometric states. Other non-stoichiometric compounds have applications in ceramics and as superconductors.

Since solids are overall electrically neutral, the defect in an ionic compound is compensated by a change in the charge of other atoms in the solid, either by changing their oxidation state, or by replacing them with atoms of different elements with a different charge.^[1]

Occurrence

Nonstoichiometry is pervasive for metal oxides, especially when the metal is not in its highest oxidation state.^[2]

Iron(II) oxides

For example, although wüstite (ferrous oxide) has an ideal (stoichiometric) formula FeO, the actual stoichiometry is closer to Fe_0.95O. The non-stoichiometry reflect the ease of oxidation of Fe²⁺ to Fe³⁺ effectively replacing a small portion of Fe²⁺ with two thirds their number of Fe³⁺. Thus for every three "missing" Fe²⁺ ions, 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 solid, three-dimensional polymers that can 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.

Tungsten oxide

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 non-stoichiometric description WO_2.95 implies a more random distribution of oxide vacancies.^[4]

Iron sulfide

The monosulfides of the transition metals are often nonstoichiometric. Best known perhaps is nominally iron(II) sulfide (the mineral pyrrhotite) with a composition Fe_(1-x)S (x = 0 to 0.2). The rare stoichiometric FeS endmember is known as the mineral troilite. Pyrrhotite is remarkable in that it has numerous polytypes, i.e. crystalline forms differing in symmetry (monoclinic or hexagonal) and composition (Fe₇S₈, Fe₉S₁₀, Fe₁₁S₁₂ and others). These materials are always iron-deficient owing to the presence of lattice defects, namely iron vacancies. Despite those defects, the composition is usually expressed as a ratio of large numbers and the crystals symmetry is relatively high. This means the iron vacancies are not randomly scattered over the crystal, but form certain regular configurations. Those vacancies strongly affect the magnetic properties of pyrrhotite: the magnetism increases with the concentration of vacancies and is absent for the stoichiometric FeS.^[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.

Applications

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 temporarily generates 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 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.

Superconductivity

Main article: Cuprate

A magnet levitating above a nitrogen-cooled high-temperature superconductor

Many superconductors are non-stoichiometric. For example, yttrium barium copper oxide, arguably the most notable high-temperature superconductor, is a non-stoichiometric solid with a formula represented by Y_xBa₂Cu₃O_7−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

Non-stoichiometric compounds are also known as berthollides (as opposed to the stoichiometric compounds or daltonides). They violate the law of definite proportions. 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.^[6]

References

↑ J. Gopalakrishnan, Chintamani Nagesa Ramachandra Rao (1997). New Directions in Solid State Chemistry. Cambridge University Press. p. 230.
↑ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 0080379419. . pp. 642-644
↑ Lesley E. Smart (2005). Solid State Chemistry: An Introduction, 3rd edition. CRC Press. p. 214. ISBN 0-7487-7516-1.
↑ Shriver, D. F.; Atkins, P. W.; Overton, T. L.; Rourke, J. P.; Weller, M. T.; Armstrong, F. A. (2006). Inorganic Chemistry. New York: W. H. Freeman. ISBN 0-7167-4878-9.
↑ Hubert Lloyd Barnes (1997). Geochemistry of hydrothermal ore deposits. John Wiley and Sons. pp. 382–390. ISBN 0-471-57144-X.
↑ Henry Marshall Leicester (1971). The Historical Background of Chemistry. Courier Dover Publications. p. 153.