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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, non-stoichiometric compounds are
chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
s, almost always solid
inorganic compound In chemistry, an inorganic compound is typically a chemical compound that lacks carbon–hydrogen bonds, that is, a compound that is not an organic compound. The study of inorganic compounds is a subfield of chemistry known as '' inorganic chemist ...
s, having
elemental An elemental is a mythic being that is described in occult and alchemical works from around the time of the European Renaissance, and particularly elaborated in the 16th century works of Paracelsus. According to Paracelsus and his subsequent fo ...
composition whose proportions cannot be represented by a ratio of small
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...
s (i.e. an
empirical formula In chemistry, the empirical formula of a chemical compound is the simplest whole number ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulfur monoxide, or SO, would simply be SO, as is th ...
); most often, in such materials, some small percentage of atoms are missing or too many atoms are packed into an otherwise perfect
lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an orna ...
work. Contrary to earlier definitions, modern understanding of non-stoichiometric compounds view them as homogeneous, and not mixtures of
stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
chemical compounds. Since the solids are overall electrically neutral, the defect is compensated by a change in the charge of other atoms in the solid, either by changing their
oxidation state In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. C ...
, or by replacing them with atoms of different elements with a different charge. Many
metal oxide An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the E ...
s and
sulfide Sulfide (British English also sulphide) is an inorganic anion of sulfur with the chemical formula S2− or a compound containing one or more S2− ions. Solutions of sulfide salts are corrosive. ''Sulfide'' also refers to chemical compounds lar ...
s have non-stoichiometric examples; for example, stoichiometric
iron(II) oxide Iron(II) oxide or ferrous oxide is the inorganic compound with the formula FeO. Its mineral form is known as wüstite. One of several iron oxides, it is a black-colored powder that is sometimes confused with rust, the latter of which consists ...
, which is rare, has the formula , whereas the more common material is nonstoichiometric, with the formula . The type of equilibrium defects in non-stoichiometric compounds can vary with attendant variation in bulk properties of the material. Non-stoichiometric compounds also exhibit special electrical or chemical properties because of the defects; for example, when atoms are missing, electrons can move through the solid more rapidly. Non-stoichiometric compounds have applications in
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
and
superconductive Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
material and in electrochemical (i.e.,
battery Battery most often refers to: * Electric battery, a device that provides electrical power * Battery (crime), a crime involving unlawful physical contact Battery may also refer to: Energy source *Automotive battery, a device to provide power t ...
) system designs.


Occurrence


Iron oxides

Nonstoichiometry is pervasive for
metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
oxides An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the E ...
, especially when the metal is not in its highest
oxidation state In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. C ...
.N. N. Greenwood & A. Earnshaw, 2012, "Chemistry of the Elements," 2nd Edn., Amsterdam, NH, NLD:Elsevier, , se

accessed 8 July 2015. age numbers marked by superscript, inline./ref> For example, although
wüstite Wüstite ( Fe O) is a mineral form of iron(II) oxide found with meteorites and native iron. It has a grey colour with a greenish tint in reflected light. Wüstite crystallizes in the isometric-hexoctahedral crystal system in opaque to transluc ...
(
ferrous oxide Iron(II) oxide or ferrous oxide is the inorganic compound with the formula FeO. Its mineral form is known as wüstite. One of several iron oxides, it is a black-colored powder that is sometimes confused with rust, the latter of which consists of ...
) has an ideal (
stoichiometric Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
) formula , the actual stoichiometry is closer to . The non-stoichiometry reflect the ease of oxidation of to effectively replacing a small portion of with two thirds their number of . Thus for every three "missing" ions, the crystal contains two 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 , where ''x'' is a small number (0.05 in the previous example) representing the deviation from the "ideal" formula. 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.


Iron sulfides

The monosulfides of the transition metals are often nonstoichiometric. Best known perhaps is nominally iron(II) sulfide (the mineral
pyrrhotite Pyrrhotite is an iron sulfide mineral with the formula Fe(1-x)S (x = 0 to 0.2). It is a nonstoichiometric variant of FeS, the mineral known as troilite. Pyrrhotite is also called magnetic pyrite, because the color is similar to pyrite and it is ...
) with a composition (''x'' = 0 to 0.2). The rare stoichiometric
endmember An endmember (also end-member or end member) in mineralogy is a mineral that is at the extreme end of a mineral series in terms of purity of its chemical composition. Minerals often can be described as solid solutions with varying compositions of ...
is known as the mineral ''
troilite Troilite is a rare iron sulfide mineral with the simple formula of FeS. It is the iron-rich endmember of the pyrrhotite group. Pyrrhotite has the formula Fe(1-x)S (x = 0 to 0.2) which is iron deficient. As troilite lacks the iron deficiency whic ...
''. Pyrrhotite is remarkable in that it has numerous
polytypes In materials science, polymorphism describes the existence of a solid material in more than one form or crystal structure. Polymorphism is a form of isomerism. Any crystalline material can exhibit the phenomenon. Allotropy refers to polymorphism ...
, i.e. crystalline forms differing in symmetry (
monoclinic In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic s ...
or
hexagonal In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A '' regular hexagon'' has ...
) and composition (, , 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 .


Palladium hydrides

Palladium hydride Palladium hydride is metallic palladium that contains a substantial quantity of hydrogen within its crystal lattice. Despite its name, it is not an ionic hydride but rather an alloy of palladium with metallic hydrogen that can be written PdHx. At ro ...
is a nonstoichiometric material of the approximate composition (0.02 < ''x'' < 0.58). This solid conducts hydrogen by virtue of the mobility of the hydrogen atoms within the solid.


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 Tungsten(VI) oxide, also known as tungsten trioxide is a chemical compound of oxygen and the transition metal tungsten, with formula WO3. The compound is also called tungstic anhydride, reflecting its relation to tungstic acid . It is a light ...
, one can generate a series of related materials that are slightly deficient in oxygen. These oxygen-deficient species can be described as , but in fact they are stoichiometric species with large unit cells with the formulas , where ''n'' = 20, 24, 25, 40. Thus, the last species can be described with the stoichiometric formula , whereas the non-stoichiometric description implies a more random distribution of oxide vacancies.


Other cases

At high temperatures (1000 °C),
titanium sulfide Titanium(II) sulfide (TiS) is an inorganic chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by che ...
s present a series of non-stoichiometric compounds. The
coordination polymer A coordination polymer is an inorganic or organometallic polymer structure containing metal cation centers linked by ligands. More formally a coordination polymer is a coordination compound with repeating coordination entities extending in 1, 2, o ...
Prussian blue Prussian blue (also known as Berlin blue, Brandenburg blue or, in painting, Parisian or Paris blue) is a dark blue pigment produced by oxidation of ferrous ferrocyanide salts. It has the chemical formula Fe CN)">Cyanide.html" ;"title="e(Cyani ...
, nominally and their analogs are well known to form in non-stoichiometric proportions. The non-stoichiometric phases exhibit useful properties vis-à-vis their ability to bind
caesium Caesium (IUPAC spelling) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
and
thallium Thallium is a chemical element with the Symbol (chemistry), symbol Tl and atomic number 81. It is a gray post-transition metal that is not found free in nature. When isolated, thallium resembles tin, but discolors when exposed to air. Chemists W ...
ions.


Applications


Oxidation catalysis

Many useful compounds are produced by the reactions of
hydrocarbon In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and hydrophobic, and their odors are usually weak or ex ...
s with
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
, a conversion that is
catalyzed Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
by metal oxides. The process operates via the transfer of "lattice" oxygen to the hydrocarbon substrate, a step that temporarily generates a vacancy (or defect). In a subsequent step, the missing oxygen is replenished by O2. Such catalysts rely on the ability of the metal oxide to form phases that are not stoichiometric.Atkins, P. W.; Overton, T. L.; Rourke, J. P.; Weller, M. T.; Armstrong, F. A., 2010, ''Shriver and Atkins' Inorganic Chemistry'' 5th Edn., pp. 65, 75, 99f, 268, 271, 277, 287, 356, 409, Oxford, OXF, GBR: Oxford University Press, , se

accessed 8 July 2015.
An analogous sequence of events describes other kinds of atom-transfer reactions including
hydrogenation Hydrogenation is a chemical reaction between molecular hydrogen (H2) and another compound or element, usually in the presence of a Catalysis, catalyst such as nickel, palladium or platinum. The process is commonly employed to redox, reduce or S ...
and
hydrodesulfurization Hydrodesulfurization (HDS) is a catalytic chemical process widely used to remove sulfur (S) from natural gas and from refined petroleum products, such as gasoline or petrol, jet fuel, kerosene, diesel fuel, and fuel oils. The purpose of remov ...
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. 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 Yttrium barium copper oxide (YBCO) is a family of crystalline chemical compounds that display high-temperature superconductivity; it includes the first material ever discovered to become superconducting above the boiling point of liquid nitrogen ...
, arguably the most notable
high-temperature superconductor High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previ ...
, is a non-stoichiometric solid with the formula Y''x''Ba2Cu3O7−''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 Nikolai Semyonovich Kurnakov (russian: Николай Семёнович Курнаков; 6 December 1860 – 19 March 1941) was a Russian chemist, who is internationally recognized as the originator of physical chemistry, physicochemical analys ...
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 Rare Earth Trifluorides, Part 2 Arxius de les Seccions de Ciències , Institut d'Estudis Catalans, 2000, p75ff. , The names come from
Claude Louis Berthollet Claude Louis Berthollet (, 9 December 1748 – 6 November 1822) was a Savoyard-French chemist who became vice president of the French Senate in 1804. He is known for his scientific contributions to theory of chemical equilibria via the mecha ...
and
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into colour blindness, which he had. Colour b ...
, 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 An F center or Farbe center (from the original German ''Farbzentrum'', where ''Farbe'' means ''color'' and ''zentrum'' means center) is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more un ...
*
Vacancy defect In crystallography, a vacancy is a type of point defect in a crystal where an atom is missing from one of the lattice sites.Ehrhart, P. (1991) "Properties and interactions of atomic defects in metals and alloys", chapter 2, p. 88 in ''Landolt-B ...


References


Further reading

*
F. Albert Cotton Frank Albert Cotton FRS (April 9, 1930 – February 20, 2007) was an American chemist. He was the W.T. Doherty-Welch Foundation Chair and Distinguished Professor of Chemistry at Texas A&M University. He authored over 1600 scientific articles. C ...
, 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, , se

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, se

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, se

accessed 8 July 2015. {{Authority control Solid-state chemistry Inorganic chemistry Non-stoichiometric compounds General chemistry