Non-stoichiometric compound

Last updated February 07, 2024

Origin of title phenomenon in crystallographic defects. Shown is a two-dimensional slice through a primitive cubic crystal system showing the regular square array of atoms on one face (open circles, o), and with these, places where atoms are missing from a regular site to create vacancies, displaced to an adjacent acceptable space to create a Frenkel pair, or substituted by a smaller or larger atom not usually seen (closed circles, * ), in each case resulting in a material that is moved toward being measurably non-stoichiometric. Defecttypes.png — **Origin of title phenomenon in crystallographic defects.** Shown is a two-dimensional slice through a primitive cubic crystal system showing the regular square array of atoms on one face (open circles, o), and with these, places where atoms are missing from a regular site to create *vacancies*, displaced to an adjacent acceptable space to create a *Frenkel pair* , or substituted by a smaller or larger atom not usually seen (closed circles, • ), *in each case resulting in a material that is moved toward being measurably non-stoichiometric.*

Non-stoichiometric compounds are chemical compounds, almost always solid inorganic compounds, having elemental composition whose proportions cannot be represented by a ratio of small natural numbers (i.e. an empirical formula); most often, in such materials, some small percentage of atoms are missing or too many atoms are packed into an otherwise perfect lattice work.^{[ not verified in body ]}

Contrary to earlier definitions, modern understanding of non-stoichiometric compounds view them as homogeneous, and not mixtures of stoichiometric chemical compounds.^{[ not verified in body ]} 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, or by replacing them with atoms of different elements with a different charge. Many metal oxides and sulfides have non-stoichiometric examples; for example, stoichiometric iron(II) oxide, which is rare, has the formula FeO, whereas the more common material is nonstoichiometric, with the formula Fe_0.95O. The type of equilibrium defects in non-stoichiometric compounds can vary with attendant variation in bulk properties of the material.^[1] 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.^{[ not verified in body ]} Non-stoichiometric compounds have applications in ceramic and superconductive material and in electrochemical (i.e., battery) system designs.^{[ citation needed ]}

Occurrence

Iron oxides

Nonstoichiometry is pervasive for metal oxides, especially when the metal is not in its highest oxidation state.^[2]^{: 642–644} 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.^{[ citation needed ]}

Iron sulfides

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−xS (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.^[4]

Palladium hydrides

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.^{[ citation needed ]}

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 non-stoichiometric description WO_2.95 implies a more random distribution of oxide vacancies.^{[ citation needed ]}

Other cases

At high temperatures (1000 °C), titanium sulfides present a series of non-stoichiometric compounds.^[2]^: 679

The coordination polymer Prussian blue, nominally Fe₇(CN)₁₈ and their analogs are well known to form in non-stoichiometric proportions.^[5]^: 114 The non-stoichiometric phases exhibit useful properties vis-à-vis their ability to bind caesium and thallium ions.^{[ citation needed ]}

Applications

Oxidation catalysis

Many useful compounds 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 (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.^[6] 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. 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.^[6]

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 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.^[6]

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.^[7] 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.^[8]

Related Research Articles

In chemistry, the law of definite proportions, sometimes called Proust's law or the law of constant composition, states that a given chemical compound always contains its component elements in fixed ratio and does not depend on its source and method of preparation. For example, oxygen makes up about ⁸/₉ of the mass of any sample of pure water, while hydrogen makes up the remaining ¹/₉ of the mass: the mass of two elements in a compound are always in the same ratio. Along with the law of multiple proportions, the law of definite proportions forms the basis of stoichiometry.

<span class="mw-page-title-main">Oxide</span> Chemical compound where oxygen atoms are combined with atoms of other elements

An oxide is a chemical compound containing at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O^2– ion with oxygen in the oxidation state of −2. Most of the Earth's crust consists of oxides. Even materials considered pure elements often develop an oxide coating. For example, aluminium foil develops a thin skin of Al₂O₃ that protects the foil from further oxidation.

In chemistry, a salt or ionic compound is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a neutral compound with no net electric charge. The constituent ions are held together by electrostatic forces termed ionic bonds.

Solid-state chemistry, also sometimes referred as materials chemistry, is the study of the synthesis, structure, and properties of solid phase materials. It therefore has a strong overlap with solid-state physics, mineralogy, crystallography, ceramics, metallurgy, thermodynamics, materials science and electronics with a focus on the synthesis of novel materials and their characterization. A diverse range of synthetic techniques, such as the ceramic method and chemical vapour depostion, make solid-state materials. Solids can be classified as crystalline or amorphous on basis of the nature of order present in the arrangement of their constituent particles. Their elemental compositions, microstructures, and physical properties can be characterized through a variety of analytical methods.

<span class="mw-page-title-main">Wüstite</span> Iron(II) oxide mineral formed under reducing conditions

Wüstite is a mineral form of mostly 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 translucent metallic grains. It has a Mohs hardness of 5 to 5.5 and a specific gravity of 5.88. Wüstite is a typical example of a non-stoichiometric compound.

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 [77 K ] at about 93 K.

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 hydrated iron(III) oxide. Iron(II) oxide also refers to a family of related non-stoichiometric compounds, which are typically iron deficient with compositions ranging from Fe_0.84O to Fe_0.95O.

Cuprates are a class of compounds that contain copper (Cu) atom(s) in an anion. They can be broadly categorized into two main types:

Cerium(IV) oxide, also known as ceric oxide, ceric dioxide, ceria, cerium oxide or cerium dioxide, is an oxide of the rare-earth metal cerium. It is a pale yellow-white powder with the chemical formula CeO₂. It is an important commercial product and an intermediate in the purification of the element from the ores. The distinctive property of this material is its reversible conversion to a non-stoichiometric oxide.

A chalcogenide is a chemical compound consisting of at least one chalcogen anion and at least one more electropositive element. Although all group 16 elements of the periodic table are defined as chalcogens, the term chalcogenide is more commonly reserved for sulfides, selenides, tellurides, and polonides, rather than oxides. Many metal ores exist as chalcogenides. Photoconductive chalcogenide glasses are used in xerography. Some pigments and catalysts are also based on chalcogenides. The metal dichalcogenide MoS₂ is a common solid lubricant.

In crystallography, a Frenkel defect is a type of point defect in crystalline solids, named after its discoverer Yakov Frenkel. The defect forms when an atom or smaller ion leaves its place in the structure, creating a vacancy and becomes an interstitial by lodging in a nearby location. In elemental systems, they are primarily generated during particle irradiation, as their formation enthalpy is typically much higher than for other point defects, such as vacancies, and thus their equilibrium concentration according to the Boltzmann distribution is below the detection limit. In ionic crystals, which usually possess low coordination number or a considerable disparity in the sizes of the ions, this defect can be generated also spontaneously, where the smaller ion is dislocated. Similar to a Schottky defect the Frenkel defect is a stoichiometric defect. In ionic compounds, the vacancy and interstitial defect involved are oppositely charged and one might expect them to be located close to each other due to electrostatic attraction. However, this is not likely the case in real material due to smaller entropy of such a coupled defect, or because the two defects might collapse into each other. Also, because such coupled complex defects are stoichiometric, their concentration will be independent of chemical conditions.

A Schottky defect is an excitation of the site occupations in a crystal lattice leading to point defects named after Walter H. Schottky. In ionic crystals, this defect forms when oppositely charged ions leave their lattice sites and become incorporated for instance at the surface, creating oppositely charged vacancies. These vacancies are formed in stoichiometric units, to maintain an overall neutral charge in the ionic solid.

<span class="mw-page-title-main">Uranate</span>

A uranate is a ternary oxide involving the element uranium in one of the oxidation states 4, 5 or 6. A typical chemical formula is M_xU_yO_z, where M represents a cation. The uranium atom in uranates(VI) has two short collinear U–O bonds and either four or six more next nearest oxygen atoms. The structures are infinite lattice structures with the uranium atoms linked by bridging oxygen atoms.

Iron shows the characteristic chemical properties of the transition metals, namely the ability to form variable oxidation states differing by steps of one and a very large coordination and organometallic chemistry: indeed, it was the discovery of an iron compound, ferrocene, that revolutionalized the latter field in the 1950s. Iron is sometimes considered as a prototype for the entire block of transition metals, due to its abundance and the immense role it has played in the technological progress of humanity. Its 26 electrons are arranged in the configuration [Ar]3d⁶4s², of which the 3d and 4s electrons are relatively close in energy, and thus it can lose a variable number of electrons and there is no clear point where further ionization becomes unprofitable.

A chemical substance is a unique form of matter with constant chemical composition and characteristic properties. Chemical substances may take the form of a single element or chemical compounds. If two or more chemical substances can be combined without reacting, they may form a chemical mixture. If a mixture is separated to isolate one chemical substance to a desired degree, the resulting substance is said to be chemically pure.

Copper sulfides describe a family of chemical compounds and minerals with the formula Cu_xS_y. Both minerals and synthetic materials comprise these compounds. Some copper sulfides are economically important ores.

A chemical compound is a chemical substance composed of many identical molecules containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound. A compound can be transformed into a different substance by a chemical reaction, which may involve interactions with other substances. In this process, bonds between atoms may be broken and/or new bonds formed.

Cerimetry or cerimetric titration, also known as cerate oximetry, is a method of volumetric chemical analysis developed by Ion Atanasiu. It is a redox titration in which an iron(II)–1,10-phenanthroline complex (ferroin) color change indicates the end point. Ferroin can be reversibly discolored in its oxidized form upon titration with a Ce⁴⁺ solution. The use of cerium(IV) salts as reagents for volumetric analysis was first proposed in the middle of 19th century, but systematic studies did not start until about 70 years later. Standard solutions can be prepared from different Ce⁴⁺ salts, but often cerium sulfate is chosen.

The strength of metal oxide adhesion effectively determines the wetting of the metal-oxide interface. The strength of this adhesion is important, for instance, in production of light bulbs and fiber-matrix composites that depend on the optimization of wetting to create metal-ceramic interfaces. The strength of adhesion also determines the extent of dispersion on catalytically active metal. Metal oxide adhesion is important for applications such as complementary metal oxide semiconductor devices. These devices make possible the high packing densities of modern integrated circuits.

Sodium cobalt oxide, also called sodium cobaltate, is any of a range of compounds of sodium, cobalt, and oxygen with the general formula Na^_xCoO^₂ for 0 < x ≤ 1. The name is also used for hydrated forms of those compounds, Na^_xCoO^₂·yH^₂O.

References

↑ Geng, Hua Y.; et al. (2012). "Anomalies in nonstoichiometric uranium dioxide induced by a pseudo phase transition of point defects". Phys. Rev. B . 85 (14): 144111. arXiv: 1204.4607 . Bibcode:2012PhRvB..85n4111G. doi:10.1103/PhysRevB.85.144111. S2CID 119288531.
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↑ The Rare Earth Trifluorides, Part 2 Arxius de les Seccions de Ciències Dmitrii N. Khitarov, Boris Pavlovich Sobolev, Irina V. Alexeeva, Institut d'Estudis Catalans, 2000, p75ff. ISBN 847283610X, ISBN 9788472836105
↑ Henry Marshall Leicester (1971). The Historical Background of Chemistry. Courier Dover Publications. p. 153. ISBN 9780486610535.