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Non-stoichiometric compound

Non-stoichiometric compound is a chemistry topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Non-stoichiometric compound rather than just read about it. In short: 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. Contrary to earlier definitions, modern understa…

Non-stoichiometric compound — main illustration
Non-stoichiometric compound — illustration

Key takeaways

  • Non-stoichiometric compound belongs to chemistry; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Non-stoichiometric compound to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Non-stoichiometric compound from memory before moving on to harder problems.

Reference excerpt

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. Contrary to earlier definitions, modern understanding of non-stoichiometric compounds view them as homogeneous, and not mixtures of stoichiometric 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, 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 Fe0.95O. 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 and superconductive material and in electrochemical (i.e., battery) system designs.

Occurrence

Iron oxides Nonstoichiometry is pervasive for metal oxides, especially when the metal is not in its highest oxidation state. For example, although wüstite (ferrous oxide) has an ideal (stoichiometric) formula FeO, the actual stoichiometry is closer to Fe0.95O. 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 Fe1−xO, 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) with a composition Fe1−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.

Palladium hydrides Palladium hydride is a nonstoichiometric material of the approximate composition PdHx (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, one can generate a series of related materials that are slightly deficient in oxygen. These oxygen-deficient species can be described as WO3−x, but in fact they are stoichiometric species with large unit cells with the formulas WnO3n−2, where n = 20, 24, 25, 40. Thus, the last species can be described with the stoichiometric formula W40O118, whereas the non-stoichiometric description WO2.95 implies a more random distribution of oxide vacancies.

Other cases At high temperatures (1000 °C), titanium sulfides present a series of non-stoichiometric compounds. The coordination polymer Prussian blue, nominally Fe7(CN)18 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 and thallium ions.

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. 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.

Superconductivity

… excerpt ends here. Continue reading the full article.

Illustrations

Non-stoichiometric compound: 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.
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 compound: Pyrrhotite, an example of a non-stoichiometric inorganic compound, with formula Fe1−xS (x = 0 to 0.2)
Pyrrhotite, an example of a non-stoichiometric inorganic compound, with formula Fe1−xS (x = 0 to 0.2)

Worked examples

Example 1 — a first encounter with Non-stoichiometric compound

Start with the simplest possible case. Write down what Non-stoichiometric compound claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Non-stoichiometric compound before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Non-stoichiometric compound ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Non-stoichiometric compound

In research
Non-stoichiometric compound appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Non-stoichiometric compound in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Non-stoichiometric compound is common in secondary-school and first-year university syllabi. It links to neighbouring topics General chemistry, Inorganic chemistry, Non-stoichiometric compounds, so understanding it makes those chapters shorter.
In everyday life
Look for Non-stoichiometric compound outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Non-stoichiometric compound in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Non-stoichiometric compound means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Non-stoichiometric compound out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Non-stoichiometric compound in simple terms?

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 missi…

Why does Non-stoichiometric compound matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Non-stoichiometric compound?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Non-stoichiometric compound.

Tags

  • General chemistry
  • Inorganic chemistry
  • Non-stoichiometric compounds
  • Solid-state chemistry

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