A Schottky defect is an excitation of the site occupations in a

crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...

leading to

point defect A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell param ...

s named after

Walter H. Schottky Walter Hans Schottky (23 July 1886 – 4 March 1976) was a German physicist who played a major early role in developing the theory of electron and ion emission phenomena, invented the screen-grid vacuum tube in 1915 while working at Siemens ...

. In ionic crystals, this defect forms when oppositely charged

ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...

s leave their lattice sites and become incorporated for instance at the surface, creating oppositely charged vacancies. These vacancies are formed in

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 ...

units, to maintain an overall neutral charge in the ionic solid.

Definition

Schottky defects consist of unoccupied anion and cation sites in a stoichiometric ratio. For a simple ionic crystal of type A⁻B⁺, a Schottky defect consists of a single anion vacancy (A) and a single cation vacancy (B), or v + v following

Kröger–Vink notation Kröger–Vink notation is a set of conventions that are used to describe electric charges and Crystal structure, lattice positions of Crystallographic defect#, point defect species in crystals. It is primarily used for ionic crystals and is particu ...

. For a more general crystal with formula A_xB_y, a Schottky cluster is formed of x vacancies of A and y vacancies of B, thus the overall stoichiometry and charge neutrality are conserved. Conceptually, a Schottky defect is generated if the crystal is expanded by one unit cell, whose a prior empty sites are filled by atoms that diffused out of the interior, thus creating vacancies in the crystal. Schottky defects are observed most frequently when there is a small difference in size between the cations and anions that make up a material.

Illustration

Chemical equations in

for the formation of Schottky defects in TiO₂ and BaTiO₃. :∅ v + 2 v :∅ v + v + 3 v This can be illustrated schematically with a two-dimensional diagram of a

sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...

crystal lattice:

Bound and dilute defects

The vacancies that make up the Schottky defects have opposite charge, thus they experience a mutually attractive

Coulomb force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...

. At low temperature, they may form bound clusters. The bound clusters are typically less mobile than the dilute counterparts, as multiple species need to move in a concerted motion for the whole cluster to migrate. This has important implications for numerous functional ceramics used in a wide range of applications, including ion conductors,

Solid oxide fuel cell A solid oxide fuel cell (or SOFC) is an electrochemical conversion device that produces electricity directly from oxidizing a fuel. Fuel cells are characterized by their electrolyte material; the SOFC has a solid oxide or ceramic electrolyte. A ...

s and

nuclear fuel Nuclear fuel is material used in nuclear power stations to produce heat to power turbines. Heat is created when nuclear fuel undergoes nuclear fission. Most nuclear fuels contain heavy fissile actinide elements that are capable of undergoing ...

Examples

This type of defect is typically observed in highly

ionic compound In chemistry, an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. The compound is neutral overall, but consists of positively charged ions called cations and negatively charged i ...

s, highly coordinated compounds, and where there is only a small difference in sizes of cations and anions of which the compound lattice is composed. Typical salts where Schottky disorder is observed are

NaCl Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...

KCl Potassium chloride (KCl, or potassium salt) is a metal halide Salt (chemistry), salt composed of potassium and chlorine. It is odorless and has a white or colorless vitreous lustre, vitreous crystal appearance. The solid dissolves readily in wa ...

, KBr,

CsCl CSCL can refer to: * Caesium chloride (CsCl), a chemical compound. * Computer Supported Collaborative Learning, a research topic on supporting collaborative learning with the assistance of computer artifacts. * China Shipping Container Lines, a c ...

and AgBr. For engineering applications, Schottky defects are important in oxides with

Fluorite structure In solid state chemistry, the fluorite structure refers to a common motif for compounds with the formula MX2. The X ions occupy the eight tetrahedral interstitial sites whereas M ions occupy the regular sites of a face-centered cubic (FCC) structure ...

, such as CeO₂, cubic ZrO₂, UO₂, ThO₂ and PuO₂.

Effect on density

Typically, the formation volume of a vacancy is positive: the lattice contraction due to the strains around the defect does not make up for the expansion of the crystal due to the additional number of sites. Thus, the density of the solid crystal is less than the theoretical density of the material.

References

Notes

{{reflist Crystallographic defects