In crystallography, a Frenkel defect is a type of

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 ...

in crystalline solids, named after its discoverer

Yakov Frenkel __NOTOC__ Yakov Il'ich Frenkel (russian: Яков Ильич Френкель; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed matter physics. He is also known as Jacov Frenkel, frequ ...

. The defect forms when an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, ...

or smaller

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 ...

(usually cation) leaves its place in the lattice, creating a vacancy and becomes an

interstitial An interstitial space or interstice is a space between structures or objects. In particular, interstitial may refer to: Biology * Interstitial cell tumor * Interstitial cell, any cell that lies between other cells * Interstitial collagenase ...

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 In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability th ...

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 (usually the cation) is dislocated. Similar to a

Schottky defect 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 inc ...

the Frenkel defect is a

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 equ ...

defect (does not change the over all stoichiometry of the compound). 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.

Effect on density

Even though Frenkel defects involve only the migration of the ions within the crystal, the total volume and thus the density is not necessarily changed: in particular for close-packed systems, the lattice expansion due to the strains induced by the interstitial atom typically dominates over the lattice contraction due to the vacancy, leading to a decrease of density.

Examples

Frenkel defects are exhibited in ionic solids with a large size difference between the anion and cation (with the cation usually smaller due to an increased

effective nuclear charge In atomic physics, the effective nuclear charge is the actual amount of positive (nuclear) charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevent ...

) Some examples of solids which exhibit Frenkel defects: *

zinc sulfide Zinc sulfide (or zinc sulphide) is an inorganic compound with the chemical formula of ZnS. This is the main form of zinc found in nature, where it mainly occurs as the mineral sphalerite. Although this mineral is usually black because of various ...

, *

silver(I) chloride Silver chloride is a chemical compound with the chemical formula Ag Cl. This white crystalline solid is well known for its low solubility in water (this behavior being reminiscent of the chlorides of Tl+ and Pb2+). Upon illumination or heating, ...

, *

silver(I) bromide Silver bromide (AgBr) is a soft, pale-yellow, water-insoluble salt well known (along with other silver halides) for its unusual sensitivity to light. This property has allowed silver halides to become the basis of modern photographic materials. A ...

(also shows Schottky defects), *

silver(I) iodide Silver iodide is an inorganic compound with the formula Ag I. The compound is a bright yellow solid, but samples almost always contain impurities of metallic silver that give a gray coloration. The silver contamination arises because AgI is hig ...

. These are due to the comparatively smaller size of Zn^2+ and Ag+ ions. For example, consider a lattice formed by X^''n''− and M^''n''+ ions. Suppose an M ion leaves the M sublattice, leaving the X sublattice unchanged. The number of interstitials formed will equal the number of vacancies formed. One form of a Frenkel defect reaction in MgO with the oxide anion leaving the lattice and going into the

interstitial site In crystallography, interstitial sites, holes or voids are the empty space that exists between the packing of atoms (spheres) in the crystal structure. The holes are easy to see if you try to pack circles together; no matter how close you get ...

written in

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 ...

: :Mg + O → O + v + Mg This can be illustrated with the example of the sodium chloride crystal structure. The diagrams below are schematic two-dimensional representations.

Effect on density

Examples

See also

References

Further reading