In crystallography, a Frenkel defect is a type of point defect in crystalline solids, named after its discoverer Yakov Frenkel.[1] The defect forms when an atom or smaller ion (usually cation) leaves its place in the lattice, creating a vacancy and becomes an interstitial by lodging in a nearby location.[2] 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.[citation needed] 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.[citation needed] Similar to a Schottky defect the Frenkel defect is a stoichiometric 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.[3] Also, because such coupled complex defects are stoichiometric, their concentration will be independent of chemical conditions.[4]
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.[citation needed]
Examples
The Frenkel defect within the NaCl structure
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)
Some examples of solids which exhibit Frenkel defects:
These are due to the comparatively smaller size of and ions.
For example, consider a lattice formed by Xn− and Mn+ 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 written in Kröger–Vink notation:
Mg× Mg + O× O → O i + v•• O + Mg× Mg
This can be illustrated with the example of the sodium chloride crystal structure. The diagrams below are schematic two-dimensional representations.
^Frenkel, Yakov (1926). "Über die Wärmebewegung in festen und flüssigen Körpern (About the thermal motion in solids and liquids)". Zeitschrift für Physik. Springer. 35 (8): 652–669. Bibcode:1926ZPhy...35..652F. doi:10.1007/BF0137981.
^Ashcroft and Mermin (1976). Solid State chemistry. Cengage Learning. pp. 620. ISBN0030839939.
^Gorai, Prashun; Stevanovic, Vladan. "Comment on "Understanding the Intrinsic P-Type Behavior and Phase Stability of Thermoelectric α-Mg3Sb2"". ACS Applied Energy Materials. doi:10.1021/acsaem.9b01918.
^Anand, Shashwat; Toriyama, Micheal; Wolverton, Chris; Snyder, Jeff. "A Convergent Understanding of Charged Defects". Accounts of Materials Research. doi:10.1021/accountsmr.2c00044.
frenkel, defect, crystallography, type, point, defect, crystalline, solids, named, after, discoverer, yakov, frenkel, defect, forms, when, atom, smaller, usually, cation, leaves, place, lattice, creating, vacancy, becomes, interstitial, lodging, nearby, locati. In crystallography a Frenkel defect is a type of point defect in crystalline solids named after its discoverer Yakov Frenkel 1 The defect forms when an atom or smaller ion usually cation leaves its place in the lattice creating a vacancy and becomes an interstitial by lodging in a nearby location 2 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 citation needed 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 citation needed Similar to a Schottky defect the Frenkel defect is a stoichiometric 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 3 Also because such coupled complex defects are stoichiometric their concentration will be independent of chemical conditions 4 Contents 1 Effect on density 2 Examples 3 See also 4 References 5 Further readingEffect on density EditEven 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 citation needed Examples Edit The Frenkel defect within the NaCl structure 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 Some examples of solids which exhibit Frenkel defects zinc sulfide silver I chloride silver I bromide also shows Schottky defects silver I iodide These are due to the comparatively smaller size of Zn 2 displaystyle ce Zn 2 and Ag displaystyle ce Ag ions For example consider a lattice formed by Xn and Mn 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 written in Kroger Vink notation Mg Mg O O O displaystyle prime prime i v O Mg MgThis can be illustrated with the example of the sodium chloride crystal structure The diagrams below are schematic two dimensional representations The defect free NaCl structure Two Frenkel defects within the NaCl structureSee also EditDeep level transient spectroscopy DLTS Schottky defect Wigner effect Crystallographic defectReferences Edit Frenkel Yakov 1926 Uber die Warmebewegung in festen und flussigen Korpern About the thermal motion in solids and liquids Zeitschrift fur Physik Springer 35 8 652 669 Bibcode 1926ZPhy 35 652F doi 10 1007 BF0137981 Ashcroft and Mermin 1976 Solid State chemistry Cengage Learning pp 620 ISBN 0030839939 Gorai Prashun Stevanovic Vladan Comment on Understanding the Intrinsic P Type Behavior and Phase Stability of Thermoelectric a Mg3Sb2 ACS Applied Energy Materials doi 10 1021 acsaem 9b01918 Anand Shashwat Toriyama Micheal Wolverton Chris Snyder Jeff A Convergent Understanding of Charged Defects Accounts of Materials Research doi 10 1021 accountsmr 2c00044 Further reading EditKittel Charles 2005 Introduction to Solid State Physics 8th ed Wiley pp 585 588 ISBN 0 471 41526 X Retrieved from https en wikipedia org w index php title Frenkel defect amp oldid 1108562946, wikipedia, wiki, book, books, library,
