Frenkel defect

Last updated

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 structure, 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

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 structural expansion due to the strains induced by the interstitial atom typically dominates over the structural contraction due to the vacancy, leading to a decrease of density.[ citation needed ]

Examples

The Frenkel defect within the NaCl structure NaCl - Frenkel defect.jpg
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 structure 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 structure 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.

The defect-free NaCl structure Nacllattice.svg
The defect-free NaCl structure
Two Frenkel defects within the NaCl structure Naclfrenkeldefect.svg
Two Frenkel defects within the NaCl structure

See also

Related Research Articles

<span class="mw-page-title-main">Crystallographic defect</span> Disruption of the periodicity of a crystal lattice

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 parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect. Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization.

<span class="mw-page-title-main">Ionic bonding</span> Chemical bonding involving attraction between ions

Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding, along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be more complex, e.g. molecular ions like NH+
4
or SO2−
4
. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal to obtain a full valence shell for both atoms.

<span class="mw-page-title-main">Salt (chemistry)</span> Chemical compound involving ionic bonding

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.

<span class="mw-page-title-main">Hydride</span> Molecule with a hydrogen bound to a more electropositive element or group

In chemistry, a hydride is formally the anion of hydrogen (H), a hydrogen atom with two electrons. The term is applied loosely. At one extreme, all compounds containing covalently bound H atoms are called hydrides: water (H2O) is a hydride of oxygen, ammonia is a hydride of nitrogen, etc. For inorganic chemists, hydrides refer to compounds and ions in which hydrogen is covalently attached to a less electronegative element. In such cases, the H centre has nucleophilic character, which contrasts with the protic character of acids. The hydride anion is very rarely observed.

<span class="mw-page-title-main">F-center</span> Type of crystallographic defect

An F center or Farbe center is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more unpaired electrons. Electrons in such a vacancy in a crystal lattice tend to absorb light in the visible spectrum such that a material that is usually transparent becomes colored. The greater the number of F centers, the more intense the color of the compound. F centers are a type of color center.

<span class="mw-page-title-main">Cubic crystal system</span> Crystallographic system where the unit cell is in the shape of a cube

In crystallography, the cubiccrystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.

<span class="mw-page-title-main">Silver bromide</span> Chemical compound

Silver bromide (AgBr) is a soft, pale-yellow, water-insoluble salt well known for its unusual sensitivity to light. This property has allowed silver halides to become the basis of modern photographic materials. AgBr is widely used in photographic films and is believed by some to have been used for making the Shroud of Turin. The salt can be found naturally as the mineral bromargyrite.

<span class="mw-page-title-main">Vacancy defect</span> Crystallographic defect; an atom missing from a lattice site

In crystallography, a vacancy is a type of point defect in a crystal where an atom is missing from one of the lattice sites. Crystals inherently possess imperfections, sometimes referred to as crystallographic defects.

Ionic radius, rion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), with 1 Å = 100 pm. Typical values range from 31 pm (0.3 Å) to over 200 pm (2 Å).

<span class="mw-page-title-main">Non-stoichiometric compound</span> Chemical compounds that cannot be represented by an empirical formula

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 ; most often, in such materials, some small percentage of atoms are missing or too many atoms are packed into an otherwise perfect lattice work.

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.

Kröger–Vink notation is a set of conventions that are used to describe electric charges and lattice positions of point defect species in crystals. It is primarily used for ionic crystals and is particularly useful for describing various defect reactions. It was proposed by F. A. Kröger and H. J. Vink.

Beta-alumina solid electrolyte (BASE) is a fast ion conductor material used as a membrane in several types of molten salt electrochemical cell. Currently there is no known substitute available. β-Alumina exhibits an unusual layered crystal structure which enables very fast ion transport. β-Alumina is not an isomorphic form of aluminium oxide (Al2O3), but a sodium polyaluminate. It is a hard polycrystalline ceramic, which, when prepared as an electrolyte, is complexed with a mobile ion, such as Na+, K+, Li+, Ag+, H+, Pb2+, Sr2+ or Ba2+ depending on the application. β-Alumina is a good conductor of its mobile ion yet allows no non-ionic (i.e., electronic) conductivity. The crystal structure of the β-alumina provides an essential rigid framework with channels along which the ionic species of the solid can migrate. Ion transport involves hopping from site to site along these channels. Since the 1970's this technology has been thoroughly developed, resulting in interesting applications. Its special characteristics on ion and electrical conductivity make this material extremely interesting in the field of energy storage.

In chemistry, a Zintl phase is a product of a reaction between a group 1 or group 2 and main group metal or metalloid. It is characterized by intermediate metallic/ionic bonding. Zintl phases are a subgroup of brittle, high-melting intermetallic compounds that are diamagnetic or exhibit temperature-independent paramagnetism and are poor conductors or semiconductors.

<span class="mw-page-title-main">Ion</span> Particle, atom or molecule with a net electrical charge

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 convention. The net charge of an ion is not zero because its total number of electrons is unequal to its total number of protons.

<span class="mw-page-title-main">Solid state ionics</span>

Solid-state ionics is the study of ionic-electronic mixed conductor and fully ionic conductors and their uses. Some materials that fall into this category include inorganic crystalline and polycrystalline solids, ceramics, glasses, polymers, and composites. Solid-state ionic devices, such as solid oxide fuel cells, can be much more reliable and long-lasting, especially under harsh conditions, than comparable devices with fluid electrolytes.

A metal ion in aqueous solution or aqua ion is a cation, dissolved in water, of chemical formula [M(H2O)n]z+. The solvation number, n, determined by a variety of experimental methods is 4 for Li+ and Be2+ and 6 for most elements in periods 3 and 4 of the periodic table. Lanthanide and actinide aqua ions have higher solvation numbers (often 8 to 9), with the highest known being 11 for Ac3+. The strength of the bonds between the metal ion and water molecules in the primary solvation shell increases with the electrical charge, z, on the metal ion and decreases as its ionic radius, r, increases. Aqua ions are subject to hydrolysis. The logarithm of the first hydrolysis constant is proportional to z2/r for most aqua ions.

Transition metal oxides are compounds composed of oxygen atoms bound to transition metals. They are commonly utilized for their catalytic activity and semiconducting properties. Transition metal oxides are also frequently used as pigments in paints and plastics, most notably titanium dioxide. Transition metal oxides have a wide variety of surface structures which affect the surface energy of these compounds and influence their chemical properties. The relative acidity and basicity of the atoms present on the surface of metal oxides are also affected by the coordination of the metal cation and oxygen anion, which alter the catalytic properties of these compounds. For this reason, structural defects in transition metal oxides greatly influence their catalytic properties. The acidic and basic sites on the surface of metal oxides are commonly characterized via infrared spectroscopy, calorimetry among other techniques. Transition metal oxides can also undergo photo-assisted adsorption and desorption that alter their electrical conductivity. One of the more researched properties of these compounds is their response to electromagnetic radiation, which makes them useful catalysts for redox reactions, isotope exchange and specialized surfaces.

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.

<span class="mw-page-title-main">Interstitial site</span> Empty space between atoms in a crystal lattice

In crystallography, interstitial sites, holes or voids are the empty space that exists between the packing of atoms (spheres) in the crystal structure.

References

  1. 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/BF01379812. S2CID   121391169.
  2. Ashcroft and Mermin (1976). Solid State chemistry. Cengage Learning. pp.  620. ISBN   0030839939.
  3. Gorai, Prashun; Stevanovic, Vladan (2020). "Comment on "Understanding the Intrinsic P-Type Behavior and Phase Stability of Thermoelectric α-Mg3Sb2"". ACS Applied Energy Materials. 3: 106–108. doi: 10.1021/acsaem.9b01918 . S2CID   211212284.
  4. Anand, Shashwat; Toriyama, Micheal; Wolverton, Chris; Snyder, Jeff (2022). "A Convergent Understanding of Charged Defects". Accounts of Materials Research. 3 (7): 685–696. doi:10.1021/accountsmr.2c00044. S2CID   249932959.

Further reading