Frenkel defect and Wigner effect

A Frenkel defect, Frenkel pair, or Frenkel disorder is a type of point defect in a crystal lattice. The defect forms when an atom or ion leaves its place in the lattice, creating a vacancy, and becomes an interstitial by lodging in a nearby location not usually occupied by an atom. Frenkel defects occur due to thermal vibrations, and it is theorized that there will be no defects in a crystal at 0 K. The phenomenon is named after the Soviet physicist Yakov Frenkel, who discovered it in 1926.

For example, consider a lattice formed by X and M 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 oxygen ion leaving the lattice and going into the interstitial site written in Kröger–Vink notation:

+→++

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

Two Frenkel defects within the NaCl structure

Wigner effect: The Wigner effect (named for its discoverer, E. P. Wigner), also known as the discomposition effect, is the displacement of atoms in a solid caused by neutron radiation. Any solid can be affected by the Wigner effect, but the effect is of most concern in neutron moderators, such as graphite, that are used to slow down fast neutrons. The material surrounding the moderator receives a much smaller amount of neutron radiation, and from slower neutrons, and is not as worrisome.

An interstitial atom and its associated vacancy are known as a Frenkel defect.

Explanation:

To create the Wigner effect, neutrons that collide with the atoms in a crystal structure must have enough energy to displace them from the lattice. This amount (threshold displacement energy) is approximately 25 eV. A neutron's energy can vary widely but it is not uncommon to have energies up to and exceeding 10 MeV (10,000,000 eV) in the center of a nuclear reactor. A neutron with a significant amount of energy will create a displacement cascade in a matrix via elastic collisions. For example a 1 MeV neutron striking graphite will create 900 displacements, however not all displacements will create defects because some of the struck atoms will find and fill the vacancies that were either small pre-existing voids or vacancies newly formed by the other struck atoms.

The atoms that do not find a vacancy come to rest in non-ideal locations; that is, not along the symmetrical lines of the lattice. These atoms are referred to as interstitial atoms, or simply interstitials. Because these atoms are not in the ideal location they have an energy associated with them, much like a ball at the top of a hill has gravitational potential energy. When large amounts of interstitials have accumulated they pose a risk of releasing all of their energy suddenly, creating a temperature spike. Sudden unplanned increases in temperature can present a large risk for certain types of nuclear reactors with low operating temperatures and were the indirect cause of the Windscale fire. Accumulation of energy in irradiated graphite has been recorded as high as 2.7 kJ/g, but is typically much lower than this.[1] Despite some reports[which?], Wigner energy buildup had nothing to do with the Chernobyl disaster: This reactor, like all contemporary power reactors, operated at a high enough temperature to allow the displaced graphite structure to realign itself before any potential energy could be stored.

Some Extrinsic defects and Intrinsic defects.

Various elemental analyses of diamond reveal a wide range of impurities. They however mostly originate from inclusions of foreign materials in diamond, which could be nanometer-small and invisible in an optical microscope. Also, virtually any element can be hammered into diamond by ion implantation. More essential are elements which can be introduced into the diamond lattice as isolated atoms (or small atomic clusters) during the diamond growth. By 2008, those elements are nitrogen, boron, hydrogen, silicon, phosphorus, nickel, cobalt and perhaps sulfur. Manganese and tungsten have been unambiguously detected in diamond, but they might originate from foreign inclusions. Detection of isolated iron in diamond has later been re-interpreted in terms of micro-particles of ruby produced during the diamond synthesis.Oxygen is believed to be a major impurity in diamond, but it has not been spectroscopically identified in diamond yet.[citation needed] Two electron paramagnetic resonance centers (OK1 and N3) have been assigned to nitrogen-oxygen complexes. However, the assignment is indirect and the corresponding concentrations are rather low (few parts per million).

• Nitrogen:The most common impurity in diamond is nitrogen, which can comprise up to 1% of a diamond by mass.[11] Previously, all lattice defects in diamond were thought to be the result of structural anomalies; later research revealed nitrogen to be present in most diamonds and in many different configurations. Most nitrogen enters the diamond lattice as a single atom (i.e. nitrogen-containing molecules dissociate before incorporation), however, molecular nitrogen incorporates into diamond as well. Absorption of light and other material properties of diamond are highly dependent upon nitrogen content and aggregation state. Although all aggregate configurations cause absorption in the infrared, diamonds containing aggregated nitrogen are usually colorless, i.e. have little absorption in the visible spectrum.
• Boron:Diamonds containing boron as a substitutional impurity are termed type IIb. Only one percent of natural diamonds are of this type, and most are blue to grey.Boron is acceptor in diamond: boron atoms have one less available electron than the carbon atoms; therefore, each boron atom substituting for a carbon atom creates an electron hole in the band gap that can accept an electron from the valence band. This allows red light absorption, and due to the small energy (0.37 eV)needed for the electron to leave the valence band, holes can be thermally released from the boron atoms to the valence band even at room temperatures. These holes can move in an electric field and render the diamond electrically conductive (i.e., a p-type semiconductor). Few boron atoms are required for this to happen—a typical ratio is one boron atom per 1,000,000 carbon atoms.Boron-doped diamonds transmit light down to ~250 nm and absorb some red and infrared light (hence the blue color); they may phosphoresce blue after exposure to shortwave ultraviolet light.[28] Apart from optical absorption, boron acceptors have been detected by electron paramagnetic resonance.

Intrinsic defects

The easiest way to produce intrinsic defects in diamond is by displacing carbon atoms through irradiation with high-energy particles, such as alpha (helium), beta (electrons) or gamma particles, protons, neutrons, ions, etc. The irradiation can occur in the laboratory or in the nature (see Diamond enhancement - Irradiation); it produces primary defects named frenkel defects (carbon atoms knocked off their normal lattice sites to interstitial sites) and remaining lattice vacancies. An important difference between the vacancies and interstitials in diamond is that whereas interstitials are mobile during the irradiation, even at liquid nitrogen temperatures,however vacancies start migrating only at temperatures ~700 0C.

Vacancies and interstitials can also be produced in diamond by plastic deformation, though in much smaller concentrations.

• Isolated carbon interstitial: Isolated interstitial has never been observed in diamond and is considered unstable. Its interaction with a regular carbon lattice atom produces a "split-interstitial", a defect where two carbon atoms share a lattice site and are covalently bonded with the carbon neighbors. This defect has been thoroughly characterized by electron paramagnetic resonance (R2 center)[58] and optical absorption,and unlike most other defects in diamond, it does not produce photoluminescence.
• Interstitial complexes:The isolated split-interstitial moves through the diamond crystal during irradiation. When it meets other interstitials it aggregates into larger complexes of two and three split-interstitials, identified by electron paramagnetic resonance (R1 and O3 centers),[60][61] optical absorption and photoluminescence.
• Vacancy-Interstitial complexes:Most high-energy particles, beside displacing carbon atom from the lattice site, also pass it enough surplus energy for a rapid migration through the lattice. However, when relatively gentle gamma irradiation is used, this extra energy is minimal. Thus the interstitials remain near the original vacancies and form vacancy-interstitials pairs identified through optical absorption.Vacancy-di-interstitial pairs have been also produced, though by electron irradiation and through a different mechanism:[65] Individual interstitials migrate during the irradiation and aggregate to form di-interstitials; this process occurs preferentially near the lattice vacancies.
• Isolated vacancy:Pure diamonds, before and after irradiation and annealing. Clockwise from left bottom: 1) Initial (2×2 mm) 2-4) Irradiated by different doses of 2-MeV electrons 5-6) Irradiated by different doses and annealed at 800 °C. Isolated vacancy is the most studied defect in diamond, both experimentally and theoretically. Its most important practical property is optical absorption, like in the color centers, which gives diamond green, or sometimes even green-blue color (in pure diamond). The characteristic feature of this absorption is a series of sharp lines called GR1-8, where GR1 line at 741 nm is the most prominent and important. The vacancy behaves as a deep electron donor/acceptor, whose electronic properties depend on the charge state. The energy level for the +/0 states is at 0.6 eV and for the 0/- states is at 2.5 eV above the valence band.[66]
• Multivacancy complexes:Upon annealing of pure diamond at ~700 0C, vacancies migrate and form divacancies, characterized by optical absorption and electron paramagnetic resonance.[67] Similar to single interstitials, divacancies do not produce photoluminescence. Divacancies, in turn, anneal out at ~900 0C creating multivacancy chains detected by EPR[68] and presumably hexavacancy rings. The latter should be invisible to most spectroscopies, and indeed, they have not been detected thus far.[68] Annealing of vacancies changes diamond color from green to yellow-brown. Similar mechanism (vacancy aggregation) is also believed to cause brown color of plastically deformed natural diamonds.

Pure diamonds, before and after irradiation and annealing. Clockwise from left bottom: 1) Initial (2×2 mm) 2-4) Irradiated by different doses of 2-MeV electrons 5-6) Irradiated by different doses and annealed at 800 °C.

Cristallographic defects in diamond.

Imperfections in the crystal lattice of diamond are common. Such crystallographic defects in diamond may be the result of lattice irregularities or extrinsic substitutional or interstitial impurities, introduced during or after the diamond growth. They affect the material properties of diamond and determine to which type a diamond is assigned; the most dramatic effects are on the diamond color and electrical conductivity, as explained by the band theory.

The defects can be detected by different types of spectroscopy, including electron paramagnetic resonance (EPR), luminescence induced by light (photoluminescence, PL) or electron beam (cathodoluminescence, CL), and absorption of light in the infrared (IR), visible and UV parts of the spectrum. Absorption spectrum is used not only to identify the defects, but also to estimate their concentration; it can also distinguish natural from synthetic or enhanced diamonds.[1]

The number of defects in diamond whose microscopic structure has been reliably identified is rather large (many dozens), and only the major ones are briefly mentioned in this article.

Labeling of diamond centers:

There is a tradition in diamond spectroscopy to label a defect-induced spectrum by a numbered acronym (e.g. GR1). This tradition has been followed in general with some notable deviations, such as A, B and C centers. Many acronyms are confusing though:

• Some symbols are too similar (e.g., 3H and H3).
• Accidentally, same labels were given to different centers detected by EPR and optical techniques (e.g., N3 EPR center and N3 optical center have no relation).
• Whereas some acronyms are logical, such as N3 (N for natural, i.e. observed in natural diamond) or H3 (H for heated, i.e. observed after irradiation and heating), many are not. In particular, there is no clear distinction between the meaning of labels GR (general radiation), R (radiation) and TR (type-II radiation).

Defect symmetry:

The symmetry of defects in crystals is described by the point groups. They differ from the space groups describing the symmetry of crystals by absence of translations, and thus are much fewer in number. In diamond, only defects of the following symmetries have been observed thus far: tetrahedral (Td), tetragonal (D2d), trigonal (D3d,C3v), rhombic (C2v), monoclinic (C2h, C1h, C2) and triclinic (C1 or CS).

The defect symmetry allows predicting many optical properties. For example, one-phonon (infrared) absorption in pure diamond lattice is forbidden because the lattice has an inversion center. However, introducing any defect (even "very symmetrical", such as N-N substitutional pair) breaks the crystal symmetry resulting in defect-induced infrared absorption, which is the most common tool to measure the defect concentrations in diamond.

An interesting symmetry related phenomenon has been observed that when diamond is produced by the high-pressure high-temperature synthesis, non-tetrahedral defects align to the direction of the growth. Such alignment has been also been observed in gallium arsenide and thus is not unique to diamond.

Line defects and Planar defects.

Line defects can be described by gauge theories.

• Dislocations are linear defects around which some of the atoms of the crystal lattice are misaligned. There are two basic types of dislocations, the edge dislocation and the screw dislocation. "Mixed" dislocations, combining aspects of both types, are also common. An edge dislocation is shown. The dislocation line is presented in blue, the Burgers vector b in black. Edge dislocations are caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the adjacent planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. The analogy with a stack of paper is apt: if a half a piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable at the edge of the half sheet. The screw dislocation is more difficult to visualise, but basically comprises a structure in which a helical path is traced around the linear defect (dislocation line) by the atomic planes of atoms in the crystal lattice. The presence of dislocation results in lattice strain (distortion). The direction and magnitude of such distortion is expressed in terms of a Burgers vector (b). For an edge type, b is perpendicular to the dislocation line, whereas in the cases of the screw type it is parallel. In metallic materials, b is aligned with close-packed crytallographic directions and its magnitude is equivalent to one interatomic spacing. Dislocations can move if the atoms from one of the surrounding planes break their bonds and rebond with the atoms at the terminating edge. It is the presence of dislocations and their ability to readily move (and interact) under the influence of stresses induced by external loads that leads to the characteristic malleability of metallic materials. Dislocations can be observed using transmission electron microscopy, field ion microscopy and atom probe techniques. Deep level transient spectroscopy has been used for studying the electrical activity of dislocations in semiconductors, mainly silicon.

• Disclinations are line defects corresponding to "adding" or "subtracting" an angle around a line. Basically, this means that if you track the crystal orientation around the line defect, you get a rotation. Usually they play a role only in liquid crystals.

An edge dislocation is shown. The dislocation line is presented in blue, the Burgers vector b in black.

Planar defects:

• Grain boundaries occur where the crystallographic direction of the lattice abruptly changes. This usually occurs when two crystals begin growing separately and then meet.
• Anti-phase boundaries occur in ordered alloys: in this case, the crystallographic direction remains the same, but each side of the boundary has an opposite phase: For example if the ordering is usually ABABABAB, an anti phase boundary takes the form of ABABBABA.
• Stacking faults occur in a number of crystal structures, but the common example is in close-packed structures. Face-centered cubic (fcc) structures differ from hexagonal close packed (hcp) structures only in stacking order: both structures have close packed atomic planes with sixfold symmetry—the atoms form equilateral triangles. When stacking one of these layers on top of another, the atoms are not directly on top of one another—the first two layers are identical for hcp and fcc, and labelled AB. If the third layer is placed so that its atoms are directly above those of the first layer, the stacking will be ABA—this is the hcp structure, and it continues ABABABAB. However there is another location for the third layer, such that its atoms are not above the first layer. Instead, the fourth layer is placed so that its atoms are directly above the first layer. This produces the stacking ABCABCABC, and is actually a cubic arrangement of the atoms. A stacking fault is a one or two layer interruption in the stacking sequence, for example if the sequence ABCABABCAB were found in an fcc structure.

Crystallographic defect and point defects.

Crystalline solids have a very regular atomic structure: that is, the local positions of atoms with respect to each other are repeated at the atomic scale. These arrangements are called crystal structures, and their study is called crystallography. However, most crystalline materials are not perfect: the regular pattern of atomic arrangement is interrupted by crystallographic defects. The various types of defects are enumerated here.

Point defects are defects which are not extended in space in any dimension. There is no strict limit for how small a "point" defect should be, but typically the term is used to describe defects which involve at most a few extra or missing atoms without an ordered structure of the defective positions. Larger defects in an ordered structure are usually considered dislocation loops. For historical reasons, many point defects especially in ionic crystals are called 'centers': for example the vacancy in many ionic solids is called an F-center. These dislocations allow for ionic transport through crystals leading to electrochemical reactions which are frequently specified using Kröger–Vink Notation.

• Vacancies are sites which are usually occupied by an atom but which are unoccupied. If a neighboring atom moves to occupy the vacant site, the vacancy moves in the opposite direction to the site which used to be occupied by the moving atom. The stability of the surrounding crystal structure guarantees that the neighboring atoms will not simply collapse around the vacancy. In some materials, neighboring atoms actually move away from a vacancy, because they can form better bonds with atoms in the other directions. A vacancy (or pair of vacancies in an ionic solid) is sometimes called a Schottky defect.
• Interstitials are atoms which occupy a site in the crystal structure at which there is usually not an atom. They are generally high energy configurations. Small atoms in some crystals can occupy interstices without high energy, such as hydrogen in palladium.Schematic illustration of some simple point defect types in a monatomic solid
• A nearby pair of a vacancy and an interstitial is often called a Frenkel defect or Frenkel pair. This is caused when an ion moves into an interstitial site and creates a vacancy.
• Impurities occur because materials are never 100% pure. In the case of an impurity, the atom is often incorporated at a regular atomic site in the crystal structure. This is neither a vacant site nor is the atom on an interstitial site and it is called a substitutional defect. The atom is not supposed to be anywhere in the crystal, and is thus an impurity. There are two different types of substitutional defects. Isovalent substitution and aliovalent substitution. Isovalent substitution is where the ion that is substituting the original ion is of the same oxidation state as the ion it is replacing. Aliovalent substitution is where the ion that is substituting the original ion is of a different oxidation state as the ion it is replacing. Aliovalent substitutions change the overall charge within the ionic compound, but the ionic compound must be neutral. Therefore a charge compensation mechanism is required. Hence either one of the metals is partially or fully oxidised or reduced, or ion vacancies are created.
• Antisite defects occur in an ordered alloy or compound. For example, some alloys have a regular structure in which every other atom is a different species; for illustration assume that type A atoms sit on the corners of a cubic lattice, and type B atoms sit in the center of the cubes. If one cube has an A atom at its center, the atom is on a site usually occupied by an atom, but it is not the correct type. This is neither a vacancy nor an interstitial, nor an impurity.
• Topological defects are regions in a crystal where the normal chemical bonding environment is topologically different from the surroundings. For instance, in a perfect sheet of graphite (graphene) all atoms are in rings containing six atoms. If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed. An example is the Stone Wales defect in nanotubes, which consists of two adjacent 5-membered and two 7-membered atom rings.Schematic illustration of defects in a compound solid, using GaAs as an example.
• Also amorphous solids may contain defects. These are naturally somewhat hard to define, but sometimes their nature can be quite easily understood. For instance, in ideally bonded amorphous silica all Si atoms have 4 bonds to O atoms and all O atoms have 2 bonds to Si atom. Thus e.g. an O atom with only one Si bond (a dangling bond) can be considered a defect in silica.
• Complexes can form between different kinds of point defects. For example, if a vacancy encounters an impurity, the two may bind together if the impurity is too large for the lattice. Interstitials can form 'split interstitial' or 'dumbbell' structures where two atoms effectively share an atomic site, resulting in neither atom actually occupying the site.

Schematic illustration of some simple point defect types in a monatomic solid

Schematic illustration of defects in a compound solid, using GaAs as an example.

Did you know?

How do impurities affect the structure and properties of a solid?

You already know that to obtain a perfectly pure substance is almost impossible. Purification is a costly process. In general, analytical reagent-grade chemicals are of high purity, and yet few of them are better than 99.9% pure. This means that a foreign atom or molecule is present for every 1000 host atoms or molecules in the crystal.

Perhaps the most demanding of purity is in the electronic industry. Silicon crystals of 99.999 (called 5 nines) or better are required for IC chips productions. These crystal are doped with nitrogen group elements of P and As or boron group elemnts B, Al etc to form n- aand p-type semiconductors. In these crystals, the impurity atom substitute atoms of the host crystals.

Presence minute foreign atoms with one electron more or less than the valence four silicon and germanium host atoms is the key of making n- aand p-type semiconductors. Having many simiconductors connected in a single chip makes the integrated circuit a very efficient information processor. The electronic properties change dramatically due to these impurities. This is further described in Inorganic Chemistry by Swaddle.

In other bulk materials, the presence of impurity usually leads to a lowering of melting point. For example, Hall and Heroult tried to electorlyze natural aluminum (aluminium) compounds. They discovered that using a 5% mixture of Al2O3 (melting point 273 K) in cryolite Na3AlF6 (melting point 1273 K) reduced the melting point to 1223 K, and that enabled the production of aluminum in bulk. Recent modifications lowered melting temperatures below 933 K.

Some types of glass are made by mixing silica (SiO2), alumina (Al2O3), calcium oxide (CaO), and sodium oxide (Na2O). They are softer, but due to lower melting points, they are cheaper to produce.

What are color centers and how do they affect electric conductivity of solids?

Color centers are imperfections in crystals that cause color (defects that cause color by absorption of light). Due to defects, metal oxides may also act as semiconductors, because there are many different types of electron traps. Electrons in defect region only absorb light at certain range of wavelength. The color seen are due to lights not absorbed.

For example, a diamond with C vacancies (missing carbon atoms) absorbs light, and these centers give green color as shown here. Replacement of Al3+ for Si4+ in quartz give rise to the color of smoky quartz.

A high temperature phase of ZnOx, (x <>

Some non-stoichiometric solids are engineered to be n-type or p-type semiconductors. Nickel oxide NiO gain oxygen on heating in air, resulting in having Ni3+ sites acting as electron trap, a p-type semiconductor. On the other hand, ZnO lose oxygen on heating, and the excess Zn metal atoms in the sample are ready to give electrons. The solid is an n-type semiconductor.

Microcracks

A Microcrack occurs where internal broken bonds create new surfaces.

They are about 10 µm in size and there is a tendancy to form on the surface of a solid rather than in the bulk.

They also form at grain boundaries and other regions of disorder. The region across which the bonds are broken is known as the separation plane.

Microcracks are formed when there is abrasion (or impacts) with dust particles.They are important in determining how, and where, a solid may fracture. When a crystal has more than one type of atom, there will be Chemical as well as Physical disorder in the grain-boundaries.

Volume Defects:

Volume defects are Voids, i.e. the absence of a number of atoms to form internal surfaces in the crystal. They have similar properties to microcracks because of the broken bonds at the surface.

Amorphous materials and Polymers:

Since they are not just distortions from a perfect crystal structure, Microcracks and Voids can exist in both Crystalline and Amorphous solids.

Polymers can have partly crystalline regions so may also have all of these kinds of defects.

Planar defects and Boundaries

A Planar Defect is a discontinuity of the perfect crystal structure across a plane.

Grain Boundaries:

A Grain Boundary is a general planar defect that separates regions of different crystalline orientation (i.e. grains) within a polycrystalline solid.

The atoms in the grain boundary will not be in perfect crystalline arrangement.

Grain boundaries are usually the result of uneven growth when the solid is crystallising.

Grain sizes vary from 1 µm to 1 mm.

Tilt Boundaries:

A Tilt Boundary, between two slightly mis-aligned grains appears as an array of edge dislocations.

Twin Boundaries:

A Twin Boundary happens when the crystals on either side of a plane are mirror images of each other.

The boundary between the twinned crystals will be a single plane of atoms.

There is no region of disorder and the boundary atoms can be viewed as belonging to the crystal structures of both twins

Twins are either grown-in during crystallisation, or the result of mechanical or thermal work.

Line defects

Dislocation

A Dislocation is a line discontinuity in the regular crystal structure.

There are two basic types: Edge dislocations, and Screw dislocations.

• An Edge dislocation in a Metal may be regarded as the insertion (or removal) of an extra half plane of atoms in the crystal structure.

The regions surrounding the dislocation line are made of essentially perfect crystal.

The only severe disruption to the crystal structure occurs along the dislocation line (perpendicular to the page).

Note that perpendicular to the page, the line may step up or down. These steps are known as jogs.

• A Screw Dislocation changes the character of the atom planes.The atom planes no longer exist separately from each other.

They form a single surface, like a screw thread, which "spirals" from one end of the crystal to the other.

(It is actually a helical structure because it winds up in 3D, not like a spiral that is flat.)

In the average crystal structure, there are ~1012 m of dislocation lines per m3 of crystal.

Combinations of edge and screw dislocations are often formed as edge dislocations can be formed by branching off a screw dislocation.

Crystalline defects

The ideal crystal has an infinite 3D repetition of identical units, which may be atoms or molecules.

Real crystals are limited in size, and they have some disorder in stacking which are called defects.

Point Defects:

• A Point Defect involves a single atom change to the normal crystal array.
• There are three major types of point defect: Vacancies, Interstitials and Impurities.
• They may be built-in with the original crystal growth, or activated by heat.
• They may be the result of radiation, or electric current etc, etc.

Vacancies:

A Vacancy is the absence of an atom from a site normally occupied in the lattice.

Interstitials:

An Interstitial is an atom on a non-lattice site.

There needs to be enough room for it, so this type of defect occurs in open covalent structures, or metallic structures with large atoms.

Impurities:

An Impurity is the substitution of a regular lattice atom with an atom that does not normally occupy that site.

The atom may come from within the crystal, (e.g. a Chlorine atom on a Sodium site in a NaCl crystal) or from the addition of impurities.

The concentration of point defects in a crystal is typically between 0.1% and 1% of the atomic sites, however extremely pure materials can now be grown.

The concentrations and movement of point defects in a solid are very important in controlling colour and deformation.