![MoS2 antisites&vacancies](https://upload.wikimedia.org/wikipedia/commons/a/a3/MoS2_antisites%26vacancies.jpg)
A crystallographic defect is an interruption of the regular patterns of arrangement of
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, and ...
s or
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s in
crystalline solids
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...
. The positions and orientations of particles, which are repeating at fixed distances determined by the
unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
parameters in crystals, exhibit a periodic
crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pat ...
, but this is usually imperfect.
[Ehrhart, P. (1991]
Properties and interactions of atomic defects in metals and alloys
, volume 25 of Landolt-Börnstein, New Series III, chapter 2, p. 88, Springer, Berlin Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological
homotopy
In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a deforma ...
establishes a mathematical method of characterization.
Point defects
Point defects are defects that occur only at or around a single lattice point. They are not extended in space in any dimension. Strict limits for how small a point defect is are generally not defined explicitly. However, these defects typically involve at most a few extra or missing atoms. Larger defects in an ordered structure are usually considered
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
loops. For historical reasons, many point defects, especially in ionic crystals, are called ''centers'': for example a vacancy in many ionic solids is called a luminescence center, a color center, or
F-center
An F center or Farbe center (from the original German ''Farbzentrum'', where ''Farbe'' means ''color'' and ''zentrum'' means center) is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more un ...
. These dislocations permit ionic transport through crystals leading to electrochemical reactions. These are frequently specified using
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 ...
.
*
Vacancy defect
In crystallography, a vacancy is a type of point defect in a crystal where an atom is missing from one of the lattice sites.Ehrhart, P. (1991) "Properties and interactions of atomic defects in metals and alloys", chapter 2, p. 88 in ''Landolt-B ...
s are lattice sites which would be occupied in a perfect crystal, but are vacant. 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 experience attraction from atoms in the surroundings. A vacancy (or pair of vacancies in an ionic solid) is sometimes called 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 incor ...
.
*
Interstitial defect
In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure. When the atom is of the same type as those already ...
s are atoms that occupy a site in the crystal structure at which
there is usually not an atom. They are generally high energy configurations. Small atoms (mostly impurities) in some crystals can occupy interstices without high energy, such as
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
in
palladium
Palladium is a chemical element with the symbol Pd and atomic number 46. It is a rare and lustrous silvery-white metal discovered in 1803 by the English chemist William Hyde Wollaston. He named it after the asteroid Pallas, which was itself na ...
.
*A nearby pair of a vacancy and an interstitial is often called a
Frenkel defect
In crystallography, a Frenkel defect is a type of point defect in crystalline solids, named after its discoverer Yakov Frenkel. The defect forms when an atom or smaller ion (usually cation) leaves its place in the lattice, creating a vacancy a ...
or Frenkel pair. This is caused when an ion moves into an interstitial site and creates a vacancy.
*Due to fundamental limitations of material purification methods, materials are never 100% pure, which by definition induces defects in crystal structure. 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. In some cases where the radius of the substitutional atom (ion) is substantially smaller than that of the atom (ion) it is replacing, its equilibrium position can be shifted away from the lattice site. These types of substitutional defects are often referred to as
off-center ions. 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 than 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 when atoms of different type exchange positions. 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 a B atom, and is thus an antisite defect. 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
Graphene () is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. ) 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.
*Also
amorphous
In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal.
Etymology
The term comes from the Greek ''a'' ("wi ...
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
Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
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
In chemistry, a dangling bond is an unsatisfied valence on an immobilized atom. An atom with a dangling bond is also referred to as an immobilized free radical or an immobilized radical, a reference to its structural and chemical similarity to a f ...
) can be considered a defect in silica. Moreover, defects can also be defined in amorphous solids based on empty or densely packed local atomic neighbourhoods, and the properties of such 'defects' can be shown to be similar to normal vacancies and interstitials in crystals.
*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.
Line defects
Line defects can be described by gauge theories.
Dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
s are linear defects, around which 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.
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
In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as , that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.
The vecto ...
(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 crystallographic 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
Ductility is a List of materials properties, mechanical property commonly described as a material's amenability to Drawing (manufacturing), drawing (e.g. into wire). In materials science, ductility is defined by the degree to which a materia ...
of metallic materials.
Dislocations can be observed using
transmission electron microscopy
Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a g ...
,
field ion microscopy
The Field ion microscope (FIM) was invented by Müller in 1951. It is a type of microscope that can be used to image the arrangement of atoms at the surface of a sharp metal tip.
On October 11, 1955, Erwin Müller and his Ph.D. student, Kanwar ...
and
atom probe
The atom probe was introduced at th14th Field Emission Symposium in 1967by Erwin Wilhelm Müller and J. A. Panitz. It combined a field ion microscope with a mass spectrometer having a single particle detection capability and, for the first time, ...
techniques.
Deep-level transient spectroscopy has been used for studying the electrical activity of dislocations in semiconductors, mainly
silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic tab ...
.
Disclination In crystallography, a disclination is a line defect in which rotational symmetry is violated. In analogy with dislocations in crystals, the term, ''disinclination'', for liquid crystals first used by Frederick Charles Frank and since then has been m ...
s 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 were thought to play a role only in liquid crystals, but recent developments suggest that they might have a role also in solid materials, e.g. leading to the self-healing of
cracks.
Planar defects
![Schema fcc hcp](https://upload.wikimedia.org/wikipedia/commons/a/a0/Schema_fcc_hcp.png)
*
Grain boundaries
In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional crystallographic defect, defects in the crystal structure, and tend to decrease the ...
occur where the crystallographic direction of the lattice abruptly changes. This usually occurs when two crystals begin growing separately and then meet.
*
Antiphase 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 (
hexagonal close-packed
In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occu ...
crystal), an antiphase boundary takes the form of ABABBABA.
*
Stacking fault
In crystallography, a stacking fault is a planar defect that can occur in crystalline materials.Fine, Morris E. (1921). "Introduction to Chemical and Structural Defects in Crystalline Solids", in ''Treatise on Solid State Chemistry Volume 1'', Spr ...
s occur in a number of crystal structures, but the common example is in
close-packed
In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occu ...
structures. They are formed by a local deviation of the stacking sequence of layers in a crystal. An example would be the ABABCABAB stacking sequence.
*A
twin boundary
Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly ...
is a defect that introduces a plane of mirror symmetry in the ordering of a crystal. For example, in
cubic close-packed crystals, the stacking sequence of a twin boundary would be ABCABCBACBA.
*On planes of
single crystal
In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "Re ...
s, steps between atomically flat terraces can also be regarded as planar defects. It has been shown that such defects and their geometry have significant influence on the adsorption of organic molecules
Bulk defects
* Three-dimensional macroscopic or bulk defects, such as pores, cracks, or inclusions
* Voids — small regions where there are no atoms, and which can be thought of as clusters of vacancies
* Impurities can cluster together to form small regions of a different phase. These are often called
precipitate
In an aqueous solution, precipitation is the process of transforming a dissolved substance into an insoluble solid from a super-saturated solution. The solid formed is called the precipitate. In case of an inorganic chemical reaction leading ...
s.
Mathematical classification methods
A successful mathematical classification method for physical lattice defects, which works not only with the theory of dislocations and other defects in crystals but also, e.g., for
disclination In crystallography, a disclination is a line defect in which rotational symmetry is violated. In analogy with dislocations in crystals, the term, ''disinclination'', for liquid crystals first used by Frederick Charles Frank and since then has been m ...
s in liquid crystals and for excitations in superfluid
3He, is the topological
homotopy
In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a deforma ...
theory.
Computer simulation methods
Density functional theory
Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
, classical
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the ...
and
kinetic Monte Carlo
The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with known transition rates among states. It ...
simulations are widely used to study the properties of defects in solids with computer simulations.
Simulating jamming of hard spheres of different sizes and/or in containers with non-commeasurable sizes using the
Lubachevsky–Stillinger algorithm
Lubachevsky-Stillinger (compression) algorithm (LS algorithm, LSA, or LS protocol) is a numerical procedure suggested by F. H. Stillinger and B.D. Lubachevsky that simulates or imitates a physical process of compressing an assembly of hard particl ...
can be an effective technique for demonstrating some types of crystallographic defects.
See also
*
Bjerrum defect
A Bjerrum defect is a crystallographic defect which is specific to ice, and which is partly responsible for the electrical properties of ice. It was first proposed by Niels Bjerrum in 1952 in order to explain the electrical polarization of ice in ...
*
Crystallographic defects in diamond
Imperfections in the crystal lattice of diamond are common. Such defects may be the result of lattice irregularities or extrinsic substitutional or interstitial impurities, introduced during or after the diamond growth. The defects affect the ...
*
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 ...
*
F-center
An F center or Farbe center (from the original German ''Farbzentrum'', where ''Farbe'' means ''color'' and ''zentrum'' means center) is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more un ...
References
Further reading
*
Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is professor of theoretical physics at the Free University of Berlin, Germany (since 1968)Honorary Doctorat the
West University of Timișoaraandat thin Bishkek. He is alsHonorary Memberof th For his contributio ...
, ''Gauge Fields in Condensed Matter'', Vol. II
"Stresses and defects" pp. 743–1456, World Scientific (Singapore, 1989); Paperback
*
Hermann Schmalzried
Hermann Schmalzried (born January 21, 1932 in Koblenz) is a German chemist known for his work in physical chemistry, especially on the thermodynamics and kinetics of solid state chemistry.
Education and career
Schmalzried received his diploma ...
: ''Solid State Reactions''. Verlag Chemie, Weinheim 1981, .
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