Crystallographic defect in the context of Recrystallization temperature

A solid solution, a term commonly used for metals, is a homogeneous mixture of two compounds in solid state and having a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word "solution" is used to describe the intimate mixing of components at the atomic level and distinguishes these homogeneous materials from physical mixtures of components. Two terms are mainly associated with solid solutions – solvents and solutes, depending on the relative abundance of the atomic species.

The solute may incorporate into the solvent crystal lattice substitutionally, by replacing a solvent particle in the lattice, or interstitially, by fitting into the space between solvent particles.

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. The absence of the defects associated with grain boundaries can give monocrystals unique properties, particularly mechanical, optical and electrical, which can also be anisotropic, depending on the type of crystallographic structure. These properties, in addition to making some gems precious, are industrially used in technological applications, especially in optics and electronics.

Because entropic effects favor the presence of some imperfections in the microstructure of solids, such as impurities, inhomogeneous strain and crystallographic defects such as dislocations, perfect single crystals of meaningful size are exceedingly rare in nature. The necessary laboratory conditions often add to the cost of production. On the other hand, imperfect single crystals can reach enormous sizes in nature: several mineral species such as beryl, gypsum and feldspars are known to have produced crystals several meters across.

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

Contrary to earlier definitions, modern understanding of non-stoichiometric compounds view them as homogeneous, and not mixtures of stoichiometric chemical compounds. Since the solids are overall electrically neutral, the defect is compensated by a change in the charge of other atoms in the solid, either by changing their oxidation state, or by replacing them with atoms of different elements with a different charge. Many metal oxides and sulfides have non-stoichiometric examples; for example, stoichiometric iron(II) oxide, which is rare, has the formula FeO, whereas the more common material is nonstoichiometric, with the formula Fe_0.95O. The type of equilibrium defects in non-stoichiometric compounds can vary with attendant variation in bulk properties of the material. Non-stoichiometric compounds also exhibit special electrical or chemical properties because of the defects; for example, when atoms are missing, electrons can move through the solid more rapidly. Non-stoichiometric compounds have applications in ceramic and superconductive material and in electrochemical (i.e., battery) system designs.

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 allows atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.

The two primary types of dislocations are sessile dislocations which are immobile and glissile dislocations which are mobile. Examples of sessile dislocations are the stair-rod dislocation and the Lomer–Cottrell junction. The two main types of mobile dislocations are edge and screw dislocations.

In condensed-matter physics, a collision cascade (also known as a displacement cascade or a displacement spike) is a set of nearby adjacent energetic (much higher than ordinary thermal energies) collisions of atoms induced by an energetic particle in a solid or liquid.

If the maximum atom or ion energies in a collision cascade are higher than the threshold displacement energy of the material (tens of eVs or more), the collisions can permanently displace atoms from their lattice sites and produce defects. The initial energetic atom can be, e.g., an ion from a particle accelerator, an atomic recoil produced by a passing high-energy neutron, electron or photon, or be produced when a radioactive nucleus decays and gives the atom a recoil energy.

An intrinsic semiconductor, also called a pure semiconductor, undoped semiconductor or i-type semiconductor, is a semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p. This may be the case even after doping the semiconductor, though only if it is doped with both donors and acceptors equally. In this case, n = p still holds, and the semiconductor remains intrinsic, though doped. This means that some conductors are both intrinsic as well as extrinsic but only if n (electron donor dopant/excited electrons) is equal to p (electron acceptor dopant/vacant holes that act as positive charges).

The electrical conductivity of chemically pure semiconductors can still be affected by crystallographic defects of technological origin (like vacancies), some of which can behave similar to dopants. Their effect can often be neglected, though, and the number of electrons in the conduction band is then exactly equal to the number of holes in the valence band. The conduction of current of intrinsic semiconductor is enabled purely by electron excitation across the band-gap, which is usually small at room temperature except for narrow-bandgap semiconductors, like Hg
_0.8Cd
_0.2Te.

Ionic conductivity (denoted by λ) is the movement of ions through a solid material, a phenomenon central to solid-state ionics. It is denoted by λ and measured in siemens per meter (S/m). While perfect crystals of inorganic compounds are typically electrical insulators, ionic conduction arises when defects are introduced—either intrinsically through thermal activation or extrinsically via doping with aliovalent impurities. These defects enable ion migration by providing pathways through the crystal lattice. Solid ionic conductors, known as solid electrolytes, are critical components in technologies such as all-solid-state batteries, supercapacitors, fuel cells, and thin-film microelectronic devices. The ionic conductivity (σ) follows an Arrhenius-type relationship with temperature, governed by activation energy barriers influenced by crystal structure and defect chemistry. Ionic conduction is one mechanism of current.

In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship.

In metallurgy, solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element (the alloying element) to the crystalline lattice of another element (the base metal), forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms (e.g. the precipitation of intermetallic compounds).

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 present they are known as a self-interstitial defect. Alternatively, small atoms in some crystals may occupy interstitial sites, such as hydrogen in palladium. Interstitials can be produced by bombarding a crystal with elementary particles having energy above the displacement threshold for that crystal, but they may also exist in small concentrations in thermodynamic equilibrium. The presence of interstitial defects can modify the physical and chemical properties of a material.

Electron backscatter diffraction (EBSD) is a scanning electron microscopy (SEM) technique used to study the crystallographic structure of materials. EBSD is carried out in a scanning electron microscope equipped with an EBSD detector comprising at least a phosphorescent screen, a compact lens and a low-light camera. In the microscope an incident beam of electrons hits a tilted sample. As backscattered electrons leave the sample, they interact with the atoms and are both elastically diffracted and lose energy, leaving the sample at various scattering angles before reaching the phosphor screen forming Kikuchi patterns (EBSPs). The EBSD spatial resolution depends on many factors, including the nature of the material under study and the sample preparation. They can be indexed to provide information about the material's grain structure, grain orientation, and phase at the micro-scale. EBSD is used for impurities and defect studies, plastic deformation, and statistical analysis for average misorientation, grain size, and crystallographic texture. EBSD can also be combined with energy-dispersive X-ray spectroscopy (EDS), cathodoluminescence (CL), and wavelength-dispersive X-ray spectroscopy (WDS) for advanced phase identification and materials discovery.

The change and sharpness of the electron backscatter patterns (EBSPs) provide information about lattice distortion in the diffracting volume. Pattern sharpness can be used to assess the level of plasticity. Changes in the EBSP zone axis position can be used to measure the residual stress and small lattice rotations. EBSD can also provide information about the density of geometrically necessary dislocations (GNDs). However, the lattice distortion is measured relative to a reference pattern (EBSP₀). The choice of reference pattern affects the measurement precision; e.g., a reference pattern deformed in tension will directly reduce the tensile strain magnitude derived from a high-resolution map while indirectly influencing the magnitude of other components and the spatial distribution of strain. Furthermore, the choice of EBSP₀ slightly affects the GND density distribution and magnitude.

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 structure, creating a vacancy and becomes an interstitial 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 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 the Frenkel defect is a stoichiometric defect (does not change the overall 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.