Diffusionless transformationDiffusionless transformations, also referred to as displacive transformations, are solid-state changes in the crystal structure that do not rely on the diffusion of atoms over long distances. Instead, they occur due to coordinated shifts in atomic positions, where atoms move by a distance less than the span between neighboring atoms while maintaining their relative arrangement. An illustrative instance of this is the martensitic transformation observed in steel.
Heat treatingHeat treating (or heat treatment) is a group of industrial, thermal and metalworking processes used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass. Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve the desired result such as hardening or softening of a material.
Phase transitionIn chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.
Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
NucleationIn thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled (at atmospheric pressure) below 0 °C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0 °C often stay completely free of ice for long periods (supercooling).
Alpha particleAlpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways. Alpha particles are named after the first letter in the Greek alphabet, α. The symbol for the alpha particle is α or α2+. Because they are identical to helium nuclei, they are also sometimes written as He2+ or 42He2+ indicating a helium ion with a +2 charge (missing its two electrons).
Transformation (function)In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations.
Single crystalIn 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.
NanoparticleA nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At the lowest range, metal particles smaller than 1 nm are usually called atom clusters instead.
Recrystallization (metallurgy)In materials science, recrystallization is a process by which deformed grains are replaced by a new set of defect-free grains that nucleate and grow until the original grains have been entirely consumed. Recrystallization is usually accompanied by a reduction in the strength and hardness of a material and a simultaneous increase in the ductility. Thus, the process may be introduced as a deliberate step in metals processing or may be an undesirable byproduct of another processing step.
AtomAn atom is a particle that consists of a nucleus of protons and neutrons surrounded by a cloud of electrons. The atom is the basic particle of the chemical elements, and the chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element. Atoms are extremely small, typically around 100 picometers across.
Abnormal grain growthAbnormal or discontinuous grain growth, also referred to as exaggerated or secondary recrystallisation grain growth, is a grain growth phenomenon through which certain energetically favorable grains (crystallites) grow rapidly in a matrix of finer grains resulting in a bimodal grain size distribution. In ceramic materials this phenomenon can result in the formation of elongated prismatic, acicular (needle-like) grains in a densified matrix with implications for improved fracture toughness through the impedance of crack propagation.
NanomaterialsNanomaterials describe, in principle, materials of which a single unit is sized (in at least one dimension) between 1 and 100 nm (the usual definition of nanoscale). Nanomaterials research takes a materials science-based approach to nanotechnology, leveraging advances in materials metrology and synthesis which have been developed in support of microfabrication research. Materials with structure at the nanoscale often have unique optical, electronic, thermo-physical or mechanical properties.
Grain growthIn materials science, grain growth is the increase in size of grains (crystallites) in a material at high temperature. This occurs when recovery and recrystallisation are complete and further reduction in the internal energy can only be achieved by reducing the total area of grain boundary. The term is commonly used in metallurgy but is also used in reference to ceramics and minerals. The behaviors of grain growth is analogous to the coarsening behaviors of grains, which implied that both of grain growth and coarsening may be dominated by the same physical mechanism.
CrystallizationCrystallization is the process by which solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. Some ways by which crystals form are precipitating from a solution, freezing, or more rarely deposition directly from a gas. Attributes of the resulting crystal depend largely on factors such as temperature, air pressure, and in the case of liquid crystals, time of fluid evaporation. Crystallization occurs in two major steps.
Grain boundary strengtheningIn materials science, grain-boundary strengthening (or Hall–Petch strengthening) is a method of strengthening materials by changing their average crystallite (grain) size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain has an effect on how stress builds up in the adjacent grain, which will eventually activate dislocation sources and thus enabling deformation in the neighbouring grain as well.
Möbius transformationIn geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0. Geometrically, a Möbius transformation can be obtained by first performing stereographic projection from the plane to the unit two-sphere, rotating and moving the sphere to a new location and orientation in space, and then performing stereographic projection (from the new position of the sphere) to the plane.
SuperalloyA superalloy, or high-performance alloy, is an alloy with the ability to operate at a high fraction of its melting point. Key characteristics of a superalloy include mechanical strength, thermal creep deformation resistance, surface stability, and corrosion and oxidation resistance. The crystal structure is typically face-centered cubic (FCC) austenitic. Examples of such alloys are Hastelloy, Inconel, Waspaloy, Rene alloys, Incoloy, MP98T, TMS alloys, and CMSX single crystal alloys.
BerylliumBeryllium is a chemical element with the symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other elements to form minerals. Gemstones high in beryllium include beryl (aquamarine, emerald, red beryl) and chrysoberyl. It is a relatively rare element in the universe, usually occurring as a product of the spallation of larger atomic nuclei that have collided with cosmic rays.
