Phase diagramA phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium. Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.
Crystal structureIn crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure.
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.
MetastabilityIn chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation.
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.
MoleculeA 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 biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.
Cubic crystal systemIn crystallography, the cubic (or isometric) crystal 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. There are three main varieties of these crystals: Primitive cubic (abbreviated cP and alternatively called simple cubic) Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated cF or fcc) Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals.
Phase portraitIn mathematics, a phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space. This reveals information such as whether an attractor, a repellor or limit cycle is present for the chosen parameter value.
CrystalA 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, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography.
Crystal structure predictionCrystal structure prediction (CSP) is the calculation of the crystal structures of solids from first principles. Reliable methods of predicting the crystal structure of a compound, based only on its composition, has been a goal of the physical sciences since the 1950s. Computational methods employed include simulated annealing, evolutionary algorithms, distributed multipole analysis, random sampling, basin-hopping, data mining, density functional theory and molecular mechanics.
Stable manifoldIn mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set. The gravitational tidal forces acting on the rings of Saturn provide an easy-to-visualize physical example. The tidal forces flatten the ring into the equatorial plane, even as they stretch it out in the radial direction.
Isobaric counterdiffusionIn physiology, isobaric counterdiffusion (ICD) is the diffusion of different gases into and out of tissues while under a constant ambient pressure, after a change of gas composition, and the physiological effects of this phenomenon. The term inert gas counterdiffusion is sometimes used as a synonym, but can also be applied to situations where the ambient pressure changes. It has relevance in mixed gas diving and anesthesiology.
SolubilityIn chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubility of a substance in a specific solvent is generally measured as the concentration of the solute in a saturated solution, one in which no more solute can be dissolved. At this point, the two substances are said to be at the solubility equilibrium.
Crystal systemIn crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.
Diatomic moleculeDiatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide () or nitric oxide (), the molecule is said to be heteronuclear. The bond in a homonuclear diatomic molecule is non-polar.
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.
Succinic acidSuccinic acid (səkˈsɪnᵻk) is a dicarboxylic acid with the chemical formula (CH2)2(CO2H)2. In living organisms, succinic acid takes the form of an anion, succinate, which has multiple biological roles as a metabolic intermediate being converted into fumarate by the enzyme succinate dehydrogenase in complex 2 of the electron transport chain which is involved in making ATP, and as a signaling molecule reflecting the cellular metabolic state. Succinate is generated in mitochondria via the tricarboxylic acid cycle (TCA).
Decompression theoryDecompression theory is the study and modelling of the transfer of the inert gas component of breathing gases from the gas in the lungs to the tissues and back during exposure to variations in ambient pressure. In the case of underwater diving and compressed air work, this mostly involves ambient pressures greater than the local surface pressure, but astronauts, high altitude mountaineers, and travellers in aircraft which are not pressurised to sea level pressure, are generally exposed to ambient pressures less than standard sea level atmospheric pressure.
RutileRutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite. Rutile has one of the highest refractive indices at visible wavelengths of any known crystal and also exhibits a particularly large birefringence and high dispersion. Owing to these properties, it is useful for the manufacture of certain optical elements, especially polarization optics, for longer visible and infrared wavelengths up to about 4.
Phase spaceIn dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the direct product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.
