Post-transition metalThe metallic elements in the periodic table located between the transition metals to their left and the chemically weak nonmetallic metalloids to their right have received many names in the literature, such as post-transition metals, poor metals, other metals, p-block metals and chemically weak metals. The most common name, post-transition metals, is generally used in this article. Physically, these metals are soft (or brittle), have poor mechanical strength, and usually have melting points lower than those of the transition metals.
TantalumTantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as tantalium, it is named after Tantalus, a figure in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that is highly corrosion-resistant. It is part of the refractory metals group, which are widely used as components of strong high-melting-point alloys. It is a group 5 element, along with vanadium and niobium, and it always occurs in geologic sources together with the chemically similar niobium, mainly in the mineral groups tantalite, columbite and coltan.
Tantalum pentoxideTantalum pentoxide, also known as tantalum(V) oxide, is the inorganic compound with the formula Ta2O5. It is a white solid that is insoluble in all solvents but is attacked by strong bases and hydrofluoric acid. Ta2O5 is an inert material with a high refractive index and low absorption (i.e. colourless), which makes it useful for coatings. It is also extensively used in the production of capacitors, due to its high dielectric constant.
Zintl phaseIn chemistry, a Zintl phase is a product of a reaction between a group 1 (alkali metal) or group 2 (alkaline earth metal) and main group metal or metalloid (from groups 13, 14, 15, or 16). It is characterized by intermediate metallic/ionic bonding. Zintl phases are a subgroup of brittle, high-melting intermetallic compounds that are diamagnetic or exhibit temperature-independent paramagnetism and are poor conductors or semiconductors. This type of solid is named after German chemist Eduard Zintl who investigated them in the 1930s.
RadonRadon is a chemical element with the symbol Rn and atomic number 86. It is a radioactive, colourless, odourless, tasteless noble gas. It occurs naturally in minute quantities as an intermediate step in the normal radioactive decay chains through which thorium and uranium slowly decay into various short-lived radioactive elements and eventually into stable lead. Radon itself is the immediate decay product of radium. Its most stable isotope, 222Rn, has a half-life of only 3.8 days, making it one of the rarest elements.
HafniumHafnium is a chemical element with the symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in many zirconium minerals. Its existence was predicted by Dmitri Mendeleev in 1869, though it was not identified until 1923, by Dirk Coster and George de Hevesy, making it the penultimate stable element to be discovered (the last being rhenium in 1925). Hafnium is named after Hafnia, the Latin name for Copenhagen, where it was discovered.
Period 4 elementA period 4 element is one of the chemical elements in the fourth row (or period) of the periodic table of the chemical elements. The periodic table is laid out in rows to illustrate recurring (periodic) trends in the chemical behaviour of the elements as their atomic number increases: a new row is begun when chemical behaviour begins to repeat, meaning that elements with similar behaviour fall into the same vertical columns. The fourth period contains 18 elements beginning with potassium and ending with krypton – one element for each of the eighteen groups.
KryptonKrypton (from κρυπτός 'the hidden one') is a chemical element with the symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace amounts in the atmosphere and is often used with other rare gases in fluorescent lamps. Krypton is chemically inert. Krypton, like the other noble gases, is used in lighting and photography. Krypton light has many spectral lines, and krypton plasma is useful in bright, high-powered gas lasers (krypton ion and excimer lasers), each of which resonates and amplifies a single spectral line.
Wave equationThe (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields - as they occur in classical physics - such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media.
Orthonormal basisIn mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.
Miller indexMiller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and l, the Miller indices. They are written (hkl), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to , where are the basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Period 5 elementA period 5 element is one of the chemical elements in the fifth row (or period) of the periodic table of the chemical elements. The periodic table is laid out in rows to illustrate recurring (periodic) trends in the chemical behaviour of the elements as their atomic number increases: a new row is begun when chemical behaviour begins to repeat, meaning that elements with similar behaviour fall into the same vertical columns. The fifth period contains 18 elements, beginning with rubidium and ending with xenon.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
Standard basisIn mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors Similarly, the standard basis for the three-dimensional space is formed by vectors Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction.
Schrödinger equationThe Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics.
Helmholtz equationIn mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation where ∇2 is the Laplace operator, k2 is the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number. The Helmholtz equation has a variety of applications in physics, including the wave equation and the diffusion equation, and it has uses in other sciences.
Reciprocal latticeIn physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality , where is the momentum vector and is the reduced Planck constant.
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.
Acid dissociation constantIn chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted K_a) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction HA A^- + H^+ known as dissociation in the context of acid–base reactions. The chemical species HA is an acid that dissociates into , the conjugate base of the acid and a hydrogen ion, .
