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Hubbard Model
The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other pushes it away from its neighbors. Its Hamiltonian thus has two terms: a kinetic term allowing for tunneling ("hopping") of particles between lattice sites and a potential term reflecting on-site interaction. The particles can either be fermions, as in Hubbard's original work, or bosons, in which case the model is referred to as the "Bose–Hubbard model". The Hubbard model is a useful approximation for particles in a periodic potential at sufficiently low temperatures, where all the particles may be assumed to be in the lowest Bloch band, and long-range interactions between the particles can be ignored. If interactions between particles at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-temperature Superconductivity
High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previously known superconductors, which function at even colder temperatures close to absolute zero. In absolute terms, these "high temperatures" are still far below ambient, and therefore require cooling. The first high-temperature superconductor was discovered in 1986, by IBM researchers Bednorz and Müller, who were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-c materials are type-II superconductors. The major advantage of high-temperature superconductors is that they can be cooled by using liquid nitrogen, as opposed to the previously known superconductors which require expensive and hard-to-handle coolants, primarily liquid helium. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrogen Atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe. In everyday life on Earth, isolated hydrogen atoms (called "atomic hydrogen") are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary ( diatomic) hydrogen gas, H2. "Atomic hydrogen" and "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms). Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen (or any) atom can exist, contrary to the predictions of classical physics. Attempts to develop a theore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Parameter
A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal. A simple cubic crystal has only one lattice constant, the distance between atoms, but in general lattices in three dimensions have six lattice constants: the lengths ''a'', ''b'', and ''c'' of the three cell edges meeting at a vertex, and the angles ''α'', ''β'', and ''γ'' between those edges. The crystal lattice parameters ''a'', ''b'', and ''c'' have the dimension of length. The three numbers represent the size of the unit cell, that is, the distance from a given atom to an identical atom in the same position and orientation in a neighboring cell (except for very simple crystal structures, this will not necessarily be disance to the nearest neighbor). Their SI unit is the meter, and they are traditionally specified in angstroms (Å); an angstrom being 0.1 nanome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every atom of that element. The atomic number can be used to uniquely identify ordinary chemical elements. In an ordinary uncharged atom, the atomic number is also equal to the number of electrons. For an ordinary atom, the sum of the atomic number ''Z'' and the neutron number ''N'' gives the atom's atomic mass number ''A''. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of the nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number ''A''. Atoms with the same atomic number but dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyrochlore
Pyrochlore () is a mineral group of the niobium end member of the pyrochlore supergroup. The general formula, (where A and B are metals), represent a family of phases isostructural to the mineral pyrochlore. Pyrochlores are an important class of materials in diverse technological applications such as luminescence, ionic conductivity, nuclear waste immobilization, high temperature thermal barrier coatings, automobile exhaust gas control, catalysts, solid oxide fuel cell, ionic/electrical conductors etc. Occurrence The mineral is associated with the metasomatic end stages of magmatic intrusions. Pyrochlore crystals are usually well formed (euhedral), occurring usually as octahedra of a yellowish or brownish color and resinous luster. It is commonly metamict due to radiation damage from included radioactive elements. Pyrochlore occurs in pegmatites associated with nepheline syenites and other alkalic rocks. It is also found in granite pegmatites and greisens. It is characteristical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rare-earth
The rare-earth elements (REE), also called the rare-earth metals or (in context) rare-earth oxides or sometimes the lanthanides (yttrium and scandium are usually included as rare earths), are a set of 17 nearly-indistinguishable lustrous silvery-white soft heavy metals. Compounds containing rare earths have diverse applications in electrical and electronic components, lasers, glass, magnetic materials, and industrial processes. Scandium and yttrium are considered rare-earth elements because they tend to occur in the same ore deposits as the lanthanides and exhibit similar chemical properties, but have different electronic and magnetic properties. These metals tarnish slowly in air at room temperature and react slowly with cold water to form hydroxides, liberating hydrogen. They react with steam to form oxides, and at elevated temperature (400°C) ignite spontaneously. These elements and their compounds have no biological function other than in several specialized enzymes, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typically ductile (can be drawn into wires) and malleable (they can be hammered into thin sheets). These properties are the result of the ''metallic bond'' between the atoms or molecules of the metal. A metal may be a chemical element such as iron; an alloy such as stainless steel; or a molecular compound such as polymeric sulfur nitride. In physics, a metal is generally regarded as any substance capable of conducting electricity at a temperature of absolute zero. Many elements and compounds that are not normally classified as metals become metallic under high pressures. For example, the nonmetal iodine gradually becomes a metal at a pressure of between 40 and 170 thousand times atmospheric pressure. Equally, some materials regarded as metals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2. In relativistic mechanics, this is a good approximation only when ''v'' is much less than the speed of light. The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound. History and etymology The adjective ''kinetic'' has its roots in the Greek word κίνησις ''kinesis'', m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric-field Screening
In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases (classical plasmas), electrolytes, and charge carriers in electronic conductors (semiconductors, metals). In a fluid, with a given permittivity , composed of electrically charged constituent particles, each pair of particles (with charges and ) interact through the Coulomb force as \mathbf = \frac\hat, where the vector is the relative position between the charges. This interaction complicates the theoretical treatment of the fluid. For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable. The difficulty lies in the fact that even though the Coulomb force diminishes with distance as , the average number of particles at each distance is proportional to , assuming the fluid is fairly isotropic. As a result, a charge fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Band Structure
In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ''forbidden bands''). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). Why bands and band gaps occur The electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two or more atoms join together to form a molecule, their atomic orbitals overlap and hybridize. Similarly, if a large number ''N'' of identical atoms come ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal
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, 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. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and "rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
