|
Wigner–Seitz Radius
The Wigner–Seitz radius r_, named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid (for first group metals). In the more general case of metals having more valence electrons, r_ is the radius of a sphere whose volume is equal to the volume per a free electron.* This parameter is used frequently in condensed matter physics to describe the density of a system. Worth to mention, r_ is calculated for bulk materials. Formula In a 3-D system with N free electrons in a volume V, the Wigner–Seitz radius is defined by :\frac \pi r_^3 = \frac = \frac\,, where n is the particle density of free electrons. Solving for r_ we obtain :r_ = \left(\frac\right)^. The radius can also be calculated as :r_= \left(\frac\right)^\frac\,, where M is molar mass, Z is amount of free electrons per atom, \rho is mass density, and N_ is the Avogadro constant. This parameter is normally reported in atomic units, i.e., in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Wigner
Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". A graduate of the Technical University of Berlin, Wigner worked as an assistant to Karl Weissenberg and Richard Becker at the Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen. Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. Along the way he performed ground-breaking work in pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone in the mathematical formulation of quantum mechanics. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frederick Seitz
Frederick Seitz (July 4, 1911 – March 2, 2008) was an American physicist and a pioneer of solid state physics and lobbyist. Seitz was the 4th president of Rockefeller University from 1968–1978, and the 17th president of the United States National Academy of Sciences from 1962–1969. Seitz was the recipient of the National Medal of Science, NASA's Distinguished Public Service Award, and other honors. He founded the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana–Champaign and several other material research laboratories across the United States. Seitz was also the founding chairman of the George C. Marshall Institute, a tobacco industry consultant, and a prominent climate change denier. Background and personal life Born in San Francisco on July 4, 1911, Seitz graduated from Lick-Wilmerding High School in the middle of his senior year, and went on to study physics at Stanford University obtaining his bachelor's degree in three years, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holt, Rinehart And Winston
Holt McDougal is an American publishing company, a division of Houghton Mifflin Harcourt, that specializes in textbooks for use in high schools. The Holt name is derived from that of U.S. publisher Henry Holt (1840–1926), co-founder of the earliest ancestor business, but Holt McDougal is distinct from contemporary Henry Holt and Company, which claims the history from 1866. The companies publish different kinds of books. History Holt, Rinehart and Winston (HRW) was created in March 1960 by the merger of Henry Holt and Company of New York City (established 1866 as Leypoldt and Holt); Rinehart & Company of New York, descendant of Farrar & Rinehart (est. 1929); and the John C. Winston Company of Philadelphia (est. 1884). ''The Wall Street Journal'' reported on March 1, 1960, that Holt stockholders had approved the merger, last of the three approvals. "Henry Holt is the surviving concern, but will be known as Holt, Rinehart, Winston, Inc.""Henry Holt Merger". ''The Wall Street ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Density (particle Count)
The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density. ''Population density'' is an example of areal number density. The term number concentration (symbol: lowercase ''n'', or ''C'', to avoid confusion with amount of substance indicated by uppercase '' N'') is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations. Definition Volume number density is the number of specified objects per unit volume: :n = \frac, where ''N'' is the total number of objects in a volume ''V''. Here it is assumed that ''N'' is large enough that rounding of the count to the nearest integer does not introduce much of an error, however ''V'' is chosen to be small enough that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molar Mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an ''average'' of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities. The molecular mass and formula mass are commonly used as a synonym of molar mass, particularly for molecular compounds; however, the most authoritative sources define it differently. The difference is that molecular mass is the mass of one specific particle or molecul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Avogadro Constant
The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining constant with an exact value of . It is named after the Italian scientist Amedeo Avogadro by Stanislao Cannizzaro, who explained this number four years after Avogadro's death while at the Karlsruhe Congress in 1860. The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted or , which is the number of particles that are contained in one mole, exactly . The Avogadro number is the approximate number of nucleons ( protons or neutrons) in one gram of ordinary matter. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is approximately the number of nucleons in one c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Units
The Hartree atomic units are a system of natural units of measurement which is especially convenient for atomic physics and computational chemistry calculations. They are named after the physicist Douglas Hartree. By definition, the following four fundamental physical constants may each be expressed as the numeric value 1 multiplied by a coherent unit of this system: * Reduced Planck constant: \hbar, also known as the atomic unit of action * Elementary charge: e, also known as the atomic unit of charge * Bohr radius: a_0, also known as the atomic unit of length * Electron mass: m_\text, also known as the atomic unit of mass Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts. Defining constants Each unit in this system can be expressed as a product of powers of four physical constants without a multiplying constant. This makes it a coherent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohr Radius
The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is The number in parenthesis denotes the uncertainty of the last digits. Definition and value The Bohr radius is defined as a_0 = \frac = \frac = \frac , where * \varepsilon_0 is the permittivity of free space, * \hbar is the reduced Planck constant, * m_ is the mass of an electron, * e is the elementary charge, * c is the speed of light in vacuum, and * \alpha is the fine-structure constant. The CODATA value of the Bohr radius (in SI units) is History In the Bohr model for atomic structure, put forward by Niels Bohr in 1913, electrons orbit a central nucleus under electrostatic attraction. The original derivation posited that electrons have orbital angular momentum in integer multiples of the reduced Planck co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wigner–Seitz Cell
The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. It is used in the study of crystalline materials in crystallography. The unique property of a crystal is that its atoms are arranged in a regular three-dimensional array called a lattice. All the properties attributed to crystalline materials stem from this highly ordered structure. Such a structure exhibits discrete translational symmetry. In order to model and study such a periodic system, one needs a mathematical "handle" to describe the symmetry and hence draw conclusions about the material properties consequent to this symmetry. The Wigner–Seitz cell is a means to achieve this. A Wigner–Seitz cell is an example of a primitive cell, which is a unit cell containing exactly one lattice point. For any given lattice, there are an infinite number of possible primitive cells. However there is only on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wigner Crystal
A Wigner crystal is the solid (crystalline) phase of electrons first predicted by Eugene Wigner in 1934. A gas of electrons moving in a uniform, inert, neutralizing background (i.e. Jellium Model) will crystallize and form a lattice if the electron density is less than a critical value. This is because the potential energy dominates the kinetic energy at low densities, so the detailed spatial arrangement of the electrons becomes important. To minimize the potential energy, the electrons form a bcc (body-centered cubic) lattice in 3 D, a triangular lattice in 2D and an evenly spaced lattice in 1D. Most experimentally observed Wigner clusters exist due to the presence of the external confinement, i.e. external potential trap. As a consequence, deviations from the b.c.c or triangular lattice are observed. A crystalline state of the 2D electron gas can also be realized by applying a sufficiently strong magnetic field. However, it is still not clear whether it is the Wigner crystalli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
