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Lyddane–Sachs–Teller Relation
In condensed matter physics, the Lyddane–Sachs–Teller relation (or LST relation) determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) (\omega_\text) of an ionic crystal to the natural frequency of the transverse optical lattice vibration (\omega_\text) for long wavelengths (zero wavevector). The ratio is that of the static permittivity \varepsilon_ to the permittivity for frequencies in the visible range \varepsilon_. The Lyddane–Sachs–Teller relation is named after the physicists R. H. Lyddane, Robert G. Sachs, and Edward Teller. Origin and limitations The Lyddane–Sachs–Teller relation applies to optical lattice vibrations that have an associated net polarization density, so that they can produce long ranged electromagnetic fields (over ranges much longer than the inter-atom distances). The relation assumes an idealized polar ("infrared active") optical lattice vibration that gives a contribution to the frequency-depende ... [...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 matter phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retarded Potential
In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light ''c'', so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution (the point of cause) to another point in space (where the effect is measured), see figure below. In the Lorenz gauge The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: : \Box \varphi = \dfrac \,,\quad \Box \mathbf = \mu_0\mathbf where φ(r, ''t'') is the electric potential and A(r, ''t'') is the magnetic vector potential, for an arbitrary source of charge density ρ(r, ''t'') and current density J(r, ''t''), and \Box is the D'Alembert operator. Solving these gives the retarded potentials below (all ... [...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 Stree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introduction To Solid State Physics
''Introduction to Solid State Physics'', known colloquially as ''Kittel'', is a classic condensed matter physics textbook written by American physicist Charles Kittel in 1953. The book has been highly influential and has seen widespread adoption; Marvin L. Cohen remarked in 2019 that Kittel's content choices in the original edition played a large role in defining the field of solid-state physics. It was also the first proper textbook covering this new field of physics. The book is published by John Wiley and Sons and, as of 2018, it is in its ninth edition and has been reprinted many times as well as translated into over a dozen languages, including Chinese, French, German, Hungarian, Indonesian, Italian, Japanese, Korean, Malay, Romanian, Russian, Spanish, and Turkish. In some later editions, the eighteenth chapter, titled ''Nanostructures'', was written by Paul McEuen. Along with its rival ''Ashcroft and Mermin'', the book is considered a standard textbook in condensed matter p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reststrahlen Effect
The reststrahlen effect (German: “residual rays”) is a reflectance phenomenon in which electromagnetic radiation within a narrow energy band cannot propagate within a given medium due to a change in refractive index concurrent with the specific absorbance band of the medium in question; this narrow energy band is termed the ''reststrahlen band''. As a result of this inability to propagate, normally incident reststrahlen band radiation experiences strong-reflection or total-reflection from that medium. The energies at which reststrahlen bands occur vary and are particular to the individual compound. Numerous physical attributes of a compound will have an effect on the appearance of the reststrahlen band. These include phonon band-gap, particle/grain size, strongly absorbing compounds, compounds with optically opaque bands in the infrared. Appearance "The term Reststrahlen was coined following the observation by Heinrich Rubens (more than a century ago) that repeated reflect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes Shift
__NOTOC__ Stokes shift is the difference (in energy, wavenumber or frequency units) between positions of the band maxima of the absorption and emission spectra (fluorescence and Raman being two examples) of the same electronic transition. It is named after Irish physicist George Gabriel Stokes. Sometimes Stokes shifts are given in wavelength units, but this is less meaningful than energy, wavenumber or frequency units because it depends on the absorption wavelength. For instance, a 50 nm Stokes shift from absorption at 300 nm is larger in terms of energy than a 50 nm Stokes shift from absorption at 600 nm. When a system (be it a molecule or atom) absorbs a photon, it gains energy and enters an excited state. One way for the system to relax is to emit a photon, thus losing its energy (another method would be the loss of energy as translational mode energy (via vibrational-translational or electronic-translational collisional processes with other atoms or molecules)). When the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raman Spectroscopy
Raman spectroscopy () (named after Indian physicist C. V. Raman) is a spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified. Raman spectroscopy relies upon inelastic scattering of photons, known as Raman scattering. A source of monochromatic light, usually from a laser in the visible, near infrared, or near ultraviolet range is used, although X-rays can also be used. The laser light interacts with molecular vibrations, phonons or other excitations in the system, resulting in the energy of the laser photons being shifted up or down. The shift in energy gives information about the vibrational modes in the system. Infrared spectroscopy typically yields similar yet complementary information. Typically, a sample is illuminated with a laser beam. Electr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NaCl
Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g/mol respectively, 100 g of NaCl contains 39.34 g Na and 60.66 g Cl. Sodium chloride is the salt most responsible for the salinity of seawater and of the extracellular fluid of many multicellular organisms. In its edible form, salt (also known as ''table salt'') is commonly used as a condiment and food preservative. Large quantities of sodium chloride are used in many industrial processes, and it is a major source of sodium and chlorine compounds used as feedstocks for further chemical syntheses. Another major application of sodium chloride is de-icing of roadways in sub-freezing weather. Uses In addition to the familiar domestic uses of salt, more dominant applications of the approximately 250 million tonnes per year production (2008 da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group 4 Element
Group 4 is the second group of transition metals in the periodic table. It contains the four elements titanium (Ti), zirconium (Zr), hafnium (Hf), and rutherfordium (Rf). The group is also called the titanium group or titanium family after its lightest member. As is typical for early transition metals, zirconium and hafnium have only the group oxidation state of +4 as a major one, and are quite electropositive and have a less rich coordination chemistry. Due to the effects of the lanthanide contraction, they are very similar in properties. Titanium is somewhat distinct due to its smaller size: it has a well-defined +3 state as well (although +4 is more stable). All the group 4 elements are hard, refractory metals. Their inherent reactivity is completely masked due to the formation of a dense oxide layer that protects them from corrosion, as well as attack by many acids and alkalis. The first three of them occur naturally. Rutherfordium is strongly radioactive: it does not occur na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Energy Levels
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy of the level. It is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same energy eigenvalue. When this is the case, energy alone is not enough to characterize what state the system is in, and other quantum numbers are needed to characterize the exact state when distinction is desired. In classical mechanics, this can be understood in terms of different possible trajectories corresponding to the same energy. Degeneracy plays a fundamental role in quantum statistical mechanics. For an -particle system in three dimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Zero
In complex analysis (a branch of mathematics), a pole is a certain type of singularity (mathematics), singularity of a complex-valued function of a complex number, complex variable. In some sense, it is the simplest type of singularity. Technically, a point is a pole of a function if it is a zero of a function, zero of the function and is holomorphic function, holomorphic in some neighbourhood (mathematics), neighbourhood of (that is, complex differentiable in a neighbourhood of ). A function is meromorphic function, meromorphic in an open set if for every point of there is a neighborhood of in which either or is holomorphic. If is meromorphic in , then a zero of is a pole of , and a pole of is a zero of . This induces a duality between ''zeros'' and ''poles'', that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at infinity, then the sum of the multiplicity (mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). In physics, the term "light" may refer more broadly to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, microwaves and radio waves are also light. The primary properties of light are intensity, propagation direction, frequency or wavelength spectrum and polarization. Its speed in a vacuum, 299 792 458 metres a second (m/s), is one of the fundamental constants of nature. Like all types of electromagnetic radiation, visible light propagates by massless elementary particles called photons that represents the quanta of electromagnetic field, and can be analyzed as both waves and par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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