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Bethe–Slater Curve
The Bethe–Slater curve is a heuristic explanation for why certain metals are ferromagnetic and others are antiferromagnetic. It assumes a Heisenberg model of magnetism, and explains the differences in exchange energy of transition metals as due to the ratio of the interatomic distance ''a'' to the radius ''r'' of the ''3d'' electron shell. When the magnetically important ''3d'' electrons of adjacent atoms are relatively close to each other, the exchange interaction, J_, is negative, but when they are further away, the exchange interaction becomes positive, before slowly dropping off. The idea of relating exchange energy to inter-atomic distance was first proposed by John C. Slater in 1930, and illustrated as a curve on a graph in a review by Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic
A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Context Gigerenzer & Gaissmaier (2011) state that sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone). In physics, multiple types of material magnetism have been distinguished. Ferromagnetism (along with the similar effec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933. Generally, antiferromagnetic order may exist at sufficiently low temperatures, but vanishes at and above the Néel temperature – named after Louis Néel, who had first identified this type of magnetic ordering. Above the Néel temperature, the material is typically paramagnetic. Measurement When no external field is applied, the antiferromagnetic structure corresponds to a vanishing total magnetization. In an external magnetic field, a kind of ferrimagnetic behavior may be displayed in the antiferromagnetic phase, with the absolute value of one of the sublattice magne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Heisenberg Model
In statistical physics, the classical Heisenberg model, developed by Werner Heisenberg, is the n = 3 case of the ''n''-vector model, one of the models used to model ferromagnetism and other phenomena. Definition The classical Heisenberg model can be formulated as follows: take a d-dimensional lattice, and place a set of spins of unit length, :\vec_i \in \mathbb^3, , \vec_i, =1\quad (1), on each lattice node. The model is defined through the following Hamiltonian: : \mathcal = -\sum_ \mathcal_ \vec_i \cdot \vec_j\quad (2) where : \mathcal_ = \begin J & \mboxi, j\mbox \\ 0 & \mbox\end is a coupling between spins. Properties * The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model. * In the continuum limit the Heisenberg model (2) gives the following equation of motion :: \vec_=\vec\wedge \vec_. :This equation is called the continuous classical Heisenberg ferromagnet equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exchange Energy
In chemistry and physics, the exchange interaction is a quantum mechanical constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences cannot always be predicted based on classical ideas of force. Both bosons and fermions can experience the exchange interaction. The wave function of indistinguishable particles is subject to exchange symmetry: the wave function either changes sign (for fermions) or remains unchanged (for bosons) when two particles are exchanged. The exchange symmetry alters the expectation value of the distance between two indistinguishable particles when their wave functions overlap. For fermions the expectation value of the distance increases, and for bosons it decreases (compared to distinguishable particles). The exchange interaction arises from the combination of exchange symmetry and the Coulomb interaction. For an electron in an electron gas, the excha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition Metals
In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinide elements (the f-block) are called inner transition metals and are sometimes considered to be transition metals as well. They are lustrous metals with good electrical and thermal conductivity. Most (with the exception of group 11 and group 12) are hard and strong, and have high melting and boiling temperatures. They form compounds in any of two or more different oxidation states and bind to a variety of ligands to form coordination complexes that are often coloured. They form many useful alloys and are often employed as catalysts in elemental form or in compounds such as coordination complexes and oxides. Most are strongly paramagnetic because of their unpaired d electrons, as are many of their compounds. All of the elements that are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Shell
In chemistry and atomic physics, an electron shell may be thought of as an orbit that electrons follow around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on further and further from the nucleus. The shells correspond to the principal quantum numbers (''n'' = 1, 2, 3, 4 ...) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, ...). Each period on the conventional periodic table of elements represents an electron shell. Each shell can contain only a fixed number of electrons: the first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18, continuing as the general formula of the ''n''th shell being able to hold up to 2( ''n''2) electrons. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John C
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope John ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German Theoretical physics, theoretical physicist who pioneered developments in Atomic physics, atomic and Quantum mechanics, quantum physics, and also educated and mentored many students for the new era of theoretical physics. He served as doctoral advisor and Postdoctoral researcher, postdoc advisor to seven Nobel Prize winners and supervised at least 30 other famous physicists and chemists. Only J. J. Thomson's record of mentorship offers a comparable list of high-achieving students. He introduced the second quantum number, azimuthal quantum number, and the third quantum number, magnetic quantum number. He also introduced the fine-structure constant and pioneered X-ray wave theory. Early life and education Sommerfeld was born in 1868 to a family with deep ancestral roots in Prussia. His mother Cäcilie Matthias (1839–1902) was the daughter of a Potsdam builder. His father Franz Sommerfeld (1820� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Bethe
Hans Albrecht Eduard Bethe (; ; July 2, 1906 – March 6, 2005) was a German-American physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics and solid-state physics, and received the Nobel Prize in Physics in 1967 for his work on the theory of stellar nucleosynthesis. For most of his career, Bethe was a professor at Cornell University.James C. Keck Collected Works and Biography () has the class notes taken by one of Bethe's students at Cornell from the graduate courses on Nuclear Physics and on Applications of Quantum Mechanics he taught in the spring of 1947. In 1931, Bethe developed the Bethe ansatz, which is a method for finding the exact solutions for the Eigenvalue, eigenvalues and Eigenvector, eigenvectors of certain one-dimensional quantum many-body models. In 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Structure
The term magnetic structure of a material pertains to the ordered arrangement of magnetic spins, typically within an ordered crystallographic lattice. Its study is a branch of solid-state physics. Magnetic structures Most solid materials are non-magnetic, that is, they do not display a magnetic structure. Due to the Pauli exclusion principle, each state is occupied by electrons of opposing spins, so that the charge density is compensated everywhere and the spin degree of freedom is trivial. Still, such materials typically do show a weak magnetic behaviour, e.g. due to diamagnetism or Pauli paramagnetism. The more interesting case is when the material's electron spontaneously break above-mentioned symmetry. For ferromagnetism in the ground state, there is a common spin quantization axis and a global excess of electrons of a given spin quantum number, there are more electrons pointing in one direction than in the other, giving a macroscopic magnetization (typically, the majority ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
