James Friauf
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James Friauf
James Byron Friauf (1896 1972) was an American electrical engineer who first determined the crystal structure of MgZn2 in 1927. Friauf was a professor of physics at the Carnegie Institute of Technology, now Carnegie Mellon University. He had received training in the determination of the structure of crystals as a student at California Institute of Technology where he studied with Roscoe Gilkey Dickinson. The structure Friauf discovered consists of intra-penetrating icosahedra, which coordinate the Zn atoms, and 16-vertex polyhedra that coordinate the Mg atoms. The latter type of polyhedron is called a Friauf polyhedron and is, actually, an inter-penetrating tetrahedron and a 12-vertex truncated polyhedron. MgZn2 is a member of the largest class of single intermetallic structures, since referred to as the Laves phases Laves phases are intermetallic phases that have composition AB2 and are named for Fritz Laves who first described them. The phases are classified on the ...
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Electrical Engineer
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is now divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control, and electrica ...
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Magnesium Zincide
Magnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic table) it occurs naturally only in combination with other elements and it almost always has an oxidation state of +2. It reacts readily with air to form a thin passivation coating of magnesium oxide that inhibits further corrosion of the metal. The free metal burns with a brilliant-white light. The metal is obtained mainly by electrolysis of magnesium salts obtained from brine. It is less dense than aluminium and is used primarily as a component in strong and lightweight alloys that contain aluminium. In the cosmos, magnesium is produced in large, aging stars by the sequential addition of three helium nuclei to a carbon nucleus. When such stars explode as supernovas, much of the magnesium is expelled into the interstellar medium where it ...
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Carnegie Institute Of Technology
Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology in 1912 and began granting four-year degrees in the same year. In 1967, the Carnegie Institute of Technology merged with the Mellon Institute of Industrial Research, founded in 1913 by Andrew Mellon and Richard B. Mellon and formerly a part of the University of Pittsburgh. Carnegie Mellon University has operated as a single institution since the merger. The university consists of seven colleges and independent schools: Carnegie Mellon College of Engineering, The College of Engineering, Carnegie Mellon College of Fine Arts, College of Fine Arts, Dietrich College of Humanities and Social Sciences, Mellon College of Science, Tepper School of Business, Heinz College, Heinz College of Information Systems and Public Policy, and the Carnegie Mell ...
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Carnegie Mellon University
Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology in 1912 and began granting four-year degrees in the same year. In 1967, the Carnegie Institute of Technology merged with the Mellon Institute of Industrial Research, founded in 1913 by Andrew Mellon and Richard B. Mellon and formerly a part of the University of Pittsburgh. Carnegie Mellon University has operated as a single institution since the merger. The university consists of seven colleges and independent schools: The College of Engineering, College of Fine Arts, Dietrich College of Humanities and Social Sciences, Mellon College of Science, Tepper School of Business, Heinz College of Information Systems and Public Policy, and the School of Computer Science. The university has its main campus located 5 miles (8 km) from Downto ...
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California Institute Of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasionally referred to as "CIT", most notably in its alma mater, but this is uncommon. is a private research university in Pasadena, California. Caltech is ranked among the best and most selective academic institutions in the world, and with an enrollment of approximately 2400 students (acceptance rate of only 5.7%), it is one of the world's most selective universities. The university is known for its strength in science and engineering, and is among a small group of institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began attracting influential scientists such as George Ellery H ...
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Roscoe Gilkey Dickinson
Roscoe Gilkey Dickinson (May 3, 1894 – July 13, 1945) was an American chemist, known primarily for his work on X-ray crystallography. As professor of chemistry at the California Institute of Technology (Caltech), he was the doctoral advisor of Nobel laureate Linus Pauling and of Arnold O. Beckman, inventor of the pH meter. Dickinson received his undergraduate education at the Massachusetts Institute of Technology and, in 1920, became the first person to receive a PhD from Caltech (which had recently changed its name from Throop College). For his dissertation he had studied the crystal structures of wulfenite, scheelite, sodium chlorate, and sodium bromate. His graduate advisor was Arthur Amos Noyes. References External links Dickinson's Ph.D. thesisof digitized materials related to Dickinson's and Linus Pauling Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educ ...
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Icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non- stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles. Regular icosahedra There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have icosahedral symmetry. The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a ''great icosahedron''. Convex regular icosahedron The convex regular icosahedron is usually referred to simply as the ''regular icosahedron'', one of the five regular Platonic solids, and is represented by its Schläfli symbol , con ...
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhedr ...
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Friauf Polyhedron
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by truncation (geometry), truncating all 4 vertices of a regular tetrahedron at one third of the original edge length. A deeper truncation, removing a tetrahedron of half the original edge length from each vertex, is called Rectification (geometry), rectification. The rectification of a tetrahedron produces an octahedron. A ''truncated tetrahedron'' is the Goldberg polyhedron containing triangular and hexagonal faces. A ''truncated tetrahedron'' can be called a cantic cube, with Coxeter diagram, , having half of the vertices of the cantellated cube (rhombicuboctahedron), . There are two dual positions of this construction, and combining them creates the uniform compound of two truncated tetrahedra. Area and volume The area ''A'' and the volume ''V'' of a truncated tetrahedron of edge leng ...
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Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet (geometry), facet in place of each vertex. The term originates from Kepler's names for the Archimedean solids. Uniform truncation In general any polyhedron (or polytope) can also be truncated with a degree of freedom as to how deep the cut is, as shown in Conway polyhedron notation truncation operation. A special kind of truncation, usually implied, is a uniform truncation, a truncation operator applied to a regular polyhedron (or regular polytope) which creates a resulting uniform polyhedron (uniform polytope) with equal edge lengths. There are no degrees of freedom, and it represents a fixed geometric, just like the regular polyhedra. In general all single ringed uniform polytopes have a uniform truncation. For example, the icosidodecahedron, represented as Schläfli symbols r or \begin 5 \\ 3 \end, and Coxeter-Dynkin diagram or has a uniform truncation, the truncate ...
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Intermetallic
An intermetallic (also called an intermetallic compound, intermetallic alloy, ordered intermetallic alloy, and a long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elements. Intermetallics are generally hard and brittle, with good high-temperature mechanical properties. They can be classified as stoichiometric or nonstoichiometic intermetallic compounds. Although the term "intermetallic compounds", as it applies to solid phases, has been in use for many years, its introduction was regretted, for example by Hume-Rothery in 1955. Definitions Research definition Schulze in 1967 defined intermetallic compounds as ''solid phases containing two or more metallic elements, with optionally one or more non-metallic elements, whose crystal structure differs from that of the other constituents''. Under this definition, the following are included: #Electron (or Hume-Rothery) compounds #Size packing phases. e.g. Lav ...
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Laves Phases
Laves phases are intermetallic phases that have composition AB2 and are named for Fritz Laves who first described them. The phases are classified on the basis of geometry alone. While the problem of packing spheres of equal size has been well-studied since Gauss, Laves phases are the result of his investigations into packing spheres of two sizes. Laves phases fall into three Strukturbericht types: cubic MgCu2 (C15), hexagonal MgZn2 (C14), and hexagonal MgNi2 (C36). The latter two classes are unique forms of the hexagonal arrangement, but share the same basic structure. In general, the A atoms are ordered as in diamond, hexagonal diamond, or a related structure, and the B atoms form tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ... around the A atoms for the AB2 stru ...
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