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Law Of Rational Indices
The law of rational indices is an Empirical research, empirical law in the field of crystallography concerning crystal structure. The law states that "when referred to three intersecting axes all faces occurring on a crystal can be described by numerical indices which are integers, and that these integers are usually small numbers." The law is also named the ''law of rational intercepts'' or the ''second law of crystallography''. Definition The International Union of Crystallography (IUCr) gives the following definition: "The law of rational indices states that the intercepts, ''OP'', ''OQ'', ''OR'', of the natural faces of a crystal form with the unit-cell axes a, b, c are inversely proportional to prime integers, , , . They are called the Miller index, Miller indices of the face. They are usually small because the corresponding lattice planes are among the densest and have therefore a high interplanar spacing and low indices." History The law of constancy of interfacial ang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal System
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices (an infinite array of discrete points). Space groups (symmetry groups of a configuration in space) are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are ''triclinic'', ''monoclinic'', ''orthorhombic'', ''tetragonal'', ''trigonal'', ''hexagonal'', and ''cubic''. Informally, two crystals are in the same crystal system if they have similar symmetries (though there are many exceptions). Classifications Crystals can be classified in three ways: lattice systems, crystal systems and crystal families. The various classifications are often confused: in particular the trigonal crystal system i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.UN announcement "International Year of Crystallography" iycr2014.org. 12 July 2012 Crystallography is a broad topic, and many of its subareas, such as X-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals of crystal structure to the mathematics of Crystal system, crystal geometry, including those that are Aperiodic crystal, not periodic or quasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Symmetry (crystallography)
The law of symmetry is a law in the field of crystallography concerning crystal structure. The law states that all crystals of the same substance possess the same elements of symmetry. The law is also named the ''law of constancy of symmetry'', ''René Just Haüy, Haüy's law'' or the ''third law of crystallography''. Definition The way in which the law of symmetry was originally defined by Haüy in 1815 was based on his law of rational indices, law of decrements and his conception of crystals being assembled of tiny parallelepipeds (''molécules intégrantes'') stacked up in three dimensions without leaving any gaps. The modern definition of the law of symmetry is based on symmetry elements, and is more in the German dynamistic crystallographic tradition of Christian Samuel Weiss, Moritz Ludwig Frankenheim and Johann F. C. Hessel. Weiss and his followers studied the external symmetry of crystals rather than their internal structure. René Just Haüy first lectured about his la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Constancy Of Interfacial Angles
The law of constancy of interfacial angles (; ) is an Empirical research, empirical law in the fields of crystallography and mineralogy concerning the shape, or morphology, of crystals. The law states that the angles between adjacent corresponding faces of crystals of a particular substance are always constant despite the different shapes, sizes, and mode of growth of crystals. The law is also named the ''first law of crystallography'' or ''Nicolas Steno, Steno's law''. Definition The International Union of Crystallography (IUCr) gives the following definition: "The law of the constancy of interfacial angles (or 'first law of crystallography') states that the angles between the crystal faces of a given species are constant, whatever the lateral extension of these faces and the origin of the crystal, and are characteristic of that species." The law is valid at constant temperature and pressure. This law is important in identifying different mineral species as small changes in at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasicrystal
A quasiperiodicity, quasiperiodic crystal, or quasicrystal, is a structure that is Order and disorder (physics), ordered but not Bravais lattice, periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold. Aperiodic tilings were discovered by mathematicians in the early 1960s, and some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography, the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,—that also brought in 1982, with the crystallographic Fourier t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bravais Lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_3 \mathbf_3, where the ''ni'' are any integers, and a''i'' are ''primitive translation vectors'', or ''primitive vectors'', which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique. A fundamental aspect of any Bravais lattice is that, for any choice of direction, the lattice appears exactly the same from each of the discrete lattice points when looking in that chosen direction. The Bravais lattice concept is used to formally define a ''crystalline arrangement'' and its (finite) frontiers. A crystal is made up of one or more atoms, called the ''basis'' or ''motif'', at each lattice point. The ''basis'' may consist of atoms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombic Dodecahedron Assembled From Cubic Blocks
Rhombic may refer to: *Rhombus, a quadrilateral whose four sides all have the same length (often called a diamond) * Rhombic antenna, a broadband directional antenna most commonly used on shortwave frequencies * polyhedra formed from rhombuses, such as the rhombic dodecahedron or the rhombic triacontahedron or the rhombic dodecahedral honeycomb or the rhombic icosahedron or the rhombic hexecontahedron or the rhombic enneacontahedron or the trapezo-rhombic dodecahedron In geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex polytope, convex dodecahedron with 6 rhombus, rhombic and 6 trapezoidal faces. It has symmetry. A concave form can be constructed with an identical ne ... * other things that exhibit the shape of a rhombus, such as rhombic tiling, Rhombic Chess, rhombic drive, Rhombic Skaapsteker, rhombic egg eater, rhombic night adder, forest rhombic night adder {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Auguste Bravais
Auguste Bravais (; 23 August 1811, Annonay, Ardèche – 30 March 1863, Le Chesnay, France) was a French physicist known for his work in crystallography, the conception of Bravais lattices, and the formulation of Bravais law. Bravais also studied magnetism, the northern lights, meteorology, geobotany, phyllotaxis, astronomy, statistics and hydrography. He studied at the Collège Stanislas in Paris before joining the École Polytechnique in 1829, where he was a classmate of groundbreaking mathematician Évariste Galois, whom Bravais actually beat in a scholastic mathematics competition. Towards the end of his studies he became a naval officer, and sailed on the ''Finistere'' in 1832 as well as the ''Loiret'' afterwards. He took part in hydrographic work along the Algerian Coast. He participated in the ''Recherche'' expedition and helped the ''Lilloise'' in Spitzbergen and Lapland. Bravais taught a course in applied mathematics for astronomy in the Faculty of Sciences in Lyon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Samuel Weiss
Christian Samuel Weiss (26 February 1780 – 1 October 1856) was a German mineralogist born in Leipzig. Following graduation, he worked as a physics instructor in Leipzig from 1803 until 1808. and in the meantime, conducted geological studies of mountain formations in Tyrol, Switzerland and France (1806–08).Christian Samuel Weiss — Humboldt-Universität zu Berlin biographical information In 1810 he became a professor of at the , where in 1818/19 and 1832/33, he served as university [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Hallowes Miller
Prof William Hallowes Miller FRS HFRSE LLD DCL (6 April 180120 May 1880) was a Welsh mineralogist and laid the foundations of modern crystallography. Miller indices are named after him, the method having been described in his ''Treatise on Crystallography'' (1839). The mineral known as millerite is named after him. Life and work Miller was born in 1801 at Velindre near Llandovery, Carmarthenshire, South Wales. He was educated at St John's College, Cambridge, where he graduated in 1826 as fifth wrangler. He became a Fellow there in 1829. For a few years Miller was occupied as a college tutor and during this time he published treatises on hydrostatics and hydrodynamics. Miller also gave special attention to crystallography, and at 31 years old, on the resignation of William Whewell he succeeded in 1832 to the professorship of mineralogy, a post he held until 1870. Miller's chief work, on ''Crystallography'', was published in 1839. He was elected to the Royal Society in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axel Gadolin
Axel Vilhelmovich Gadolin (; 12June 1828 – 15December 1892) was a Finnish/Russian lieutenant general, and also a scientist in the field of artillery, metallurgy, mineralogy and crystallography. Gadolin was a professor at the Mikhailov Artillery Academy and the Saint Petersburg Institute of Technology, doctor of mineralogy from Saint Petersburg University, and academician of the St. Petersburg Academy of Sciences. He was awarded the Lomonosov Prize in 1868 for his work on crystallographic point groups. Career Gadolin was born in Somero in the Grand Duchy of Finland on 12June 1828. He was the nephew of the chemist Johan Gadolin. Gadolin combined his military career with a scientific career in mineralogy, crystallography, and artillery sciences. Gadolin received his initial education at the Finnish Cadet School. In 1847 he was a second lieutenant in the Russian artillery service. Gadolin graduated from the Mikhailov Artillery Academy in 1849 and remained their to teach; his i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
