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X-ray Crystallography
X-ray
X-ray
crystallography is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays
X-rays
to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder, and various other information. Since many materials can form crystals—such as salts, metals, minerals, semiconductors, as well as various inorganic, organic, and biological molecules— X-ray
X-ray
crystallography has been fundamental in the development of many scientific fields
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Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.[1][2] In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word crystal derives from the Ancient Greek
Ancient Greek
word κρύσταλλος (krustallos), meaning both "ice" and "rock crystal",[3] from κρύος (kruos), "icy cold, frost".[4][5] Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid
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Snow
Snow
Snow
refers to forms of ice crystals that precipitate from the atmosphere (usually from clouds) and undergo changes on the Earth's surface.[2] It pertains to frozen crystalline water throughout its life cycle, starting when, under suitable conditions, the ice crystals form in the atmosphere, increase to millimeter size, precipitate and accumulate on surfaces, then metamorphose in place, and ultimately melt, slide or sublimate away. Snowstorms
Snowstorms
organize and develop by feeding on sources of atmospheric moisture and cold air. Snowflakes nucleate around particles in the atmosphere by attracting supercooled water droplets, which freeze in hexagonal-shaped crystals. Snowflakes take on a variety of shapes, basic among these are platelets, needles, columns and rime. As snow accumulates into a snowpack, it may blow into drifts. Over time, accumulated snow metamorphoses, by sintering, sublimation and freeze-thaw
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Fourier Transform
The Fourier transform
Fourier transform
(FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes. The Fourier transform
Fourier transform
of a function of time itself is a complex-valued function of frequency, whose absolute value represents the amount of that frequency present in the original function, and whose complex argument is the phase offset of the basic sinusoid in that frequency. The Fourier transform
Fourier transform
is called the frequency domain representation of the original signal. The term Fourier transform
Fourier transform
refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time
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Neutron
5000000000000000000♠0 e 3021799999999999999♠(−2±8)×10−22 e (experimental limits)[4]Electric dipole moment < 6974290000000000000♠2.9×10−26 e⋅cm (experimental upper limit)Electric polarizability 6997116000000000000♠1.16(15)×10−3 fm3Magnetic moment 3026033763500000000♠−0.96623650(23)×10−26 J·T−1[3] 3002895812437000000♠−1.04187563(25)×10−3 μB[3] 2999808695726999999♠−1.91304273(45) μN[3]Magnetic polarizability 6996370000000000000♠3.7(20)×10−4 fm3Spin 1/2Isospin −1/2Parity +1Condensed I(JP) = 1/2(1/2+)The neutron is a subatomic particle, symbol n or n0, with no net electric charge and a mass slightly larger than that of a proton. Protons and neutrons constitute the nuclei of atoms
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Fourier Transformation
The Fourier transform
Fourier transform
(FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes. The Fourier transform
Fourier transform
of a function of time itself is a complex-valued function of frequency, whose absolute value represents the amount of that frequency present in the original function, and whose complex argument is the phase offset of the basic sinusoid in that frequency. The Fourier transform
Fourier transform
is called the frequency domain representation of the original signal. The term Fourier transform
Fourier transform
refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time
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Small-angle X-ray Scattering
Small-angle X-ray scattering (SAXS) is a small-angle scattering technique by which nanoscale density differences in a sample can be quantified. This means that it can determine nanoparticle size distributions, resolve the size and shape of (monodisperse) macromolecules, determine pore sizes, characteristic distances of partially ordered materials, and much more. This is achieved by analyzing the elastic scattering behaviour of X-rays when travelling through the material, recording their scattering at small angles (typically 0.1 - 10°, hence the "Small-angle" in its name)
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Nanocrystalline
A nanocrystalline (NC) material is a polycrystalline material with a crystallite size of only a few nanometers. These materials fill the gap between amorphous materials without any long range order and conventional coarse-grained materials. Definitions vary, but nanocrystalline material is commonly defined as a crystallite (grain) size below 100 nm. Grain sizes from 100–500 nm are typically considered "ultrafine" grains. The grain size of a NC sample can be estimated using x-ray diffraction. In materials with very small grain sizes, the diffraction peaks will be broadened. This broadening can be related to a crystallite size using the Scherrer equation
Scherrer equation
(applicable up to ~50 nm), a Williamson-Hall plot, or more sophisticated methods such as the Warren-Averbach method or computer modeling of the diffraction pattern
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Elastic Scattering
Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials). Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not
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Wavelength
In physics, the wavelength is the spatial period of a wave—the distance over which the wave's shape repeats,[1][2] and thus the inverse of the spatial frequency. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.[3][4] Wavelength
Wavelength
is commonly designated by the Greek letter
Greek letter
lambda (λ)
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Johannes Kepler
Johannes Kepler
Johannes Kepler
(/ˈkɛplər/;[1] German: [joˈhanəs ˈkɛplɐ]; December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer. Kepler is a key figure in the 17th-century scientific revolution. He is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe
Tycho Brahe
in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein
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Tetrahedron
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 ordinary convex polyhedra and the only one that has fewer than 5 faces.[1] The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper
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Monochromatic
Monochrome[1] describes paintings, drawings, design, or photographs in one color or values of one color.[2] A monochromatic object or image reflects colors in shades of limited colors or hues. Images using only shades of grey (with or without black or white) are called grayscale or black-and-white. However, scientifically speaking, monochromatic light refers to visible light of a narrow band of wavelengths (see spectral color).Contents1 Application 2 In physics 3 See also 4 ReferencesApplication[edit]A photograph of a parrot rendered with a monochrome palette of a limited number of shadesFor an image, the term monochrome is usually taken to mean the same as black and white or, more likely, grayscale, but may also be used to refer to other combinations containing only tones of a single color, such as green-and-white or green-and-black
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Tridymite
Tridymite
Tridymite
is a high-temperature polymorph of silica and usually occurs as minute tabular white or colorless pseudo-hexagonal crystals, or scales, in cavities in felsic volcanic rocks. Its chemical formula is SiO2. Tridymite
Tridymite
was first described in 1868 and the type location is in Hidalgo, Mexico. The name is from the Greek tridymos for triplet as tridymite commonly occurs as twinned crystal trillings[1] (compound crystals comprising three twinned crystal components).Contents1 Structure 2 Mars 3 See also 4 References 5 External linksStructure[edit] Crystal structure
Crystal structure
of α-tridymiteβ-tridymite Tridymite
Tridymite
can occur in seven crystalline forms. Two of the most common at standard pressure are known as α and β
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Polymorphism (materials Science)
In materials science, polymorphism is the ability of a solid material to exist in more than one form or crystal structure. Polymorphism can potentially be found in any crystalline material including polymers, minerals, and metals, and is related to allotropy, which refers to chemical elements. The complete morphology of a material is described by polymorphism and other variables such as crystal habit, amorphous fraction or crystallographic defects. Polymorphism is relevant to the fields of pharmaceuticals, agrochemicals, pigments, dyestuffs, foods, and explosives. When polymorphism exists as a result of a difference in crystal packing, it is called packing polymorphism. Polymorphism can also result from the existence of different conformers of the same molecule in conformational polymorphism. In pseudopolymorphism the different crystal types are the result of hydration or solvation
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Nicolas Steno
Nicolas Steno (Danish: Niels Steensen; Latinized to Nicolaus Stenonis or Nicolaus Stenonius[notes 2]; 1 January 1638 – 25 November 1686[9][10] [NS: 11 January 1638 – 5 December 1686][9]) was a Danish scientist, a pioneer in both anatomy and geology who became a Catholic bishop in his later years. Steno was trained in the classical texts on science; however, by 1659 he seriously questioned accepted knowledge of the natural world.[11] Importantly he questioned explanations for tear production, the idea that fossils grew in the ground and explanations of rock formation
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