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Scherrer Equation
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis. It is named after Paul Scherrer. It is used in the determination of size of crystals in the form of powder. The Scherrer equation can be written as: :\tau = \frac where: * \tau is the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size, which may be smaller or equal to the particle size; * K is a dimensionless shape factor, with a value close to unity. The shape factor has a typical value of about 0.9, but varies with the actual shape of the crystallite; * \lambda is the X-ray wavelength; * \beta is the line broadening at half the maximum intensity (FWHM), after subtracting the instrumental line broadening, in radians. This quantity is also sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-ray Crystallography
X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring the angles and intensities of the X-ray diffraction, a crystallography, crystallographer can produce a three-dimensional picture of the density of electrons within the crystal and the positions of the atoms, as well as their chemical bonds, crystallographic disorder, and other information. X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences between various materials, especially minerals and alloys. The method has also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X-ray crystall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grain Size
Grain size (or particle size) is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain. A single grain can be composed of several crystals. Granular material can range from very small colloidal particles, through clay, silt, sand, gravel, and cobbles, to boulders. Krumbein phi scale Size ranges define limits of classes that are given names in the Wentworth scale (or Udden–Wentworth scale named after geologists Chester K. Wentworth and Johan A. Udden) used in the United States. The Krumbein ''phi'' (φ) scale, a modification of the Wentworth scale created by W. C. Krumbein in 1934, is a logarithmic scale computed by the equation :\varphi=-\log_2, where :\varphi is the Krumbein phi scale, :D is the diameter In geometry, a diameter of a circle i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. More precisely, the PDF is used to specify the probability of the random variable falling ''within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paracrystalline
In materials science, paracrystalline materials are defined as having short- and medium-range ordering in their lattice (similar to the liquid crystal phases) but lacking crystal-like long-range ordering at least in one direction. Origin and definition The words "paracrystallinity" and "paracrystal" were coined by the late Friedrich Rinne in the year 1933. Their German equivalents, e.g. "Parakristall", appeared in print one year earlier. A general theory of paracrystals has been formulated in a basic textbook, and then further developed/refined by various authors. Rolf Hosemann's definition of an ideal paracrystal is: "The electron density distribution of any material is equivalent to that of a paracrystal when there is for every building block one ideal point so that the distance statistics to other ideal points are identical for all of these points. The electron configuration of each building block around its ideal point is statistically independent of its counterpart in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
André Guinier
André Guinier (1 August, 1911 – 3 July, 2000) was a French physicist and crystallographer who did pioneering work in the field of X-ray diffraction and solid-state physics. He was credited for the discovery and developments of small-angle X-ray scattering (SAXS) into an indispensable tool for materials science and crystallography. Education and career Guinier was born in Nancy, France, his father Philibert Guinier was a botanist and director of the Nancy branch of the French National School of Forestry. Guinier studied at Lycée Henri-Poincaré before entering the École Normale Supérieure (ENS), where he studied physics from 1930 to 1934. After graduation, he worked as an agrégé-preparateur in the physics laboratory of ENS. In 1939, Guinier discovered SAXS and received his doctorate with a thesis on X-ray crystallography under Charles Mauguin. He then worked at the Conservatoire National des Arts et Métiers, where he became deputy director of the test laboratory in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye–Waller Factor
The Debye–Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x-ray scattering or coherent neutron scattering caused by thermal motion. It is also called the B factor, atomic B factor, or temperature factor. Often, "Debye–Waller factor" is used as a generic term that comprises the Lamb–Mössbauer factor of incoherent neutron scattering and Mössbauer spectroscopy. The DWF depends on the scattering vector q. For a given q, DWF(q) gives the fraction of elastic scattering; 1 – DWF(q) correspondingly gives the fraction of inelastic scattering (strictly speaking, this probability interpretation is not true in general). In diffraction studies, only the elastic scattering is useful; in crystals, it gives rise to distinct Bragg reflection peaks. Inelastic scattering events are undesirable as they cause a diffuse background — unless the energies of scattered particles are analysed, in which case they c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-Ray Diffraction Pattern
X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering, when there is no change in the energy of the waves. The resulting map of the directions of the X-rays far from the sample is called a diffraction pattern. It is different from X-ray crystallography which exploits X-ray diffraction to determine the arrangement of atoms in materials, and also has other components such as ways to map from experimental diffraction measurements to the positions of atoms. This article provides an overview of X-ray diffraction, starting with the early history of x-rays and the discovery that they have the right spacings to be diffracted by crystals. In many cases these diffraction patterns can be Interpreted using a single scattering or kinematical theory with conservation of energy (wave vector). Many different types of X-ray sources exist, ranging from ones u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nanocrystal
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 to 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 (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. The crystallite size can be measured directly using transmission electron microscopy. Synthesis Nanocrystalline materials can be prepared in se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Lindo Patterson
Arthur Lindo Patterson (23 July 1902, Nelson, New Zealand – 6 November 1966, Philadelphia, Pennsylvania) was a pioneering British X-ray crystallographer. Patterson was born to British parents in New Zealand in 1902. Shortly afterwards the family moved to Montreal, Canada and later to London, England. In 1920 Patterson moved to Canada for college at McGill University, Montreal. Firstly he concentrated on Mathematics and but then changed his major to Physics. He received his bachelor's degree in 1923 and a master's in 1924. His master's thesis was on the production of hard X-rays by interaction of radium β rays with solids. From 1924 to 1926 he worked in London in the laboratory of W. H. Bragg, where he learnt the art of crystal structure analysis. In 1926 Patterson moved to the Kaiser Wilhelm Institute for Fibrous Materials Chemistry (later the Fritz Haber Institute) in the Dahlem neighbourhood of Berlin, where he worked on the X-ray crystallography of cellulose fibres. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Powder Diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer. Powder diffraction stands in contrast to single crystal diffraction techniques, which work best with a single, well-ordered crystal. Explanation The most common type of powder diffraction is with X-rays, the focus of this article, although some aspects of neutron powder diffraction are mentioned. (Powder electron diffraction is more complex due to dynamical diffraction and is not discussed further herein.) Typical diffractometers use electromagnetic radiation (waves) with known wavelength and frequency, which is determined by their source. The source is often X-rays, and neutrons are also common sources, with their frequency determined by their de Broglie wavelength. When these waves reach the sample, the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure Factor S(q) For Stack Of N=31 Planes With Separation (1D Lattice Constant) A = 1
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as organism, biological organisms, minerals and chemical substance, chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a Complex network, network featuring many-to-many Link (geometry), links, or a lattice (order), lattice featuring connections between components that are neighbors in space. Load-bearing Buildings, aircraft, skeletons, Ant colony, anthills, beaver dams, bridges and salt domes are all examples of Structural load, load-bearing structures. The results of construction are divided into buildings and nonbuilding structure, non-building structures, and make up the infrastructure of a human society. Built str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure Factor
In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns) obtained in X-ray, electron and neutron diffraction experiments. Confusingly, there are two different mathematical expressions in use, both called 'structure factor'. One is usually written S(\mathbf); it is more generally valid, and relates the observed diffracted intensity per atom to that produced by a single scattering unit. The other is usually written F or F_ and is only valid for systems with long-range positional order — crystals. This expression relates the amplitude and phase of the beam diffracted by the (hk\ell) planes of the crystal ((hk\ell) are the Miller indices of the planes) to that produced by a single scattering unit at the vertices of the primitive unit cell. F_ is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
