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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 determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident 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 crystallographic 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 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 among various mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallinity
Crystallinity refers to the degree of structural order in a solid. In a crystal, the atoms or molecules are arranged in a regular, periodic manner. The degree of crystallinity has a big influence on hardness, density, Transparency and translucency, transparency and diffusion. In an ideal gas, the relative positions of the atoms or molecules are completely random. Amorphous materials, such as liquids and glasses, represent an intermediate case, having order over short distances (a few atomic or molecular spacings) but not over longer distances. Many materials, such as glass-ceramics and some polymers, can be prepared in such a way as to produce a mixture of crystalline and Amorphous solid, amorphous regions. In such cases, crystallinity is usually specified as a percentage of the volume of the material that is crystalline. Even within materials that are completely crystalline, however, the degree of structural perfection can vary. For instance, most metallic alloys are crystalline ... [...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 ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
André Guinier
André Guinier (1 August 1911 – 3 July 2000) was a French physicist who did important work in the field of X-ray diffraction and solid-state physics. He worked at the Conservatoire National des Arts et Métiers, then taught at the University of Paris and later at the University of Paris-Sud in Orsay, where he co-founded the Laboratory of Solid State Physics. He was elected to the French Academy of Sciences in 1971 and won the Gregori Aminoff Prize in 1985. In the field of small-angle scattering he discovered the relationship of particle size to intensity which is called Guinier's Law. He developed the Guinier camera for use in X-ray diffraction and contributed to the development of the electron microprobe by Raimond Castaing. Together with Prof George Dawson Preston he also gives his name to the Guinier-Preston zone Publications *Guinier, André (1955) ''Small-angle scattering of X-rays''. OCLC number: 01646250. *Guinier, André (1963). "X-ray Diffraction. In Crystals, Imp ... [...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 crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident 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 crystallographic 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 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 among various mat ... [...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. In ... [...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 A diffractometer produces electromagnetic radiation (waves) with known wavelength and frequency, which is determined by their source. The source is often x-rays, because they are the only kind of energy with the optimal wavelength for inter-atomic-scale diffraction. However, electrons and neutrons are also common sources, with their frequency determined by their de Broglie wavelength. When these waves reach the sample, the incoming beam is either reflected off the surface, or can enter the lattice and be diffracted by the atoms present in the sample. If the atoms are ... [...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 biological organisms, minerals and 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 network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space. Load-bearing Buildings, aircraft, skeletons, anthills, beaver dams, bridges and salt domes are all examples of load-bearing structures. The results of construction are divided into buildings and non-building structures, and make up the infrastructure of a human society. Built structures are broadly divided by their varying design approaches and standards, into categories including building structures, archi ... [...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] |
Laser Diffraction Analysis
Laser diffraction analysis, also known as laser diffraction spectroscopy, is a technology that utilizes diffraction patterns of a laser beam passed through any object ranging from nanometers to millimeters in size to quickly measure geometrical dimensions of a particle. This particle size analysis process does not depend on volumetric flow rate, the amount of particles that passes through a surface over time. Fraunhofer vs. Mie Theory Laser diffraction analysis is originally based on the Fraunhofer diffraction theory, stating that the intensity of light scattered by a particle is directly proportional to the particle size. The angle of the laser beam and particle size have an inversely proportional relationship, where the laser beam angle increases as particle size decreases and vice versa. The Mie scattering model, or Mie theory, is used as alternative to the Fraunhofer theory since the 1990s. Commercial laser diffraction analyzers leave to the user the choice of using either ... [...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) 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 of the particle or grain in millimeters (Krumbein and Monk's equation) and :D_0 is a reference diameter, equal to 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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