In crystallography, mosaicity is a measure of the spread of crystal plane orientations. A mosaic crystal is an idealized model of an imperfect crystal, imagined to consist of numerous small perfect crystals (crystallites) that are to some extent randomly misoriented. Empirically, mosaicities can be determined by measuring rocking curves. Diffraction by mosaics is described by the Darwin–Hamilton equations.
The mosaic crystal model goes back to a theoretical analysis of X-ray diffraction by C. G. Darwin (1922). Currently, most studies follow Darwin in assuming a Gaussian distribution of crystallite orientations centered on some reference orientation. The mosaicity is commonly equated with the standard deviation of this distribution.
An important application of mosaic crystals is in monochromators for x-ray and neutron radiation. The mosaicity enhances the reflected flux, and allows for some phase-space transformation.
Pyrolitic graphite (PG) can be produced in form of mosaic crystals (HOPG: highly ordered PG) with controlled mosaicity of up to a few degrees.
To describe diffraction by a thick mosaic crystal, it is usually assumed that the constituent crystallites are so thin that each of them reflects at most a small fraction of the incident beam. Primary extinction and other dynamical diffraction effects can then be neglected. Reflections by different crystallites add incoherently, and can therefore be treated by classical transport theory. When only beams within the scattering plane are considered, then they obey the Darwin–Hamilton equations (Darwin 1922, Hamilton 1957),
where are the directions of the incident and diffracted beam, are the corresponding currents, μ is the Bragg reflectivity, and σ accounts for losses by absorption and by thermal and elastic diffuse scattering. A generic analytical solution has been obtained remarkably late (Sears 1997; for the case σ=0 Bacon/Lowde 1948). An exact treatment must allow for three-dimensional trajectories of multiply reflected radiation. The Darwin–Hamilton equations are then replaced by a Boltzmann equation with a very special transport kernel. In most cases, resulting corrections to the Darwin–Hamilton–Sears solutions are rather small (Wuttke 2014).
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.
In X-ray crystallography, wide-angle X-ray scattering (WAXS) or wide-angle X-ray diffraction (WAXD) is the analysis of Bragg peaks scattered to wide angles, which are caused by sub-nanometer-sized structures. It is an X-ray-diffraction method and commonly used to determine a range of information about crystalline materials. The term WAXS is commonly used in polymer sciences to differentiate it from SAXS but many scientists doing "WAXS" would describe the measurements as Bragg/X-ray/powder diffraction or crystallography.
Uranium carbide, a carbide of uranium, is a hard refractory ceramic material. It comes in several stoichiometries (x differs in UCx), such as uranium methanide (UC, CAS number 12070-09-6), uranium sesquicarbide (U2C3, CAS number 12076-62-9), and uranium acetylide (UC2, CAS number 12071-33-9).
Hugo M. Rietveld was a Dutch crystallographer who is famous for his publication on the full profile refinement method in powder diffraction, which became later known as the Rietveld refinement method. The method is used for the characterisation of crystalline materials from X-ray powder diffraction data. The Rietveld refinement uses a least squares approach to refine a theoretical line profile until it matches the measured profile. The introduction of this technique which used the full profile instead of individual reflections was a significant step forward in the diffraction analysis of powder samples.
The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice, atomic crystal structures or nanometer scaled multi-layers or self arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics.
Dynamical Theory of Crystal Lattices is a book in solid state physics, authored collaboratively by Max Born and Kun Huang. The book was originally started by Born in c. 1940, and was finished in the 1950s by Huang in consultation with Born. The text is considered a classical treatise on the subject of lattice dynamics, phonon theory, and elasticity in crystalline solids, but excluding metals and other complex solids with order/disorder phenomena. J. D. Eshelby, Melvin Lax, and A. J. C. Wilson reviewed the book in 1955, among several others.
Complex metallic alloys (CMAs) or complex intermetallics (CIMs) are intermetallic compounds characterized by the following structural features:
Diffraction topography is a quantum beam imaging technique based on Bragg diffraction. Diffraction topographic images ("topographies") record the intensity profile of a beam of X-rays diffracted by a crystal. A topography thus represents a two-dimensional spatial intensity mapping of reflected X-rays, i.e. the spatial fine structure of a Laue reflection. This intensity mapping reflects the distribution of scattering power inside the crystal; topographs therefore reveal the irregularities in a non-ideal crystal lattice. X-ray diffraction topography is one variant of X-ray imaging, making use of diffraction contrast rather than absorption contrast which is usually used in radiography and computed tomography (CT). Topography is exploited to a lesser extends with neutrons and other quantum beams. In the electron microscope community, such technique is called dark field imaging or diffraction contrast imaging.
The International Union of Crystallography (IUCr) is an organisation devoted to the international promotion and coordination of the science of crystallography. The IUCr is a member of the International Council for Science (ICSU).
Acta Crystallographica is a series of peer-reviewed scientific journals, with articles centred on crystallography, published by the International Union of Crystallography (IUCr). Originally established in 1948 as a single journal called Acta Crystallographica, there are now six independent Acta Crystallographica titles:
A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or molecules. They are characterized by symmetry, morphology, and directionally dependent physical properties. A crystal structure describes the arrangement of atoms, ions, or molecules in a crystal.
Arthur William Pryor was an Australian physicist known for his contributions to neutron diffraction and infrared laser isotope separation. Pryor authored and co-authored a number of papers in the field of crystallography and he also co-authored, with B. T. M. Willis, the book Thermal Vibrations in Crystallography.
William Houlder Zachariasen, more often known as W. H. Zachariasen, was a Norwegian-American physicist, specializing in X-ray crystallography and famous for his work on the structure of glass.
Topologically close pack (TCP) phases, also known as Frank-Kasper (FK) phases, are one of the largest groups of intermetallic compounds, known for their complex crystallographic structure and physical properties. Owing to their combination of periodic and aperiodic structure, some TCP phases belong to the class of quasicrystals. Applications of TCP phases as high-temperature structural and superconducting materials have been highlighted; however, they have not yet been sufficiently investigated for details of their physical properties. Also, their complex and often non-stoichiometric structure makes them good subjects for theoretical calculations.
Americium(III) bromide or americium tribromide is the chemical compound composed of americium and bromine with the formula AmBr3, with americium in a +3 oxidation state. The compound is a crystalline solid.
In crystallography, direct methods is a set of techniques used for structure determination using diffraction data and a priori information. It is a solution to the crystallographic phase problem, where phase information is lost during a diffraction measurement. Direct methods provides a method of estimating the phase information by establishing statistical relationships between the recorded amplitude information and phases of strong reflections.
Quantum crystallography is a branch of crystallography that investigates crystalline materials within the framework of quantum mechanics, with analysis and representation, in position or in momentum space, of quantities like wave function, electron charge and spin density, density matrices and all properties related to them. Like the quantum chemistry, Quantum crystallography involves both experimental and computational work. The theoretical part of quantum crystallography is based on quantum mechanical calculations of atomic/molecular/crystal wave functions, density matrices or density models, used to simulate the electronic structure of a crystalline material. While in quantum chemistry, the experimental works mainly rely on spectroscopy, in quantum crystallography the scattering techniques play the central role, although spectroscopy as well as atomic microscopy are also sources of information.
Aafje Looijenga-Vos was a Dutch crystallographer. She was a professor for general chemistry and later for structural chemistry at the University of Groningen.
Isidor Fankuchen was an American pioneer of crystallography. Known to his friends as "Fan" he was from a Jewish family of Dutch origin and trained in Cornell and under W.L. Bragg and J.D. Bernal. He was one of the founders of the International Union of Crystallography (1945). His name has mistakenly been recorded also as Isadore van Kueken.
Hans-Beat Bürgi is a Swiss chemist and crystallographer. He was a professor for crystallography at the University of Bern from 1979 to 2007.