Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word crystallography is derived from the Ancient Greek word κρύσταλλος (; "clear ice, rock-crystal"), with its meaning extending to all solids with some degree of transparency, and γράφειν (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography.
Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on physical measurements of their geometry using a goniometer. This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.
Crystallographic methods now depend on analysis of the diffraction patterns of a sample targeted by a beam of some type. X-rays are most commonly used; other beams used include electrons or neutrons. Crystallographers often explicitly state the type of beam used, as in the terms X-ray crystallography, neutron diffraction and electron diffraction. These three types of radiation interact with the specimen in different ways.
X-rays interact with the spatial distribution of electrons in the sample.
Electrons are charged particles and therefore interact with the total charge distribution of both the atomic nuclei and the electrons of the sample.
Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero.
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In group theory, geometry, representation theory and molecular geometry, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, as transformations of an object in space, rotations, reflections and inversions are all symmetry operations. Such symmetry operations are performed with respect to symmetry elements (for example, a point, line or plane).
Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and l, the Miller indices. They are written (hkl), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to , where are the basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice.
In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties, such as whether or not it has a dipole moment, as well as its allowed spectroscopic transitions. To do this it is necessary to use group theory. This involves classifying the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule.
Ce cours permet l'acquisition des notions essentielles relatives à la structure de la matière, aux équilibres et à la réactivité chimique en liaison avec les propriétés mécaniques, thermiques, électri
The student has a basic understanding of the physical and physicochemical principles which result from the chainlike structure of synthetic macromolecules. The student can predict major characteristic
Active in quality control, industrial crystals and automation. Scientific Visual offers automated quality control tools for industrial crystals, identifying imperfections in raw crystals to optimize processing and reduce waste.
Covers the fundamentals of electron diffraction and its applications in understanding crystal structures and symmetry, including lattice vectors, lattice planes, and dark-field imaging techniques.
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization. History of mineralogy Early writing on mineralogy, especially on gemstones, comes from ancient Babylonia, the ancient Greco-Roman world, ancient and medieval China, and Sanskrit texts from ancient India and the ancient Islamic world.
Symmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.
Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight he ...
Cupredoxins are widely occurring copper-binding proteins with a typical Greek-key beta barrel fold. They are generally described as electron carriers that rely on a T1 copper centre coordinated by four ligands provided by the folded polypeptide. The discov ...
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Aerosols formed and grown by gas-to-particle processes are a major contributor to smog and haze in megacities, despite the competition between growth and loss rates. Rapid growth rates from ammonium nitrate formation have the potential to sustain particle ...