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For the book of poetry, see Crystallography (book). Crystallography is a book of Poetry and Prose published in 1994 and revised in 2003 by Canadian author Christian Bök

Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. In older usage, it is the scientific study of crystals. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating

Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on the geometry of the crystals. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or The former is carried out using a goniometer. A goniometer is an instrument that either measures angle or allows an object to be rotated to a precise angular position The position in 3D space of each crystal face is plotted on a stereographic net, e. g. Wulff net or Lambert net. In Geometry, the stereographic projection is a particular mapping ( function) that projects a Sphere onto a plane The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk In fact, the pole to each face is plotted on the net. Each point is labelled with its Miller index. Miller indices are a notation system in Crystallography for planes and directions in crystal (Bravais lattices In particular a family of Lattice planes The final plot allows the symmetry of the crystal to be established.

Crystallographic methods now depend on the analysis of the diffraction patterns that emerge from a sample that is targeted by a beam of some type. Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle The beam is not always electromagnetic radiation, even though X-rays are the most common choice. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. For some purposes electrons or neutrons are used, which is possible due to the wave properties of the particles. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. Crystallographers often explicitly state the type of illumination used when referring to a method, as with the terms X-ray diffraction, neutron diffraction and electron diffraction. X-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystallographic structure chemical composition Neutron diffraction is a crystallographic method for the determination of the atomic and/or magnetic structure of a material Electron diffraction is a technique used to study matter by firing Electrons at a sample and observing the resulting Interference pattern

These three types of radiation interact with the specimen in different ways. X-rays interact with the spatial distribution of the valence electrons, while electrons are charged particles and therefore feel the total charge distribution of both the atomic nuclei and the surrounding electrons. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. In chemistry valence electrons are the Electrons contained in the outermost or valence, Electron shell of an Atom. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, a charged particle is a particle with an Electric charge. The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current They are therefore also scattered by magnetic fields. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.

Contents

Theory

In several cases, an image of a microscopic object is generated by focusing the rays of the visible spectrum using a lens, as in light microscopy. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging A microscope ( Greek: ( micron) = small + ( skopein) = to look or see is an instrument for viewing objects that are However, because the wavelength of visible light is long compared to atomic bond lengths and atoms themselves, it is necessary to use radiation with shorter wavelengths, such as X-rays. A chemical bond is the physical process responsible for the attractive interactions between Atoms and Molecules and which confers stability to diatomic and polyatomic History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny Employing shorter wavelengths implies abandoning microscopy and true imaging, however, because there exists no material from which a lens capable of focusing this type of radiation can be created. (That said, scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold). A zone plate is a device used to focus light Unlike lenses however zone plates use Diffraction instead of Refraction. Generally, in diffraction-based imaging, the only wavelengths used are those that are too short to be focused. This difficulty is the reason that crystals must be used.

Because of their highly ordered and repetitive structure, crystals are an ideal material for analyzing the structure of solids. To use X-ray diffraction as an example, a single X-ray photon diffracting off of one electron cloud will not generate a strong enough signal for the equipment to detect. However, many X-rays diffracting off many electron clouds in approximately the same relative position and orientation throughout the crystal will result in constructive interference and hence a detectable signal. In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern

Notation

See Miller index for a full treatment of this topic. Miller indices are a notation system in Crystallography for planes and directions in crystal (Bravais lattices In particular a family of Lattice planes

Technique

Some materials studied using crystallography, proteins for example, do not occur naturally as crystals. Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl Typically, such molecules are placed in solution and allowed to crystallize over days, weeks, or months through vapor diffusion. Diffusion is the net movement of particles (typically molecules from an area of high concentration to an area of low concentration by uncoordinated random movement A drop of solution containing the molecule, buffer, and precipitants is sealed in a container with a reservoir containing a hygroscopic solution. Hygroscopy is the ability of a substance to attract Water Molecules from the surrounding environment through either absorption or Adsorption Water in the drop diffuses to the reservoir, slowly increasing the concentration and allowing a crystal to form. If the concentration were to rise more quickly, the molecule would simply precipitate out of solution, resulting in disorderly granules rather than an orderly and hence usable crystal. Precipitation is the formation of a Solid in a Solution during a Chemical reaction.

Once a crystal is obtained, data can be collected using a beam of radiation. Although many universities that engage in crystallographic research have their own X-ray producing equipment, synchrotrons are often used as X-ray sources, because of the purer and more complete patterns such sources can generate. This article is mostly concerned with applications of Synchrotron radiation. Synchrotron sources also have a much higher intensity of X-ray beams, so data collection takes a fraction of the time normally necessary at weaker sources.

Producing an image from a diffraction pattern requires sophisticated mathematics and often an iterative process of modelling and refinement. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In this process, the mathematically predicted diffraction patterns of an hypothesized or "model" structure are compared to the actual pattern generated by the crystalline sample. Ideally, researchers make several initial guesses, which through refinement all converge on the same answer. Models are refined until their predicted patterns match to as great a degree as can be achieved without radical revision of the model. This is a painstaking process, made much easier today by computers.

The mathematical methods for the analysis of diffraction data only apply to patterns, which in turn result only when waves diffract from orderly arrays. Hence crystallography applies for the most part only to crystals, or to molecules which can be coaxed to crystalize for the sake of measurement. In spite of this, a certain amount of molecular information can be deduced from the patterns that are generated by fibers and powders, which while not as perfect as a solid crystal, may exhibit a degree of order. Powder diffraction is a scientific technique using X-ray, Neutron, or Electron Diffraction on powder or Microcrystalline samples for This level of order can be sufficient to deduce the structure of simple molecules, or to determine the coarse features of more complicated molecules (the double-helical structure of DNA, for example, was deduced from an X-ray diffraction pattern that had been generated by a fibrous sample). Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known

Crystallography in materials engineering

Crystallography is a tool that is often employed by materials scientists. In single crystals, the effects of the crystalline arrangement of atoms is often easy to see macroscopically, because the natural shapes of crystals reflect the atomic structure. In addition, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding crystallographic defects. Crystalline solids have a very regular atomic structure that is the local positions of atoms with respect to each other are repeated at the atomic scale Mostly, materials do not occur in a single crystalline, but poly-crystalline form, such that the powder diffraction method plays a most important role in structural determination. Powder diffraction is a scientific technique using X-ray, Neutron, or Electron Diffraction on powder or Microcrystalline samples for

A number of other physical properties are linked to crystallography. For example, the minerals in clay form small, flat, platelike structures. Clay is a naturally occurring material composed primarily of fine-grained Minerals which show plasticity through a variable range of Water content, and Clay can be easily deformed because the platelike particles can slip along each other in the plane of the plates, yet remain strongly connected in the direction perpendicular to the plates. Such mechanisms can be studied by crystallographic texture measurements. In Materials science, texture is the distribution of crystallographic orientations of a sample

In another example, iron transforms from a body-centered cubic (bcc) structure to a face-centered cubic (fcc) structure called austenite when it is heated. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 The cubic crystal system (or isometric) is a Crystal system where the Unit cell is in the shape of a Cube. The cubic crystal system (or isometric) is a Crystal system where the Unit cell is in the shape of a Cube. Austenite (or gamma phase iron is a metallic non-magnetic solid solution of Iron and an Alloying element The fcc structure is a close-packed structure, and the bcc structure is not, which explains why the volume of the iron decreases when this transformation occurs.

Crystallography is useful in phase identification: That is, when performing some kind of processing on a material, it is often desired to find out what compounds and what phases are present in the material. Each phase has a characteristic arrangement of atoms. Techniques like X-ray diffraction can be used to identify which patterns are present in the material, and thus which compounds are present (note: the determination of the "phases" within a material should not be confused with the more general problem of "phase determination," which refers to the phase of waves as they diffract from planes within a crystal, and which is a necessary step in the interpretation of complicated diffraction patterns).

Crystallography covers the enumeration of the symmetry patterns which can be formed by atoms in a crystal and for this reason has a relation to group theory and geometry. See symmetry group. The Symmetry group of an object ( Image, signal, etc eg in 1D 2D or 3D is the group of all Isometries under which it is

Biology

X-ray crystallography is the primary method for determining the molecular conformations of biological macromolecules, particularly protein and nucleic acids such as DNA and RNA. X-ray crystallography is a method of determining the arrangement of Atoms within a Crystal, in which a beam of X-rays strikes a crystal and scatters The term macromolecule by definition implies "large Molecule " Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl A nucleic acid is a Macromolecule composed of chains of monomeric Nucleotides In Biochemistry these Molecules carry Genetic information Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known Ribonucleic acid ( RNA) is a Nucleic acid that consists of a long chain of Nucleotide units In fact, the double-helical structure of DNA was deduced from crystallographic data. The first crystal structure of a macromolecule was solved in 1958 (Kendrew, J. C. et al. (1958) A three-dimensional model of the myoglobin molecule obtained by X-ray analysis (Nature 181, 662–666). The Protein Data Bank (PDB) is a freely accessible repository for the structures of proteins and other biological macromolecules. The Protein Data Bank ( PDB) is a repository for 3-D structural data of Proteins and Nucleic acids These data typically obtained by X-ray crystallography Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl Computer programs like RasMol or Pymol can be used to visualize biological molecular structures. RasMol is a computer program written for Molecular graphics visualization intended and used primarily for the PyMOL is an open-source user-sponsored molecular visualization system created by Warren Lyford DeLano and commercialized by DeLano Scientific LLC which is a private

Electron crystallography has been used to determine some protein structures, most notably membrane proteins and viral capsids. Electron crystallography is a method to determine the arrangement of atoms in solids using an Electron microscope. Also see Transmembrane protein. A membrane protein is a Protein molecule that is attached to or associated with the membrane For the leaf bug see Miridae. A capsid is the protein shell of a virus.

Scientists of note

See also

External links

Dictionary

crystallography

-noun

  1. The experimental science of determining the arrangement of atoms in solids.
  2. The study of crystals.
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