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Encyclopedia > Crystallography

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. In older usage, it is the scientific study of crystals. Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... For other uses, see Solid (disambiguation). ... Quartz crystal Synthetic bismuth crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid in which the constituent atoms, molecules...


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. The former is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wolff net or Lambert net. In fact, 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. Sphere symmetry group o. ... A goniometer is an instrument that either measures angles or allows an object to be rotated to a precise angular position. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Examples of directions Miller indices are a notation used to describe lattice planes and directions in a crystal. ...


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. The beam is not always electromagnetic radiation, even though X-rays are the most common choice. For some purposes electrons or neutrons are used, which is possible due to the wave properties of the particles. 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. The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... It has been suggested that this article or section be merged with light. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... e- redirects here. ... This article or section does not adequately cite its references or sources. ... X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of x-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. ... Neutron diffraction is a crystallography technique that uses neutrons to determine the atomic structure of a material. ... This article is in need of attention from an expert on the subject. ...


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. Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero. They are therefore also scattered by magnetic fields. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies. In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... In chemistry, valence electrons are the electrons contained in the valence shell of an atom, and which are likely to participate in a chemical reaction through bonding with other atoms or molecules. ... e- redirects here. ... In physics, a charged particle is a particle with an electric charge. ... The nucleus (atomic nucleus) is the center of an atom. ... This article or section does not adequately cite its references or sources. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... A bar magnet. ... For other senses of this term, see magnetic field (disambiguation). ...

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. 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. 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). 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. The visible spectrum is the portion of the optical spectrum (light or electromagnetic spectrum) that is visible to the human eye. ... A lens. ... Robert Hookes microscope (1665) - an engineered device used to study living systems. ... A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... An example of a zone plate Zone plates are a device used to focus light. ...


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. Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...


Notation

See Miller index for a full treatment of this topic. Examples of directions Miller indices are a notation used to describe lattice planes and directions in a crystal. ...

  • Coordinates in square brackets such as [100] denote a direction (in real space).
  • Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are equivalent due to symmetry operations. If it refers to a cubic system, this example could mean [100], [010], [001] or the negative of any of those directions.
  • Miller indices in parentheses such as (100) denote a plane, in a cubic system the normal to the (hkl) plane is the direction [hkl].
  • Indices in curly brackets or braces such as {100} denote a family of plane normals which are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.

For technical reasons, :) and some similar combinations starting with : redirect here. ... A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ...

Technique

Some materials studied using crystallography, proteins for example, do not occur naturally as crystals. Typically, such molecules are placed in solution and allowed to crystallize over days, weeks, or months through vapor diffusion. A drop of solution containing the molecule, buffer, and precipitants is sealed in a container with a reservoir containing a hygroscopic solution. 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. A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... This article or section does not adequately cite its references or sources. ... A hygroscopic substance is a substance that absorbs water readily from its surroundings. ...


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. 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. Synchrotron radiation emerging from a beam port. ...


Producing an image from a diffraction pattern requires sophisticated mathematics and often an iterative process of modelling and refinement. 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. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...


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. 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). To meet Wikipedias quality standards, this article or section may require cleanup. ... The structure of part of a DNA double helix Deoxyribonucleic acid (DNA) is a nucleic acid that contains the genetic instructions for the development and function of living organisms. ...


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. Mostly, materials do not occur in a syngle crystalline, but poly-crystalline form, such that the powder diffraction method plays a most important role in structural determination. 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. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...


A number of other physical properties are linked to crystallography. For example, the minerals in clay form small, flat, platelike structures. 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. The Gay Head cliffs in Marthas Vineyard are made almost entirely of clay. ... 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. 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. General Name, Symbol, Number iron, Fe, 26 Chemical series transition metals Group, Period, Block 8, 4, d Appearance lustrous metallic with a grayish tinge Standard atomic weight 55. ... In crystallography, the cubic crystal system is the most symmetric of the 7 crystal systems. ... In crystallography, the cubic crystal system is the most symmetric of the 7 crystal systems. ... Iron-carbon phase diagram, showing the conditions under which austenite (γ) is stable in carbon steel. ...


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 (e. ...


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. 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. RasMol can be used to visualize biological molecular structures. X-ray crystallography or single-crystal X-ray diffraction is an analytical technique which uses the diffraction pattern produced by bombarding a single crystal with X-rays to solve the crystal structure. ... A macromolecule is a large molecule with a large molecular mass bonded covalently, but generally the use of the term is restricted to polymers and molecules which structurally include polymers. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... A nucleic acid is a complex, high-molecular-weight biochemical macromolecule composed of nucleotide chains that convey genetic information. ... The structure of part of a DNA double helix Deoxyribonucleic acid (DNA) is a nucleic acid that contains the genetic instructions for the development and function of living organisms. ... This article or section does not adequately cite its references or sources. ... The Protein Data Bank (PDB) is a repository for 3-D structural data of proteins and nucleic acids. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... RasMol is a computer program written for molecular graphics visualization intended and used primarily for the depiction and exploration of biological macromolecule structures, such as those found in the Protein Data Bank. ...


Electron crystallography has been used to determine some protein structures, most notably membrane proteins and viral capsids. To meet Wikipedias quality standards, this article or section may require cleanup. ... A membrane protein is a protein molecule that is attached to, or associated with the membrane of a cell or an organelle. ... The outer shell of a virus is called the capsid. ...


Scientists of note

// Pierre Curie (Paris, France, May 15, 1859 – April 19, 1906, Paris) was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity and radioactivity. ... Don Craig Wiley, 1944-2001, American crystallographer. ... René Just Haüy (February 28, 1743 – June 3, 1822), French mineralogist, commonly styled the Abbé Haüy, from being an honorary canon of Notre Dame, was born at St Just, in the départment of Oise. ... William Hallowes Miller (April 6, 1801 - May 20, 1880), British mineralogist and crystallographer, was born at Velindre near Llandovery, Carmarthenshire. ... Sir William Henry Bragg OM, Cantab, OKW (Westward, Cumbria, England July 2, 1862 – March 10, 1942) was an English physicist and chemist, educated at King Williams College, Isle of Man, and Trinity College, Cambridge. ... Sir William Lawrence Bragg CH, FRS, (31 March 1890 – 1 July 1971) was an Australian physicist who shared the Nobel Prize in Physics in 1915 with his father Sir William Henry Bragg. ... Boris Nikolaevich Delaunay (March 15, 1890 in Petersburg &#8211; July 17, 1980 in Moscow) (or Delone; Russian language: &#1041;&#1086;&#1088;&#1080;&#1089; &#1053;&#1080;&#1082;&#1086;&#1083;&#1072;&#1077;&#1074;&#1080;&#1095; &#1044;&#1077;&#1083;&#1086;&#1085;&#1077;), was a Soviet/Russian mathematician. ... Robert Huber is a German biochemist and Nobel laureate. ... Dorothy Mary Crowfoot Hodgkin, OM , FRS (12 May 1910 – 29 July 1994) was a British founder of protein crystallography. ... Max Ferdinand Perutz, OM (May 19, 1914 – February 6, 2002) was an Austrian-British molecular biologist. ... Christian Bök (born Book, 1966- ), is a Canadian experimental poet. ...

See also

In crystallography, atomic packing factor is the fraction of volume in a crystal structure that is occupied by atoms. ... Quartz crystal Synthetic bismuth crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid in which the constituent atoms, molecules... Crystal engineering is the design and synthesis of molecular solid-state structures with desired properties, based on an understanding and exploitation of intermolecular interactions. ... Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. ... A crystal system is a category of space groups, which characterize symmetry of structures in three dimensions with translational symmetry in three directions, having a discrete symmetry group. ... A crystallite is a domain of solid-state matter that has the same structure as a single crystal. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... A crystallographic group is a topologically discrete subgroup of the group of isometries of some geometric space (typically, not necessarily a Euclidean space) with a compact fundamental domain. ... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... The dynamical theory of diffraction describes the interaction of wave fields with a regular lattice. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The symmetry group of an object (e. ... X-ray crystallography or single-crystal X-ray diffraction is an analytical technique which uses the diffraction pattern produced by bombarding a single crystal with X-rays to solve the crystal structure. ...

External links


  Results from FactBites:
 
Crystallography - Wikipedia, the free encyclopedia (1484 words)
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.
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.
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.
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