Crystallography

Crystallography

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Encyclopedia
Crystallography is the experimental science of the arrangement of atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s in solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

s. The word "crystallography" derives from the Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

 words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.

Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on their geometry. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry
Symmetry
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 perfection...

 of the crystal in question. The former is carried out using a goniometer
Goniometer
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry is derived from two Greek words, gōnia, meaning angle, and metron, meaning measure....

. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert net
Lambert azimuthal equal-area projection
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk . It accurately represents area in all regions of the sphere, but it does not accurately represent angles...

. In fact, the pole
Pole figure
A pole figure is a graphical representation of the orientation of objects in space. For example, pole figures in the form of stereographic projections are used to represent the orientation distribution of crystallographic lattice planes in crystallography and texture analysis in materials...

 to each face is plotted on the net. Each point is labelled with its Miller index
Miller index
Miller indices form a notation system in crystallography for planes and directions in crystal lattices.In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written , and each index denotes a plane orthogonal to a direction in the...

. The final plot allows the symmetry of the crystal to be established.

Crystallographic methods now depend on the analysis of the diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 patterns of a sample targeted by a beam of some type. Although X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s are most commonly used, the beam is not always electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

. For some purposes electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s or neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s are used. This is facilitated by 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
Neutron diffraction
Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material: A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of...

and electron diffraction
Electron diffraction
Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as 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-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s interact with the spatial distribution of the valence electrons, while electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s are charged particle
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...

s and therefore feel the total charge distribution of both the atomic nuclei and the surrounding electrons. Neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...

 of neutrons is non-zero. They are therefore also scattered by magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s. When neutrons are scattered from hydrogen-containing materials, they produce diffraction patterns with high noise levels. However, the material can sometimes be treated to substitute hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 for deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.

Theory


Generally, an image of a small object is made using a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

 to focus the illuminating radiation, as is done with the rays of the visible spectrum in light microscopy
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...

. However, the wavelength of visible light (about 4000 to 7000 angstrom
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....

s) is three orders of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...

 longer than the length of typical atomic bonds
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

 and atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s themselves (about 1 to 2 angstroms). Therefore, obtaining information about the spatial arrangement of atoms requires the use of radiation with shorter wavelengths, such as X-rays or neutrons beam. Employing shorter wavelengths implied 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, and by critical-angle reflection inside long tapered capillaries.) Diffracted x-ray or neutrons beams cannot be focused to produce images, so the sample structure must be reconstructed from the diffraction pattern. Sharp features in the diffraction pattern arise from periodic, repeating structure in the sample, which are often very strong due to coherent reflection of many photons from many regularly spaced instances of similar structure, while non-periodic components of the structure result in diffuse (and usually weak) diffraction features. Said more simply, areas with a higher density and repetition of atom order tend to reflect more light toward one point in space when compared to those areas with fewer atoms and less repetition.

Because of their highly ordered and repetitive structure, crystals give diffraction patterns of sharp Bragg reflection spots, and are ideal for analyzing the structure of solids.

Notation



  • Coordinates in square bracket
    Bracket
    Brackets are tall punctuation marks used in matched pairs within text, to set apart or interject other text. In the United States, "bracket" usually refers specifically to the "square" or "box" type.-List of types:...

    s
    such as [100] denote a direction vector (in real space).

  • Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are related by symmetry operations. In the cubic crystal system for example, <100> would mean [100], [010], [001] or the negative of any of those directions.

  • Miller indices in parentheses such as (100) denote a plane of the crystal structure, and regular repetitions of that plane with a particular spacing. In the cubic system, the normal
    Surface normal
    A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

     to the (hkl) plane is the direction [hkl], but in lower-symmetry cases, the normal to (hkl) is not parallel to [hkl].

  • Indices in curly brackets or braces such as {100} denote a family of planes and their normals which are equivalent in cubic materials due to symmetry operations, much the way angle brackets denote a family of directions. In non-cubic materials, is not necessarily perpendicular to {hkl}.

Technique


Some materials studied using crystallography, protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s 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
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

. 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
Precipitation (chemistry)
Precipitation is the formation of a solid in a solution or inside anothersolid during a chemical reaction or by diffusion in a solid. When the reaction occurs in a liquid, the solid formed is called the precipitate, or when compacted by a centrifuge, a pellet. The liquid remaining above the solid...

 out of solution, resulting in disorderly granules rather than an orderly and hence usable crystal.

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, synchrotron
Synchrotron light
A synchrotron light source is a source of electromagnetic radiation produced by a synchrotron, which is artificially produced for scientific and technical purposes by specialized particle accelerators, typically accelerating electrons...

s 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. Complementary neutron crystallography techniques are used to enhance hydrogen atoms positions. Such techniques are available in Neutron facilities
Neutron facilities
A neutron research facility is a big laboratory operating a large-scale neutron source that provides thermal neutrons to a suite of research instruments.The neutron source is either a research reactor or a spallation source.- Research practice :...

.

Producing an image from a diffraction pattern requires sophisticated mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 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.

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 crystallize 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
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.-Explanation:...

, 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. For example, the double-helical structure of DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...

 was deduced from an X-ray diffraction pattern that had been generated by a fibrous sample.

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 defect
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...

s. Mostly, materials do not occur in a single crystalline, but poly-crystalline form, such that the powder diffraction
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.-Explanation:...

 method plays a most important role in structural determination.

A number of other physical properties are linked to crystallography. For example, the minerals in clay
Clay
Clay is a general term including many combinations of one or more clay minerals with traces of metal oxides and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure.- Formation :Clay minerals...

 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
Texture (crystalline)
In materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample. A sample in which these orientations are fully random is said to have no texture. If the crystallographic orientations are not random, but have some preferred orientation, then the...

 measurements.

In another example, iron
Iron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

 transforms from a body-centered cubic (bcc) structure to a face-centered cubic (fcc) structure called austenite
Austenite
Austenite, also known as gamma phase iron, is a metallic non-magnetic allotrope of iron or a solid solution of iron, with an alloying element. In plain-carbon steel, austenite exists above the critical eutectoid temperature of ; other alloys of steel have different eutectoid temperatures...

 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.

Crystallography is useful in phase identification. When performing any process on a material, it may be 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 or neutron diffraction can be used to identify which patterns are present in the material, and thus which compounds are present.

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
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

.

Biology


X-ray crystallography
X-ray crystallography
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 causes the beam of light to spread into many specific directions. From the angles and intensities of these diffracted beams, a crystallographer can produce a...

 is the primary method for determining the molecular conformations of biological macromolecule
Macromolecule
A macromolecule is a very large molecule commonly created by some form of polymerization. In biochemistry, the term is applied to the four conventional biopolymers , as well as non-polymeric molecules with large molecular mass such as macrocycles...

s, particularly protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

 and nucleic acid
Nucleic acid
Nucleic acids are biological molecules essential for life, and include DNA and RNA . Together with proteins, nucleic acids make up the most important macromolecules; each is found in abundance in all living things, where they function in encoding, transmitting and expressing genetic information...

s such as DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...

 and RNA
RNA
Ribonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....

. In fact, the double-helical structure of DNA was deduced from crystallographic data. The first crystal structure of a macromolecule was solved in 1958. A three-dimensional model of the myoglobin molecule obtained by X-ray analysis. The Protein Data Bank
Protein Data Bank
The Protein Data Bank is a repository for the 3-D structural data of large biological molecules, such as proteins and nucleic acids....

 (PDB) is a freely accessible repository for the structures of protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s and other biological macromolecules. Computer programs like RasMol
RasMol
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...

 or Pymol
PyMOL
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 software company dedicated to creating useful tools that become universally accessible to scientific and educational communities...

 can be used to visualize biological molecular structures.
Neutron crystallography is often used to help refine structures obtained by x-ray methods or to solve a specific bond; the methods are often viewed as complementary, as x-rays are sensitive to electron positions and scatter most strongly off heavy atoms, while neutrons are sensitive to nucleus positions and scatter strongly off many light isotopes, including hydrogen and deuterium.
Electron crystallography
Electron crystallography
Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope .- Comparison with X-ray crystallography :...

 has been used to determine some protein structures, most notably membrane protein
Membrane protein
A membrane protein is a protein molecule that is attached to, or associated with the membrane of a cell or an organelle. More than half of all proteins interact with membranes.-Function:...

s and viral capsids.

Scientists of note


  • William Barlow
  • John Desmond Bernal
  • William Henry Bragg
    William Henry Bragg
    Sir William Henry Bragg OM, KBE, PRS was a British physicist, chemist, mathematician and active sportsman who uniquely shared a Nobel Prize with his son William Lawrence Bragg - the 1915 Nobel Prize in Physics...

  • William Lawrence Bragg
    William Lawrence Bragg
    Sir William Lawrence Bragg CH OBE MC FRS was an Australian-born British physicist and X-ray crystallographer, discoverer of the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure. He was joint winner of the Nobel Prize for Physics in 1915. He was knighted...

  • Auguste Bravais
    Auguste Bravais
    Auguste Bravais was a French physicist, well known for his work in crystallography...

  • Martin Julian Buerger
  • Francis Crick
    Francis Crick
    Francis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...

  • Pierre Curie
    Pierre Curie
    Pierre Curie was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity and radioactivity, and Nobel laureate. He was the son of Dr. Eugène Curie and Sophie-Claire Depouilly Curie ...

  • Peter Debye
    Peter Debye
    Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

  • Boris Delone
  • Jack Dunitz
  • Paul Peter Ewald
    Paul Peter Ewald
    Paul Peter Ewald was a German-born U.S. crystallographer and physicist, a pioneer of X-ray diffraction methods.-Education:...

  • Evgraf Stepanovich Fedorov
    Yevgraf Fyodorov
    Yevgraf Stepanovich Fyodorov, sometimes spelled Evgraf Stepanovich Fedorov , was a Russian mathematician, crystallographer, and mineralogist....

  • Rosalind Franklin
    Rosalind Franklin
    Rosalind Elsie Franklin was a British biophysicist and X-ray crystallographer who made critical contributions to the understanding of the fine molecular structures of DNA, RNA, viruses, coal and graphite...

  • Georges Friedel
    Georges Friedel
    Georges Friedel was a French mineralogist and crystallographer.- Life :Georges was the son of the famous chemist Charles Friedel...

  • Paul Heinrich von Groth
    Paul Heinrich von Groth
    Paul Heinrich von Groth was a German mineralogist. His most important contribution to science was his systematic classification of minerals based on their chemical compositions and crystal structures....

  • René Just Haüy
    René Just Haüy
    René Just Haüy – 3 June 1822 in Paris) was a French mineralogist, commonly styled the Abbé Haüy after he was made an honorary canon of Notre Dame. He is often referred to as the "Father of Modern Crystallography." -Biography:...

  • Carl Hermann
    Carl Hermann
    Carl Hermann was a German professor of crystallography. With Charles-Victor Mauguin, he invented an international standard notation for crystallographic groups known as the Hermann–Mauguin notation or International notation.Born in the north German port town of Wesermünde to parents both of...

  • Johann Friedrich Christian Hessel
    Johann F. C. Hessel
    Johann Friedrich Christian Hessel was a German physician and professor of mineralogy at the University of Marburg....

  • Dorothy Crowfoot Hodgkin
    Dorothy Crowfoot Hodgkin
    Dorothy Mary Hodgkin OM, FRS , née Crowfoot, was a British chemist, credited with the development of protein crystallography....

  • Robert Huber
    Robert Huber
    Robert Huber is a German biochemist and Nobel laureate.He was born 20 February 1937 in Munich where his father, Sebastian, was a bank cashier. He was educated at the Humanistisches Karls-Gymnasium from 1947 to 1956 and then studied chemistry at the Technische Hochschule, receiving his diploma in 1960...

  • Aaron Klug
    Aaron Klug
    Sir Aaron Klug, OM, PRS is a Lithuanian-born British chemist and biophysicist, and winner of the 1982 Nobel Prize in Chemistry for his development of crystallographic electron microscopy and his structural elucidation of biologically important nucleic acid-protein complexes.-Biography:Klug was...

  • Max von Laue
    Max von Laue
    Max Theodor Felix von Laue was a German physicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals...

  • Kathleen Lonsdale
    Kathleen Lonsdale
    Dame Kathleen Lonsdale, DBE FRS was a crystallographer, who established the structure of benzene by X-ray diffraction methods in 1929, and hexachlorobenzene by Fourier spectral methods in 1931...

  • Ernest-François Mallard
    Ernest-François Mallard
    Ernest-François Mallard was a French mineralogist and a member of the French Academy of Sciences.-References:...

  • Charles-Victor Mauguin
    Charles-Victor Mauguin
    French professor of mineralogy Charles-Victor Mauguin was inventor of an international standard notation for crystallographic groups known as the Hermann–Mauguin notation or International notation....

  • William Hallowes Miller
    William Hallowes Miller
    William Hallowes Miller FRS , British mineralogist and crystallographer.- Life and work :Miller was born in 1801 at Velindre near Llandovery, Carmarthenshire. He was educated at St John's College, Cambridge, where he graduated in 1826 as fifth wrangler. He became a Fellow there in 1829...

  • Friedrich Mohs
    Friedrich Mohs
    Carl Friedrich Christian Mohs was a German geologist/mineralogist.- Career :Mohs, born in Gernrode, Germany, studied chemistry, mathematics and physics at the University of Halle and also studied at the Mining Academy in Freiberg, Saxony...

  • Paul Niggli
  • Arthur Lindo Patterson
    Arthur Lindo Patterson
    Arthur Lindo Patterson 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...

  • Max Perutz
    Max Perutz
    Max Ferdinand Perutz, OM, CH, CBE, FRS was an Austrian-born British molecular biologist, who shared the 1962 Nobel Prize for Chemistry with John Kendrew, for their studies of the structures of hemoglobin and globular proteins...

  • Hugo Rietveld
    Hugo Rietveld
    Hugo M. Rietveld is a Dutch crystallographer and one of the most prominent crystallographers of the 20th century. He is famous for his invention of the Rietveld refinement method, which is used for the characterisation of crystalline materials from powder diffraction data...

  • Jean-Baptiste L. Romé de l'Isle
    Jean-Baptiste L. Romé de l'Isle
    Jean-Baptiste Louis Romé de l'Isle was a French mineralogist, considered one of the creators of modern crystallography....

  • Paul Scherrer
    Paul Scherrer
    Paul Scherrer was a Swiss physicist. Born in Herisau, Switzerland, he studied at Göttingen, Germany, before becoming a lecturer there. Later, Scherrer became head of the Department of Physics at ETH Zürich....

  • Arthur Moritz Schönflies
  • Dan Shechtman
    Dan Shechtman
    Dan Shechtman is the Philip Tobias Professor of Materials Science at the Technion – Israel Institute of Technology, an Associate of the US Department of Energy's Ames Laboratory, and Professor of Materials Science at Iowa State University. On April 8, 1982, while on sabbatical at the U.S...

  • Tej P. Singh
  • Constance Tipper
    Constance Tipper
    Constance Fligg Elam Tipper was a British metallurgist and crystallographer.Constance Tipper specialized in the investigation of metal strength and its effect on engineering problems. During the Second World War, she investigated the causes of brittle fracture in Liberty Ships...

  • Christian Samuel Weiss
    Christian Samuel Weiss
    Christian Samuel Weiss was a German mineralogist born in Leipzig. After graduation he was a physics instructor in Leipzig from 1803 until 1808...

  • Don Craig Wiley
    Don Craig Wiley
    Don Craig Wiley was an American microbiologist.Wiley was world-renowned for finding new ways to help the human immune system battle such viral scourges as smallpox, influenza, AIDS, Ebola, and herpes simplex. His research was honored with the 1993 Cancer Research Institute William B. Coley Award...

  • Ralph Walter Graystone Wyckoff
    Ralph Walter Graystone Wyckoff
    Ralph Walter Graystone Wyckoff, Sr. was an American scientist and pioneer of X-ray crystallography. He was elected Foreign member of the Royal Society, on April 19, 1951....

  • Ada Yonath
    Ada Yonath
    Ada E. Yonath is an Israeli crystallographer best known for her pioneering work on the structure of the ribosome. She is the current director of the Helen and Milton A. Kimmelman Center for Biomolecular Structure and Assembly of the Weizmann Institute of Science. In 2009, she received the Nobel...



See also


  • Atomic packing factor
    Atomic packing factor
    In crystallography, atomic packing factor or packing fraction is the fraction of volume in a crystal structure that is occupied by atoms. It is dimensionless and always less than unity. For practical purposes, the APF of a crystal structure is determined by assuming that atoms are rigid spheres...

  • Condensed matter physics
    Condensed matter physics
    Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...

  • Crystal engineering
    Crystal engineering
    Crystal engineering is the design and synthesis of molecular solid-state structures with desired properties, based on an understanding and exploitation of intermolecular interactions. The two main strategies currently in use for crystal engineering are based on hydrogen bonding and coordination...

  • Crystal growth
    Crystal growth
    A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. Crystal growth is a major stage of a crystallization process, and consists in the addition of new atoms, ions, or polymer strings into...

  • Crystal optics
    Crystal optics
    Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be...

  • Crystal system
    Crystal system
    In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals...

  • Crystal
    Crystal
    A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

  • Crystallite
    Crystallite
    Crystallites are small, often microscopic crystals that, held together through highly defective boundaries, constitute a polycrystalline solid. Metallurgists often refer to crystallites as grains.- Details :...

  • Crystallization processes
  • Crystallographic database
    Crystallographic database
    A crystallographic database is a database specifically designed to store information about crystals and crystal structures. 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,...

  • Crystallographic group
  • Dynamical theory of diffraction
    Dynamical theory of diffraction
    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...

  • Electron crystallography
    Electron crystallography
    Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope .- Comparison with X-ray crystallography :...

  • Euclidean plane isometry
    Euclidean plane isometry
    In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length...

  • Fixed points of isometry groups in Euclidean space
    Fixed points of isometry groups in Euclidean space
    A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space....

  • Fractional coordinates
    Fractional coordinates
    In crystallography, a fractional coordinate system is a coordinate system in which the edges of the unit cell are used as the basic vectors to describe the positions of atomic nuclei...

  • Group action
    Group action
    In algebra and geometry, a group action is a way of describing symmetries of objects using groups. The essential elements of the object are described by a set, and the symmetries of the object are described by the symmetry group of this set, which consists of bijective transformations of the set...

  • Laser-heated pedestal growth
    Laser-heated pedestal growth
    Laser-heated pedestal growth is a crystal growth technique. The technique can be viewed as a miniature floating zone, where the heat source is replaced by a powerful CO2 or YAG laser...

  • Materials science
    Materials science
    Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates...

  • Metallurgy
    Metallurgy
    Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. It is also the technology of metals: the way in which science is applied to their practical use...

  • Mineralogy
    Mineralogy
    Mineralogy is the study of chemistry, crystal structure, and physical properties of minerals. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization.-History:Early writing...

  • Neutron crystallography
  • NMR crystallography
  • Neutron diffraction at OPAL
    OPAL
    OPAL is a 20 megawatt pool-type nuclear research reactor that was officially opened on 20 April 2007 at the Australian Nuclear Science and Technology Organisation Research Establishment at Lucas Heights, located in South Sydney, Australia.The main reactor uses are:* Irradiation of target...

  • Neutron diffraction at the ILL
  • Permutation group
    Permutation group
    In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G ; the relationship is often written as...

  • Point group
    Point group
    In geometry, a point group is a group of geometric symmetries that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O...

  • Quasicrystal
    Quasicrystal
    A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...

  • Solid state chemistry
  • Space group
    Space group
    In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...

  • Symmetric group
    Symmetric group
    In mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself...



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