Crystallography is the experimental science of determining the arrangement of atomAtom
|-! bgcolor=gray | Properties|-||}The atom is a basic unit of matter consisting of a dense, central atomic nucleus surrounded by a electron cloud of electric charge electrons....
s in solidSolid
A solid object is in the states of matter characterized by resistance to deformation and changes of volume. In other words, it has high values both of Young's modulus and of shear modulus; this contrasts e.g....
s. In older usage, it is the scientific study of crystalCrystal
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....
s. The word "crystallography" is derived from the GreekGreek language
Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write.
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 symmetrySymmetry
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 goniometerGoniometer
A goniometer is an instrument that either measures angle or allows an object to be rotated to a precise angular position. The term goniometry is derived from two Greek words, gonia, meaning angle and metron, meaning Measurement....
. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert netLambert 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 to each face is plotted on the net. Each point is labelled with its Miller indexMiller index
Miller indices are a notation system in crystallography for planes and directions in Bravais lattices.In particular, a family of lattice planes is determined by three integers , , and , the Miller indices....
. The final plot allows the symmetry of the crystal to be established.
Crystallographic methods now depend on the analysis of the diffractionDiffraction
Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle. It is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings....
patterns that emerge from a sample that is targeted by a beam of some type. The beam is not always electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation takes the form of wave propagation waves in a vacuum or in matter. EM radiation has an electric field and magnetic field component which oscillate in phase perpendicular to each other and to the direction of energy Wave propagation....
, even though X-rayX-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 10 to 0.01 nanometers, corresponding to frequency in the range 30 Hertz to 30 Hertz and energies in the range 120 Electron volt to 120 keV....
s are the most common choice. For some purposes electronElectron
The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s or neutronNeutron
The neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutrons are usually found in atomic nucleus....
s 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 diffractionNeutron diffraction
Neutron diffraction is a method for the determination of the atomic and/or magnetic structure of a material. It can be equally well applied to study crystalline solids , gasses, liquids or amorphous materials....
and electron diffractionElectron diffraction
Electron diffraction is a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern. This phenomenon occurs due to the wave-particle duality, which states that a particle of matter can be described as a wave....
.
These three types of radiation interact with the specimen in different ways. X-rayX-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 10 to 0.01 nanometers, corresponding to frequency in the range 30 Hertz to 30 Hertz and energies in the range 120 Electron volt to 120 keV....
s interact with the spatial distribution of the valence electrons, while electronElectron
The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s are charged particleCharged 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 properties are quite different from solids, liq...
s and therefore feel the total charge distribution of both the atomic nuclei and the surrounding electrons. NeutronNeutron
The neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutrons are usually found in atomic nucleus....
s are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic momentMagnetic moment
In physics, astronomy, chemistry, and electrical engineering, the term magnetic moment of a system usually refers to its magnetic dipole moment, and is a measure of the strength of the system's net Magnetism....
of neutrons is non-zero. They are therefore also scattered by magnetic fieldMagnetic field
A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
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 hydrogenHydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the chemical symbol H. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly combustion and explosive Diatomic molecule gas with the molecular formula H2....
for deuteriumDeuterium
Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen ....
. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies.
Theory
An image of a small object is usually generated by using a lensLens (optics)
A lens is an optics device with perfect or approximate axial symmetry which transmittance and refraction light, converging or diverging the beam....
to focus the illuminating radiation, as is done with the rays of the visible spectrum in light microscopyMicroscope
A microscope is an Laboratory equipment for viewing objects that are too small to be seen by the naked or unaided eye. The science of investigating small objects using such an instrument is called microscopy....
. However, the wavelength of visible light (about 4000 to 7000 Angstroms) is three orders of magnitudeOrder of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed Geometric progression to the class preceding it....
longer then the length of typical atomic bondsChemical bond
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....
and atomAtom
|-! bgcolor=gray | Properties|-||}The atom is a basic unit of matter consisting of a dense, central atomic nucleus surrounded by a electron cloud of electric charge electrons....
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. 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 beams cannot be focussed 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.
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
See Miller indexMiller index
Miller indices are a notation system in crystallography for planes and directions in Bravais lattices.In particular, a family of lattice planes is determined by three integers , , and , the Miller indices....
for a full treatment of this topic.
Coordinates in square bracketBracket
Brackets are punctuation marks used in pairs to set apart or interject text within other text. In computer science, the term is sometimes said to strictly apply to the square or box type....
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 normalSurface normal
A surface normal, or simply normal, to a Flatness is a vector which 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 space to that surface at P....
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 denote a family of planes and their normals which are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.
Technique
Some materials studied using crystallography, proteinProtein
Proteins are organic compounds made of amino acids arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid Residue ....
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 diffusionDiffusion
Molecular diffusion, often called simply diffusion, is a net transport of molecules from a region of higher concentration to one of lower concentration by random molecular motion....
. 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 precipitatePrecipitation (chemistry)
Precipitation is the formation of a solid in a solution during a chemical reaction. When the reaction occurs, the solid formed is called the precipitate, and the liquid remaining above the solid is called the supernate....
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, synchrotronSynchrotron light
A synchrotron light source is a source of electromagnetic radiation produced by synchrotron radiation, 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.
Producing an image from a diffraction pattern requires sophisticated mathematicsMathematics
Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
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 powdersPowder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials....
, 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 DNADNA
Deoxyribonucleic acid is a nucleic acid that contains the genetics instructions used in the development and functioning of all known living organisms and some viruses....
, for example, 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 defectCrystallographic defect
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....
s. Mostly, materials do not occur in a single crystalline, but poly-crystalline form, such that the powder diffractionPowder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials....
method plays a most important role in structural determination.
A number of other physical properties are linked to crystallography. For example, the minerals in clayClay
Clay is a naturally occurring material composed primarily of fine-grained minerals, which show plasticity through a variable range of water content, and which can be hardened when dried and/or fired....
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 textureTexture (crystalline)
In materials science, texture is the distribution of crystallographic orientations of a sample. A sample in which these orientations are fully random is said to have no texture....
measurements.
In another example, ironIron
Iron is a chemical element with the symbol Fe and atomic number 26. Iron is a Group 8 element and period 4 element. Iron is lustrous and silvery in color....
transforms from a body-centered cubic (bcc) structure to a face-centered cubic (fcc) structure called austeniteAustenite
Austenite is a metallic non-magnetic solid solution of iron and an alloying element. In plain-carbon steel, austenite exists above the critical eutectoid temperature of 1000 K ; 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 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 groupSymmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with Function composition as the operation. It is a subgroup of the isometry group of the space concerned....
.
Biology
X-ray crystallographyX-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 scatters into many different directions....
is the primary method for determining the molecular conformations of biological macromoleculeMacromolecule
The term macromolecule by definition implies "large molecule". In the context of biochemistry, the term may be applied to the four conventional biopolymers , as well as non-polymeric molecules with large molecular mass such as macrocycles....
s, particularly proteinProtein
Proteins are organic compounds made of amino acids arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid Residue ....
and nucleic acidNucleic acid
A nucleic acid is a macromolecule composed of chains of monomeric nucleotides. In biochemistry these molecules carry genetic information or form structures within Cell ....
s such as DNADNA
Deoxyribonucleic acid is a nucleic acid that contains the genetics instructions used in the development and functioning of all known living organisms and some viruses....
and RNARNA
Ribonucleic acid is a type of molecule that consists of a long chain of nucleotide units. Each nucleotide consists of a nucleobase, a ribose sugar, and a phosphate....
. 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 (NatureNature (journal)
Nature is a prominent scientific journal, first published on 4 November 1869. Although most scientific journals are now highly specialized, Nature is one of the few journals, along with other weekly journals such as Science and Proceedings of the National Academy of Sciences, that still publishes original research articles ac...
181, 662–666). The Protein Data BankProtein 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. . The data, typically obtained by X-ray crystallography or Protein NMR and submitted by biologists and biochemistry from around the world, are released into the public domain, and can be accessed at no charge...
(PDB) is a freely accessible repository for the structures of proteinProtein
Proteins are organic compounds made of amino acids arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid Residue ....
s and other biological macromolecules. Computer programs like RasMolRasMol
RasMol is a computer program written for molecular graphics visualization intended and used primarily for the depiction and exploration of Structural biology, such as those found in the Protein Data Bank....
or PymolPyMOL
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.
Electron crystallographyElectron crystallography
Electron crystallography is a method to determine the arrangement of atoms in solids using an electron microscope. It can complement X-ray crystallography for studies of very small crystals , both inorganic, organic and proteins, such as membrane proteins, that cannot easily form the large 3-dimensional crystals required for that process....
has been used to determine some protein structures, most notably membrane proteinMembrane 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....
s and viral capsids.
Scientists of note
See also
Further reading
Applied Computational Powder Diffraction Data Analysis
External links
Introduction to Crystallography and Mineral Crystal Systems
Crystallographic Teaching Pamphlets
Crystal Lattice Structures
Freely Available Crystallographic Software for Academia
NetSci Software Listing for Crystallography
SINCRIS Information Server for Crystallography
ORTEP a professional grade viewer for use on a PC which is based on the FORTRAN code which came from..
Vega Science Trust Interviews on Crystallography Freeview video interviews with Max Pertuz, Rober Huber and Aaron Klug.
Commission on Crystallographic Teaching, Pamphlets
Crystallography site of Steffen Weber with lots of Java Applets
IUCr Online Dictionary of Crystallography
American Crystallographic Association
Laue Measurement of Single-Crystal Turbine Blades
Ames Laboratory, US DOE Crystallography Research Resources
The source of this article is Wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.
AbsoluteAstronomy.com © 2009. All Rights Reserved.
Comments: 0