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Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the
Ancient Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...
word (; "clear ice, rock-crystal"), and (; "to write"). In July 2012, the
United Nations The United Nations (UN) is the Earth, global intergovernmental organization established by the signing of the Charter of the United Nations, UN Charter on 26 June 1945 with the stated purpose of maintaining international peace and internationa ...
recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.UN announcement "International Year of Crystallography"
iycr2014.org. 12 July 2012
Crystallography is a broad topic, and many of its subareas, such as
X-ray crystallography X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring th ...
, are themselves important scientific topics. Crystallography ranges from the fundamentals of
crystal structure In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat ...
to the mathematics of crystal geometry, including those that are not periodic or
quasicrystal A quasiperiodicity, quasiperiodic crystal, or quasicrystal, is a structure that is Order and disorder (physics), ordered but not Bravais lattice, periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks trans ...
s. At the atomic scale it can involve the use of
X-ray diffraction X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering, when there is no change in the energy of the waves. ...
to produce experimental data that the tools of
X-ray crystallography X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring th ...
can convert into detailed positions of atoms, and sometimes electron density. At larger scales it includes experimental tools such as orientational imaging to examine the relative orientations at the grain boundary in materials. Crystallography plays a key role in many areas of biology, chemistry, and physics, as well new developments in these fields.


History and timeline

Before the 20th century, the study of
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s was based on physical measurements of their geometry using a goniometer. This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the
symmetry Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant und ...
of the crystal in question. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established. The discovery of
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
s and
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s in the last decade of the 19th century enabled the determination of crystal structures on the atomic scale, which brought about the modern era of crystallography. The first X-ray diffraction experiment was conducted in 1912 by Max von Laue, while electron diffraction was first realized in 1927 in the Davisson–Germer experiment and parallel work by George Paget Thomson and Alexander Reid. These developed into the two main branches of crystallography,
X-ray crystallography X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring th ...
and
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
diffraction. The quality and throughput of solving crystal structures greatly improved in the second half of the 20th century, with the developments of customized instruments and phasing algorithms. Nowadays, crystallography is an
interdisciplinary field Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several fields such as sociology, anthropology, psychology, economi ...
, supporting theoretical and experimental discoveries in various domains. Modern-day scientific instruments for crystallography vary from laboratory-sized equipment, such as
diffractometer A diffractometer is a measuring instrument for analyzing the structure of a material from the scattering pattern produced when a beam of radiation or particles (such as X-rays or neutrons) interacts with it. Principle A typical diffractometer c ...
s and
electron microscope An electron microscope is a microscope that uses a beam of electrons as a source of illumination. It uses electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing it ...
s, to dedicated large facilities, such as photoinjectors, synchrotron light sources and
free-electron laser A free-electron laser (FEL) is a fourth generation light source producing extremely brilliant and short pulses of radiation. An FEL functions much as a laser but employs relativistic electrons as a active laser medium, gain medium instead of using ...
s.


Methodology

Crystallographic methods depend mainly on analysis of the
diffraction Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...
patterns of a sample targeted by a beam of some type.
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
s are most commonly used; other beams used include
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s or
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
s. Crystallographers often explicitly state the type of beam used, as in the terms ''
X-ray diffraction X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering, when there is no change in the energy of the waves. ...
,
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 Neutron temperature, thermal or ...
'' and '' electron diffraction''. These three types of radiation interact with the specimen in different ways. * X-rays interact with the spatial distribution of electrons in the sample. * Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition the
magnetic moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...
of neutrons is non-zero, so they are also scattered by
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
s. When neutrons are scattered from
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
-containing materials, they produce diffraction patterns with high noise levels, which can sometimes be resolved by substituting
deuterium Deuterium (hydrogen-2, symbol H or D, also known as heavy hydrogen) is one of two stable isotopes of hydrogen; the other is protium, or hydrogen-1, H. The deuterium nucleus (deuteron) contains one proton and one neutron, whereas the far more c ...
for hydrogen. * Electrons are
charged particle In physics, a charged particle is a particle with an electric charge. For example, some elementary particles, like the electron or quarks are charged. Some composite particles like protons are charged particles. An ion, such as a molecule or atom ...
s and therefore interact with the total charge distribution of both the
atomic nuclei The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. Aft ...
and the electrons of the sample. It is hard to focus x-rays or neutrons, but since electrons are charged they can be focused and are used in
electron microscope An electron microscope is a microscope that uses a beam of electrons as a source of illumination. It uses electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing it ...
to produce magnified images. There are many ways that
transmission electron microscopy Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a g ...
and related techniques such as scanning transmission electron microscopy, high-resolution electron microscopy can be used to obtain images with in many cases atomic resolution from which crystallographic information can be obtained. There are also other methods such as
low-energy electron diffraction Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of single crystal, single-crystalline materials by bombardment with a collimated beam of low-energy electrons (30–200 eV) and observation o ...
, low-energy electron microscopy and reflection high-energy electron diffraction which can be used to obtain crystallographic information about surfaces.


Applications in various areas


Materials science

Crystallography is used by materials scientists to characterize different materials. 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 A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in Crystal, crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the Crysta ...
s. Most materials do not occur as a single crystal, but are poly-crystalline in nature (they exist as an aggregate of small crystals with different orientations). As such, powder diffraction techniques, which take diffraction patterns of samples with a large number of crystals, play an important role in structural determination. Other physical properties are also linked to crystallography. For example, the minerals in
clay Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolinite, ). Most pure clay minerals are white or light-coloured, but natural clays show a variety of colours from impuriti ...
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. Crystallographic studies help elucidate the relationship between a material's structure and its properties, aiding in developing new materials with tailored characteristics. This understanding is crucial in various fields, including metallurgy, geology, and materials science. Advancements in crystallographic techniques, such as electron diffraction and X-ray crystallography, continue to expand our understanding of material behavior at the atomic level. In another example,
iron Iron is a chemical element; it has symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, forming much of Earth's o ...
transforms from a
body-centered cubic In crystallography, the cubic (or isometric) crystal system is a crystal system where the Crystal structure#Unit cell, unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There ...
(bcc) structure called ferrite to a
face-centered cubic In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties o ...
(fcc) structure called austenite when it is heated. The fcc structure is a close-packed structure unlike the bcc structure; thus the volume of the iron decreases when this transformation occurs. Crystallography is useful in phase identification. When manufacturing or using a material, it is generally desirable to know what compounds and what phases are present in the material, as their composition, structure and proportions will influence the material's properties. Each phase has a characteristic arrangement of atoms. X-ray or neutron diffraction can be used to identify which structures 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 is related to
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...
.


Biology

X-ray crystallography X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring th ...
is the primary method for determining the molecular conformations of biological
macromolecule A macromolecule is a "molecule of high relative molecular mass, the structure of which essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass." Polymers are physi ...
s, particularly
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metab ...
and
nucleic acid Nucleic acids are large biomolecules that are crucial in all cells and viruses. They are composed of nucleotides, which are the monomer components: a pentose, 5-carbon sugar, a phosphate group and a nitrogenous base. The two main classes of nuclei ...
s such as
DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...
and
RNA Ribonucleic acid (RNA) is a polymeric molecule that is essential for most biological functions, either by performing the function itself (non-coding RNA) or by forming a template for the production of proteins (messenger RNA). RNA and deoxyrib ...
. The first crystal structure of a macromolecule was solved in 1958, a three-dimensional model of the myoglobin molecule obtained by X-ray analysis. 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 even off many light isotopes, including hydrogen and deuterium. Electron diffraction has been used to determine some protein structures, most notably membrane proteins and viral capsids. Macromolecular structures determined through X-ray crystallography (and other techniques) are housed in the
Protein Data Bank The Protein Data Bank (PDB) is a database for the three-dimensional structural data of large biological molecules such as proteins and nucleic acids, which is overseen by the Worldwide Protein Data Bank (wwPDB). This structural data is obtained a ...
(PDB)–a freely accessible repository for the structures of proteins and other biological macromolecules. There are many molecular graphics codes available for visualising these structures.


Notation

* Coordinates in ''square
bracket A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. They come in four main pairs of shapes, as given in the box to the right, which also gives their n ...
s'' such as 00/nowiki> 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 00 10 01/nowiki> 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 to the (hkl) plane is the direction kl but in lower-symmetry cases, the normal to (hkl) is not parallel to kl * Indices in ''curly brackets'' or ''braces'' such as denote a family of planes and their normals. In cubic materials the symmetry makes them equivalent, just as the way angle brackets denote a family of directions. In non-cubic materials, is not necessarily perpendicular to .


Reference literature

The ''International Tables for Crystallography'' is an eight-book series that outlines the standard notations for formatting, describing and testing crystals. The series contains books that covers analysis methods and the mathematical procedures for determining organic structure through x-ray crystallography, electron diffraction, and neutron diffraction. The International tables are focused on procedures, techniques and descriptions and do not list the physical properties of individual crystals themselves. Each book is about 1000 pages and the titles of the books are: :Vol A - ''Space Group Symmetry'', :Vol A1 - ''Symmetry Relations Between Space Groups'', :Vol B - ''Reciprocal Space'', :Vol C - ''Mathematical, Physical, and Chemical Tables'', :Vol D - ''Physical Properties of Crystals'', :Vol E - ''Subperiodic Groups'', :Vol F - ''Crystallography of Biological Macromolecules'', and :Vol G - ''Definition and Exchange of Crystallographic Data''.


Notable scientists


See also

* Atomic packing factor *
Crystal structure In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat ...
* Crystallographer * Crystallographic database * Crystallographic point group *
Crystallographic group In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...
* Dana classification system * Electron crystallography * Electron diffraction * Fractional coordinates *
Low-energy electron diffraction Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of single crystal, single-crystalline materials by bombardment with a collimated beam of low-energy electrons (30–200 eV) and observation o ...
* Neutron crystallography * Neutron diffraction at OPAL * Neutron diffraction at the ILL * NMR crystallography *
Point group In geometry, a point group is a group (mathematics), mathematical group of symmetry operations (isometry, isometries in a Euclidean space) that have a Fixed point (mathematics), fixed point in common. The Origin (mathematics), coordinate origin o ...
* Precession electron diffraction *
Quasicrystal A quasiperiodicity, quasiperiodic crystal, or quasicrystal, is a structure that is Order and disorder (physics), ordered but not Bravais lattice, periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks trans ...
* Reflection high-energy electron diffraction *
Space group In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...
*
Symmetric group In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric grou ...
* Timeline of crystallography *
Transmission electron microscopy Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a g ...
*
X-ray crystallography X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring th ...


References


External links


Free book, Geometry of Crystals, Polycrystals and Phase Transformations

American Crystallographic Association






{{Authority control Chemistry Condensed matter physics Instrumental analysis Materials science Neutron-related techniques Synchrotron-related techniques