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A crystal or crystalline solid is a
solid Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structur ...
material whose constituents (such as
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s,
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s, or ions) are arranged in a highly ordered microscopic structure, forming a
crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
that extends in all directions. In addition, macroscopic
single crystal In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "Re ...
s are usually identifiable by their geometrical shape, consisting of flat
faces The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affe ...
with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as
crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics ( condensed matter physics). The wor ...
. The process of crystal formation via mechanisms of
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 of the ...
is called
crystallization Crystallization is the process by which solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. Some ways by which crystals form are precipitating from a solution, freezing, or more rarely deposi ...
or
solidification Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liqu ...
. The word ''crystal'' derives from the
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
word (), meaning both " ice" and "
rock crystal Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...
", from (), "icy cold, frost". Examples of large crystals include
snowflake A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, which falls through the Earth's atmosphere as snow.Knight, C.; Knight, N. (1973). Snow crystals. Scientific American, vol. 228, no. ...
s,
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, b ...
s, and
table salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of salts; salt in the form of a natural crystalline mineral is known as rock salt or halite. Salt is present in vast quantitie ...
. Most inorganic solids are not crystals but
polycrystal A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
s, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most
metals A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typical ...
, rocks,
ceramics A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
, and ice. A third category of solids is
amorphous solid In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' (" ...
s, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
, wax, and many
plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adapta ...
s. Despite the name, lead crystal, crystal glass, and related products are ''not'' crystals, but rather types of glass, i.e. amorphous solids. Crystals, or crystalline solids, are often used in
pseudoscientific Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claim ...
practices such as
crystal therapy Crystal healing is a pseudoscientific alternative-medicine practice that uses semiprecious stones and crystals such as quartz, agate, amethyst or opal. Adherents of the practice claim that these have healing powers, but there is no scientific ...
, and, along with
gemstone A gemstone (also called a fine gem, jewel, precious stone, or semiprecious stone) is a piece of mineral crystal which, in cut and polished form, is used to make jewelry or other adornments. However, certain rocks (such as lapis lazuli, opal, ...
s, are sometimes associated with spellwork in
Wicca Wicca () is a modern Pagan religion. Scholars of religion categorise it as both a new religious movement and as part of the occultist stream of Western esotericism. It was developed in England during the first half of the 20th century and w ...
n beliefs and related religious movements.


Crystal structure (microscopic)

The scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pattern ...
. A crystal is a solid where the atoms form a periodic arrangement. (
Quasicrystal A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...
s are an exception, see
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor *Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ( ...
). Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a ''
polycrystalline A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
'' structure. In the final block of ice, each of the small crystals (called "
crystallite A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
s" or "grains") is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does ''not'' have a periodic arrangement of atoms, because the periodic pattern is broken at the
grain boundaries In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and therma ...
. Most macroscopic
inorganic In chemistry, an inorganic compound is typically a chemical compound that lacks carbon–hydrogen bonds, that is, a compound that is not an organic compound. The study of inorganic compounds is a subfield of chemistry known as ''inorganic chemist ...
solids are polycrystalline, including almost all
metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
s,
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain, ...
s, ice, rocks, etc. Solids that are neither crystalline nor polycrystalline, such as
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
, are called ''
amorphous solid In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' (" ...
s'', also called
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
y, vitreous, or noncrystalline. These have no periodic order, even microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the
latent heat of fusion In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state fro ...
, but forming a crystal does. A crystal structure (an arrangement of atoms in a crystal) is characterized by its ''unit cell'', a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are
stacked ''Stacked'' is an American television sitcom that aired on Fox from April 13, 2005 to January 11, 2006. Premise ''Stacked'' was described as the opposite of ''Cheers'', instead of a smart person in a "dumb" place, it is based on the concept of ...
in three-dimensional space to form the crystal. The symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries (230 is commonly cited, but this treats chiral equivalents as separate entities), called crystallographic space groups. These are grouped into 7
crystal system In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their poin ...
s, such as
cubic crystal system 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 ...
(where the crystals may form cubes or rectangular boxes, such as
halite Halite (), commonly known as rock salt, is a type of salt, the mineral (natural) form of sodium chloride ( Na Cl). Halite forms isometric crystals. The mineral is typically colorless or white, but may also be light blue, dark blue, purple, p ...
shown at right) or
hexagonal crystal system In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crysta ...
(where the crystals may form hexagons, such as ordinary water ice).


Crystal faces and shapes

Crystals are commonly recognized, macroscopically, by their shape, consisting of flat faces with sharp angles. These shape characteristics are not ''necessary'' for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is often present and easy to see.
Euhedral Euhedral crystals (also known as idiomorphic or automorphic crystals) are those that are well-formed, with sharp, easily recognised faces. The opposite is anhedral (also known as '' xenomorphic'' or ''allotriomorphic''): a rock with an anhedr ...
crystals are those that have obvious, well-formed flat faces. Anhedral crystals do not, usually because the crystal is one grain in a polycrystalline solid. The flat faces (also called
facet Facets () are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cut ...
s) of a
euhedral Euhedral crystals (also known as idiomorphic or automorphic crystals) are those that are well-formed, with sharp, easily recognised faces. The opposite is anhedral (also known as '' xenomorphic'' or ''allotriomorphic''): a rock with an anhedr ...
crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are
planes Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes' ...
of relatively low
Miller index Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers ''h'', ''k'', and ''� ...
. This occurs because some surface orientations are more stable than others (lower
surface energy In surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less ener ...
). As a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. (See diagram on right.) One of the oldest techniques in the science of
crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics ( condensed matter physics). The wor ...
consists of measuring the three-dimensional orientations of the faces of a crystal, and using them to infer the underlying
crystal symmetry In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns t ...
. A crystal's crystallographic forms are sets of possible faces of the crystal that are related by one of the symmetries of the crystal. For example, crystals of
galena Galena, also called lead glance, is the natural mineral form of lead(II) sulfide (PbS). It is the most important ore of lead and an important source of silver. Galena is one of the most abundant and widely distributed sulfide minerals. It cr ...
often take the shape of cubes, and the six faces of the cube belong to a crystallographic form that displays one of the symmetries of the isometric crystal system. Galena also sometimes crystallizes as octahedrons, and the eight faces of the octahedron belong to another crystallographic form reflecting a different symmetry of the isometric system. A crystallographic form is described by placing the Miller indices of one of its faces within brackets. For example, the octahedral form is written as , and the other faces in the form are implied by the symmetry of the crystal. Forms may be closed, meaning that the form can completely enclose a volume of space, or open, meaning that it cannot. The cubic and octahedral forms are examples of closed forms. All the forms of the isometric system are closed, while all the forms of the monoclinic and triclinic crystal systems are open. A crystal's faces may all belong to the same closed form, or they may be a combination of multiple open or closed forms. A crystal's habit is its visible external shape. This is determined by the
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pattern ...
(which restricts the possible facet orientations), the specific crystal chemistry and bonding (which may favor some facet types over others), and the conditions under which the crystal formed.


Occurrence in nature


Rocks

By volume and weight, the largest concentrations of crystals in the Earth are part of its solid
bedrock In geology, bedrock is solid rock that lies under loose material ( regolith) within the crust of Earth or another terrestrial planet. Definition Bedrock is the solid rock that underlies looser surface material. An exposed portion of be ...
. Crystals found in rocks typically range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are occasionally found. , the world's largest known naturally occurring crystal is a crystal of
beryl Beryl ( ) is a mineral composed of beryllium aluminium silicate with the chemical formula Be3Al2Si6O18. Well-known varieties of beryl include emerald and aquamarine. Naturally occurring, hexagonal crystals of beryl can be up to several ...
from Malakialina,
Madagascar Madagascar (; mg, Madagasikara, ), officially the Republic of Madagascar ( mg, Repoblikan'i Madagasikara, links=no, ; french: République de Madagascar), is an island country in the Indian Ocean, approximately off the coast of East Afric ...
, long and in diameter, and weighing . Some crystals have formed by
magmatic Magma () is the molten or semi-molten natural material from which all igneous rocks are formed. Magma is found beneath the surface of the Earth, and evidence of magmatism has also been discovered on other terrestrial planets and some natural sa ...
and
metamorphic Metamorphic rocks arise from the transformation of existing rock to new types of rock in a process called metamorphism. The original rock (protolith) is subjected to temperatures greater than and, often, elevated pressure of or more, causi ...
processes, giving origin to large masses of crystalline rock. The vast majority of
igneous rocks Igneous rock (derived from the Latin word ''ignis'' meaning fire), or magmatic rock, is one of the three main rock types, the others being sedimentary and metamorphic. Igneous rock is formed through the cooling and solidification of magma or ...
are formed from molten magma and the degree of crystallization depends primarily on the conditions under which they solidified. Such rocks as
granite Granite () is a coarse-grained ( phaneritic) intrusive igneous rock composed mostly of quartz, alkali feldspar, and plagioclase. It forms from magma with a high content of silica and alkali metal oxides that slowly cools and solidifies un ...
, which have cooled very slowly and under great pressures, have completely crystallized; but many kinds of
lava Lava is molten or partially molten rock (magma) that has been expelled from the interior of a terrestrial planet (such as Earth) or a moon onto its surface. Lava may be erupted at a volcano or through a fracture in the crust, on land or ...
were poured out at the surface and cooled very rapidly, and in this latter group a small amount of amorphous or
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
y matter is common. Other crystalline rocks, the metamorphic rocks such as
marble Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite. Marble is typically not foliated (layered), although there are exceptions. In geology, the term ''marble'' refers to metamorphose ...
s,
mica-schist Schist ( ) is a medium-grained metamorphic rock showing pronounced schistosity. This means that the rock is composed of mineral grains easily seen with a low-power hand lens, oriented in such a way that the rock is easily split into thin flakes ...
s and
quartzite Quartzite is a hard, non- foliated metamorphic rock which was originally pure quartz sandstone.Essentials of Geology, 3rd Edition, Stephen Marshak, p 182 Sandstone is converted into quartzite through heating and pressure usually related to tec ...
s, are recrystallized. This means that they were at first fragmental rocks like
limestone Limestone ( calcium carbonate ) is a type of carbonate sedimentary rock which is the main source of the material lime. It is composed mostly of the minerals calcite and aragonite, which are different crystal forms of . Limestone forms w ...
,
shale Shale is a fine-grained, clastic sedimentary rock formed from mud that is a mix of flakes of clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4) and tiny fragments (silt-sized particles) of other minerals, especiall ...
and
sandstone Sandstone is a clastic sedimentary rock composed mainly of sand-sized (0.0625 to 2 mm) silicate grains. Sandstones comprise about 20–25% of all sedimentary rocks. Most sandstone is composed of quartz or feldspar (both silicat ...
and have never been in a
molten Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which ...
condition nor entirely in solution, but the high temperature and pressure conditions of
metamorphism Metamorphism is the transformation of existing rock (the protolith) to rock with a different mineral composition or texture. Metamorphism takes place at temperatures in excess of , and often also at elevated pressure or in the presence of ch ...
have acted on them by erasing their original structures and inducing recrystallization in the solid state. Other rock crystals have formed out of precipitation from fluids, commonly water, to form druses or
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...
veins.
Evaporite An evaporite () is a water- soluble sedimentary mineral deposit that results from concentration and crystallization by evaporation from an aqueous solution. There are two types of evaporite deposits: marine, which can also be described as ocean ...
s such as
halite Halite (), commonly known as rock salt, is a type of salt, the mineral (natural) form of sodium chloride ( Na Cl). Halite forms isometric crystals. The mineral is typically colorless or white, but may also be light blue, dark blue, purple, p ...
,
gypsum Gypsum is a soft sulfate mineral composed of calcium sulfate dihydrate, with the chemical formula . It is widely mined and is used as a fertilizer and as the main constituent in many forms of plaster, blackboard or sidewalk chalk, and drywa ...
and some limestones have been deposited from aqueous solution, mostly owing to
evaporation Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. High concentration of the evaporating substance in the surrounding gas significantly slows down evaporation, such as when h ...
in arid climates.


Ice

Water-based ice in the form of
snow Snow comprises individual ice crystals that grow while suspended in the atmosphere—usually within clouds—and then fall, accumulating on the ground where they undergo further changes. It consists of frozen crystalline water throughou ...
,
sea ice Sea ice arises as seawater freezes. Because ice is less dense than water, it floats on the ocean's surface (as does fresh water ice, which has an even lower density). Sea ice covers about 7% of the Earth's surface and about 12% of the world's o ...
, and
glacier A glacier (; ) is a persistent body of dense ice that is constantly moving under its own weight. A glacier forms where the accumulation of snow exceeds its ablation over many years, often centuries. It acquires distinguishing features, such a ...
s are common crystalline/polycrystalline structures on Earth and other planets. A single
snowflake A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, which falls through the Earth's atmosphere as snow.Knight, C.; Knight, N. (1973). Snow crystals. Scientific American, vol. 228, no. ...
is a single crystal or a collection of crystals, while an
ice cube An ice cube is a small piece of ice, which is typically rectangular as viewed from above and trapezoidal as viewed from the side. Ice cubes are products of mechanical refrigeration and are usually produced to cool beverages. They may be p ...
is a
polycrystal A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
.


Organigenic crystals

Many living
organisms In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells ( cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fu ...
are able to produce crystals, for example
calcite Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratc ...
and
aragonite Aragonite is a carbonate mineral, one of the three most common naturally occurring crystal forms of calcium carbonate, (the other forms being the minerals calcite and vaterite). It is formed by biological and physical processes, including pre ...
in the case of most
mollusc Mollusca is the second-largest phylum of invertebrate animals after the Arthropoda, the members of which are known as molluscs or mollusks (). Around 85,000  extant species of molluscs are recognized. The number of fossil species is est ...
s or
hydroxylapatite Hydroxyapatite, also called hydroxylapatite (HA), is a naturally occurring mineral form of calcium apatite with the formula Ca5(PO4)3(OH), but it is usually written Ca10(PO4)6(OH)2 to denote that the crystal unit cell comprises two entities. ...
in the case of
vertebrate Vertebrates () comprise all animal taxa within the subphylum Vertebrata () ( chordates with backbones), including all mammals, birds, reptiles, amphibians, and fish. Vertebrates represent the overwhelming majority of the phylum Chordata, with ...
s.


Polymorphism and allotropy

The same group of atoms can often solidify in many different ways. Polymorphism is the ability of a solid to exist in more than one crystal form. For example, water ice is ordinarily found in the hexagonal form Ice Ih, but can also exist as the cubic Ice Ic, the
rhombohedral In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be us ...
ice II, and many other forms. The different polymorphs are usually called different '' phases''. In addition, the same atoms may be able to form noncrystalline phases. For example, water can also form
amorphous ice Amorphous ice (non-crystalline or "vitreous" ice) is an amorphous solid form of water. Common ice is a crystalline material wherein the molecules are regularly arranged in a hexagonal lattice, whereas amorphous ice has a lack of long-range ord ...
, while SiO2 can form both
fused silica Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non- crystalline) form. This differs from all other commercial glasses in which other ingredients are added which ch ...
(an amorphous glass) and
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...
(a crystal). Likewise, if a substance can form crystals, it can also form polycrystals. For pure chemical elements, polymorphism is known as
allotropy Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the ...
. For example,
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, b ...
and
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
are two crystalline forms of
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
, while
amorphous carbon Amorphous carbon is free, reactive carbon that has no crystalline structure. Amorphous carbon materials may be stabilized by terminating dangling-π bonds with hydrogen. As with other amorphous solids, some short-range order can be observed. Amor ...
is a noncrystalline form. Polymorphs, despite having the same atoms, may have wildly different properties. For example, diamond is among the hardest substances known, while graphite is so soft that it is used as a lubricant. Polyamorphism is a similar phenomenon where the same atoms can exist in more than one
amorphous solid In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' (" ...
form.


Crystallization

Crystallization is the process of forming a crystalline structure from a fluid or from materials dissolved in a fluid. (More rarely, crystals may be deposited directly from gas; see
thin-film deposition A thin film is a layer of material ranging from fractions of a nanometer (monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ap ...
and
epitaxy Epitaxy refers to a type of crystal growth or material deposition in which new crystalline layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited crystalline film is called an epit ...
.) Crystallization is a complex and extensively-studied field, because depending on the conditions, a single fluid can solidify into many different possible forms. It can form a
single crystal In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "Re ...
, perhaps with various possible phases, stoichiometries, impurities, defects, and
habits A habit (or wont as a humorous and formal term) is a routine of behavior that is repeated regularly and tends to occur subconsciously.
. Or, it can form a
polycrystal A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
, with various possibilities for the size, arrangement, orientation, and phase of its grains. The final form of the solid is determined by the conditions under which the fluid is being solidified, such as the chemistry of the fluid, the
ambient pressure Ambient or Ambiance or Ambience may refer to: Music and sound * Ambience (sound recording), also known as atmospheres or backgrounds * Ambient music, a genre of music that puts an emphasis on tone and atmosphere * ''Ambient'' (album), by Moby * ...
, the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
, and the speed with which all these parameters are changing. Specific industrial techniques to produce large single crystals (called ''
boules ''Boules'' () is a collective name for a wide range of games similar to bowls and bocce (In French: jeu or jeux, in Croatian: boćanje and in Italian: gioco or giochi) in which the objective is to throw or roll heavy balls (called in France, ...
'') include the Czochralski process and the
Bridgman technique Bridgman is a surname, and may refer to: * David Bridgman, Australian architect * Elijah Coleman Bridgman (1801–1861), American missionary in China * Frederick Arthur Bridgman (1847-1928), American artist * George Bridgman (1865-1943), anatomis ...
. Other less exotic methods of crystallization may be used, depending on the physical properties of the substance, including
hydrothermal synthesis Hydrothermal synthesis includes the various techniques of crystallizing substances from high-temperature aqueous solutions at high vapor pressures; also termed "hydrothermal method". The term " hydrothermal" is of geologic origin. Geochemists and ...
, sublimation, or simply solvent-based crystallization. Large single crystals can be created by geological processes. For example, selenite crystals in excess of 10  m are found in the Cave of the Crystals in Naica, Mexico. For more details on geological crystal formation, see above. Crystals can also be formed by biological processes, see above. Conversely, some organisms have special techniques to ''prevent'' crystallization from occurring, such as
antifreeze protein Antifreeze proteins (AFPs) or ice structuring proteins refer to a class of polypeptides produced by certain animals, plants, fungi and bacteria that permit their survival in temperatures below the freezing point of water. AFPs bind to small ...
s.


Defects, impurities, and twinning

An ''ideal'' crystal has every atom in a perfect, exactly repeating pattern. However, in reality, most crystalline materials have a variety of
crystallographic defect A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell para ...
s, places where the crystal's pattern is interrupted. The types and structures of these defects may have a profound effect on the properties of the materials. A few examples of crystallographic defects include
vacancy defect In crystallography, a vacancy is a type of point defect in a crystal where an atom is missing from one of the lattice sites.Ehrhart, P. (1991) "Properties and interactions of atomic defects in metals and alloys", chapter 2, p. 88 in ''Landolt-B� ...
s (an empty space where an atom should fit),
interstitial defect In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure. When the atom is of the same type as those alread ...
s (an extra atom squeezed in where it does not fit), and
dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to s ...
s (see figure at right). Dislocations are especially important in materials science, because they help determine the mechanical strength of materials. Another common type of crystallographic defect is an
impurity In chemistry and materials science, impurities are chemical substances inside a confined amount of liquid, gas, or solid, which differ from the chemical composition of the material or compound. Firstly, a pure chemical should appear thermody ...
, meaning that the "wrong" type of atom is present in a crystal. For example, a perfect crystal of
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, b ...
would only contain
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
atoms, but a real crystal might perhaps contain a few
boron Boron is a chemical element with the symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the '' boron group'' it has t ...
atoms as well. These boron impurities change the diamond's color to slightly blue. Likewise, the only difference between
ruby A ruby is a pinkish red to blood-red colored gemstone, a variety of the mineral corundum ( aluminium oxide). Ruby is one of the most popular traditional jewelry gems and is very durable. Other varieties of gem-quality corundum are called ...
and
sapphire Sapphire is a precious gemstone, a variety of the mineral corundum, consisting of aluminium oxide () with trace amounts of elements such as iron, titanium, chromium, vanadium, or magnesium. The name sapphire is derived via the Latin "sa ...
is the type of impurities present in a
corundum Corundum is a crystalline form of aluminium oxide () typically containing traces of iron, titanium, vanadium and chromium. It is a rock-forming mineral. It is a naturally transparent material, but can have different colors depending on the pr ...
crystal. In
semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way ...
s, a special type of impurity, called a
dopant A dopant, also called a doping agent, is a trace of impurity element that is introduced into a chemical material to alter its original electrical or optical properties. The amount of dopant necessary to cause changes is typically very low. Whe ...
, drastically changes the crystal's electrical properties.
Semiconductor device A semiconductor device is an electronic component that relies on the electronic properties of a semiconductor material (primarily silicon, germanium, and gallium arsenide, as well as organic semiconductors) for its function. Its conductivit ...
s, such as
transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch ...
s, are made possible largely by putting different semiconductor dopants into different places, in specific patterns. Twinning is a phenomenon somewhere between a crystallographic defect and a
grain boundary In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and therma ...
. Like a grain boundary, a twin boundary has different crystal orientations on its two sides. But unlike a grain boundary, the orientations are not random, but related in a specific, mirror-image way.
Mosaicity In crystallography, mosaicity is a measure of the spread of crystal plane orientations. A mosaic crystal is an idealized model of an imperfect crystal, imagined to consist of numerous small perfect crystals (crystallites) that are to some extent ra ...
is a spread of crystal plane orientations. A
mosaic crystal In crystallography, mosaicity is a measure of the spread of crystal plane orientations. A mosaic crystal is an idealized model of an imperfect crystal, imagined to consist of numerous small perfect crystals (crystallites) that are to some extent ra ...
consists of smaller crystalline units that are somewhat misaligned with respect to each other.


Chemical bonds

In general, solids can be held together by various types of
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
s, such as
metallic bond Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. It may be des ...
s,
ionic bond Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds ...
s,
covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between ato ...
s,
van der Waals bond In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and th ...
s, and others. None of these are necessarily crystalline or non-crystalline. However, there are some general trends as follows.
Metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
s are almost always polycrystalline, though there are exceptions like
amorphous metal An amorphous metal (also known as metallic glass, glassy metal, or shiny metal) is a solid metallic material, usually an alloy, with disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a high ...
and single-crystal metals. The latter are grown synthetically. (A microscopically-small piece of metal may naturally form into a single crystal, but larger pieces generally do not.)
Ionic compound In chemistry, an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. The compound is neutral overall, but consists of positively charged ions called cations and negatively charged ...
materials are usually crystalline or polycrystalline. In practice, large
salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of salts; salt in the form of a natural crystalline mineral is known as rock salt or halite. Salt is present in vast quant ...
crystals can be created by solidification of a
molten Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which ...
fluid, or by crystallization out of a solution. Covalently bonded solids (sometimes called covalent network solids) are also very common, notable examples being
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, b ...
and
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...
. Weak
van der Waals force In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and ...
s also help hold together certain crystals, such as crystalline
molecular solid A molecular solid is a solid consisting of discrete molecules. The cohesive forces that bind the molecules together are van der Waals forces, dipole-dipole interactions, quadrupole interactions, π-π interactions, hydrogen bonding, halogen bo ...
s, as well as the interlayer bonding in
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
.
Polymer A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
materials generally will form crystalline regions, but the lengths of the molecules usually prevent complete crystallization—and sometimes polymers are completely amorphous.


Quasicrystals

A
quasicrystal A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...
consists of arrays of atoms that are ordered but not strictly periodic. They have many attributes in common with ordinary crystals, such as displaying a discrete pattern in
x-ray diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
, and the ability to form shapes with smooth, flat faces. Quasicrystals are most famous for their ability to show five-fold symmetry, which is impossible for an ordinary periodic crystal (see crystallographic restriction theorem). The
International Union of Crystallography The International Union of Crystallography (IUCr) is an organisation devoted to the international promotion and coordination of the science of crystallography. The IUCr is a member of the International Council for Science (ICSU). Objectives T ...
has redefined the term "crystal" to include both ordinary periodic crystals and quasicrystals ("any solid having an essentially discrete
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
diagram"). Quasicrystals, first discovered in 1982, are quite rare in practice. Only about 100 solids are known to form quasicrystals, compared to about 400,000 periodic crystals known in 2004. The 2011
Nobel Prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...
was awarded to
Dan Shechtman Dan Shechtman ( he, דן שכטמן; born January 24, 1941)Dan Shechtman
. (PDF). Retri ...
for the discovery of quasicrystals.


Special properties from anisotropy

Crystals can have certain special electrical, optical, and mechanical properties that
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
and
polycrystal A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
s normally cannot. These properties are related to the
anisotropy Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
of the crystal, i.e. the lack of rotational symmetry in its atomic arrangement. One such property is the
piezoelectric effect Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word '' ...
, where a voltage across the crystal can shrink or stretch it. Another is
birefringence Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefri ...
, where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
,
electrical permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in r ...
, and
Young's modulus Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied ...
, may be different in different directions in a crystal. For example,
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
crystals consist of a stack of sheets, and although each individual sheet is mechanically very strong, the sheets are rather loosely bound to each other. Therefore, the mechanical strength of the material is quite different depending on the direction of stress. Not all crystals have all of these properties. Conversely, these properties are not quite exclusive to crystals. They can appear in
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
es or
polycrystal A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...
s that have been made
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
by working or
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
—for example, stress-induced birefringence.


Crystallography

''
Crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics ( condensed matter physics). The wor ...
'' is the science of measuring the
crystal structure In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pattern ...
(in other words, the atomic arrangement) of a crystal. One widely used crystallography technique is
X-ray diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
. Large numbers of known crystal structures are stored in
crystallographic database A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or ...
s.


Image gallery

File:Insulincrystals.jpg,
Insulin Insulin (, from Latin ''insula'', 'island') is a peptide hormone produced by beta cells of the pancreatic islets encoded in humans by the ''INS'' gene. It is considered to be the main anabolic hormone of the body. It regulates the metabolism ...
crystals grown in earth orbit. File:Hoar frost macro2.jpg,
Hoar frost Frost is a thin layer of ice on a solid surface, which forms from water vapor in an above-freezing atmosphere coming in contact with a solid surface whose temperature is below freezing, and resulting in a phase change from water vapor (a ga ...
: A type of ice crystal (picture taken from a distance of about 5 cm). File:Gallium crystals.jpg,
Gallium Gallium is a chemical element with the Symbol (chemistry), symbol Ga and atomic number 31. Discovered by France, French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in boron group, group 13 of the periodic table and is similar to ...
, a metal that easily forms large crystals. File:Apatite-Rhodochrosite-Fluorite-169799.jpg, An apatite crystal sits front and center on cherry-red rhodochroite rhombs, purple fluorite cubes, quartz and a dusting of brass-yellow pyrite cubes. File:Monokristalines Silizium für die Waferherstellung.jpg,
Boules ''Boules'' () is a collective name for a wide range of games similar to bowls and bocce (In French: jeu or jeux, in Croatian: boćanje and in Italian: gioco or giochi) in which the objective is to throw or roll heavy balls (called in France, ...
of
silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ...
, like this one, are an important type of industrially-produced
single crystal In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "Re ...
. File:Bornite-Chalcopyrite-Pyrite-180794.jpg, A specimen consisting of a bornite-coated chalcopyrite crystal nestled in a bed of clear quartz crystals and lustrous pyrite crystals. The bornite-coated crystal is up to 1.5 cm across. File:Calcite-millerite association.jpg, Needle-like
millerite Millerite is a nickel sulfide mineral, Ni S. It is brassy in colour and has an acicular habit, often forming radiating masses and furry aggregates. It can be distinguished from pentlandite by crystal habit, its duller colour, and general la ...
crystals partially encased in
calcite Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratc ...
crystal and oxidized on their surfaces to zaratite; from the
Devonian The Devonian ( ) is a geologic period and system of the Paleozoic era, spanning 60.3 million years from the end of the Silurian, million years ago (Mya), to the beginning of the Carboniferous, Mya. It is named after Devon, England, wh ...
Milwaukee Formation of
Wisconsin Wisconsin () is a state in the upper Midwestern United States. Wisconsin is the 25th-largest state by total area and the 20th-most populous. It is bordered by Minnesota to the west, Iowa to the southwest, Illinois to the south, Lake M ...


See also

*
Atomic packing factor In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. In atomi ...
*
Anticrystal An anticrystal is a theoretical solid that is completely disordered, making it the opposite of a crystal. The mechanical properties of even a slightly disordered solid can have more in common with an anticrystal than with a crystal. All naturall ...
*
Cocrystal Cocrystals are "solids that are crystalline single phase materials composed of two or more different molecular or ionic compounds generally in a stoichiometric ratio which are neither solvates nor simple salts." A broader definition is that cocryst ...
* Colloidal crystal *
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 of the ...
*
Crystal oscillator A crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. The oscillator frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable clock ...
*
Liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. Th ...
*
Time crystal In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is alrea ...


References


Further reading

* * * * * {{Authority control