TheInfoList

In
crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek language, Greek words ''crystallon'' "cold drop, frozen drop" ...

, the cubic (or isometric) crystal system is a
crystal system In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek language, Greek words ''crystallon'' "col ...
where the
unit cell In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space t ...

is in the shape of a
cube In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...

. This is one of the most common and simplest shapes found in
crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformatio ...

s and
mineral In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. (2 ...

s. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Note that although the ''unit cell'' in these crystals is conventionally taken to be a cube, the primitive unit cell often is not.

Bravais lattices

The three Bravais lattices in the cubic crystal system are: The primitive cubic system (cP) consists of one lattice point on each corner of the cube. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom ( × 8). The body-centered cubic system (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell ( × 8 + 1). The face-centered cubic system (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell ( × 8 from the corners plus  × 6 from the faces). Each sphere in a cF lattice has
coordination numberIn chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/m ...

12. Coordination number is the number of nearest neighbours of a central atom in the structure. The face-centered cubic system is closely related to the
hexagonal close packed In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or Lattice (group), lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fractio ...
(hcp) system, where two systems differ only in the relative placements of their hexagonal layers. The 11plane of a face-centered cubic system is a hexagonal grid. Attempting to create a C-centered cubic crystal system (i.e., putting an extra lattice point in the center of each horizontal face) would result in a simple
tetragonal In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, froze ...
Bravais lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of Translation operator (quantum mechanics)#Discrete Translational Symmetry, discrete translation operations described in t ...
.

Crystal classes

The ''isometric crystal system'' class names,
point groups In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space tha ...
(in Schönflies notation,
Hermann–Mauguin notationIn geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that ...
,
orbifold In the mathematical disciplines of topology s, which have only one surface and one edge, are a kind of object studied in topology. In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (nu ...
, and
Coxeter notation In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space tha ...
), type, examples, International Tables for Crystallography space group number, and
space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchan ...
s are listed in the table below. There are a total 36 cubic space groups. Other terms for hexoctahedral are: normal class, holohedral, ditesseral central class,
galena Galena, also called lead glance, is the natural mineral form of lead(II) sulfide Lead is a chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scienti ...

type.

Voids in the unit cell

Voids in the unit cell are also known as interstitial sites or holes. They are the empty space that exists between the packing of atoms (spheres) in the unit cells. The holes are easy to see if you try to pack circles together. No matter how close you get them or how you arrange them, you will have empty space in between. The same is true in a unit cell, no matter how the atoms are arranged, there will be interstitial sites present between the atoms. These sites or holes can be filled with other atoms.  The picture with packed circles is only a 2D representation.  In a crystal lattice, the atoms (spheres) would be packed in a 3D arrangement.  This results in different shaped interstitial sites depending on the arrangement of the atoms in the lattice. A simple cubic unit cell, with stacks of atoms arranged as if at the eight corners of a cube would form a single cubic hole or void in the center. A close packed unit cell, both face-centered cubic and hexagonal close packed, can form two different shaped holes.  Looking at the three green spheres in the hexagonal packing illustration, they form a triangle shaped hole.  If an atom is arranged on top of this triangular hole it forms a tetrahedral interstitial hole. If the three atoms in the layer above are rotated and their triangular hole sits on top of this one, it forms an octahedral interstitial hole. In a close-packed structure there are 4 atoms per unit cell and it will have 4 octahedral voids (1:1 ratio) and 8 tetrahedral voids (1:2 ratio) per unit cell. The tetrahedral void is smaller in size and could fit an atom with a radius 0.225 times the size of the atoms making up the lattice.  An octahedral void could fit an atom with a radius 0.441 times the size of the atoms making up the lattice. An atom that fills this empty space could be larger than this ideal radius ratio, which would lead to a distorted lattice due to pushing out the surrounding atoms, but it cannot be smaller than this ratio. A body-centered
cubic Cubic may refer to: Science and mathematics * Cube (algebra) In arithmetic and algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathema ...

unit cell has six
octahedral In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space ...

voids located at the center of each face of the unit cell, and twelve further ones located at the midpoint of each edge of the same cell, for a total of six net octahedral voids. Additionally, there are 24
tetrahedral In , a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular , is a composed of four , six straight , and four . The tetrahedron is the simplest of all the ordinary and the only one that has fewer than 5 faces. The t ...

voids located in a square spacing around each octahedral void, for a total of twelve net tetrahedral voids. These tetrahedral voids are not local maxima and are not technically voids, but they do occasionally appear in multi-atom unit cells. One important characteristic of a crystalline structure is its
atomic packing factorIn crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, frozen dr ...
. This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts on the next. The atomic packing factor is the proportion of space filled by these spheres. Assuming one atom per lattice point, in a primitive cubic lattice with cube side length ''a'', the sphere radius would be and the atomic packing factor turns out to be about 0.524 (which is quite low). This means that the volume of the unit cell actually occupied by atoms is only 52.4%. Similarly, in a ''bcc'' lattice, the atomic packing factor is 0.680, and in ''fcc'' it is 0.740. The ''fcc'' value is the highest theoretically possible value for any lattice, although there are other lattices which also achieve the same value, such as hexagonal close packed (''hcp'') and one version of tetrahedral ''bcc''. As a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the
orbital hybridization In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they unde ...
demands certain bond angles.) Accordingly, the primitive cubic structure, with especially low atomic packing factor, is rare in nature, but is found in
polonium Polonium is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical eleme ...

. The ''bcc'' and ''fcc'', with their higher densities, are both quite common in nature. Examples of ''bcc'' include
iron Iron () is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behav ...

,
chromium Chromium is a chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science tha ...

,
tungsten Tungsten, or wolfram, is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, ch ...

, and
niobium Niobium, also known as columbium, is a chemical element with the Symbol (chemistry), symbol Nb (formerly Cb) and atomic number 41. Niobium is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs scale of mineral har ...

. Examples of ''fcc'' include
aluminium Aluminium (aluminum in and ) is a with the  Al and  13. Aluminium has a density lower than those of other common , at approximately one third that of . It has a great affinity towards , and of on the surface when exposed to air ...

,
copper Copper is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elem ...

,
gold Gold is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elemen ...

and
silver Silver is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical ele ...

.

Multi-element compounds

Compounds that consist of more than one element (e.g.
binary compound In materials chemistry, a binary phase or binary compound is a chemical compound containing two different elements. Some binary phase compounds are molecular, e.g. carbon tetrachloride (CCl4). More typically binary phase refers to extended solids ...
s) often have crystal structures based on a cubic crystal system. Some of the more common ones are listed here.

Caesium chloride structure

One structure is the "interpenetrating primitive cubic" structure, also called the "caesium chloride" structure. This structure is often confused for a body-centered cubic structure, because the arrangement of atoms is the same. The true structure is shown in the graphic showing two individual primitive cubic structures that are superimposed within each other with the corner of one structure in the center of the cube of the other structure.  It helps to convince yourself that it is not body-centered cubic because there is no translational symmetry along the ½, ½, ½, plane, the chloride would be translated into a cesium, not another chloride. It works the same way for the NaCl structure described in the next section.  If you take out the Cl atoms, the leftover Na atoms still form an FCC structure, not a simple cubic structure. In the unit cell of CsCl, each ion is at the center of a cube of ions of the opposite kind, so the co - ordination number is eight. Altogether, the arrangement of atoms is the same as body-centered cubic, but with alternating types of atoms at the different lattice sites. Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its cubic void. In addition to caesium chloride itself, the structure also appears in certain other
alkali halidesAlkali metal halides, or alkali halides, are the family of inorganic compounds with the chemical formula MX, where M is an alkali metal and X is a halogen. These compounds are the often commercially significant sources of these metals and halides. T ...
when prepared at low temperatures or high pressures.Seitz, ''Modern Theory of Solids'' (1940), p.49 Generally, this structure is more likely to be formed from two elements whose ions are of roughly the same size (for example, ionic radius of Cs+ = 167 pm, and Cl = 181 pm). The
coordination numberIn chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/m ...

of each atom in the structure is 8: the central cation is coordinated to 8 anions on the corners of a cube as shown, and similarly, the central anion is coordinated to 8 cations on the corners of a cube. The
space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchan ...
of the
caesium chloride Caesium chloride or cesium chloride is the inorganic compound In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, struc ...

(CsCl) structure is called Pmm (in
Hermann–Mauguin notationIn geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that ...
), or "221" (in the International Tables for Crystallography). The Strukturbericht designation is "B2". Other compounds showing caesium chloride like structure are ,
CsI CSI may refer to: Places * Chhatrapati Shivaji International Airport Chhatrapati is a royal title from the Indian subcontinent that was mainly used by the Marathas. It is often taken to be the equivalent of emperor An emperor (from la, im ...
, high-temperature
RbCl Ribulose-1,5-bisphosphate carboxylase-oxygenase, commonly known by the abbreviations RuBisCo, rubisco, RuBPCase, or RuBPco, is an enzyme involved in the first major step of carbon fixation, a process by which atmospheric carbon dioxide is converte ...
, AlCo, AgZn, BeCu, MgCe, RuAl and SrTl.

Rock-salt structure

The
space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchan ...
of the rock-salt (NaCl) structure is called Fmm (in
Hermann–Mauguin notationIn geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that ...
), or "225" (in the International Tables for Crystallography). The Strukturbericht designation is "B1". In the rock-salt or
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salt (chemistry), salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With Molar mass, molar ...
(
halite Halite (), commonly known as rock salt, is a type of salt Salt is a mineral In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition a ...

) structure, each of the two atom types forms a separate face-centered cubic lattice, with the two lattices interpenetrating so as to form a 3D checkerboard pattern. Earlier it was stated that there is one octahedral hole per atom in a cubic close packed structure.  In sodium chloride there is a 1:1 ratio of sodium to chlorine atoms.  The structure can also be described as an FCC lattice of sodium with chlorine occupying each octahedral void or vice versa. Examples of compounds with this structure include sodium chloride itself, along with almost all other alkali halides, and "many divalent metal oxides, sulfides, selenides, and tellurides". More generally, this structure is more likely to be formed if the cation is somewhat smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732). The coordination number of each atom in this structure is 6: each cation is coordinated to 6 anions at the vertices of an
octahedron In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral tri ...

, and similarly, each anion is coordinated to 6 cations at the vertices of an octahedron. The interatomic distance (distance between cation and anion, or half the unit cell length ''a'') in some rock-salt-structure crystals are: 2.3 Å (2.3 × 10−10 m) for NaF, 2.8 Å for NaCl, and 3.2 Å for SnTe. Most of the
alkali metal The alkali metals consist of the chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structur ...
hydride In chemistry, a hydride is formally the anion of hydrogen, H−. The term is applied loosely. At one extreme, all chemical compound, compounds containing covalent bond, covalently bound H atoms are called hydrides: water (H2O) is a hydride of o ...

s and
halide A halide is a binary phase, of which one part is a halogen atom and the other part is an chemical element, element or radical (chemistry), radical that is less electronegative (or more electropositive) than the halogen, to make a, e.g., fluoride, ...
s have the rock salt structure, though a few have the
caesium chloride Caesium chloride or cesium chloride is the inorganic compound In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, struc ...

structure instead. Other compounds showing rock salt like structure are MgO, PbS, AgF, AgCl, AgBr and ScN.

Fluorite structure

Much like the rock salt structure, the
fluorite structureIn solid state chemistry, the fluorite structure refers to a common motif for compounds with the formula MX2. The X ions occupy the eight tetrahedral interstitial sites whereas M ions occupy the regular sites of a face-centered cubic 200px, A netwo ...

(AB2) is also an Fmm structure but has 1:2 ratio of ions. The anti-fluorite structure is nearly identical, except the positions of the anions and cations are switched in the structure. They are designated
Wyckoff positions In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, frozen d ...
4a and 8c whereas the rock-salt structure positions are 4a and 4b.

Zincblende structure

The
space group In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchan ...
of the Zincblende structure is called F3m (in
Hermann–Mauguin notationIn geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that ...
), or 216. The Strukturbericht designation is "B3".The Zincblende (B3) Structure
The Zincblende structure (also written "zinc blende") is named after the mineral zincblende (
sphalerite Sphalerite is a sulfide mineral The sulfide minerals are a class of s containing (S2−) or (S22−) as the major . Some sulfide minerals are economically important as metal s. The sulfide class also includes the , the , the , the , the bi ...

), one form of
zinc sulfide Zinc sulfide (or zinc sulphide) is an inorganic compound 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. However, the distinction is not ...

(β-ZnS). As in the rock-salt structure, the two atom types form two interpenetrating face-centered cubic lattices. However, it differs from rock-salt structure in how the two lattices are positioned relative to one another. The zincblende structure has
tetrahedral In , a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular , is a composed of four , six straight , and four . The tetrahedron is the simplest of all the ordinary and the only one that has fewer than 5 faces. The t ...

coordination Coordination may refer to: * Coordination (linguistics) In linguistics, coordination is a complex syntactic In linguistics, syntax () is the set of rules, principles, and processes that govern the structure of Sentence (linguistics), sentence ...

: Each atom's nearest neighbors consist of four atoms of the opposite type, positioned like the four vertices of a
regular tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular Pyramid (geometry), pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (g ...
. Earlier it was mentioned that there are 2 tetrahedral interstitial sites per atom in an FCC structure, but in zinc sulfide the ratio of zinc to sulfur is 1:1.  That is explained by the fact that not all of the interstitial sites have to be occupied.   In the zincblende structure, only half of the tetrahedral voids will be filled. Altogether, the arrangement of atoms in zincblende structure is the same as
diamond cubic The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, including α-tin, the se ...
structure, but with alternating types of atoms at the different lattice sites. Examples of compounds with this structure include zincblende itself,
lead(II) nitrate Lead(II) nitrate is an inorganic compound In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, prop ...
, many compound semiconductors (such as
gallium arsenide 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 ta ...

and
cadmium telluride Cadmium telluride (CdTe) is a stable crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a ...
), and a wide array of other binary compounds.

Iron monosilicide structure

The space group of the iron monosilicide structure is P213 (No. 198), and the Strukturbericht designation is B20. This is a
chiral Chirality is a property of important in several branches of science. The word ''chirality'' is derived from the (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from its ; that is, i ...
structure, and is sometimes associated with helimagnetic properties. There are four atoms of each element for a total of eight atoms in the unit cell. Examples occur among the transition metal silicides and germanides, as well as a few other compounds such as gallium palladide.

Weaire–Phelan structure

The
Weaire–Phelan structure In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that ...
has Pmn (223) symmetry. It has 3 orientations of stacked
tetradecahedron 240px, A tetradecahedron with ''D2d'' symmetry, existing in the Weaire–Phelan structure A tetradecahedron is a polyhedron In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -me ...
s with cells in the gaps. It is found as a
crystal structure In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek language, Greek words ''crystallon'' "co ...

in
chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

where it is usually known as the "Type I
clathrate A clathrate is a chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched a ...
structure".
Gas hydrates Clathrate hydrates, or gas hydrates, clathrates, hydrates, etc., are crystalline water-based solids physically resembling ice, in which small Chemical polarity, non-polar molecules (typically gases) or Chemical polarity, polar molecules with large ...
formed by methane, propane, and carbon dioxide at low temperatures have a structure in which
water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known li ...

molecules lie at the nodes of the Weaire–Phelan structure and are
hydrogen bond A hydrogen bond (or H-bond) is a primarily electrostatic Electrostatics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department ...

ed together, and the larger gas molecules are trapped in the polyhedral cages.

*
Atomium The Atomium ( ) is a landmark building in Brussels Brussels (french: Bruxelles or ; nl, Brussel ), officially the Brussels-Capital Region (All text and all but one graphic show the English name as Brussels-Capital Region.) (french: link=n ...

: building which is a model of a ''bcc'' unit cell, with vertical body diagonal. *
Crystal structure In crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek language, Greek words ''crystallon'' "co ...

*
Dislocations In materials science The interdisciplinary field of materials science, also commonly termed materials science and engineering, covers the design and discovery of new materials, particularly solids. The intellectual origins of materials scienc ...

*
Reciprocal lattice In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is usually a periodic spatial fun ...