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 of these crystals:
Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals. However, fcc stands for a face-centered-cubic Bravais lattice, which is not necessarily close-packed when a motif is set onto the lattice points. E.g. the diamond and the zincblende lattices are fcc but not close-packed. Each is subdivided into other variants listed below. Although the unit cells in these crystals are conventionally taken to be cubes, the primitive unit cells often are not.
The three Bravais latices in the cubic crystal system are:
Bravais lattice | Primitive cubic | Body-centered cubic | Face-centered cubic |
---|---|---|---|
Pearson symbol | cP | cI | cF |
Unit cell |
The primitive cubic lattice (cP) consists of one lattice point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom (1⁄8 × 8). [1]
The body-centered cubic lattice (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 two lattice points per unit cell (1⁄8 × 8 + 1). [1]
The face-centered cubic lattice (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 four lattice points per unit cell (1⁄8 × 8 from the corners plus 1⁄2 × 6 from the faces).
The face-centered cubic lattice is closely related to the hexagonal close packed (hcp) system, where two systems differ only in the relative placements of their hexagonal layers. The [111] plane of a face-centered cubic lattice is a hexagonal grid.
Attempting to create a base-centered cubic lattice (i.e., putting an extra lattice point in the center of each horizontal face) results in a simple tetragonal Bravais lattice.
Coordination number (CN) is the number of nearest neighbors of a central atom in the structure. [1] Each sphere in a cP lattice has coordination number 6, in a cI lattice 8, and in a cF lattice 12.
Atomic packing factor (APF) is the fraction of volume that is occupied by atoms. The cP lattice has an APF of about 0.524, the cI lattice an APF of about 0.680, and the cF lattice an APF of about 0.740.
The isometric crystal system class names, point groups (in Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation), type, examples, international tables for crystallography space group number, [2] and space groups are listed in the table below. There are a total 36 cubic space groups.
No. | Point group | Type | Example | Space groups | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Name [3] | Schön. | Intl | Orb. | Cox. | Primitive | Face-centered | Body-centered | |||
195–197 | Tetartoidal | T | 23 | 332 | [3,3]+ | enantiomorphic | Ullmannite, Sodium chlorate | P23 | F23 | I23 |
198–199 | P213 | I213 | ||||||||
200–204 | Diploidal | Th | 2/m3 (m3) | 3*2 | [3+,4] | centrosymmetric | Pyrite | Pm3, Pn3 | Fm3, Fd3 | I3 |
205–206 | Pa3 | Ia3 | ||||||||
207–211 | Gyroidal | O | 432 | 432 | [3,4]+ | enantiomorphic | Petzite | P432, P4232 | F432, F4132 | I432 |
212–214 | P4332, P4132 | I4132 | ||||||||
215–217 | Hextetrahedral | Td | 43m | *332 | [3,3] | Sphalerite | P43m | F43m | I43m | |
218–220 | P43n | F43c | I43d | |||||||
221–230 | Hexoctahedral | Oh | 4/m32/m (m3m) | *432 | [3,4] | centrosymmetric | Galena, Halite | Pm3m, Pn3n, Pm3n, Pn3m | Fm3m, Fm3c, Fd3m, Fd3c | Im3m, Ia3d |
Other terms for hexoctahedral are: normal class, holohedral, ditesseral central class, galena type.
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 demands certain bond angles.) Accordingly, the primitive cubic structure, with especially low atomic packing factor, is rare in nature, but is found in polonium. [4] [5] The bcc and fcc, with their higher densities, are both quite common in nature. Examples of bcc include iron, chromium, tungsten, and niobium. Examples of fcc include aluminium, copper, gold and silver.
Another important cubic crystal structure is the diamond cubic structure, which can appear in carbon, silicon, germanium, and tin. Unlike fcc and bcc, this structure is not a lattice, since it contains multiple atoms in its primitive cell. Other cubic elemental structures include the A15 structure found in tungsten, and the extremely complicated structure of manganese.
Compounds that consist of more than one element (e.g. binary compounds) often have crystal structures based on the cubic crystal system. Some of the more common ones are listed here. These structures can be viewed as two or more interpenetrating sublattices where each sublattice occupies the interstitial sites of the others.
One structure is the "interpenetrating primitive cubic" structure, also called a "caesium chloride" or B2 structure. This structure is often confused for a body-centered cubic structure because the arrangement of atoms is the same. However, the caesium chloride structure has a basis composed of two different atomic species. In a body-centered cubic structure, there would be translational symmetry along the [111] direction. In the caesium chloride structure, translation along the [111] direction results in a change of species. The structure can also be thought of as two separate simple cubic structures, one of each species, that are superimposed within each other. The corner of the chloride cube is the center of the caesium cube, and vice versa. [6]
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 coordination number is eight. 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. 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 halides when prepared at low temperatures or high pressures. [7] 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 space group of the caesium chloride (CsCl) structure is called Pm3m (in Hermann–Mauguin notation), or "221" (in the International Tables for Crystallography). The Strukturbericht designation is "B2". [8]
There are nearly a hundred rare earth intermetallic compounds that crystallize in the CsCl structure, including many binary compounds of rare earths with magnesium, [9] and with elements in groups 11, 12, [10] [11] and 13. Other compounds showing caesium chloride like structure are CsBr, CsI, high-temperature RbCl, AlCo, AgZn, BeCu, MgCe, RuAl and SrTl.[ citation needed ]
The space group of the rock-salt or halite (sodium chloride) structure is denoted as Fm3m (in Hermann–Mauguin notation), or "225" (in the International Tables for Crystallography). The Strukturbericht designation is "B1". [12]
In the rock-salt 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. The rock-salt structure has octahedral coordination: Each atom's nearest neighbors consist of six atoms of the opposite type, positioned like the six vertices of a regular octahedron. 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. [6]
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". [7] According to the radius ratio rule, 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 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, [13] 2.8 Å for NaCl, [14] and 3.2 Å for SnTe. [15] Most of the alkali metal hydrides and halides have the rock salt structure, though a few have the caesium chloride structure instead.
Hydrides | Fluorides | Chlorides | Bromides | Iodides | |
---|---|---|---|---|---|
Lithium | Lithium hydride | Lithium fluoride [16] | Lithium chloride | Lithium bromide | Lithium iodide |
Sodium | Sodium hydride | Sodium fluoride [16] | Sodium chloride | Sodium bromide | Sodium iodide |
Potassium | Potassium hydride | Potassium fluoride [16] | Potassium chloride | Potassium bromide | Potassium iodide |
Rubidium | Rubidium hydride | Rubidium fluoride | Rubidium chloride | Rubidium bromide | Rubidium iodide |
Caesium | Caesium hydride | Caesium fluoride | (CsCl structure) | ||
Oxides | Sulfides | Selenides | Tellurides | Polonides | |
---|---|---|---|---|---|
Magnesium | Magnesium oxide | Magnesium sulfide | Magnesium selenide [17] | Magnesium telluride [18] | (NiAs structure) |
Calcium | Calcium oxide | Calcium sulfide | Calcium selenide [19] | Calcium telluride | Calcium polonide [20] |
Strontium | Strontium oxide | Strontium sulfide | Strontium selenide | Strontium telluride | Strontium polonide [20] |
Barium | Barium oxide | Barium sulfide | Barium selenide | Barium telluride | Barium polonide [20] |
Carbides | Nitrides | |
---|---|---|
Titanium | Titanium carbide | Titanium nitride |
Zirconium | Zirconium carbide | Zirconium nitride |
Hafnium | Hafnium carbide | Hafnium nitride [46] |
Vanadium | Vanadium carbide | Vanadium nitride |
Niobium | Niobium carbide | Niobium nitride |
Tantalum | Tantalum carbide | (CoSn structure) |
Chromium | (unstable) [47] | Chromium nitride |
Many transition metal monoxides also have the rock salt structure (TiO, VO, CrO, MnO, FeO, CoO, NiO, CdO). The early actinoid monocarbides also have this structure (ThC, PaC, UC, NpC, PuC). [37]
Much like the rock salt structure, the fluorite structure (AB2) is also an Fm3m 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 4a and 8c whereas the rock-salt structure positions are 4a and 4b. [48] [49]
The space group of the Zincblende structure is called F43m (in Hermann–Mauguin notation), or 216. [50] [51] The Strukturbericht designation is "B3". [52]
The Zincblende structure (also written "zinc blende") is named after the mineral zincblende (sphalerite), one form of zinc sulfide (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 coordination: Each atom's nearest neighbors consist of four atoms of the opposite type, positioned like the four vertices of a regular tetrahedron. In zinc sulfide the ratio of zinc to sulfur is 1:1. [6] Altogether, the arrangement of atoms in zincblende structure is the same as diamond cubic structure, but with alternating types of atoms at the different lattice sites. The structure can also be described as an FCC lattice of zinc with sulfur atoms occupying half of the tetrahedral voids or vice versa. [6]
Examples of compounds with this structure include zincblende itself, lead(II) nitrate, many compound semiconductors (such as gallium arsenide and cadmium telluride), and a wide array of other binary compounds.[ citation needed ] The boron group pnictogenides usually have a zincblende structure, though the nitrides are more common in the wurtzite structure, and their zincblende forms are less well known polymorphs. [53] [54]
Fluorides | Chlorides | Bromides | Iodides | |
---|---|---|---|---|
Copper | Copper(I) fluoride | Copper(I) chloride | Copper(I) bromide | Copper(I) iodide |
Sulfides | Selenides | Tellurides | Polonides | |
---|---|---|---|---|
Beryllium | Beryllium sulfide | Beryllium selenide | Beryllium telluride | Beryllium polonide [55] [56] |
Zinc | Zinc sulfide | Zinc selenide | Zinc telluride | Zinc polonide |
Cadmium | Cadmium sulfide | Cadmium selenide | Cadmium telluride | Cadmium polonide |
Mercury | Mercury sulfide | Mercury selenide | Mercury telluride | – |
This group is also known as the II-VI family of compounds, most of which can be made in both the zincblende (cubic) or wurtzite (hexagonal) form.
Nitrides | Phosphides | Arsenides | Antimonides | |
---|---|---|---|---|
Boron | Boron nitride* | Boron phosphide | Boron arsenide | Boron antimonide |
Aluminium | Aluminium nitride* | Aluminium phosphide | Aluminium arsenide | Aluminium antimonide |
Gallium | Gallium nitride* | Gallium phosphide | Gallium arsenide | Gallium antimonide |
Indium | Indium nitride* | Indium phosphide | Indium arsenide | Indium antimonide |
This group is also known as the III-V family of compounds.
The Heusler structure, based on the structure of Cu2MnAl, is a common structure for ternary compounds involving transition metals. It has the space group Fm3m (No. 225), and the Strukturbericht designation is L21. Together with the closely related half-Heusler and inverse-Huesler compounds, there are hundreds of examples.
The space group of the iron monosilicide structure is P213 (No. 198), and the Strukturbericht designation is B20. This is a chiral 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.
Silicides | Germanides | |
---|---|---|
Manganese | Manganese monosilicide | Manganese germanide |
Iron | Iron monosilicide | Iron germanide |
Cobalt | Cobalt monosilicide | Cobalt germanide |
Chromium | Chromium(IV) silicide | Chromium(IV) germanide |
A Weaire–Phelan structure has Pm3n (223) symmetry.
It has three orientations of stacked tetradecahedrons with pyritohedral cells in the gaps. It is found as a crystal structure in chemistry where it is usually known as a "type I clathrate structure". Gas hydrates formed by methane, propane, and carbon dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are hydrogen bonded together, and the larger gas molecules are trapped in the polyhedral cages.
Caesium is a chemical element; it has symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of 28.5 °C, which makes it one of only five elemental metals that are liquid at or near room temperature. Caesium has physical and chemical properties similar to those of rubidium and potassium. It is pyrophoric and reacts with water even at −116 °C (−177 °F). It is the least electronegative stable element, with a value of 0.79 on the Pauling scale. It has only one stable isotope, caesium-133. Caesium is mined mostly from pollucite. Caesium-137, a fission product, is extracted from waste produced by nuclear reactors. It has the largest atomic radius of all elements whose radii have been measured or calculated, at about 260 picometers.
In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.
Sodium chloride, commonly known as edible salt, is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chlorine ions. It is transparent or translucent, brittle, hygroscopic, and occurs as the mineral halite. In its edible form, it is commonly used as a condiment and food preservative. Large quantities of sodium chloride are used in many industrial processes, and it is a major source of sodium and chlorine compounds used as feedstocks for further chemical syntheses. Another major application of sodium chloride is deicing of roadways in sub-freezing weather.
Caesium fluoride is an inorganic compound with the formula CsF. A hygroscopic white salt, caesium fluoride is used in the synthesis of organic compounds as a source of the fluoride anion. The compound is noteworthy from the pedagogical perspective as caesium also has the highest electropositivity of all commonly available elements and fluorine has the highest electronegativity.
In crystallography, 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 semiconductors silicon and germanium, and silicon–germanium alloys in any proportion. There are also crystals, such as the high-temperature form of cristobalite, which have a similar structure, with one kind of atom at the positions of carbon atoms in diamond but with another kind of atom halfway between those.
Caesium chloride or cesium chloride is the inorganic compound with the formula CsCl. This colorless salt is an important source of caesium ions in a variety of niche applications. Its crystal structure forms a major structural type where each caesium ion is coordinated by 8 chloride ions. Caesium chloride dissolves in water. CsCl changes to NaCl structure on heating. Caesium chloride occurs naturally as impurities in carnallite, sylvite and kainite. Less than 20 tonnes of CsCl is produced annually worldwide, mostly from a caesium-bearing mineral pollucite.
Ionic radius, rion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), with 1 Å = 100 pm. Typical values range from 31 pm (0.3 Å) to over 200 pm (2 Å).
Rubidium chloride is the chemical compound with the formula RbCl. This alkali metal halide salt is composed of rubidium and chlorine, and finds diverse uses ranging from electrochemistry to molecular biology.
In 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/molecule/atom is called a ligand. This number is determined somewhat differently for molecules than for crystals.
For elements that are solid at standard temperature and pressure the first table gives the crystalline structure of the most thermodynamically stable form(s) in those conditions. Each element is shaded by a color representing its respective Bravais lattice, except that all orthorhombic lattices are grouped together.
Yttrium boride refers to a crystalline material composed of different proportions of yttrium and boron, such as YB2, YB4, YB6, YB12, YB25, YB50 and YB66. They are all gray-colored, hard solids having high melting temperatures. The most common form is the yttrium hexaboride YB6. It exhibits superconductivity at relatively high temperature of 8.4 K and, similar to LaB6, is an electron cathode. Another remarkable yttrium boride is YB66. It has a large lattice constant (2.344 nm), high thermal and mechanical stability, and therefore is used as a diffraction grating for low-energy synchrotron radiation (1–2 keV).
In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes two crystal systems and two lattice systems. While commonly confused, the trigonal crystal system and the rhombohedral lattice system are not equivalent. In particular, there are crystals that have trigonal symmetry but belong to the hexagonal lattice.
Few compounds of californium have been made and studied. The only californium ion that is stable in aqueous solutions is the californium(III) cation. The other two oxidation states are IV (strong oxidizing agents) and II (strong reducing agents). The element forms a water-soluble chloride, nitrate, perchlorate, and sulfate and is precipitated as a fluoride, oxalate or hydroxide. If problems of availability of the element could be overcome, then CfBr2 and CfI2 would likely be stable.
Berkelium forms a number of chemical compounds, where it normally exists in an oxidation state of +3 or +4, and behaves similarly to its lanthanide analogue, terbium. Like all actinides, berkelium easily dissolves in various aqueous inorganic acids, liberating gaseous hydrogen and converting into the trivalent oxidation state. This trivalent state is the most stable, especially in aqueous solutions, but tetravalent berkelium compounds are also known. The existence of divalent berkelium salts is uncertain and has only been reported in mixed lanthanum chloride-strontium chloride melts. Aqueous solutions of Bk3+ ions are green in most acids. The color of the Bk4+ ions is yellow in hydrochloric acid and orange-yellow in sulfuric acid. Berkelium does not react rapidly with oxygen at room temperature, possibly due to the formation of a protective oxide surface layer; however, it reacts with molten metals, hydrogen, halogens, chalcogens and pnictogens to form various binary compounds. Berkelium can also form several organometallic compounds.
Cr23C6 is the prototypical compound of a common crystal structure, discovered in 1933 as part of the chromium-carbon binary phase diagram. Over 85 known compounds adopt this structure type, which can be described as a NaCl-like packing of chromium cubes and cuboctahedra.
In crystallography, interstitial sites, holes or voids are the empty space that exists between the packing of atoms (spheres) in the crystal structure.
In crystallography, a Strukturbericht designation or Strukturbericht type is a system of detailed crystal structure classification by analogy to another known structure. The designations were intended to be comprehensive but are mainly used as supplement to space group crystal structures designations, especially historically. Each Strukturbericht designation is described by a single space group, but the designation includes additional information about the positions of the individual atoms, rather than just the symmetry of the crystal structure. While Strukturbericht symbols exist for many of the earliest observed and most common crystal structures, the system is not comprehensive, and is no longer being updated. Modern databases such as Inorganic Crystal Structure Database index thousands of structure types directly by the prototype compound. These are essentially equivalent to the old Stukturbericht designations.
Potassium trichloridocuprate(II) is a salt with chemical formula KCuCl3, more properly [K+]2[Cu2Cl2−6].
Samarium compounds are compounds formed by the lanthanide metal samarium (Sm). In these compounds, samarium generally exhibits the +3 oxidation state, such as SmCl3, Sm(NO3)3 and Sm(C2O4)3. Compounds with samarium in the +2 oxidation state are also known, for example SmI2.
Protactinium compounds are compounds containing the element protactinium. These compounds usually have protactinium in the +5 oxidation state, although these compounds can also exist in the +2, +3 and +4 oxidation states.