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The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice, and is the union of the hexagonal crystal system and the trigonal crystal system. There are 52 space groups associated with it, which are exactly those whose Bravais lattice is either hexagonal or rhombohedral.
| + Hexagonal crystal family ! Bravais lattice ! Hexagonal ! Rhombohedral |
In the hexagonal family, the crystal is conventionally described by a right rhombus prism unit cell with two equal axes ( a by a), an included angle of 120° ( γ) and a height ( c, which can be different from a) perpendicular to the two base axes.
The hexagonal unit cell for the rhombohedral Bravais lattice is the R-centered cell, consisting of two additional lattice points which occupy one body diagonal of the unit cell. There are two ways to do this, which can be thought of as two notations which represent the same structure. In the usual so-called obverse setting, the additional lattice points are at coordinates (, , ) and (, , ), whereas in the alternative reverse setting they are at the coordinates (,,) and (,,). In either case, there are 3 lattice points per unit cell in total and the lattice is non-primitive.
The Bravais lattices in the hexagonal crystal family can also be described by rhombohedral axes. The unit cell is a rhombohedron (which gives the name for the rhombohedral lattice). This is a unit cell with parameters a = b = c; α = β = γ ≠ 90°. In practice, the hexagonal description is more commonly used because it is easier to deal with a coordinate system with two 90° angles. However, the rhombohedral axes are often shown (for the rhombohedral lattice) in textbooks because this cell reveals the m symmetry of the crystal lattice.
The rhombohedral unit cell for the hexagonal Bravais lattice is the D-centered cell, consisting of two additional lattice points which occupy one body diagonal of the unit cell with coordinates (, , ) and (, , ). However, such a description is rarely used.
| 18 | 1 | Hexagonal |
The hexagonal crystal family consists of two : trigonal and hexagonal. A crystal system is a set of in which the point groups themselves and their corresponding are assigned to a lattice system (see table in Crystal system#Crystal classes).
The trigonal crystal system consists of the 5 point groups that have a single three-fold rotation axis, which includes space groups 143 to 167. These 5 point groups have 7 corresponding space groups (denoted by R) assigned to the rhombohedral lattice system and 18 corresponding space groups (denoted by P) assigned to the hexagonal lattice system. Hence, the trigonal crystal system is the only crystal system whose point groups have more than one lattice system associated with their space groups.
The hexagonal crystal system consists of the 7 point groups that have a single six-fold rotation axis. These 7 point groups have 27 space groups (168 to 194), all of which are assigned to the hexagonal lattice system.
The unit cell volume is given by a2 c•sin(60°)
Among the compounds that can take the wurtzite structure are wurtzite itself (ZnS with up to 8% iron instead of zinc), silver iodide (AgI), zinc oxide (ZnO), cadmium sulfide (CdS), cadmium selenide (CdSe), silicon carbide (α-SiC), gallium nitride (GaN), aluminium nitride (AlN), boron nitride (w-BN) and other semiconductors. In most of these compounds, wurtzite is not the favored form of the bulk crystal, but the structure can be favored in some nanocrystal forms of the material.
In materials with more than one crystal structure, the prefix "w-" is sometimes added to the empirical formula to denote the wurtzite crystal structure, as in w-BN.
Each of the two individual atom types forms a sublattice which is hexagonal close-packed (HCP-type). When viewed all together, the atomic positions are the same as in lonsdaleite (hexagonal diamond). Each atom is tetrahedrally coordinated. The structure can also be described as an HCP lattice of zinc with sulfur atoms occupying half of the tetrahedral voids or vice versa.
The wurtzite structure is Centrosymmetry (i.e., lacks inversion symmetry). Due to this, wurtzite crystals, such as GaN, InN, and AlN, can have properties such as piezoelectricity and pyroelectricity, which centrosymmetric crystals lack. The polar nature of these crystals enables electronic devices such as the high electron mobility transistors (HEMT).
Compounds adopting the NiAs structure are generally the , , Antimony and of .
The following are the members of the nickeline group:http://www.mindat.org/min-2901.html Mindat.org
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