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R = n 1 a 1 + n 2 a 2 + n 3 a 3, where n 1, n 2, and n 3 are integers and a 1, a 2, and a 3 are three non-coplanar vectors, called primitive vectors. These lattices are classified by the space group of the lattice itself, viewed as a collection of points; there are 14 Bravais lattices in three dimensions; each belongs to one lattice system only.
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base ( a by a ) and height ( c , which is different from a ).
By definition, the syntax (hkℓ) denotes a plane that intercepts the three points a 1 /h, a 2 /k, and a 3 /ℓ, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell (in the basis of the lattice vectors).
The possible screw axes are: 2 1, 3 1, 3 2, 4 1, 4 2, 4 3, 6 1, 6 2, 6 3, 6 4, and 6 5. Wherever there is both a rotation or screw axis n and a mirror or glide plane m along the same crystallographic direction, they are represented as a fraction n m {\textstyle {\frac {n}{m}}} or n/m .
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base ( a by b ) and height ( c ), such that a , b , and c are distinct.
1 p1 2 p 1: Monoclinic/inclined 3 p112 4 p11m 5 p11a 6 p112/m 7 p112/a Monoclinic/orthogonal 8 p211 9 p2 1 11 10 c211 11 pm11 12 pb11 13 cm11 14 p2/m11 15 p2 1 /m11 16 p2/b11 17 p2 1 /b11 18 c2/m11 Orthorhombic; 19 p222 20 p2 1 22 21 p2 1 2 1 2 22 c222 23 pmm2 24 pma2 25 pba2 26 cmm2 27 pm2m 28 pm2 1 b 29 pb2 1 m 30 pb2b 31 pm2a 32 pm2 1 n 33 ...
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. [2]
Brookite is the orthorhombic variant of titanium dioxide (TiO 2), which occurs in four known natural polymorphic forms (minerals with the same composition but different structure). The other three of these forms are akaogiite ( monoclinic ), anatase ( tetragonal ) and rutile ( tetragonal ).