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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.
At near-IR wavelengths, the characteristics of the 1.65, 3.1, and 4.53 μm water absorption lines are dependent on the ice temperature and crystal order. [161] The peak strength of the 1.65 μm band as well as the structure of the 3.1 μm band are particularly useful in identifying the crystallinity of water ice.
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.
In mathematics, a layer group is a three-dimensional extension of a wallpaper group, with reflections in the third dimension.It is a space group with a two-dimensional lattice, meaning that it is symmetric over repeats in the two lattice directions.