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The unit cell is defined as the smallest repeating unit having the full symmetry of the crystal structure. [2] The geometry of the unit cell is defined as a parallelepiped , providing six lattice parameters taken as the lengths of the cell edges ( a , b , c ) and the angles between them (α, β, γ).
The point symmetry of a structure can be further described as follows. Consider the points that make up the structure, and reflect them all through a single point, so that (x,y,z) becomes (−x,−y,−z). This is the 'inverted structure'. If the original structure and inverted structure are identical, then the structure is centrosymmetric.
Each crystallographic point group defines the (geometric) crystal class of the crystal. The point group of a crystal determines, among other things, the directional variation of physical properties that arise from its structure, including optical properties such as birefringency , or electro-optical features such as the Pockels effect .
Crystal faces vary in their underlying lattice density. Three faces are shown with their Miller indices. The phenomenon of the constancy of interfacial angles is important because it is an outward sign of the inherent symmetry and ordered arrangement of atoms, ions or molecules within a crystal structure.
Rotating model of the diamond cubic crystal structure 3D ball-and-stick model of a diamond lattice Pole figure in stereographic projection of the diamond lattice showing the 3-fold symmetry along the [111] direction. In crystallography, the diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as ...
Identical symmetry to the β-Po structure, distinguished based on details about the basis vectors of its unit cell. This structure can also be considered to be a distorted hcp lattice with the nearest neighbours in the same plane being approx 16% farther away [18] β-Po: A i: Rhombohedral: R 3 m (No. 166) 1 (rh.) 3 (hex.)
Crystallography ranges from the fundamentals of crystal structure to the mathematics of crystal geometry, including those that are not periodic or quasicrystals. At the atomic scale it can involve the use of X-ray diffraction to produce experimental data that the tools of X-ray crystallography can convert into detailed positions of atoms, and ...
In some cases, the full symmetry of a crystal structure is not obvious from the primitive cell, in which cases a conventional cell may be used. A conventional cell (which may or may not be primitive) is a unit cell with the full symmetry of the lattice and may include more than one lattice point.