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The crystal lattice parameters a, b, and c have the dimension of length. The three numbers represent the size of the unit cell , that is, the distance from a given atom to an identical atom in the same position and orientation in a neighboring cell (except for very simple crystal structures, this will not necessarily be distance to the nearest ...
The lengths of principal axes/edges, of unit cell and angles between them are lattice constants, also called lattice parameters or cell parameters. The symmetry properties of crystal are described by the concept of space groups. [1] All possible symmetric arrangements of particles in three-dimensional space may be described by 230 space groups.
Crystal structures are republished owing to corrections for symmetry errors, improvements of lattice and atomic parameters, and differences in diffraction technique or experimental conditions. As of 2016, there are about 1,000,000 molecule and crystal structures known and published, approximately half of them in open access .
The unit cells are specified according to six lattice parameters which are the relative lengths of the cell edges (a, b, c) and the angles between them (α, β, γ), where α is the angle between b and c, β is the angle between a and c, and γ is the angle between a and b.
Similar to the ideal hcp structure, the perfect dhcp structure should have a lattice parameter ratio of = In the real dhcp structures of 5 lanthanides (including β-Ce) / variates between 1.596 (Pm) and 1.6128 (Nd). For the four known actinides dhcp lattices the corresponding number vary between 1.620 (Bk) and 1.625 (Cf).
A lattice in which the conventional basis is primitive is called a primitive lattice, while a lattice with a non-primitive conventional basis is called a centered lattice. The choice of an origin and a basis implies the choice of a unit cell which can further be used to describe a crystal pattern.
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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. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.