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Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.
Lattice models in biophysics represent a class of statistical-mechanical models which consider a biological macromacromolecule (such as DNA, protein, actin, ...
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 positions of particles inside the unit cell are described by the fractional coordinates ( x i , y i , z i ) along the cell edges, measured from a reference ...
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by n cells are counted as 1 / n of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain 1 / 8 of each of them. [3]
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.
Lattice proteins are highly simplified models of protein-like heteropolymer chains on lattice conformational space which are used to investigate protein folding. [1] Simplification in lattice proteins is twofold: each whole residue ( amino acid ) is modeled as a single "bead" or "point" of a finite set of types (usually only two), and each ...
An example of the tetragonal crystals, wulfenite Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system. In crystallography, the tetragonal crystal system is one of the 7 crystal systems.
For the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism; [1] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes.