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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.
An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics. However, digital physics considers nature fundamentally discrete at the Planck scale, which imposes upper limit to the density of information , aka Holographic principle .
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 ...
The vector lattice (lattice) is defined as the infinite set consisting of all of the translation vectors of a crystal pattern. Each of the vectors in the vector lattice are called lattice vectors. From the vector lattice it is possible to construct a point lattice.
In either case, one needs to choose the three lattice vectors a 1, a 2, and a 3 that define the unit cell (note that the conventional unit cell may be larger than the primitive cell of the Bravais lattice, as the examples below illustrate). Given these, the three primitive reciprocal lattice vectors are also determined (denoted b 1, b 2, and b 3).
Examples of quantitative properties and qualitative phenomena that are explored with interatomic potentials include lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behavior, as well as chemical reactions.
Here, a A (1-x) B x is the lattice parameter of the solid solution, a A and a B are the lattice parameters of the pure constituents, and x is the molar fraction of B in the solid solution. Vegard's law is seldom perfectly obeyed; often deviations from the linear behavior are observed. A detailed study of such deviations was conducted by King. [3]
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]