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2. Lattice constant - Wikipedia

   en.wikipedia.org/wiki/Lattice_constant

   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.

3. Fractional coordinates - Wikipedia

   en.wikipedia.org/wiki/Fractional_coordinates

   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.

4. Crystal structure - Wikipedia

   en.wikipedia.org/wiki/Crystal_structure

   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 ...

5. Lattice (order) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(order)

   A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).

6. Metric lattice - Wikipedia

   en.wikipedia.org/wiki/Metric_lattice

   Example valuation function on the cube lattice which makes it a metric lattice. In the mathematical study of order , a metric lattice L is a lattice that admits a positive valuation : a function v ∈ L → ℝ satisfying, for any a , b ∈ L , [ 1 ] v ( a ) + v ( b ) = v ( a ∧ b ) + v ( a ∨ b ) {\displaystyle v(a)+v(b)=v(a\wedge b)+v(a\vee ...

7. Lattice model (physics) - Wikipedia

   en.wikipedia.org/wiki/Lattice_model_(physics)

   Physical lattice models frequently occur as an approximation to a continuum theory, either to give an ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics.

8. Lattice (group) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(group)

   In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.

9. Hexagonal lattice - Wikipedia

   en.wikipedia.org/wiki/Hexagonal_lattice

   The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb ...