enhetcellens

Enhetcellens, in Swedish crystallography, refers to the unit cell: the smallest repeating unit that, by translations along three independent vectors, builds the entire crystal lattice. Its geometry is defined by lattice parameters a, b, c and angles α, β, γ. The unit cell establishes the periodicity and symmetry of the crystal and provides a convenient description of atom positions within the lattice.

Unit cells can be primitive or centered. Based on lattice centering they give rise to the 14 Bravais lattices. Common centering types include primitive (P), body-centered (I), and face-centered (F); others such as base-centered (C) occur in certain crystal systems. The choice of cell is not unique: multiple conventional cells can describe the same lattice; the choice often reflects symmetry and convenience for visualization.

Inside the unit cell, atoms occupy fractional coordinates relative to the cell vectors; these positions, together with the lattice, constitute the basis. The full crystal is produced by repeating the basis via all lattice translations. The number Z of formula units per cell is used to relate cell content to macroscopic properties.

Volume of the unit cell is V = abc sqrt(1 - cos^2 α - cos^2 β - cos^2 γ + 2 cos α cos β cos γ). The density ρ of the crystal can be computed as ρ = Z M / (N_A V), where M is the molar mass and N_A is Avogadro's number.

Unit cells are determined experimentally by diffraction techniques, notably X-ray diffraction, sometimes complemented by electron or neutron diffraction. Knowledge of the unit cell and the basis is central to crystallography, materials science, and solid-state chemistry for understanding structure–property relationships.