Lattice

From Online Dictionary of Crystallography

Jump to: navigation, search

مشبك (Ar). Réseau (Fr). Gitter (Ge). Reticolo (It). 格子 (Ja). Решётка (Ru). Red (Sp).


A lattice in the vector space Vn is the set of all integral linear combinations t = u1a1 + u2a2 + ... + ukak of a system (a1, a2, ... , ak) of linearly independent vectors in Vn.

If k = n, i.e. if the linearly independent system is a basis of Vn, the lattice is often called a full lattice. In crystallography, lattices are almost always full lattices, therefore the attribute 'full' is usually suppressed.

See also

  • Crystallographic basis
  • Chapters 1.3.2 and 3.1 of International Tables for Crystallography, Volume A, 6th edition