The minimum distance parametrization of crystal lattices

Abstract

A general parametrization for all three-dimensional crystal lattices is presented in this paper which guarantees that the three primitive vectors constructed by the parametrization are the three shortest possible, linearly independent lattice vectors existing in the whole lattice. The parameter space of this so-called minimum distance parametrization (MDP) can easily be confined to contain only lattices whose shortest distance between lattice points is not smaller than a given arbitrary length. Together with the also provided extension to general crystal structures the MDP represents a means to parametrize all (and only those) crystal structures allowed for hard core particles.