BLAF - a robust program for tracking out admittable Bravais lattice(s) from the experimental unit-cell data

Abstract

BLAF represents an original computer program to devise the Bravais lattice symmetry or possible pseudo-symmetries (with allowance for large axial and angular distortions) of an experimental unit cell. The matrix approach to symmetry formulated by Himes & Mighell [Acta Cryst. (1987). A43, 375–384] is further developed and employed to analyse admittable mappings of a lattice onto itself. Solutions of the matrix equations G = MtGM, where G is the metric tensor of the Buerger reduced lattice, are integral matrices M with det(M) = + 1 and −1 < tr(M) ≤ 3, composing the seven axial hemihedral point groups 432, 622, 422, 32, 222, 2, 1. For non-triclinic symmetries these matrices carry information about important symmetry directions in the lattice, subsequently used in building up an overall transformation matrix to find a conventional (symmetry-conditioned) unit cell. The average of the generated G tensors in accordance with the particular point-group rules is a tensor Gav bearing information about the symmetry-constrained lattice parameters. Gruber's [Acta Cryst. (1989), A45, 123–131] algorithms have been used to evaluate both Buerger cells and the Niggli cell of a triclinic lattice. BLAF is realised as a separate module suitable for incorporation in the commonly used crystallographic program packages and in the form of two subroutines: enBLAF – to tackle the lattice symmetry problem by automated single-crystal diffractometers; and rBLAF – to be used for lattice symmetry analysis in, for example, programs for autoindexing of powder data. Applications of the three modules are demonstrated in several test examples.