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.

Structural, Thermodynamic and Kinetic (Hysteresis) Aspects of the Enantiotropic First-Order Phase Transformations of N-Anilinophthalimide and N-(N'-Methylanilino)phthalimide

“…Using BLAF (Macicek & Yordanov, 1992) these values can be converted into a 'dummy' reduced cell with a = 5.704, b = 8.276, c = 14.114 A, ot = 74.38,/3 = 87.68, y = 75.35 °. The cell given by Barlow et al (1979) can be reduced to give a = 5.…”

K0.12Na0.54Ag0.34Nb4O9AsO4

“…Data collection: CAD-4 EXPRESS (Duisenberg, 1992;Macíček & Yordanov, 1992); cell refinement: CAD-4 EXPRESS; data reduction: XCAD4 (Harms & Wocadlo, 1995); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1998); software used to prepare material for publication: WinGX (Farrugia, 1999 (Piffard et al, 1985), être utilisé comme tamis moléculaires ou bien en catalyse hétérogène (Ledain et al, 1997), a conduit à s'intéresser aux composés à charpentes ouvertes mixtes constituées d'octaèdres MO 6 [M = Sb (Lachgar et al, 1986), Nb (Hizaoui et al, 1999), Mo (Hajji et al, 2004)] et de tétraèdres XO 4 [X = P (Zid et al, 2003), As (Harrison et al, 1994)]. C'est dans ce cadre que nous avons entrepris l'étude des systèmes A-Nb-As-O (A = alcalin, argent) dans lesquels nous avons précédemment caractérisé les phases suivantes: K 3 NbAs 2 O 9 (Zid et al, 1989), Ag 3 Nb 3 As 2 O 14 (Ben Amor & Zid, 2006), K 2 Nb 2 As 2 O 11 (Zid et al, 1988) et KNb 4 AsO 13 (Haddad et al, 1988).…”

Structure cristalline d'un nouveau dichromate organique : [C6H18N2]3[C2O4][Cr2O7]2·4 H2O

“…• troisième étape : protonation de la base Les paramètres de la maille ont été affinés par la méthode des moindres carrés portant sur les données angulaires de 25 réflexions (10,22 < θ < 14,93°) à l'aide du programme CAD4-Express [3,4]. Les intensités ont été mesurées selon les conditions indiquées dans le Tableau 1.…”