Premium
The conversion of reduced cells to conventional cells by algebraic means
Author(s) -
Bucksch R.
Publication year - 1971
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889871006526
Subject(s) - simple (philosophy) , orthogonality , transformation (genetics) , transformation matrix , matrix (chemical analysis) , algebraic number , quadratic equation , mathematics , algebra over a field , algebraic expression , pure mathematics , mathematical analysis , physics , chemistry , geometry , classical mechanics , philosophy , biochemistry , chromatography , kinematics , epistemology , gene
A simple vector algebraic method is presented which permits the symmetry of a primitive reduced cell to be recognized by systematically checking the coefficients of its quadratic form for only seven conditions and deriving from them orthogonality relations among certain lattice vectors. In this way also the matrix of the transformation of the reduced cell to the conventional cell is found. The centring properties of the conventional cell can be derived from this matrix with the aid of simple criteria. The use of rather lengthy tables of special reduced forms and of the corresponding transformation matrices which are often unreliable owing to printing errors is no longer necessary.