The use of Buerger's algorithm in crystallographic calculations

Abstract

SummaryBuerger (Zeits. Krist., 1957, vol. 109, p. 42) describes an algorithm for deriving data for the reduced unit cell from those obtained for an arbitrary crystal setting. It is shown that indices can be added to the algorithm so that one also derives the transformation matrix for the change of setting. Conversely, a known transformation matrix forms a set of instructions for using the algorithm to transform unit cell data, whether X-ray or morphological, from the initial to the final setting, One can thus use the algorithm to calculate the lengths of any unit cell vectors and the angles between them, and, using reciprocal cell data, to obtain any interfacial angles. Worked examples of these applications show that the proposed calculation method is shorter and simpler than those at present accepted.