An Ab-Initio Indexing Method Using Conway’ s Topograph and Mathematical Ideas Behind It

Abstract

Conway’s topograph is a graph derived of the lattice-basis reduction theory, and provides an approachable visualization of the theory. The author used the topograph to visualize, simplify, and speedup the algorithms of the powder indexing software CONOGRAPH, and then applied the same ideas to ab-initio indexing of electron backscatter diffraction (EBSD) images. The purpose of this paper is to illustrate how the topograph and the reduction theory can be used in multiple ways in computational crystallography, which has been rarely covered in the course of mathematical crystallography, unlike the use of space groups.