A Mathematician’s View of Powder Structure Analysis and its Uniqueness of Solutions

Abstract

The uniqueness of solutions is one of the conditions proposed by J. Hadamart to judge whether an inverse problem is well-posed or not. In order to reflect on ab-initio powder structure analysis and powder indexing from this aspect, we introduce several mathematical theorems and their translation into statements on the uniqueness of solutions. As another application of mathematics, a new thorough search algorithm for powder indexing is presented. It is robust to false peaks caused by impurities.