Converse-transformation analysis

Converse-transformation theory and NIST*LATTICE open a new approach to study many theoretical and practical problems in crystallography. In this approach a new operator, the converse-transformation operator, is defined. The focus of this approach is based on the calculation of groups of matrices relating two lattices and subsequent analysis of these matrices to deduce crystallographic relationships. An efficient algorithm has been designed that has the ability to find all matrices (H) that relate ANY two cells (no matter how skewed) to within any specified tolerances (t) of the cell parameters. A Fortran program, NIST*LATTICE, that enables this new approach to be used is available to the scientific community. There are many immediate applications of converse-transformation analysis including the full automation of the single-crystal diffractometer and phase characterization using lattice-matching techniques.