Application of Gradient Steepest Descent Method to the Problem of Crystal Lattice Parametric Identification

Abstract

Abstract. The objective of this paperwork is the development of a crystal lattice parameter identification algorithm, which allows obtaining a more accurate solution compared to the Bravais unit cell estimation algorithm. To achieve the objective, we suggest solving the parameter identification problem using the steepest descent gradient method. The study of the parameter identification accuracy was conducted on a large number of modeled crystal lattices using the edges and angles similarity measures for Bravais unit cells.Keywords: crystal lattice, Bravais unit cell, Wigner-Seitz unit cell, similarity measure, translation vector, parameter identification, gradient steepest descent method.Citation: Shirokanev AS, Kirsh DV, Kupriyanov AV. Application of gradient steepest descent method to the problem of crystal lattice parametric identification.

Performance Analysis of Steepest Descent-Line Search Condition Combinations in Nonlinear Least Squares Fitting of CMM Data

“…In addition to this study, regarding as the step length, Kalousek [5] released a random step length selection procedure for the SD method. On the other hand, the crystal lattice parameters were found by implementing the SD method in [6]. Another application of the SD method on the sensor placement problem was completed by Akbarzadeh et al [7].…”