Deterministic combinatorial calculation of lattice parameters using Python

Abstract

Introduction: Determining lattice parameters is crucial for characterizing crystalline materials, as these constants dictate their physical and chemical behavior. While Rietveld refinement is the standard, it can be unnecessarily complex when the goal is limited to finding lattice parameters, particularly for low-symmetry systems or massive datasets. Materials and methods: This paper proposes a deterministic mathematical combinatorial method implemented in open-source Python libraries that calculates initial unit cell parameters directly. It bypasses global pattern modeling by solving localized equation systems derived from previously indexed interplanar distances. Results: The algorithm was systematically validated across six crystal systems (from cubic to monoclinic) by benchmarking calculated cell metrics against reference data from seven distinct entries in the Inorganic Crystal Structure Database (ICSD), exhibiting algebraic self-consistency in recovering ideal unit cell metrics. Conclusions: By providing a rapid, lightweight, and mathematically transparent alternative to complex black-box deep learning architectures or holistic profile fitting, this modular approach enhances crystallographic accessibility, with the full source code publicly available on GitHub to ensure reproducibility.