Novel aspects of higher dimensional structural description of trigonal, pentagonal and their related phases

TL;DR

This paper introduces a higher-dimensional framework for describing trigonal, decagonal, and related phases, unifying their structural models and aiding the study of phase transformations.

Contribution

It presents a four-dimensional model for trigonal phases and compares it with models for decagonal phases, enhancing understanding of their structural relationships.

Findings

Four-dimensional model for trigonal phase developed

Unified description of trigonal and decagonal phases achieved

Zone rules formulated for all cases

Abstract

A four dimensional description for the trigonal phase is presented. It has been demonstrated that it is possible to model one dimensional quasiperiodic structure with trigonal symmetry apart from recovering the Miller-Bravais scheme for the description of hexagonal phases. A similar discussion on the two classes of decagonal phases having 10/m and 105 symmetries will be given. The distinction in the six dimensional models of the two classes of solids has been pointed out. The zone rules for all the cases have been formulated. The critical comparison for the structural description of trigonal, decagonal and related phases in terms of higher dimension is made. The unification achieved in the higher dimensional structural models of various phases has been emphasized. The importance of such models for the study of structural phase transformation has been indicated.