Interpreting the 4-index Notation for Hexagonal Systems
Philip B. Allen
TL;DR
This paper clarifies the mathematical basis of the 4-index notation used in hexagonal systems, enhancing its clarity and utility for describing reciprocal lattice vectors and crystal faces.
Contribution
It provides a detailed explanation of the mathematical foundation of the 4-index notation, making it more understandable and practical for researchers.
Findings
Simplifies the understanding of 4-index notation.
Improves the usefulness of the notation in crystallography.
Clarifies the mathematical basis of the notation.
Abstract
A four index notation (e.g. (10-11) is often used to denote reciprocal lattice vectors or crystal faces of hexagonal crystals. The purposes of this notation have never been fully explained. This note clarifies the underlying mathematics of a symmetric overcomplete basis. This simplifies and improves the usefulness of the notation.
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Taxonomy
TopicsAdvanced Physical and Chemical Molecular Interactions · Scientific Research and Discoveries · Chemical and Physical Properties of Materials