The Lyddane-Sachs-Teller relationship for polar vibrations in materials with monoclinic and triclinic crystal systems

TL;DR

This paper extends the Lyddane-Sachs-Teller relation to monoclinic and triclinic crystal systems, providing a theoretical framework validated by experimental data for monoclinic materials and promising for future triclinic studies.

Contribution

It introduces a generalized Lyddane-Sachs-Teller relation and dielectric response function for monoclinic and triclinic materials, derived from an eigen displacement vector approach.

Findings

Validated for monoclinic β-Ga₂O₃ with experimental data

Provides a theoretical basis for future triclinic material analysis

Proposes a generalized oscillator strength expression

Abstract

A generalization of the Lyddane-Sachs-Teller relation is presented for polar vibrations in materials with monoclinic and triclinic crystal systems. The generalization is derived from an eigen displacement vector summation approach, which is equivalent to the microscopic Born-Huang description of polar lattice vibrations. An expression for a general oscillator strength is also described for materials with monoclinic and triclinic crystal systems. A generalized factorized dielectric response function characteristic for monoclinic and triclinic materials is proposed. The generalized Lyddane-Sachs-Teller relation is found valid for monoclinic $\beta$-Ga$_2$O$_3$, where accurate experimental data became available recently from a comprehensive generalized ellipsometry investigation. Data for triclinic crystal systems can be measured by generalized ellipsometry as well, and are anticipated to become available soon and results can be compared with the generalized relations presented here