# Symmetry and Piezoelectricity: Evaluation of $\alpha$-Quartz coefficients

## TL;DR

This paper evaluates the piezoelectric coefficients of α-Quartz using three symmetry-based methods, highlighting Royer-Dieulesaint as the most efficient and elegant approach among them.

## Contribution

It compares three different symmetry-based methods for deriving piezoelectric coefficients of α-Quartz, emphasizing the efficiency of Royer-Dieulesaint.

## Key findings

- Royer-Dieulesaint method is the most elegant and efficient
- Fumi method is tedious
- Landau-Lifshitz method requires additional physical principles

## Abstract

Piezoelectric coefficients of $\alpha$-Quartz are derived from symmetry arguments based on Neumann's Principle with three different methods: Fumi, Landau-Lifshitz and Royer-Dieulesaint. While Fumi method is tedious and Landau-Lifshitz requires additional physical principles to evaluate the piezoelectric coefficients, Royer-Dieulesaint is the most elegant and most efficient of the three techniques.