# Size effect of soft phonon dispersion law in nanosized ferroics

## TL;DR

This paper investigates how the size of nanoscale ferroic materials influences the dispersion of soft phonon modes, revealing true size effects and predicting false effects related to flexoelectric coupling.

## Contribution

It provides analytical expressions and numerical analysis of soft phonon dispersion in nanosized ferroics, highlighting the size-dependent behavior and its impact on flexoelectric effects.

## Key findings

- Pronounced true size effect on phonon dispersion in nanoscale ferroics
- Prediction of apparent size effects in flexoelectric coupling constants
- Analytical and numerical methods for phonon dispersion analysis

## Abstract

Using Landau-Ginsburg-Devonshire theory, we derive and analyze analytical expressions for the frequency dispersion of soft phonon modes in nanosized ferroics and perform numerical calculations for a thin SrTiO3 film. We revealed the pronounced "true" size effect in the dependence of soft phonon spatial dispersion on the film thickness and predict that it can lead to the "apparent" or "false" size effect of dynamic flexoelectric coupling constants

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Source: https://tomesphere.com/paper/1812.04702