Atomic Scale Measurement of Polar Entropy

TL;DR

This study introduces a novel atomic-scale measurement of polar configurational entropy in ferroelectric materials using advanced electron microscopy, revealing how entropy influences local symmetry breaking and polar order.

Contribution

First experimental quantification of atomic-scale polar entropy in a ferroelectric crystal using aberration-corrected STEM combined with theoretical analysis.

Findings

Atomic displacements correlate with increased polar entropy near domain walls.

Entropy variability stabilizes polar order parameter.

Method enables direct entropy measurement at atomic resolution.

Abstract

Entropy is a fundamental thermodynamic quantity that is a measure of the accessible microstates available to a system, with the stability of a system determined by the magnitude of the total entropy of the system. This is valid across truly mind boggling length scales - from nanoparticles to galaxies. However, quantitative measurements of entropy change using calorimetry are predominantly macroscopic, with direct atomic scale measurements being exceedingly rare. Here for the first time, we experimentally quantify the polar configurational entropy (in meV/K) using sub-\r{a}ngstr\"{o}m resolution aberration corrected scanning transmission electron microscopy. This is performed in a single crystal of the prototypical ferroelectric $\mathsf{LiNbO_3}$ through the quantification of the niobium and oxygen atom column deviations from their paraelectric positions. Significant excursions of the niobium - oxygen polar displacement away from its symmetry constrained direction is seen in single domain regions which increases in the proximity of domain walls. Combined with first principles theory plus mean field effective Hamiltonian methods, we demonstrate the variability in the polar order parameter, which is stabilized by an increase in the magnitude of the configurational entropy. This study presents a powerful tool to quantify entropy from atomic displacements and demonstrates its dominant role in local symmetry breaking at finite temperatures in classic, nominally Ising ferroelectrics.