Schematic of electron microscopy experiments. 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.
#ENTROPY IS A MEASURE OF PLUS#
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. Significant excursions of the niobium-oxygen polar displacement away from its symmetry-constrained direction are seen in single domain regions which increase in the proximity of domain walls. Here, we experimentally quantify the polar configurational entropy (in meV/K) using sub-angstrom resolution aberration corrected scanning transmission electron microscopy in a single crystal of the prototypical ferroelectric LiNbO 3 through the quantification of the niobium and oxygen atom column deviations from their paraelectric positions. However, quantitative measurements of entropy change using calorimetry are predominantly macroscopic, with direct atomic-scale measurements being exceedingly rare. This is valid across truly mind boggling length scales, from nanoparticles to galaxies.
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.
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