Atomic-scale measurement of polar entropy

Image Caption: 
Aberration-corrected electron microscopy and entropy measurement: Top: LiNbO3 domain wall imaged from [1100] zone axis with the polar Ising niobium-oxygen displacements overlaid. Bottom: A comparison of polar entropy measured and predicted away from the wall..

 Debangshu Mukherjee,1 Sergei Prokhorenko,2,3 Leixin Miao,1 Ke Wang,1 Eric Bousquet,2 Venkatraman Gopalan1 and Nasim Alem,1 1Pennsylvania State University, University Park, PA 16802, CA 94720, 2 Theoretical Materials Physics Q-MAT CESAM, University of Liège, Belgium, 3Physics Department and Institute for Nanoscience and Engineering, University of Arkansas,  72701, USA.

Center for Nanoscale Science DMR-1420620 (primary), DARPA Grant No. HR0011727183-D18AP00010

PHYSICAL REVIEW B 100, 104102 (2019); DOI: 10.1103/PhysRevB.100.104102

Entropy is a fundamental thermodynamic quantity that measures the microstates accessible to a system, with the stability of a system determined by the size of the total entropy. 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, MRSEC researchers experimentally quantify the polar configurational entropy using sub-angstrom resolution aberration corrected scanning transmission electron microscopy.  This is done in a single crystal of the prototypical ferroelectric LiNbO3 through the quantification of niobium and oxygen atom column deviations from their paraelectric positions. Significant excursions of the niobium-oxygen polar displacement away from its symmetry-constrained direction are seen in single-domain regions which increase near domain walls. Combined with first-principles theory plus mean field effective Hamiltonian methods, the IRG demonstrates the variability in the polar order parameter, which is stabilized by an increase in 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.

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IRG1 - Layered Ferroics