186 research outputs found
Atomic Scale Measurement of Polar Entropy
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
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.Comment: 23 pages, 21 figures (5 main, 16 supplemental
Effect of the Intrinsic Width on the Piezoelectric Force Microscopy of a Single Ferroelectric Domain Wall
Intrinsic domain wall width is a fundamental parameter that reflects bulk
ferroelectric properties and governs the performance of ferroelectric memory
devices. We present closed-form analytical expressions for vertical and lateral
piezoelectric force microscopy (PFM) profiles for the conical and disc models
of the tip, beyond point charge and sphere approximations. The analysis takes
into account the finite intrinsic width of the domain wall, and dielectric
anisotropy of the material. These analytical expressions provide insight into
the mechanisms of PFM image formation and can be used for quantitative analysis
of the PFM domain wall profiles. PFM profile of a realistic domain wall is
shown to be the convolution of its intrinsic profile and resolution function of
PFM.Comment: 25 pages, 5 figures, 3 tables, 3 Appendices, To be submitted to J.
Appl. Phy
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