Premium
Order Parameter Boundary Conditions for Ferroics: Application to Flexoelectricity
Author(s) -
Ahluwalia R.,
Yudin P. V.,
Yurkov A. S.
Publication year - 2018
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201700312
Subject(s) - flexoelectricity , boundary value problem , phase boundary , boundary (topology) , polarization (electrochemistry) , context (archaeology) , coupling parameter , boundary conditions in cfd , no slip condition , physics , coupling (piping) , condensed matter physics , mechanics , mathematics , phase (matter) , robin boundary condition , materials science , mathematical analysis , mixed boundary condition , optics , chemistry , quantum mechanics , geology , liquid crystal , metallurgy , paleontology
We study boundary conditions for ferroics in the context of the Landau theory with higher order gradient terms. Such thermodynamic description requires additional boundary conditions for the order parameter gradients, that we derive here. The results are of practical importance for materials exhibiting incommensurate phases due to competing interactions and for advanced modeling for nano‐scale ferroic systems. Boundary conditions are derived for the case when the order parameter is fixed at the free surface (blocking boundary condition) as well as for the free boundary case. The application of the boundary conditions is demonstrated using phase field simulations for ferroelectrics where there is a coupling of the polarization order parameter with strain gradients.