Topological Structures in Ferroic Materials by Jan Seidel

Author:Jan Seidel
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.5)

where is the ferroelectric part of polarization, its derivatives (the subscript ‘, i’ represents the operator of spatial derivatives ), the electric displacement and is the elastic strain where is a displacement vector.

The bulk free energy density

(5.6)

is expressed for a zero strain as a six-order polynomial expansion [50], where are parameters fitted to the single crystal properties. The remaining contributions represent bilinear forms of densities of the elastic energy , where is the elastic stiffness, electrostriction energy , where are the electrostriction coefficients, gradient energy , where are the gradient energy coefficients, and electrostatic energy . Here it is clear that . The zero-strain coefficients can be expressed in terms of usually introduced stress-free coefficients as follows:

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