Instability criterion for ferroelectrics under mechanical/electric multi-fields: Ginzburg-Landau theory based modeling

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• 作者：Le Van Lich^a ; ¹ ; ^{le.lich.68m@st.kyoto-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Takahiro Shimada^a ; ¹ ; ^{shimada@me.kyoto-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Jie Wang^b ; Takayuki Kitamura^a
• 关键词：Instability criterion ; Ferroelectric material ; Ginzburg-Landau theory ; Phase-field model
• 刊名：Acta Materialia
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：112
• 期：Complete
• 页码：1-10
• 全文大小：2258 K

文摘

Ferroelectric materials interact with not only electric fields, but also with mechanical stress/strain through intriguing cross-coupling between ferroelectric polarization and ferroelastic strain. Such mechanical and/or electric multi-field interactions allow symmetry breaking of the rotationally invariant switching field and cause a variety of complicated instability phenomena in ferroelectric systems, e.g., super switching of in-plane ferroelectric nanodomains in strained thin films, labile and ultrafast switching of ferroelastic nanodomains, and ferroelectric polarization reversal via successive ferroelastic transitions. To systematically understand the nature of instabilities in ferroelectrics, here, we propose an analytical method based on Ginzburg-Landau theory to enable rigorous description of any type of instability in arbitrary morphologies and complex microstructures under a finite electric field and/or mechanical loading. The present theory yields, as an instability criterion, the condition that the minimum eigenvalue of the Hessian matrix of potential energy with respect to displacements, electrical potential, and polarization vectors must be zero. In addition, the corresponding eigenvector represents the polarization behavior at the onset of instability, which is successfully validated by application of the criterion to domain switching and successive ferroelastic transitions in PbTiO₃ ferroelectric thin film under electrical and mechanical excitation, respectively. This approach thus provides a novel insight into the cause of instability in ferroelectrics. In addition, the proposed criterion is scale-independent, which enables elucidation of the nature of various types of instability in arbitrary ferroelectric systems so that complicated instability issues in practical situations can be addressed.