Fig. 2: Energies computed by density functional theory in one typical ferroelectric oxide under constrained electric fields or constrained electric displacement fields. | npj Computational Materials

Fig. 2: Energies computed by density functional theory in one typical ferroelectric oxide under constrained electric fields or constrained electric displacement fields.

From: Interface enhanced functionalities in oxide superlattices under mechanical and electric boundary conditions

Fig. 2

In PbTiO3 a energy U(D) as a function of electric–displacement (D) and b energy F(ξ) as a function of electric-field (ξ) of PTO along [001], [110], and [111] directions. c Electric polarization of a function of electric field P(ξ) along [001], [110], or [111] directions. d Electric Contour energy profile U(D) for D in the plane along the [100] and [010] directions. e Contour energy U(D) for D constrained in the plane determined by the [110] and [001] directions. All variables are in atomic units. In d and e, the minimum at T and saddle point at O represent tetragonal and orthorhombic states, respectively. Reproduced with permission from ref. 90. Copyright [2011] {American Physical Society}.

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