The efficient and accurate description of gradient energy anisotropy remains a significant challenge in the phase-field modeling of ferroelectric/antiferroelectric (FE/AFE) composite systems. To address this limitation, we have developed a perturbation model for solving anisotropic gradient energy based on Fourier spectral methods. Through a Fourier-space perturbation scheme, we achieve the ability to treat the full anisotropic gradient energy tensor with spatial variations, overcoming limitations of previous constant-coefficient or isotropic approximations. The application of this model to FE/AFE composites demonstrates exceptional robustness and convergence efficiency. Numerical results indicate that the proposed perturbation scheme can accurately reproduce antiferroelectric phase diagrams and AFE-FE phase transition pathways under varying gradient energy parameters. Furthermore, the algorithm exhibits superior scalability, allowing for a seamless extension to three-dimensional (3D) simulation domains. This capability facilitates the visualization of complex nanodomain structures and reveals the intricate 3D evolution mechanisms of polarization textures.
Shi et al. (Sat,) studied this question.