Angle-Adjustable Phase Field Crystal Method for Modeling Crystalline Microstructures

The phase field crystal (PFC) method has emerged as an attractive continuum modeling approach which resolves system microstructures and dynamics on atomic length and diffusive time scales and effectively addresses the elastoplastic properties of the system. Most PFC models are constructed for systems of isotropic interactions, with lattice symmetry controlled by microscopic length scales, and thus are lack of angle dependency which is important for a broad range of material systems with directional interaction or bonding. Here we develop a new PFC model incorporating both the anisotropic property of angular dependence and the rotational invariance of the whole system. Our analysis is based on the property of isotropic Cartesian tensor and the complete Fourier expansion of any n-point direct correlation function that satisfies the rotational invariance condition. Applications of this new PFC model include some examples of 3D structure modeling (such as simple cubic and diamond cubic phases) via a single length scale and angle-dependent effects, and importantly, the achieving of continuous angle control in crystalline structures (such as the rhombic phase), which demonstrates the advantage of this angle-adjustable density field approach.