Angle-adjustable density field formulation for modeling crystalline microstructures

A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but challenging issue in modeling structure and dynamics of a broad range of material systems across variable scales. This generalized phase field crystal type approach is based upon the complete expansion of particle direct correlation functions and the concept of isotropic tensors. Through applications to the modeling of various two- and three-dimensional crystalline structures, our study demonstrates the capability of bond angle control in this continuum field theory and its effects on the emergence of ordered phases, and provides a systematic way of tunable angle analysis for crystalline microstructures.