Quasiperiodic [110] symmetric tilt FCC grain boundaries

In this work, we investigate $\left(110\right)$ symmetric tilt FCC grain boundaries (GBs) using a recently developed approach for quasiperiodic interfaces with the phase field crystal model. GBs at arbitrary tilt angles can be accurately obtained through our developed method. More significantly, at specific tilt angles associated with the quadratic algebraic numbers $\sqrt{2}$ and $\sqrt{3}-1$, we find that quasiperiodic GBs exhibit generalized Fibonacci sequences. The transition mechanism from quasiperiodic to periodic GBs is explored by examining the displacement of spheres and spectral convergence. We also propose an accurate method to calculate the GB energy at arbitrary tilt angles and analyze the factors affecting the energy. The results indicate that, except for periodic GBs, the variation of GB energy with tilt angle is continuous.