  In this work, we investigate [110] symmetric tilt FCC grain boundaries (GBs)
by a recently developed approach for quasiperiodic interfaces using the
Landau-Brazovskii model. On special tilt angles associated with quadratic
algebraic numbers, quasiperiodic GBs exhibit generalized Fibonacci substitution
rules. The transition mechanism from quasiperiodic GBs to periodic GBs is
explored through sphere offsets and spectral coalescence. We also propose an
accurate method to calculate the GB energy for arbitrary tilt angle and analyze
the factors affecting the GB energy. The revealing GB energy change is continue
along with tilt angle except periodic GBs.
