  The complex arrangements of atoms near grain boundaries are difficult to
understand theoretically. We propose a phenomenological (Ginzburg-Landau-like)
description of crystalline phases based on symmetries and fairly general
stability arguments. This method allows a very detailed description of defects
at the lattice scale with virtually no tunning parameters, unlike usual
phase-field methods. The model equations are directly inspired from those used
in a very different physical context, namely, the formation of periodic
patterns in systems out-of-equilibrium ({\it e.g.} Rayleigh-B\'enard
convection, Turing patterns). We apply the formalism to the study of symmetric
tilt boundaries. Our results are in quantitative agreement with those predicted
by a recent crystallographic theory of grain boundaries based on a geometrical
quasicrystal-like construction. These results suggest that frustration and
competition effects near defects in crystalline arrangements have some
universal features, of interest in solids or other periodic phases.
