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We propose a spectral viewpoint for grain boundaries that are generallyquasiperiodic. To accurately capture the spectra computationally, it is crucialto adopt the projection method for quasiperiodic functions. Armed with theLifshitz-Petrich free energy, we take the spectral viewpoint to examine tiltgrain boundaries of the hexagonal phase. Several ingredients of grainboundaries are extracted, which are not easy to obtain from real-spaceprofiles. We find that only a few spectra substantially contribute to theformation of grain boundaries. Their linear relation to the intrinsic spectraof the bulk hexagonal phase is independent of the tilt angle. By examining thefeature of the spectral intensities, we propose a definition of the interfacewidth. The widths calculated from this definition are consistent with visualestimation.

Tilt grain boundaries of hexagonal structures: a spectral viewpoint