Abstract
A computationally efficient phonon Green's-function method is described for calculation of frequency spectra of single-walled carbon nanotubes containing point defects. The method is generally applicable to defects in other nanostructures. The phonon Green's function is used to calculate line shapes of one-phonon lines in the nuclear resonant inelastic x-ray scattering from $^{57}\mathrm{Fe}$ embedded in a single-walled carbon nanotube. The line shapes are anisotropic and have some unusual features that can provide insight into the physical processes in nanomaterials at atomistic scales and can be used to characterize them. In particular, it may be possible to use the line shapes in certain directions to determine the chirality of a nanotube.
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