Reply to “Comment on ‘Understanding first-order Raman spectra of boron carbides across the homogeneity range’ ”

Abstract

In response to Werheit's Comment, we first discuss the following three points: (i) Attribution of the Raman bands with the help of calculations based on the density functional perturbation theory (DFPT), (ii) similarity of the Raman spectrum of boron carbide to the Raman spectrum of $\ensuremath{\alpha}$ rhombohedral boron, and (iii) dependence of the experimental Raman spectrum on the frequency of the excitation laser. Central to the point at stake, we also present a Raman spectrum computed for the first time on a 405-atom unit-cell of boron carbide, where the simulation cell accounts for the substitutional disorder of the polar carbon atom in the six atomic positions that are equivalent in the trigonal symmetry. We thus obtain a theoretical spectrum whose agreement with experiment is unprecedented in boron carbide, all of the features being present, with however negligible intensities for the doublet at $270/320\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. We argue that the doublet intensity seen in experiments is not purely vibrational---as computed at mechanical equilibrium---and that FT-Raman spectroscopy taken at $1.06\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ lacks the accuracy that is necessary to study vibrational modes of boron carbides.