Lattice dynamics of Hittorf's phosphorus and identification of structural groups and defects in amorphous red phosphorus

Using the force constants and bond polarisabilities of black phosphorus the dispersion, eigenvectors, and density of states for phonons, the sound velocity and the Raman spectra are calculated for polymeric violet Hittorf's phosphorus. Good agreement with Raman and Brillouin (v_s,110,exp=6.95·10⁵cm s^?1) measurements reported for the first time on oriented single crystals is found. Thus we are able to assign specific vibrational modes, such as extended wave-like vibrations and modes localised on the P₈ and P₉ structural subunits. Comparison with vibrational spectra of amorphous red phosphorus shows that the latter contains tubes similar to those of Hittorf's P. The absence of the group of lines (around 373 cm^?1) due to P₈ cages in a-Pproves that the P₈ cages are present in much reduced numbers only there, or that the weaker bonds are broken or distorted. The features at 400 cm^?1 and 455 cm^?1 in a-P might be explained by the occurrence of P₇ cages. Broken P₈ units may also be the origin of the metastable intrinsic defects giving rise to the photo-induced ESR and axial luminescence centers in amorphous phosphorus.