Abstract
We present experimental measurements and ab initio simulations of the crystalline and amorphous phases of . The calculated Raman, infrared, and vibrational density of states (VDOS) spectra are in excellent agreement with experimental measurements and contain the signatures of all the peculiar local structures of the amorphous phase, namely, bridging and nonbridging (double-bonded or terminal) oxygens and tetrahedral units associated with , and species ( denotes the various types of tetrahedra, with being the number of bridging oxygen atoms that connect the tetrahedra to the rest of the network). In order to reveal the internal structure of the vibrational spectrum, the characteristics of vibrational modes in different frequency ranges are investigated using a mode-projection approach at different symmetries based on the symmetry group. In particular, the VDOS spectrum in the range from to 870 is dominated by bending () motions related to bridging oxygen and phosphorus ( band) atoms, while the high-frequency doublet zone (–1250 ) is associated mostly with the asymmetric () and symmetric () stretching modes, and most prominent peak around 1400 (exp. 1380 ) is mainly due to asymmetric stretching vibrations supported by double-bonded oxygen atoms. The lower-frequency range below 600 is shown to arise from a mixture of bending ( and ) and rotation () modes. The scissors bending () and rotation () modes are well localized below 600 , whereas the bending modes spread further into the range –870 . The projections of the eigenmodes onto , and species yield well-defined contributions at frequencies in striking correspondence with the positions of the Raman and infrared bands.
1 More- Received 2 July 2019
- Revised 11 September 2019
DOI:https://doi.org/10.1103/PhysRevB.100.134309
©2019 American Physical Society