Theoretical study of beta-Ge3N4 and its high-pressure spinel gamma phase

nWe perform a theoretical investigation of the beta phase and the high-pres sure spinel-like gamma phase of Ge3N4. The electronic structure is found to yield direct band gaps in the optical region for both phases. The vibratio n modes and their pressure dependence of beta-Ge3N4 are determined theoreti cally, and are compared with experimental Raman spectra. All Raman-active m odes are identified and agreement of theory with experiment is excellent. A Raman silent B-u mode of the beta phase (P6(3)/m) is found to become soft under high pressure to yield a reduced symmetry (pg) P-phase derivative. Th e P structure changes further to a reduced symmetry P3 space group at highe r pressure. Theory is used to determine the optimized structural parameters and equations of state (EOS) for all phases, and the EOS yields a theoreti cal value for the beta-->gamma phase-transition pressure. The vibration mod es of the gamma phase are determined theoretically and compared to Raman me asurements.