Lattice dynamics and force constant calculation for the Raman and infra-red wave numbers of cubic bismuth-based pyrochlore compounds

Lattice dynamics computations utilizing a short-range electrostatic force-field model have been performed for the first time to investigate the fundamental Raman and infra-red wave numbers in some cubic bismuth-based composites, namely, BMN, BZN, BMT and BZT pyrochlores. The calculations of phonons involve three stretching and four bending force-field constants in Wilson GF-matrix method. The calculated phonon wave numbers agree satisfactorily with the observed spectra in the infra-red and Raman excitation zones for all these compounds. A Raman Eg mode has been assigned within the wave number range of 360-375 cm−1. The significant contributions of each force constant towards the calculated Raman and IR wave numbers have also been obtained through investigating the potential energy distribution (PED). The PED mapping for these compounds shows that the lattice dynamical properties of the Nb5+-compounds, BMN and BZN, are remarkably different from the Ta5+-compounds, BMT and BZT. This difference may be attributed to the different degree of orientational dipole disorder caused by the local hopping of the disordered atoms at the A and O′ sites in the A2O′ sub-structure as well as electro-negativity of B5+-cations in these bismuth pyrochlores.