The Raman and infrared (IR) phonons for the Ruddlesden-Popper Srn+1BnO3n+1 (B = V, Cr, Fe, Co) bilayered tetragonal compounds with n = 2 of symmetry D174h and phase I4/mmm (Z = 2) have been analyzed with Wilson's GF-Matrix Method. Theoretical assignments for the optical wavenumbers have been reported first time for the bilayered tetragonal Sr3V2O7, Sr3Cr2O7, and Sr3Co2O7 compounds by using ten short-range force constants. The appropriate optical vibrational modes have been assigned to the bilayered tetragonal Sr3Fe2O7 compound. The theoretically calculated Raman modes found in the literature are not satisfactorily matched with the experimentally observed frequencies for the bilayered tetragonal Sr3Fe2O7 compound. Using the available data of the isostructural compounds Sr3Ti2O7 and Sr3Mn2O7, we have tried to calculate and report better results for the Raman vibrational modes of the Sr3Fe2O7 compound. Also, we have compared all these three compounds together in terms of frequencies and force constants. The impact of cation-B (B = V, Cr, Fe, Co) exchange on the lattice dynamics of the tetragonal bilayered Sr3B2O7 (B = V, Cr, Fe, Co) isostructural compounds has been analyzed by comparison of the Zone centre vibrational modes, force constants, and bond lengths. For understanding the structure more clearly an attempt is also made to analyze the effect of B-cations (B = V, Cr, Fe, Co) on the affected apical bonds. For each normal mode of the bilayered tetragonal Sr3B2O7 (B = V, Cr, Fe, Co) Ruddlesden-Popper phase, the potential energy distribution (PED) has been analyzed for the significant impact of short-range force constants on different vibrational modes.
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