This thesis focuses on the vibrational spectroscopy of the aragonite and vivianite arsenate minerals (erythrite, annabergite and hörnesite), specifically the assignment of the spectra. The infrared and Raman spectra of cerussite have been assigned according to the vibrational symmetry species. The assignment of satellite bands to 18O isotopes has been discussed with respect to the use of these bands to the quantification of the isotopes. Overtone and combination bands have been assigned according to symmetry species and their corresponding fundamental vibrations. The vibrational spectra of cerussite have been compared with other aragonite group minerals and the differences explained on the basis of differing chemistry and crystal structures of these minerals. The single crystal spectra of natural erythrite has been reported and compared with the synthetic equivalent. The symmetry species of the vibrations have been assigned according to single crystal and factor group considerations. Deuteration experiments have allowed the assignment of water vibrational freque ncies to discrete water molecules in the crystal structure. Differences in the spectra of other vivianite arsenates, namely annabergite and hörnesite, have been explained by consideration of their differing chemistry and crystal structures. A novel approach to the assignment of site occupancy of ions in the erythrite - annabergite solid solution has been reported. This approach has utilised vibrational spectroscopy, in conjunction with careful consideration of the crystal structures of the minerals. It has been shown that in the erythrite - annabergite solid solution Coprefers metal site 2 contrasting nickel which prefers site 1. This study in conjunction with other studies has yielded the trend that the more electronegative metal prefers to occupy site 1, with the least electronegative metal preferring to occupy site 2. Fundamentally this thesis has increased the knowledge base of the spectroscopic properties of the aragonite and the vivianite minerals. The site occupancy of metal ion substitutions in solid solution series of the vivianite group of minerals has been further enhanced, with novel method of studying the site occupancy of ions in solid solutions has been developed. A detailed knowledge and understanding of factor group analysis applied to the study of minerals has been achieved.