Factor groups,point groups,space groups: A review of some central concepts with application to vibrational spectroscopy on crystalline solids

Although crystallographers and solid-state spectroscopists have much in common, differences in background and tradition raise obstacles for an easy communication between the two groups of scientists. The present article features the concept of theFactor Group, which has its roots in group theory and crystallography, and is essential in the analysis of vibrational spectra of solids. A unified exposition of many concepts related to the factor group is given. The calcite structure of sodium nitrate is chosen as an illustrative example. Finally, some complications in the interpretation of vibrational spectra of simple solids like the alkali metal nitrates are discussed.