The Infrared Spectra of Minerals
The principal concern of this book is the use of vibrational spectroscopy as a tool in identifying mineral species and in deriving information concerning the structure, composition and reactions of minerals and mineral products. This does not mean that the approach is purely empirical; some theoretical understanding of the vibrational spectra of solids is essential to an assessment of the significance of the variations in the spectra that can be found within what is nominally a single mineral species, but which usually includes a range of compositions and defect structures. Theory alone, however, can give only limited support to the mineral spectroscopist, and careful studies of well-characterized families of natural and synthetic minerals have played an essential role in giving concrete structural significance to spectral features. The publication of this book represents a belief that theory and practice have now reached a state of maturitity and of mutual support which justifies a more widespread application of vibrational spectroscopy to the study of minerals and inorganic materials. The wide area of theory and practice that deserves to be covered has required a careful selection of the subject matter to be incorporated in this book. Since elementary vibrational spectroscopy is now regularly included in basic chemistry courses, and since so many books cover the theory and practice of molecular spectroscopy, it has been decided to assume the very basic level of knowledge which will be found, for example, in the elementary introduction of Cross and Jones (1969). With this assumption, it has been possible to concentrate on those aspects that are peculiar to or of particular significance for mineral spectroscopy.
As explained in the previous chapter, the only crystal vibrations which, to a first approximation, can be active in the infrared and Raman are those of long wavelength, comparable to that of the exciting radiation. Their frequency is essentially identical with those of infinite wavelength (k=0) in which all unit cells execute identical vibrations, so that the vibrations of a single unit cell define those of the crystal as a whole. The number of these potentially active vibrations—the limiting optical vibrations—is given by 3n–3, where n is the number of atoms per unit cell. The assignment of a spectrum consists in correlating each infrared absorption band or Raman scattering frequency with one of these optical vibrations (or to some combination of them), and this is a problem whose difficulty obviously increases rapidly with increasing complexity of the unit cell. This task is often considerably simplified if the unit cell has some elements of symmetry, as its vibrations can then be classified in distinct symmetry species; its symmetry species determines whether or not a vibration can be active in the infrared and Raman, and also the directional properties of its infrared absorption and Raman scattering. Moreover, the symmetry species of a vibration limits the direction of motion of the atoms, and so helps us to guess the nature of the vibration. Indeed if there is only one vibration in a given symmetry species, its form can be exactly defined without calculation
Given the symmetry of the unit cell as a whole