Order–disorder Effects

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Abstract
The determination of degree of order in minerals and other crystalline materials is an important problem usually approached by X-ray diffraction techniques. Some problems, particularly that of Al–Si ordering, are difficult by X-ray methods. Other tools, particularly vibrational spectroscopy, can also provide useful information. Infrared spectra have long been known to be sensitive to short-range order. Laser Raman spectroscopy is really too new to evaluate properly, but first evidence is that Raman spectra are sensitive to intermediate or long-range order. This chapter will review present knowledge, such as it is, on the application of vibrational spectroscopy to order-disorder problems. The subject is poorly developed, and for that reason most of the treatment will be anecdotal rather than systematic. We begin with a definition of a perfectly ordered crystal. It consists of an array of atoms arranged within a Bravais lattice such that every rotational operation of the space group transforms every atom in the structure into another atom of the same kind. Likewise there is a long-range periodicity, so that operation by the translational symmetry operators of the space group transform every atom in the unit cell into an atom of the same kind at the same position in an adjacent unit cell. Perfect order is inherently tied to this idea of complete invariance of the structure under all symmetry operations of the space group. There are a number of ways in which the perfect periodicity of the structure can be lost. They are: 1. Positional disordering due to substitution 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.