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

Abstract The carbonates are a complex group of minerals built around the ion. The carbonates and the carbonate double salts are all highly anisodesmic compounds. The carbonate ion and other anions such as sulphate, phosphate, or hydroxyl have strong covalent bonds with high force constants. The separation of the vibrational spectra into internal and lattice modes is therefore a useful approximation. Each vibrational spectrum will consist of a set of internal modes for each crystallographically distinct anion, with frequencies perturbed only slightly from the free ion values, and a set of low frequency lattice modes characteristic of the particular crystal structure. In general, the internal modes will be at higher frequencies and appear in the mid-infrared region while the lattice modes appear at lower frequencies. It is for this reason that the mid-infrared spectra of all carbonate minerals tend to look alike and that the IR spectrum is a useful identification tool for this anion. Spectra of the carbonates have been included in most of the compilations of infrared spectra of inorganic compounds and minerals. These include Hunt et al. (1950), Keller et al. (1952), Miller and Wilkins (1952), Miller et al. (1960), Moenke (1962a, 1966), Alexanian et al. (1966) and Nyquist and Kagel (1971). Infrared spectra have proved useful for the qualitative identification and quantitative analysis of carbonates in rocks and other minerals. Descriptions of these analyses are given by Louisfert and Pobeguin (1952), Pobeguin (1954), Baron et al. (1957), Pobeguin (1959), Chester and Elderfield (1967),