The early descriptions of chemical bonding in minerals and geological materials utilized purely ionic models. Crystals were regarded as being made up of charged atoms or ions that could be represented by spheres of a particular radius. Based on interatomic distances obtained from the early work on crystal structures, ionic radii were calculated for the alkali halides (Wasastjerna, 1923) and then for many elements of geochemical interest by Goldschmidt (1926). Modifications to these radius values by Pauling (1927), and others took account of such factors as different coordination numbers and their effects on radii. The widespread adoption of ionic models by geochemists resulted both from the simplicity and ease of application of these models and from the success of rules based upon them. Pauling’s rules (1929) enabled the complex crystal structures of mineral groups such as the silicates to be understood and to a limited extent be predicted; Goldschmidt’s rules (1937) to some degree enabled the distribution of elements between mineral phases or mineral and melt to be understood and predicted. Such rules are further discussed in later chapters. Ionic approaches have also been used more recently in attempts to simulate the structures of complex solids, a topic discussed in detail in Chapter 3. Chemical bonding theory has, of course, been an important component of geochemistry and mineralogy since their inception. Any field with a base of experimental data as broad as that of mineralogy is critically dependent upon theory to give order to the data and to suggest priorities for the accumulation of new data. Just as the bond with predominantly ionic character was the first to be quantitatively understood within solidstate science, the ionic bonding model was the first used to interpret mineral properties. Indeed, modern studies described herein indicate that structural and energetic properties of some minerals may be adequately understood using this model. However, there are numerous indications that an ionic model is inadequate to explain many mineral properties. It also appears that some properties that may be rationalized within an ionic model may also be rationalized assuming other limiting bond types.
Mathematical analysis of cardiac electromechanics with physiological ionic model