Diffusion kinetics in minerals: Principles and applications to tectono-metamorphic processes
Diffusion is the process by which atoms or ions or ionic species migrate within a medium in the absence of a bulk flow. Diffusion in solids has been a subject of interest in the fields of solid state science (physics, chemistry and metallurgy) for nearly a century, starting with the work of Einstein on the relationship between random atomic movement and diffusion process. The phenomenological study of diffusion began even 50 years earlier, with the empirical formulation of Fick on the relationship between the diffusion flux of a component and its concentration gradient.
The subject of diffusion in the solids may be subdivided into volume, grain boundary and surface diffusion. The last topic has, however, received very little attention in the study of geological processes. The study of grain boundary diffusion is important to the understanding of many metamorphic processes including the problems of mass transport, fluid/rock interactions, thermal history and crystal growth. The interested reader is referred to Joestein (1991) for an excellent review of the subject of grain boundary diffusion and its applications to geological problems.
Diffusion controlled processes within a mineral preserve important records of the thermal and physico-chemical history of the host rocks. Volume diffusion, that is diffusion through the crystal lattices, affects development of compositional zoning in minerals, ordering of atoms in nonequivalent crystallographic sites of a mineral, formation and coarsening of exsolution lamellae, and retention of isotopic characteristics in minerals that can serve as quantitative chronometers in their thermal and growth history.
Figures & Tables
The present book shows the arguments which have been considered in the EMU School (No. 4), dealing with Energy Modelling in Minerals; these arguments have been selected in order to provide examples of application of the most advanced theories to several cases. It should be pointed out that although the ultimate solution of our problems should involve “ab initio” quantum-mechanical calculations, at present such sophisticated procedures are far from being routine. Therefore, although “ab initio” approaches will play an ever-increasing role in the future and some important and most recent examples of such approaches are illustrated here, the greatest part of the contributions is dealing with empirical atom-atom calculations. Remarkably enough, such “semi-empirical” applications are often quite successful, providing excellent (or comparatively excellent) results in spite of their more or less approximate nature. It often happens that the methods here illustrated are some steps ahead of the current level of empirical treatment, thereby indicating a possible way of improvement by figuring out routines to be adopted in practice. If some methods seem to be too speculative to be actually usable, here they also are shown, in view of their possible discussion, or just to indicate a way to obtain promising developments. Among the descriptions of practical methods and results, some purely theoretical arguments have been inserted; these arguments — although abstract — according to our opinion are fundamental for earth scientists. Owing to the present status of the art, in a number of arguments there is no unique opinion with respect to their theoretical treatment as it is explained by different authors. Instead of having all of them discarded except the one which looks to be the most appropriate to the Editor (who might sometimes be personally involved in the question), most of such controversial points have been left just as they are, in the original draft of their advocates. Accordingly, the reader might find some discrepancies between some articles and others, which may lead to some obscurity; there are, however, several good reasons in favour of our behaviour. First of all, with a few exceptions we apologize about, our attention in inviting the contributors has been extended to all the principal authors in the world, with no limitation to a group of particular friends; moreover, the presence of different opinions in the context might give rise to interesting debates and critical objections; a further point is that the validity of the different treatments is shown per se by either the level of the theory and most of all by the agreement with the corresponding experimental data. Since we have to do with an advanced school, and in line with what should be a scientific procedure, it is important to provide the user with the possibility of choosing what seems to be the most appropriate method among a number of selected possibilities, rather than yielding to the assertion that something is indeed the ultimate and unquestionable “truth”.