Quantum-mechanical simulations of the high-pressure behaviour of crystals
First-principles theoretical methods, based on the quantum mechanics of electrons in periodic atomic systems, have been an effective tool to predict the ground-state structural and energetic behaviour of crystals for at least two decades. However, more recently the computational implementation of such methods by very efficient computer software and the availability of cheap and powerful hardware have undergone impressive improvements. It is thus now possible to tackle quite complex problems of materials science, earth sciences, environmental and other applied disciplines involving crystalline compounds from a purely theoretical point of view (Pisani, 1996). In this respect, while some quantum-mechanical techniques in principle are able to account also for thermal effects (ab initio molecular dynamics), the most easily available ab initio methods neglect the role of temperature (athermal limit) but can include the physical parameter pressure very straightforwardly. A brief account of such methods will be given here, presenting some examples of applications in the fields of thermodynamics and kinetics of crystalline materials at high pressure. Comparisons of quantum-mechanical simulations with those based on atomistic potentials are available in the literature (Catti et al., 2000).
The interest of ab initio predictions of the structural and elastic properties of minerals and technological materials, and of their stability ranges, at high pressure is clear. Measurement techniques in extreme non-ambient conditions are particularly challenging and often subject to large experimental errors (cf. the Diamond-Anvil-Cell methods). The most severe problems are perhaps faced by calorimetric measurements at high pressure, and also the determination
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”.