Energy Modelling in Minerals
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”.
Conceptually, the governing principle of any energy-minimisation technique of computer modelling of crystal structure and properties is self-evident. At 0 K the atomic array corresponding to the minimum cohesion energy, which represented as the sum over all interatomic interaction energies, is thought of as the most stable structure. However, this general principle occurs to be somewhat ambiguous, when the calculated minimum energy should be compared with experimental data. Indeed, a reference state of the cohesion energy for crystals of various types could be defined in a different way. For instance, the most natural way is to compare the calculated cohesion energy of covalent and metallic crystals with the experimental atomisation energy, i.e. the energy that gains in formation of such a crystal from a gas of isolated (noninteracting) atoms.
The cohesion energy of molecular crystals (either organic or inorganic) could be most appropriately defined as the sublimation energy, i.e. in this case the reference state is a gas of isolated and noninteracting molecules.
On the other hand, the cohesion energy of an inorganic crystal or mineral is most often regarded as the lattice energy which is the energy gain in formation of a crystal from an infinitely diluted gas of isolated ions (cations and anions). It implies that such ions do exist as stable particles in the gaseous state. It holds true for all cations and for the univalent anions like H–, F–, Cl–, Br–, I–, OH–, but that is not the case for all multivalent anions like O2–, S2–, Se2–, N3– etc.