Resumen de Computational study of electronic, structural and thermodynamic properties of crystaline, amorphous and liquid materials
To understand the relationship between the structure ofmaterials at atomic or molecular scale and their macroscopic behaviour is one of the main goals of materials science. Materials properties, after all, are determined by the structure and the motion of their components (atoms, ions or entire molecules). Thiswork is framed in this general context. It is oriented to the problem of characterising thermodynamic materials properties, studying the structure and the dynamics of their constituents by means of molecular simulations. Molecular simulation, comprising molecular dynamics and Monte Carlo method, is the tool of thermal physics. Particularly, we have been interested in the task of mapping out pressu re-temperature phase diagrams. Such diagrams chart the regions of stability of the different allotropes of a material. They are hence of considerable importance in fields as widely varied as engineering, materials processing and geophysics. Nevertheless, in spite of being fundamental in both academia and industry, the phase diagrams of most materials remain relatively unknown beyond normal conditions, i.e., high temperatures and/or pressures. The reason of this is the technical challenge of performing accurate phase behaviour studies either in experiments or in simulations. In experiments, for instance, it is very difficult to reach simultaneously high temperatures and pressures. Measurements at these conditions, therefore, are subjected to large uncertainties. In simulations, on the other hand, the limitation is in the methods for performing such kind of calculations, which are computationally demanding. Nonetheless, simulations have proven to be of great assistance in the task ofmapping out phase diagrams of materials. For instance, Alf'e, Gillan & Price (1999) have estimated from first principles calculations the melting curve of iron down to the pressure regime of the Earth's core, while Vojcadlo & Alf e (2002) have obtained that of aluminium in a similar range of pressures. On the other hand, new computationalmethods have emergedwhich nowmake phase boundaries much more accessible (Watanabe & Reinhardt 1990, de Koning, Antonelli & Yip 1999). Such methods are based on free energy calculations, which is one of the main approaches have traditionally been used for estimating coexistence points. At finite temperature and/or pressure, it is the free energy that determines the relative stability of the different phases of a material. Commonly, it is obtained from estimating free energy differences between the system of interest and a reference system for which the free energy is known, by performing a series of equilibrium simulations. The mentioned novel techniques calculate free energy differences too, but instead of equilibrium simulations they use non-equilibrium simulations, decreasing thus the computational workload necessary for estimating a coexistence point. These techniques, combined with the recent method for integrating dynamically the Clausius-Clapeyron equation (de Koning, Antonelli & Yip 2001), are nowadays the most effective tools for obtaining phase boundaries from simulations. In fact, for studying thermodynamic properties of materials. Aside from the coexistence line itself, other important data can be extracted from the simulations performed with these methods, such as enthalpies, volumes or entropies. Entropies, for example, can be obtained either from evaluating the temperature derivative of the free energy, or from structural correlation functions. Correlation functions, in particular, can be a very direct and efficient way for measuring entropies, as they can be obtained from any molecular dynamics simulation. However, the entropy is related to the structure of the system through an expansion in terms of n-particle correlation functions (Ravech'e 1971, Mountain & Ravech'e 1971, Wallace 1987), and correlation functions of order higher than two are not easy to calculate. Then, the usefulness of this method depends on the convergence of this expansion. Baranyai & Evans (1989) showed that for the Lennard-Jones fluid twoparticle correlation functions contribute around 85 % to the entropy of the system, i.e., higher order correlation functions are necessary in order to estimate the entropy of this system from correlation functions. The open question here is, how this expansion works for real liquids? In this work, then, we use the methods mentioned above in order to study the thermodynamic properties of different materials, including a series of fee metals, carbon and silicon systems. These materials are of considerable importance in both academy and industry. Hence, it is desirable to characterize their thermal properties. In the particular case of metals we obtain, by using free energy calculations, the zero-pressure melting temperature of these systems as well as collection of thermodynamic and transport properties. Then using the entropies obtained from these calculations, i.e., those obtained from evaluating the temperature derivative of the free energy, we study the convergence of the entropy exps in terms of correlation functions for metallic systems. Finally, we estimate such convergence for covalent systems using liquid and amorphous silicon. Regarding carbon we study its melting boundary from the diamond phase. These studies are performed using either empirical or tight-binding potentials for describing particles interactions (Cleri & Rosato 1993, Lim, Ong & Ercolessi 1992, Justo, Bazant, Kaxiras, Bulatov & Yip 1998, Lenosky, Kress, Kwon, Voter, Edwards, Richards, Yang & Adams 1997). These methods are very attractive for these kinds of calculations, as they are computationally much less expensive than first principles methods and, in general, offer a good compromise between transferability, accuracy and efficiency. Tight-binding models, in particular, have proven to have such requirements. It is then desirable to have such a kind ofmodel potentials for studying thermal properties ofmaterials. Nonetheless, the task of calibrating tight-binding models is not trivial, specially for describing multielemental systems, when the number of parameters and considerations to take into account make this process very difficult and tedious. Then, bearing in mind that most tight-binding models are developed for single element systems, should be possible to combine such models for describing compound systems. The last part of this work, indeed, deals with this kind of problems. It is focused in the calibration of a tight-binding molecular dynamics model for describing SiC polymorphisms, using available single element tight-binding models for describing pure Si and C (Xu, Wang, Chan & Ho 1992, Kwon, Biswas, Wang, Ho & Soukolis 1994). This compound has recently attracted much interest for structural applications in nuclear physics and aerospace materials.
It is hence important to understand and characterise its thermal properties, and would be optimum to have a transferable, efficient and accurate model for approaching this task.
