SIMULATION STUDIES OF CLUSTERS AND SURFACES

Abstract

The heart of a molecular dynamics (MD) simulation is the potential from which the forces on the atoms or molecules are calculated, For many decades, computer simulations have provided workers with a viable tool to study the properties of technologically important materials. Traditionally, simple two-body potentials have been used to perform simulations. For instance, the thermal, structural and dynamical properties of rare gas solids have been widely studied both experimentally and theoretically using the popular 2-body Lennard-Jones (LJ) potential. The simplicity of the 2-body forces has made it extremely appealing in simulation studies of realistic materials. However, it is found that only a limited class of materials could be reasonably modeled with this 2-body classical potential, namely rare gas solids and some simple metals. Applications to other materials like semi-conductors, transition and noble metals have subsequently led to wrong predictions since the very important many-body effects in these materials are not accounted for. Clearly, if one wishes to describe reasonably accurate classical properties of these materials, one must necessarily include the many-body effects into the empirical classical force scheme. This many-body term would attempt to mimic the electronic effects (usually the valence or conduction electrons). In the glue model, that. we used in the present work, electronic cohesion in noble and near-noble metals is described approximately by a many-body term that depends crucially on the local atomic coordinations. The number of neighbors of a given noble metal ion represents in some way the amount of local electronic density. This many-body term thus mimics the 'gluing' effects of the conduction electrons. Some fairly successful many-body schemes, beside this model, that are commonly used include the embedded-atom model [1] , Stillinger-Weber (SW) [2] potential and Tersoff potential [3]. In this thesis, we shall employ the glue Hamiltonian model scheme for Pb [4]. However, as these are classical potentials, the electronic properties of the system could not therefore be effectively accounted for. In a quantum mechanical scheme using the Born-Oppenheimer(BO) approximation, the ground state energy of a system of atoms depends on the positions of the ions and the quantum states of the electrons and cannot be simply broken into two-body and three-body pieces for any general configuration of the ions. Recently, a scheme that incorporates ab initio calculations into MD has been proposed by Car and Parrinello [5] where forces on the ions are calculated directly from the total energy of the electronic-ion system rather than obtained by an empirical fit to experimental data. This treatment basically solves a Schrodinger equation using local density approximation (LDA) with a plane-wave basis set. However, such computation is extremely intensive, practical only to very small systems. It is with this in mind that we have adopted the following much simpler, albeit less accurate, approach: the semi-empirical tight binding molecular dynamics (TBMD). Our aim is to obtain a reasonably accurate quantum mechanical description of the material, where large and complicated atomic arrangements could be studied with much lesser computing time. In this thesis, for example, we shall apply this TBMD scheme to Si, mainly because it is a much simpler system and there exists lesser complications to deal with. In Chapter 5, we shall obtain results that are as good as the first principles density-functional calculations for Si clusters. This thesis is organized as follows. In Chapter 1, we begin with the introduction of the glue model and explain briefly the technical fitting procedures employed in modelling Pb. Some of the shortcomings of this scheme are also discussed. Chapter 2 introduces the concepts involved in the theory of total energy minimization due to Chadi [6]. A prescription proposed by Khan and Broughton [7] which incorporates the tight-binding total energy for Si into the MD scheme is given. In this thesis, we have developed a computer code to implement the said scheme to study Si clusters and Si(001) surface. In Chapter 3, we report our results on Pb clusters, modeled by the glue Hamiltonian scheme. We show that at absolute-zero, cuboctahedral clusters are more stable than icosahedral ones for all sizes [38]. An explanation for this unexpected result is offered. We have also performed a detailed study of the temperature- and size-dependent vibrational density of states [39]. In Chapter 4, we turn our attention to the recent controversy on Pb(110) surface reconstruction, and for the first time, an explanation based on our findings is suggested that may help resolve this controversy. In Chapter 5, we shall test the accuracy and reliability of the TBMD scheme by searching for and comparing ground-state equilibrium structures of Si clusters with recent ab initio results. Furthermore, we have investigated, for the first time, a detailed structural and electronic analysis of a divacancy on a reconstructed Si(001) surface, Moreover, the results have provided us with useful information on the possible mechanism that leads to the experimentally-observed phase co-existence of local c(4x2) and p(2x2) symmetries near defects. Finally, we conclude the thesis with a summary of the main results in Chapter 6.