Electrostatic Potentials for Metal Oxide Surfaces and Interfaces
- PDF / 383,872 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 91 Downloads / 222 Views
679 Mat. Res. Soc. Symp. Proc. Vol. 318. ©1994 Materials Research Society
then discuss our preliminary results for crystalline rutile titanium dioxide. Our results indicate that this approach will be able to provide physically realistic empirical potentials for future simulations on mixed metal/metal-oxide systems.
METHODS One of the dominant interactions in the metal-oxides is the Coulombic electrostatic interaction between anions and cations. Earlier models using empirical potentials included such effects by incorporating fixed atomic charges and polarizability functions into the energetics of metal-oxides. Because our ultimate goal in this work is to develop relatively simple empirical potentials for studying the adhesion of metal-oxides with metal substrates, defects, etc., any extension of such an approach must include an ability to calculate the local atomic charge (or equivalently, the valence) based on the local environment of each atom. The long-range nature of the Coulomb interaction will lead to this "local" environment typically being relatively large-scale, of the dimensions of the screening length in the metal oxides. Conceptually then, what is needed is a description of the total electrostatic energy of an array of atoms as a function of atomic charges (valences) and position. Consider expanding the energy of a neutral atom i as a Taylor series in the partial charge, q1.4 The first derivative term OE/Oqi is traditionally denoted as the electronegativity. X,4'5 The second derivative term has been associated with an atomic hardness 6 or with a self-Coulomb repulsion. 9 The local atomic energy Ei(qi) can be expressed to second order as Ei(qi) = Ej(O) + x~q° + Jjq?/2 . The electrostatic energy, E.., of a set of interacting atoms with total atomic charges qj is given by the sum of the atomic energies Ej, and the electrostatic interaction energies,Vi (Rlj; q, q,), between all pairs of atoms. The Coulomb pair interaction Vjj (Rij; qj, qy) is given by the electrostatic interaction between charge distributions pi(r; qj). The simplest model for pi(r; qj) is as a point charge of charge q1 ; this leads to Vij (Rij; qj, qj) = qiqj/Rij. Rapp6 and Goddard 9 have suggested the use of spherically symmetric Slater-type orbitals (STO) to generate a pi(r; qj) linear in qj. For the work herein, we assume an atomic charge density distribution of the form pi(r; qj) = Zj6(r - Rj) + (q, - Zj)fj(rj) , where fi is a spherically symmetric function. Zi is an effective core charge which should satisfy the condition 0 < Zi < Zj, where Zi is the total nuclear charge of the atom. For simplicity, we model the atomic densities as single exponential functions (Slater Is orbitals). Techniques for evaluating the resulting two-center Coulomb integrals are well-known.1 0 ,11 Let [ftIfj] denote a Coulomb interaction integral between the electron charge densities fi and f 1 , and [ilfj] denote a nuclear attraction between nuclear charge Zi and electron charge density fj. The total elecrostatic energy, E,,, can then be rewritten in the for
Data Loading...
