THEORETICAL INVESTIGATION OF THE TITANIUM-SESQUIOXIDE BAND STRUCTURE

SHANNON GERVASE LIEB, Purdue University

Abstract

An ab initio calculation of the band structure of titanium sesquioxide has been carried out using the tight-binding formalism. To model the essential ingredients of the solid, a simple cluster consisting of the metal and its nearest six oxides is chosen. The cluster Fock elements are brought to self-consistency with several physically meaningful constraints imposed on the final solution. These constraints are elevated in terms of the cluster as it resides in the crystal. The potential surfaces in the region of the cluster due to the remainder of the crystal is evaluated by use of a point charge approximation of those ions remaining in the crystal after removing the cluster atoms. This potential is analytically fit and the matrix elements arising among the cluster atoms with this external potential are then evaluated. Together the cluster Fock and external potential matrix elements comprise the crystal Fock matrix. The resulting band structure has the conduction bands in three major groupings. There are four sets of doubly degenerate bands lowest in energy separated by a gap from four singly degenerate bands and above them are four more doubly degenerate bands. The ordering is discussed with respect to the initial crystal Fock matrix elements and other calculations. Likewise, the band orbital energy placements are interpreted in terms of their ionization and excitation energies. This interpretation requires a scrutinization of the closed shell formalism attendant in the creation of the cluster Fock elements, since the actual electron configuration has one electron in an open shell d orbital. Finally, the band results are compared to experiment and suggestion is made as to the extension of the bandstructure to other first row transition metal oxides possessing the same structure and stoichiometry.

Degree

Ph.D.

Subject Area

Chemistry

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