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 Title: Energy density method and its applications to defect energies Author(s): Yu, Min Director of Research: Martin, Richard M.; Trinkle, Dallas R. Doctoral Committee Chair(s): Ceperley, David M. Doctoral Committee Member(s): Chiang, Tai-Chang; Martin, Richard M.; Trinkle, Dallas R. Department / Program: Physics Discipline: Physics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): energy density method defect energies weight method Au/TiO$_2$ Abstract: We propose a method to study various defects using an energy density formulation in density functional theory. Unlike traditional total energy methods that find a single energy as the difference between two calculations, this approach can provide the formation energies for more than one point defect, surface or interface in one calculation. The energy density method also provides a picture of the distribution of the energy among the surrounding atoms; although the value assigned each atom is not unique, it gives trends. One purpose of this work is to investigate the extent to which the distribution of the energy around the defect can be used to understand its properties. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package for the projector augmented wave and pseudopotential methods. The assignment of energy to an atom uses procedures related to Bader's work on Atoms in Molecules''. Although our work is different, one aspect is the same: the calculation of volume around each atom where the kinetic energy is unique. We extend the idea of Bader volume to find a charge neutral volume for the unique classical Coulomb energy. An important part of our development is a new method to construct volumes in a way that is more accurate and efficient than previous grid-based methods that require very fine grids. Our weight method works with the density on a grid and assigns volume fractions of the cell of each grid point to different atoms. For a wide range of applications, the weight method provides much precise calculations of the atomic energies with a $O(N)$ computing time. The generality of the method is demonstrated by applications to surface and point defects of semiconductors, metals, and metal oxides. The energy density perturbation around Si monovacancy reveals the strong energy concentration on \{110\} planar zigzag chains. The O interstitial in the hexagonal-close-packed Ti crystal demonstrates a Friedel oscillation in both charge density and energy density. In particular we study the interface of Au/TiO$_2$, which is a well-recognized chemical catalyst at low temperature. By comparing the work of adhesion of different interfaces at the zero temperature, we predict a stable interfacial geometry of Au(111) on the top of a new proposed TiO model with net work of adhesion of 45\,meV/\AA$^2$ and interfacial distance 2.45\,\AA. Atomic energy variation during forming interfaces demonstrates that the attraction of top Au interfacial layer leads to a stable structure. Issue Date: 2011-01-21 URI: http://hdl.handle.net/2142/18521 Rights Information: Copyright 2010 Min Yu Date Available in IDEALS: 2011-01-212013-01-22 Date Deposited: 2010-12
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