Pattern Classification Based On Multi-Hyperellipsoid Clustering.

Traditional model-based pattern classification is based on the assumption that the distribution of the training samples of each pattern class can be formulated by a single statistical function. It is difficult to make an accurate classification by the traditional method when the training samples of different classes do not bind to this assumption. The main contribution of this research is the development of a new clustering technique, called Multi-Hyperellipsoid Clustering, that is able to handle any irregular pattern distributions. The new method uses a supervised maximum likelihood estimation to derive a set of distribution functions for the training samples of each class, and then uses an improved Bayesian probability decision model to partition the pattern space. The new classifier achieved a higher rate of correct classification than the traditional method, with respect to some rather complex pattern distributions in a number of test examples

First-principles Discovery and Investigation of Novel Materials for Energy Conversion

This dissertation aims to employ density functional theory calculations to investigate energy conversion materials. The main focus of this dissertation is on the emerging photovoltaic materials halide perovskites: the third and fourth chapters discuss perovskite-derived halides A2BX6 and double perovskite halides A2MM'X6, respectively. The fifth chapter discusses a novel material for photocatalytic water splitting.In Chapter 3, we focus on a perovksite-derived halide A2BX6 for photovoltaic applications. The electronic structure and energetic stability of A2BX6 halide compounds with the cubic and tetragonal variants of the perovskite-derived K2PtCl6 prototype structure areinvestigated computationally within the frameworks of density-functional-theory and hybrid functionals(HSE06). The HSE06 calculations are undertaken for seven known A2BX6 compounds with A = K, Rb and Cs, and B = Sn, Pd, Pt, Te, and X = I. Trends in band gaps and energetic stability are identified, which are explored further employing semi-local density-functional-theory(DFT) calculations over a larger range of chemistries, characterized by A = K, Rb, Cs, B = Si, Ge, Sn, Pb, Ni, Pd, Pt, Se and Te and X = Cl, Br, I. For the systems investigated in this work, the band gap increases from iodide to bromide to chloride. Further, variations in the A site cation influences the band gap as well as the preferred degree of tetragonal distortion. Smaller A site cations such as K and Rb favor tetragonal structuraldistortions, resulting in a slightly larger band gap. For variations in the B site in the (Ni, Pd, Pt) group and the (Se, Te) group, the band gap increases with increasing cation size. However, no observed chemical trend with respect to cation size for band gap was found forthe (Si, Sn, Ge, Pb) group. The findings in this work provide guidelines for the design of halide A2BX6 compounds for potential photovoltaic applications.In Chapter 4, we focus on building a database for the double perovskite halides and employ the database to identify new materials for photovoltaic applications. Starting from a consideration of the octahedral and tolerance factors of ~2000 candidate double-perovskitecompounds, we compute structural, electronic and transport properties of ~1000 using first-principles calculations based on DFT methods. The computational results have been assembled in a database that is accessible through the Materials Project online. As one potential application, double perovskites are candidates in the search for lead-free halide photovoltaic absorbers. We present the application of our database to aid the discovery of new double perovskite halide photovoltaic materials, by combining the results with optical absorption and phonon stability calculations. Eleven compounds from three distinct classes of chemistries were identified as promising solar absorbers and the complex chemical trends for band gap within each of these are analyzed, to provide guidelines for the use of substitutional alloying as a means of further tuning the electronic structure.In Chapter 5, we focus on the SrNbO3+d structures with different oxygen compositions and discuss their electronic properties based on DFT calculations of their electronic structures and charge density distributions. Under low oxygen pressure, films formed have the SrNbO3 perovskite structure. SrNbO3 has a heavily degenerate conduction band and a high carrier density. When growing under higher oxygen pressure, the carrier density decreases and the films become more insulating. The excess oxygen leads to the formation of extraoxygen planes with a density that increases with d; at the nominal composition SrNbO3.4, these extra oxygen planes should appear every 5 unit cells. According to our calculation for SrNbO3.4, valence electrons are confined in the middle of two neighboring extra oxygen planes. These characteristics of the electronic structure lead to strong conventional plasmonic effects and strongly correlated plasmonic effects for SrNbO3 and SrNbO3.4, respectively