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The structure and dynamics of materials using machine learning

Authors: M.R.G. Marques

Ref.: PhD thesis, Martin-Luther University of Halle-Wittenberg (2020)

Abstract: In chapter 1 we start our discussion from its foundation: the many body problem and one of its most successful solutions: density functional theory. An efficient, accurate theory, that relies on an hypothesis and on an approximation. Afterwards, in chapter 2, we discuss the problems we intend to solve with density functional theory, namely structural prediction and molecular dynamics. These are the basis for the calculation of many interesting and important properties of materials. The obstacles that arise from these concern both simulation time and size, as well as the time required for a single calculation. An attempt to surpass them, by finding methods that are both accurate and efficient, revolves around machine learning, that we promptly discuss in chapter 3. In particular, we discuss applications of machine learning in material science. This leads to the core of this work: neural networks force-fields. We discuss them from their inception to the most recent research and then, in chapter 4, we present our methodology to construct neural network force-fields capable of describing the potential energy surface (PES) of solids using relatively small, unbiased training sets. To apply these force-fields in molecular dynamics and structural prediction simulations they have to provide accurate forces and stresses. Unfortunately, the high accuracy of the energy is not a sufficient condition to assure an appropriate accuracy for these derivatives of the energy. This led us to develop and implement methodologies to optimize the neural networks with respect to energies, forces, and stresses. Additionally, we use our results to show the challenges, limitations, and potential of such force-fields, and we discuss their interpretability. Moreover, our methodology permitted the study of large complex systems, such as the formation of defects in Si and the melting of metals with an accuracy comparable to density functional theory. We take on a different route in chapter 5, where we discuss and use cluster expansions to tackle the structural prediction of copper based materials. In particular, we use genetic algorithms to identify secondary phases of Cu2ZnSn(S,Se)4 (CZTS), which usually hinder the efficiency of solar cells made out of this photovoltaic material. Moreover we study the transition between the kesterite and the stannite phases in Cu2Zn1-xSnFexSe4 compounds. Our last study involved the formation of complexes of defects in CuI, a transparent conducting semiconductor (TCS). Although the role played by Cu vacancies in the p-type transparent conductivity of CuI has been properly acknowledged, the way they arrange themselves, as well as their optimal and maximum concentrations remained unclear. Our objective was to provide an answer to these unresolved questions. We note that usually these three studies are too taxing to treat only with density functional theory. Finally, at the end of this thesis we present our relevant conclusions.

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