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978-3-8439-0576-3, Reihe Physik
Tobias C. Kerscher
Of complex configurations and sizable systems: cluster expansions for multi-site, multi-system, and multi-scale challenges
233 Seiten, Dissertation Technische Universität Hamburg-Harburg (2012), Hardcover, B5
Computational materials science has to bridge the gap between the microscopic world of atoms, governed by quantum mechanics, and the macroscopic world around us. This gap is not only a separation in scale but also in temperature and configuration. In this book, the gap is overcome by the cluster expansion, which extracts many-body interactions from quantum-mechanical input of density functional theory (DFT) and sets up a generalized Ising-Hamiltonian. Combined with subsequent Monte-Carlo simulations, this procedure can model and predict the structure, the phase stability, and the ordering of systems on a quantum-mechanical basis.
The book focuses on cluster-expansion methods for high-dimensional complex configuration spaces and sizable systems: non-primitive lattices, broken symmetries, the coupling of multiple distinct systems, and methods for large-scale simulations. It presents arbitrary reference energies for multi-site problems and so-called structural bricks as an improved energy reference for surface problems; it discusses the dissection of configuration spaces into separate systems, which interact by multi-system coupling, and applies a bisection of the configuration space to adsorbates on surfaces; and it demonstrates a parallel Monte-Carlo implementation tailor-made for cluster-expansion Hamiltonians, which opens the gates for multi-scale quantum-mechanical simulations in the micrometer range.
Those concepts are applied to three physical systems: to lanthanum hydride and its metal-insulator transition; to carbon adsorption on the (100) surface of platinum-rhodium, which changes the segregation profile of the substrate; and to the B2-phase of nickel-aluminum, which is stabilized by ordered vacancies on the nickel sublattice.