ISBN 978-3-8439-0576-3

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

Zusammenfassung / Abstract

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.