3.320: Lecture 20 (Apr 21 2005)MODEL HAMILTONIANSfrom alchemy to tight-bindingApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariImages removed for copyright reasons. Cover of “Harry Potter and the Philosopher’s Stone.” Diagram of different types of knots.New jobs for the 21st century • The virtual alchemist (linear-response theory) • The nanotechnologist (tight-binding mappings) Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariOutline • Realistic descriptions of large-scale nanostructures from first-principles • Mapping electronic structure-calculations into model Hamiltonians • Ising-like models for alloys • Tight-binding orbitals for functionalized nanotubes (electronic-structure LEGO bricks)Why semiconductor alloys ? • Technological interest: tunability of materials properties. Strained layer epitaxy (Prof Fitzgerald) • Scientific interest: spontaneous multilayer ordering Array of vertical cavity lasers Superspot reflections Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariBand-gap/lattice parameter Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariConfigurational Statistical Mechanics • Energy of a configuration ? Linear-response • Thermodynamic properties ? Monte Carlo Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariDisorder as a perturbation Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariDisorder as a perturbation Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola Marzari--Apr 21 2005 3.320 Atomistic Modeling of Materials Gerbrand Ceder and Nicola MarzariApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariFormation Energies Elastic Step Configurational Step Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariFormation Energies Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariFull DFT vs. linear responseApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariPhase Diagram from Thermodynamic Integration Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariComputational EXAFS Apr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariApr 21 2005 3.320 Atomistic Modeling of Materials -- Gerbrand Ceder and Nicola MarzariEpitaxial Phase