MSE8210 Advanced Topics in Theoretical Surface and Interface Science

Transcription

1 MSE8210 Advanced Topics in Theoretical Surface and Interface Science Aloysius Soon 알로이시우스손 Course outline An introduction to fundamental concepts in theoretical surface science Processes that occur at surfaces and interfaces: critical role in manufacture and performance of advanced materials (e.g. electronic, magnetic and optical devices, sensors, catalysts and hard coatings). Focus of this course: high-level, ab initio approaches to understanding surface and interface science phenomena. First-principles electronic structure calculations and how they can be used to probe chemo-physical properties of surfaces and interfaces (Principles and concepts are IMPORTANT)

2 Lesson plan Part One: of electronic structure and condensed matter theory [3 lessons] Part Two: Metal surfaces and simple adsorption [4 lessons] Part Three: Metal alloys and their surfaces [2 lessons] Part Four: Moving towards reality ab initio atomistic thermodynamics [2 lessons] Part Five: Special lectures Open questions in theoretical surface science [2 lectures] Revision before examination Assessment Attendance = 20 % [Active class participation is crucial!!] Assignments/Student-presentation = 20 % Two assignments (Report + Oral) Mid-term project (Report + Oral) = 30 % Final examination = 30 % Note: All lectures, assignments, presentation, discussions etc. will be given in English. GOAL: Effectively communicate science in basic English

3 Lecture materials Assumption: Basic knowledge of solid-state and surface physics/chemistry, elementary band theory and basic quantum mechanics/density-functional theory Lecture notes/outline provided Reference materials Electronic Structure: Basic Theory and Practical Methods by Richard Martin For background reading Theoretical Surface Science: A Microscopic Perspective by Axel Gross Extra reading materials will be made known along the way New learning approaches Problem-based learning (PBL) is a student-centered instructional strategy in which students collaboratively solve problems and reflect on their experiences Learning is driven by challenging, open-ended problems Students work in small collaborative groups Teachers take on the role as "facilitators" of learning Project-based learning is the use of classroom projects, intended to bring about deep learning, where students use technology (e.g. the Internet, library, scholarly articles etc.) and inquiry to engage with issues and questions of interest

4 New learning approaches About Aloysius 알로이시우스 I m from Singapore and my native language is English. I do not (yet) speak/understand Korean (fluently) I value and practice open-concept teaching i.e. I do not think that scientific pursuit is only for the SMART guys, but is just as easily available for the curious and passionate that s YOU!! I am here to learn as much from YOU, as you from me. YOU have much to offer. Most importantly, I m a NEWBIE, so please be nice!!

5 About Aloysius 알로이시우스 B.Sc. (Hons) Chemistry National University of Singapore, Singapore M.Sc. Chemistry University of Auckland, New Zealand Ph.D. Physics University of Sydney, Australia Now, it s it s your turn. Tell me something about yourself MPG/AvH Fellow Physics/Chemistry Fritz-Haber-Institut der Max-Planck-Gesellschaft, Germany Computational Materials Science Experiments Modelling Theory Computational modelling of materials properties and phenomena: from the synthesis, characterisation and processing of materials, structures and devices to the numerical methodology of materials simulations (quantum and classical) Other common and closely-related fields: Condensed matter theory, Solid-state theory (both physics and chemistry), nanoscience and nanotechnology, etc. NOT an isolated field, VERY active field: Best to go hand-inhand with experiments and theory

6 Computational Materials Science From Physics Today, June, papers published since 1893 with > 1000 citations in APS journals Surface Science Study of physical and chemical phenomena that occur at the interface of two phases, including solid-liquid interfaces, solid-gas interfaces, solid-vacuum interfaces, and liquid-gas interfaces surface physics and surface chemistry The field of surface chemistry started with heterogeneous catalysis pioneered by Paul Sabatier on hydrogenation and Fritz Haber on the Haber process Most recent developments in surface sciences include the 2007 Nobel Prize of Chemistry winner Gerhard Ertl's advancements in surface chemistry, specifically his investigation of the interaction between carbon monoxide molecules and platinum surfaces

7 Theoretical Surface Science Tremendous progress in the microscopic theoretical treatment of surfaces and processes on surfaces A wide range of surface properties can now be described from first principles, i.e. without using any empirical parameters Level of sophistication and accuracy that reliable predictions for CERTAIN surface science problems is now possible Detailed theoretical understanding will have wide applications in a range of physical, chemical, biological, medical engineering and material science problems Experiments Modelling Theory Electronic structure theory Describes the behaviour of electrons in atoms, molecules and solids, namely (in hope of) solving the many-body Schrödinger equation H Ψ = E Ψ Probes the quantum nature of electrons Quantum mechanics! Usually mathematically involved, but can be (attempted to) explained at a simple level for non-experts Goal of this course! So let s try.

8 Lesson 1.1 From atoms to solids An overview electron proton neutron Classical picture planets orbiting around the sun Quantum picture Statistics came into play: Where is the most probable location of the electron? No longer orbits but orbitals (and wavefunctions)!

9 Energy 4s 3s 2s 1s 4p 3p 2p 3d Electron configuration = arrangement of electrons in an atom, molecule, or other physical structure (e.g., a crystal). Knowing this for different atoms is useful in understanding the structure of the periodic table of elements describing the chemical bonds that hold atoms together. What if we mix-and-match the orbitals of different atoms in a molecule, e.g. H 2?

10 Energy 1s H σ* σ 1s H Non-polar bond AO1 Atomic orbitals (AO) combine = molecular orbitals (MO) MO diagram represents the interaction between the AO σ* σ AO2 Semi-polar bond AO1 σ* σ Polar bond What if, now, we mix-and-match the orbitals of many (almost infinite) number of atoms, e.g. in a crystal? AO2 LUMO CBM Energy Infinite MOs HOMO VBM Fermi level Band diagram Metal Overlaping states Semiconductor Insulator Many MOs combine to form continuous bands or states Band diagrams are useful understand and characterize materials of different electronic/optical properties

11 Adapted from Atomic and Electronic Structure of Solids Efthimios Kaxiras Adapted from Atomic and Electronic Structure of Solids Efthimios Kaxiras

12 Adapted from Atomic and Electronic Structure of Solids Efthimios Kaxiras Adapted from Atomic and Electronic Structure of Solids Efthimios Kaxiras

13 Adapted from Atomic and Electronic Structure of Solids Efthimios Kaxiras Opening of the hybridization bandgap From C to Sn, atomic size increases bandgap decreases

14 direct indirect Interband transitions in a semiconductor, between valence and conduction states Intraband transitions in a metal across the Fermi level Adapted from Atomic and Electronic Structure of Solids Efthimios Kaxiras The density-of-states (dos) describes the energy levels per unit energy increment. Non-uniform across the band: Levels are packed more closely together at some energies than others as a result of overlap of the molecular orbitals. Energy What is the area under the graph? Density-of-states

15 Density-of-states Sum over all (eigen)states/orbitals with eigenvalues, ε i of the electronic hamiltonian Projected (or local) density-of-states Conduction band Fermi level Absolute 0 K Valence band Small electronic entropy Large electronic entropy The Fermi-Dirac distribution is characterized by the temperature of the electrons, and the Fermi level

16 Relative filling of the d and sp density-of-states moving across the transition metal series Cohesive energy or Atomization energy

17 (Murnaghan) Equation of State: Binding-energy relation Cohesion Energy Relative volume Types of bonding classified by cohesion strength Something measurable by both experiments and computation Special attention is to be made when choosing (1) the type of model and (2) level of theory to use

18 Very basic concepts: electronic configuration, orbitals, types of bonding, simple crystallography, band theory (bandstructure and density-of-states), etc. To be built upon for lessons to come (Not necessarily tested in the examinations, but good to know) PROMISE: Not too much tedious, difficult mathematics only equations that exemplify a concept PROMISE: A lot of readings to do! I do not expect you to immediately understand everything, but I will highlight the key points to learn