DOCSLIB.ORG

Introduction to Surface Physics Surface Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction to Surface Physics Surface Physics Chapter 9 A (Very) Short Introduction to Surface Physics Surface Physics from fundamental… Scanning probes and surface states Carbon nanotubes …to applied Microelectronics / Nanotechnology Heterogeneous Catalysis References Physics at surfaces: A. Zangwill Surface Chemistry and Catalysis: G.A. Somorjai Principles Of Adsorption And Reaction On Solid Surfaces: R.A. Masel Theoretical Surface Science: A. Groß Lecture 1: 9.1 Geometric structure of surfaces 9.2 Adsorption at Surfaces 9.3 Diffusion at Surfaces 9.1 Geometric structure of surfaces “Ideal” surfaces [001] n Cutting close-packed materials (fcc/hcp/bcc) α vicinal surfaces steps low-index surfaces (fcc) (111) (110) (100) kinks (11 13 19) (335) Relaxation and reconstruction: metals Layer relaxation General Interpretation: Smoluchowski smoothing (Finnis & Heine) +++ -- -- Relaxation and reconstruction: metals 280 Å fcc(110)-(1x2) missing row reconstruction Au(111)-22x√3 herringbone structure Relaxation and reconstruction: semiconductors Dimerization at (001) surface of group IV elements “Dangling bond minimization” 9.2 Adsorption at surfaces Adsorption at surfaces top A surface exhibits many different ‘sites’: - simple overlayers (hollow, bridge, top) bridge - adsorbate induced reconstructions (missing row, oxide formation etc.) hollows - step/kink/defect decoration fcc(111) O(2x2) O(2x1) Lateral interactions between adsorbates - multiple sites as f(θ ), bond strength = f(θ ) - ordered adlayers ((in)commensurable) - islands, domains - competitive coadsorption… 3O(2x2) O(1x1) On an atomic scale adsorption is not just “attachment” Adsorption at surfaces Complex Surface Oxide Reconstructures are also common: eg O/Ag(111) 4x4 4x4 5x5 5x3 Adsorption at surfaces General statements in this area are dangerous, but: Well converged DFT GGA calculations mostly predict the correct adsorption site …many examples STM2 1 Eg. H2O Monomer Adsorption : 1 Michaelides, et al. Phys. Rev. Lett. 90, 216102 (2003) 2Mitsui et al. Science 297, 1850 (2002) Top view N adsorption on a W{100} surface (PW91) Side view N W 0.44 (0.41±0.05) 2.19 (2.13±0.05) W 0.26 (0.27±0.06) • Calculations on adsorbate structues often exhibit the same level of accuracy as calculations on molecular species. Michaelides, et al. Phys. Rev. Lett. 90, 246103 (2003) Adsorption at surfaces •But sometimes DFT gets it wrong…especially when the potential energy surface for adsorption is smooth: •Famous example CO/Pt(111)1 and CO on other transition metal surfaces •“Standard” DFT GGA predicts 3-fold site; Experiment says hollow CO sits at the hollow •site. •There are lots of explanations (and solutions, good or otherwise!) for this error. Perhaps the best is from Kresse who says it is because “standard” GGAs get the CO HOMO-LUMO gap wrong2 top bridge hollows fcc(111) 1P.J. Feibelman, et al. J. Phys. Chem. B 105, 4018-4025 (2001). 2 Key quantities in Surface Science Adsorption: binding energy at T = 0K tot tot tot Ebind = [ E ( ) - E ( ) - E ( ) ] Physisorption (0.1-0.3 eV/atom) - Chemisorption (>0.5 eV/atom) eg Xe, Ar eg O, N DFT adsorption energies can differ from experiment substantially: Hammer et al. Physical Review B, Vol. 59, 7413 (1999)) MolecularMolecular AdsorptionAdsorption Adsorbate Structures are modified upon adsorption Eg: ice on metals: In bulk ice (Ih) – the naturally occurring form of ice every water is involved in four H bonds (remember the cohesion chapter) MolecularMolecular AdsorptionAdsorption1 When ice is adsorbed on Pd(111) most waters in the interface layer are involved in three H bonds. On other surfaces other ice structures may form…people are a lot about this these days! 1J. Cerda, et el. Phys. Rev. Lett. 93, 116101 (2004). Molecular Adsorption In general for molecular adsorption: adsorbate bonds can be modified a little (typically lengthened by up to ~0.03 A) Internal vibrations altered (typically softened by up to several hundred cm-1; this can depend on the adsorption site: CO; hydrocarbons) Dipole moment, internal electronic structure will be modified 9.3 Diffusion at surfaces Diffusion on Metal Surfaces CLICK ON MOVIE Diffusion on Metal Surfaces CLICK ON MOVIE Atoms and molecules follow low energy pathways. So do Mr Men! Diffusion at metal surfaces: surprises… Hopping mechanism Ag(100) ∆E = 0.45 eV Au(100) ∆E = 0.83 eV Exchange mechanism Ag(100) ∆E = 0.73 eV Au(100) ∆E = 0.65 eV B.D. Yu and M. Scheffler, Phys. Rev. B 56, R15569 (1997) Diffusion on Metal Surfaces1 Molecular diffusion can be more complex than atomic diffusion. The orientation of the molecule can be important and the transition state for diffusion need not necessarily be a high symmetry adsorption site. 1Michaelides et al. PRB 69, 075409 (2004) Diffusion on Metal Surfaces •STM Experiments indicate that H2O dimers diffuse about 1000 times faster than H2O monomers across a Pd(111) surface1. •DFT calculations indicate that this might be because H2O dimers can waltz2. a b c d e f CLICK ON MOVIE 1 Mitsui et al. Science 297, 1850 (2002) 2Ranea, et al. Phys. Rev. Lett. 92 136104 (2003).
Load more

Recommended publications
  • An Introduction to Topology the Classification Theorem for Surfaces by E
    An Introduction to Topology An Introduction to Topology The Classification theorem for Surfaces By E. C. Zeeman Introduction. The classification theorem is a beautiful example of geometric topology. Although it was discovered in the last century*, yet it manages to convey the spirit of present day research. The proof that we give here is elementary, and its is hoped more intuitive than that found in most textbooks, but in none the less rigorous. It is designed for readers who have never done any topology before. It is the sort of mathematics that could be taught in schools both to foster geometric intuition, and to counteract the present day alarming tendency to drop geometry. It is profound, and yet preserves a sense of fun. In Appendix 1 we explain how a deeper result can be proved if one has available the more sophisticated tools of analytic topology and algebraic topology. Examples. Before starting the theorem let us look at a few examples of surfaces. In any branch of mathematics it is always a good thing to start with examples, because they are the source of our intuition. All the following pictures are of surfaces in 3-dimensions. In example 1 by the word “sphere” we mean just the surface of the sphere, and not the inside. In fact in all the examples we mean just the surface and not the solid inside. 1. Sphere. 2. Torus (or inner tube). 3. Knotted torus. 4. Sphere with knotted torus bored through it. * Zeeman wrote this article in the mid-twentieth century. 1 An Introduction to Topology 5.
    [Show full text]
  • Surface Physics I and II
    Surface physics I and II Lectures: Mon 12-14 ,Wed 12-14 D116 Excercises: TBA Lecturer: Antti Kuronen, [email protected] Exercise assistant: Ane Lasa, [email protected] Course homepage: http://www.physics.helsinki.fi/courses/s/pintafysiikka/ Objectives ● To study properties of surfaces of solid materials. ● The relationship between the composition and morphology of the surface and its mechanical, chemical and electronic properties will be dealt with. ● Technologically important field of surface and thin film growth will also be covered. Surface physics I 2012: 1. Introduction 1 Surface physics I and II ● Course in two parts ● Surface physics I (SPI) (530202) ● Period III, 5 ECTS points ● Basics of surface physics ● Surface physics II (SPII) (530169) ● Period IV, 5 ECTS points ● 'Special' topics in surface science ● Surface and thin film growth ● Nanosystems ● Computational methods in surface science ● You can take only SPI or both SPI and SPII Surface physics I 2012: 1. Introduction 2 How to pass ● Both courses: ● Final exam 50% ● Exercises 50% ● Exercises ● Return by ● email to [email protected] or ● on paper to course box on the 2nd floor of Physicum ● Return by (TBA) Surface physics I 2012: 1. Introduction 3 Table of contents ● Surface physics I ● Introduction: What is a surface? Why is it important? Basic concepts. ● Surface structure: Thermodynamics of surfaces. Atomic and electronic structure. ● Experimental methods for surface characterization: Composition, morphology, electronic properties. ● Surface physics II ● Theoretical and computational methods in surface science: Analytical models, Monte Carlo and molecular dynamics sumilations. ● Surface growth: Adsorption, desorption, surface diffusion. ● Thin film growth: Homoepitaxy, heteroepitaxy, nanostructures.
    [Show full text]
  • Surface Water
    Chapter 5 SURFACE WATER Surface water originates mostly from rainfall and is a mixture of surface run-off and ground water. It includes larges rivers, ponds and lakes, and the small upland streams which may originate from springs and collect the run-off from the watersheds. The quantity of run-off depends upon a large number of factors, the most important of which are the amount and intensity of rainfall, the climate and vegetation and, also, the geological, geographi- cal, and topographical features of the area under consideration. It varies widely, from about 20 % in arid and sandy areas where the rainfall is scarce to more than 50% in rocky regions in which the annual rainfall is heavy. Of the remaining portion of the rainfall. some of the water percolates into the ground (see "Ground water", page 57), and the rest is lost by evaporation, transpiration and absorption. The quality of surface water is governed by its content of living organisms and by the amounts of mineral and organic matter which it may have picked up in the course of its formation. As rain falls through the atmo- sphere, it collects dust and absorbs oxygen and carbon dioxide from the air. While flowing over the ground, surface water collects silt and particles of organic matter, some of which will ultimately go into solution. It also picks up more carbon dioxide from the vegetation and micro-organisms and bacteria from the topsoil and from decaying matter. On inhabited watersheds, pollution may include faecal material and pathogenic organisms, as well as other human and industrial wastes which have not been properly disposed of.
    [Show full text]
  • 3D Modeling: Surfaces
    CS 430/536 Computer Graphics I Overview • 3D model representations 3D Modeling: • Mesh formats Surfaces • Bicubic surfaces • Bezier surfaces Week 8, Lecture 16 • Normals to surfaces David Breen, William Regli and Maxim Peysakhov • Direct surface rendering Geometric and Intelligent Computing Laboratory Department of Computer Science Drexel University 1 2 http://gicl.cs.drexel.edu 1994 Foley/VanDam/Finer/Huges/Phillips ICG 3D Modeling Representing 3D Objects • 3D Representations • Exact • Approximate – Wireframe models – Surface Models – Wireframe – Facet / Mesh – Solid Models – Parametric • Just surfaces – Meshes and Polygon soups – Voxel/Volume models Surface – Voxel – Decomposition-based – Solid Model • Volume info • Octrees, voxels • CSG • Modeling in 3D – Constructive Solid Geometry (CSG), • BRep Breps and feature-based • Implicit Solid Modeling 3 4 Negatives when Representing 3D Objects Representing 3D Objects • Exact • Approximate • Exact • Approximate – Complex data structures – Lossy – Precise model of – A discretization of – Expensive algorithms – Data structure sizes can object topology the 3D object – Wide variety of formats, get HUGE, if you want each with subtle nuances good fidelity – Mathematically – Use simple – Hard to acquire data – Easy to break (i.e. cracks represent all primitives to – Translation required for can appear) rendering – Not good for certain geometry model topology applications • Lots of interpolation and and geometry guess work 5 6 1 Positives when Exact Representations Representing 3D Objects • Exact
    [Show full text]
  • Surface Topology
    2 Surface topology 2.1 Classification of surfaces In this second introductory chapter, we change direction completely. We dis- cuss the topological classification of surfaces, and outline one approach to a proof. Our treatment here is almost entirely informal; we do not even define precisely what we mean by a ‘surface’. (Definitions will be found in the following chapter.) However, with the aid of some more sophisticated technical language, it not too hard to turn our informal account into a precise proof. The reasons for including this material here are, first, that it gives a counterweight to the previous chapter: the two together illustrate two themes—complex analysis and topology—which run through the study of Riemann surfaces. And, second, that we are able to introduce some more advanced ideas that will be taken up later in the book. The statement of the classification of closed surfaces is probably well known to many readers. We write down two families of surfaces g, h for integers g ≥ 0, h ≥ 1. 2 2 The surface 0 is the 2-sphere S . The surface 1 is the 2-torus T .For g ≥ 2, we define the surface g by taking the ‘connected sum’ of g copies of the torus. In general, if X and Y are (connected) surfaces, the connected sum XY is a surface constructed as follows (Figure 2.1). We choose small discs DX in X and DY in Y and cut them out to get a pair of ‘surfaces-with- boundaries’, coresponding to the circle boundaries of DX and DY.
    [Show full text]
  • Differential Geometry of Curves and Surfaces 3
    DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES 3. Regular Surfaces 3.1. The definition of a regular surface. Examples. The notion of surface we are going to deal with in our course can be intuitively understood as the object obtained by a potter full of phantasy who takes several pieces of clay, flatten them on a table, then models of each of them arbitrarily strange looking pots, and finally glue them together and flatten the possible edges and corners. The resulting object is, formally speaking, a subset of the three dimensional space R3. Here is the rigorous definition of a surface. Definition 3.1.1. A subset S ⊂ R3 is a1 regular surface if for any point P in S one can find an open subspace U ⊂ R2 and a map ϕ : U → S of the form ϕ(u, v)=(x(u, v),y(u, v), z(u, v)), for (u, v) ∈ U with the following properties: 1. The function ϕ is differentiable, in the sense that the components x(u, v), y(u, v) and z(u, v) have partial derivatives of any order. 2 3 2. For any Q in U, the differential map d(ϕ)Q : R → R is (linear and) injective. 3. There exists an open subspace V ⊂ R3 which contains P such that ϕ(U) = V ∩ S and moreover, ϕ : U → V ∩ S is a homeomorphism2. The pair (U, ϕ) is called a local parametrization, or a chart, or a local coordinate system around P . Conditions 1 and 2 say that (U, ϕ) is a regular patch.
    [Show full text]
  • Mostly Surfaces
    Mostly Surfaces Richard Evan Schwartz ∗ August 21, 2011 Abstract This is an unformatted version of my book Mostly Surfaces, which is Volume 60 in the A.M.S. Student Library series. This book has the same content as the published version, but the arrangement of some of the text and equations here is not as nice, and there is no index. Preface This book is based on notes I wrote when teaching an undergraduate seminar on surfaces at Brown University in 2005. Each week I wrote up notes on a different topic. Basically, I told the students about many of the great things I have learned about surfaces over the years. I tried to do things in as direct a fashion as possible, favoring concrete results over a buildup of theory. Originally, I had written 14 chapters, but later I added 9 more chapters so as to make a more substantial book. Each chapter has its own set of exercises. The exercises are embedded within the text. Most of the exercises are fairly routine, and advance the arguments being developed, but I tried to put a few challenging problems in each batch. If you are willing to accept some results on faith, it should be possible for you to understand the material without working the exercises. However, you will get much more out of the book if you do the exercises. The central object in the book is a surface. I discuss surfaces from many points of view: as metric spaces, triangulated surfaces, hyperbolic surfaces, ∗ Supported by N.S.F.
    [Show full text]
  • Basics of the Differential Geometry of Surfaces
    Chapter 20 Basics of the Differential Geometry of Surfaces 20.1 Introduction The purpose of this chapter is to introduce the reader to some elementary concepts of the differential geometry of surfaces. Our goal is rather modest: We simply want to introduce the concepts needed to understand the notion of Gaussian curvature, mean curvature, principal curvatures, and geodesic lines. Almost all of the material presented in this chapter is based on lectures given by Eugenio Calabi in an upper undergraduate differential geometry course offered in the fall of 1994. Most of the topics covered in this course have been included, except a presentation of the global Gauss–Bonnet–Hopf theorem, some material on special coordinate systems, and Hilbert’s theorem on surfaces of constant negative curvature. What is a surface? A precise answer cannot really be given without introducing the concept of a manifold. An informal answer is to say that a surface is a set of points in R3 such that for every point p on the surface there is a small (perhaps very small) neighborhood U of p that is continuously deformable into a little flat open disk. Thus, a surface should really have some topology. Also,locally,unlessthe point p is “singular,” the surface looks like a plane. Properties of surfaces can be classified into local properties and global prop- erties.Intheolderliterature,thestudyoflocalpropertieswascalled geometry in the small,andthestudyofglobalpropertieswascalledgeometry in the large.Lo- cal properties are the properties that hold in a small neighborhood of a point on a surface. Curvature is a local property. Local properties canbestudiedmoreconve- niently by assuming that the surface is parametrized locally.
    [Show full text]
  • Surface Details
    Surface Details ✫ Incorp orate ne details in the scene. ✫ Mo deling with p olygons is impractical. ✫ Map an image texture/pattern on the surface Catmull, 1974; Blin & Newell, 1976. ✫ Texture map Mo dels patterns, rough surfaces, 3D e ects. ✫ Solid textures 3D textures to mo del wood grain, stains, marble, etc. ✫ Bump mapping Displace normals to create shading e ects. ✫ Environment mapping Re ections of environment on shiny surfaces. ✫ Displacement mapping Perturb the p osition of some pixels. CPS124, 296: Computer Graphics Surface Details Page 1 Texture Maps ✫ Maps an image on a surface. ✫ Each element is called texel. ✫ Textures are xed patterns, pro cedurally gen- erated, or digitized images. CPS124, 296: Computer Graphics Surface Details Page 2 Texture Maps ✫ Texture map has its own co ordinate system; st-co ordinate system. ✫ Surface has its own co ordinate system; uv -co ordinates. ✫ Pixels are referenced in the window co ordinate system Cartesian co ordinates. Texture Space Object Space Image Space (s,t) (u,v) (x,y) CPS124, 296: Computer Graphics Surface Details Page 3 Texture Maps v u y xs t s x ys z y xs t s x ys z CPS124, 296: Computer Graphics Surface Details Page 4 Texture Mapping CPS124, 296: Computer Graphics Surface Details Page 5 Texture Mapping Forward mapping: Texture scanning ✫ Map texture pattern to the ob ject space. u = f s; t = a s + b t + c; u u u v = f s; t = a s + b t + c: v v v ✫ Map ob ject space to window co ordinate sys- tem. Use mo delview/pro jection transformations.
    [Show full text]
  • AN INTRODUCTION to the CURVATURE of SURFACES by PHILIP ANTHONY BARILE a Thesis Submitted to the Graduate School-Camden Rutgers
    AN INTRODUCTION TO THE CURVATURE OF SURFACES By PHILIP ANTHONY BARILE A thesis submitted to the Graduate School-Camden Rutgers, The State University Of New Jersey in partial fulfillment of the requirements for the degree of Master of Science Graduate Program in Mathematics written under the direction of Haydee Herrera and approved by Camden, NJ January 2009 ABSTRACT OF THE THESIS An Introduction to the Curvature of Surfaces by PHILIP ANTHONY BARILE Thesis Director: Haydee Herrera Curvature is fundamental to the study of differential geometry. It describes different geometrical and topological properties of a surface in R3. Two types of curvature are discussed in this paper: intrinsic and extrinsic. Numerous examples are given which motivate definitions, properties and theorems concerning curvature. ii 1 1 Introduction For surfaces in R3, there are several different ways to measure curvature. Some curvature, like normal curvature, has the property such that it depends on how we embed the surface in R3. Normal curvature is extrinsic; that is, it could not be measured by being on the surface. On the other hand, another measurement of curvature, namely Gauss curvature, does not depend on how we embed the surface in R3. Gauss curvature is intrinsic; that is, it can be measured from on the surface. In order to engage in a discussion about curvature of surfaces, we must introduce some important concepts such as regular surfaces, the tangent plane, the first and second fundamental form, and the Gauss Map. Sections 2,3 and 4 introduce these preliminaries, however, their importance should not be understated as they lay the groundwork for more subtle and advanced topics in differential geometry.
    [Show full text]
  • 9. 3D Object Representations
    CS3162 Introduction to Computer Graphics Helena Wong, 2001 9. 3D Object Representations Methods: § Polygon and Quadric surfaces: For simple Euclidean objects § Spline surfaces and construction: For curved surfaces § Procedural methods: Eg. Fractals, Particle systems § Physically based modeling methods § Octree Encoding § Isosurface displays, Volume rendering, etc. Classification: Boundary Representations (B-reps) eg. Polygon facets and spline patches Space-partitioning representations eg. Octree Representation Objects may also associate with other properties such as mass, volume, so as to determine their response to stress and temperature etc. 9.1 Polygon Surfaces This method simplifies and speeds up the surface rendering and display of objects. For other 3D objection representations, they are often converted into polygon surfaces before rendering. Polygon Mesh - Using a set of connected polygonally bounded planar surfaces to represent an object, which may have curved surfaces or curved edges. - The wireframe display of such object can be displayed quickly to give general indication of the surface structure. - Realistic renderings can be produced by interpolating shading patterns across the polygon surfaces to eliminate or reduce the presence of polygon edge boundaries. - Common types of polygon meshes are triangle strip and quadrilateral mesh. - Fast hardware-implemented polygon renderers are capable of displaying up to 1,000,000 or more shaded triangles per second, including the application of surface texture and special lighting effects. CS3162 Introduction to Computer Graphics Helena Wong, 2001 Polygon Tables This is the specification of polygon surfaces using vertex coordinates and other attributes: 1. Geometric data table: vertices, edges, and polygon surfaces. 2. Attribute table: eg. Degree of transparency and surface reflectivity etc.
    [Show full text]
  • Efficient Methods to Calculate Partial Sphere Surface Areas for A
    Mathematical and Computational Applications Article Efficient Methods to Calculate Partial Sphere Surface Areas for a Higher Resolution Finite Volume Method for Diffusion-Reaction Systems in Biological Modeling Abigail Bowers, Jared Bunn and Myles Kim * Department of Applied Mathematics, Florida Polytechnic University, Lakeland, FL 33805, USA; abowers@floridapoly.edu (A.B.); jbunn@floridapoly.edu (J.B.) * Correspondence: mkim@floridapoly.edu Received: 14 November 2019; Accepted: 20 December 2019; Published: 23 December 2019 Abstract: Computational models for multicellular biological systems, in both in vitro and in vivo environments, require solving systems of differential equations to incorporate molecular transport and their reactions such as release, uptake, or decay. Examples can be found from drugs, growth nutrients, and signaling factors. The systems of differential equations frequently fall into the category of the diffusion-reaction system due to the nature of the spatial and temporal change. Due to the complexity of equations and complexity of the modeled systems, an analytical solution for the systems of the differential equations is not possible. Therefore, numerical calculation schemes are required and have been used for multicellular biological systems such as bacterial population dynamics or cancer cell dynamics. Finite volume methods in conjunction with agent-based models have been popular choices to simulate such reaction-diffusion systems. In such implementations, the reaction occurs within each finite volume and finite volumes interact with one another following the law of diffusion. The characteristic of the reaction can be determined by the agents in the finite volume. In the case of cancer cell growth dynamics, it is observed that cell behavior can be different by a matter of a few cell size distances because of the chemical gradient.
    [Show full text]