Crystallography and Surface Structure E-Book

Klaus Hermann

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 439

Veröffentlichungsjahr: 2011

Beschreibung

In den Oberflächen- und Nanowissenschaften ist ein fundiertes Verständnis lokaler Geometrie und Symmetrie von Kristallen und deren Oberflächen von entscheidender Bedeutung, da die Kristallstruktur viele physikalische und chemische Parameter mitbestimmt. Studenten und Forscher in Physik, Chemie und Materialwissenschaften erhalten hierzu mit dem vorliegenden Buch sowohl eine wertvolle Einführung wie auch ein nützliches Nachschlagewerk. Das Buch führt insbesondere scheinbar disparate Beschreibungen und Notationen zusammen, die ständig von Oberflächen- und Nanowissenschaftlern benötigt werden. Professor Hermann ist als Wissenschaftler im Bereich der theoretischen Oberflächenphysik ausgewiesen und bekannt als Koautor der NIST Surface Structure Database (SSD), einer absoluten Referenz in der Struktur- und Oberflächenwissenschaft. Seine Arbeiten zur Oberflächenvisualisierung dokumentiert er auch in diesem Buch, in dem aufwändige Grafiken der zahlreichen Beispiele die mathematisch formal gewählte Herangehensweise illustrieren. Übungen mit unterschiedlichem Schwierigkeitsgrad - von einfachen Fragen bis zu kleinen Forschungsprojekten - regen die Diskussion zu den unterschiedlichen Themen an.

Leseprobe

Contents

Cover

Related Titles

Title Page

Copyright

Preface

Chapter 1: Introduction

Chapter 2: Bulk Crystals: Three-Dimensional Lattices

2.1 Basic Definitions

2.2 Representation of Bulk Crystals

2.3 Periodicity Cells of Lattices

2.4 Lattice Symmetry

2.5 Neighbor Shells

2.6 Quasicrystals

Chapter 3: Crystal Layers: Two-Dimensional Lattices

3.1 Basic Definitions, Miller Indices

3.2 Reciprocal Lattice

3.3 Netplane-Adapted Lattice Vectors

3.4 Symmetrically Appropriate Lattice Vectors: Minkowski Reduction

3.5 Miller Indices for Cubic Lattices

3.6 Alternative Definition of Miller Indices: Hexagonal Miller–Bravais Indices

3.7 Symmetry Properties of Netplanes

3.8 Crystal Systems and Bravais Lattices in Two Dimensions

3.9 Crystallographic Classification of Netplanes

Chapter 4: Ideal Single Crystal Surfaces

4.1 Basic Definitions, Termination

4.2 Morphology of Surfaces, Stepped and Kinked Surfaces

4.3 Miller Index Decomposition

4.4 Chiral Surfaces

Chapter 5: Real Crystal Surfaces

5.1 Surface Relaxation

5.2 Surface Reconstruction

5.3 Faceting

Chapter 6: Adsorbate Layers

6.1 Definition and Classification

6.2 Wood Notation of Surface Geometry

6.3 Symmetry and Domain Formation

Chapter 7: Experimental Analysis of Real Crystal Surfaces

7.1 Experimental Methods

7.2 The NIST Surface Structure Database

Chapter 8: Nanotubes

8.1 Basic Definition

8.2 Nanotubes and Symmetry

Appendix A: Mathematics of the Wood Notation

Appendix B: Mathematics of the Minkowski Reduction

Appendix C: Some Details of Number Theory

C.1 Basic Definitions

C.2 Euclid's Algorithm

C.3 Linear Diophantine Equations

C.4 Quadratic Diophantine Equations

Appendix D: Some Details of Vector Calculus and Linear Algebra

Appendix E: Parameter Tables of Crystals

Appendix F: Relevant Web Sites

References

Glossary and Abbreviations

Index

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The Author

Prof. Dr. Klaus Hermann

Fritz Haber Institute

Theory Department Berlin, Germany

Cover picture

by Klaus Hermann

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ISBN: 978-3-527-41012-5

Preface

The objective of this book is to provide students and researchers with the foundations of crystallography necessary to understand geometry and symmetry of surfaces and interfaces of crystalline materials. This includes both macroscopic single crystals and crystalline nanoparticles. Knowledge of their geometric properties is a prerequisite for the interpretation of corresponding experimental and theoretical results, which explain both their physical and their chemical behaviors. In particular, surface and interface structure is of vital importance not only for studies of properties near single crystal surfaces but also for research on thin films at solid substrates. Here, technological applications range from semiconductor devices and magnetic storage disks to heterogeneous catalysts.

Crystalline nanoparticles, such as nanotubes, nanowires, or compact particles of finite size, have recently attracted considerable interest due to their novel chemical and physical properties. Examples are carbon nanotubes, silicon nanowires, and nanosize quantum dots at semiconductor surfaces. Although these particles are of finite size in one or more dimensions, their local atom arrangement can still be close to that of extended bulk crystals. In addition, their surfaces and interfaces with other materials can be described analogously to those found for single crystal surfaces. Thus, surface crystallography, covered in this book, can also be applied to analyze geometric properties of nanoparticle surfaces.

While treatises on three-dimensional crystallography are abundant, there are only few chapters on surface crystallography available in specialized surface science reviews. In particular, comprehensive textbooks on surface structure have not yet been published. Nevertheless, students and researchers entering the field need to obtain a thorough overview of surface geometry, which includes all relevant basic crystallographic methods required for theoretical and experimental analyses. This book tries to serve this purpose. It is primarily meant for graduate and PhD students in physics, chemistry, and crystallography and will also help researchers who want to learn in more detail about the geometry at surfaces of single crystals or nanoparticles.

This book is written by a theoretical surface scientist. Therefore, the discussion of methods and approaches in the text is frequently adapted to surfaces and differs at some places from traditional crystallographic treatment. For example, number theoretical methods are used to derive appropriate transformations between equivalent lattice descriptions. Furthermore, some of the conventional concepts of surface structure are looked at from a different viewpoint and go beyond the standard treatment known inside the surface science community. Examples include the introduction of Miller indices based on netplane-adapted lattices and a thorough mathematical treatment of symmetry, which results in the 17 two-dimensional space groups. Therefore, the text can also be used as a resource complementary to the standard surface science literature.

This book project started as a manuscript of a series of lectures on surface crystallography, given by the author at several international workshops and in universities as well as research institutions where surface science and catalysis groups were engaged in research on structural properties of surfaces. Questions and discussions during the lectures were often the source of more detailed work on different sections of the manuscript and thus helped to improve its presentation. Furthermore, research visits to various surface science groups raised the author's awareness of new or incompletely treated issues to be dealt with. The author is indebted to all those who contributed with their scientific curiosity and criticism. The text has benefited from numerous discussions with surface scientists, crystallographers, and mathematicians of whom only a few are mentioned: Gerhard Ertl, Klaus Heinz, Bernhard Hornfeck, Klaus Müller, John B. Pendry, Gabor A. Somorjai, D. Phil Woodruff. Wolfgang Moritz served as an extremely valuable sparring partner in the world of crystallography. Very special thanks go to Michel A. Van Hove whose constructive criticism, rich ideas, and continuous support during the writing phase were unmatched. Without him the book would not have come out in its present form.

Finally, I am greatly indebted to my wife Hanna for her patience and loving care throughout the time it took to finish this book and beyond.

Fritz Haber Institute, Berlin

Summer 2010

Klaus Hermann

Chapter 1

Introduction

Research in many areas of materials science requires a thorough knowledge of crystalline solid-state systems on an atomic scale. These systems may represent real materials such as complex semiconductors or may act as meaningful models, for example, simulating reactive sites of catalysts. Here, physical and chemical insight depends very much on details of the geometry of local environments around atoms and of possible periodic atom arrangements inside the crystal and at its surface. As examples we mention that

chemical binding between atoms inside a crystal and at its surface strongly depends, apart from atomic parameters, on local geometry [1, 2]. This is very often expressed by local coordination describing the number and arrangement of nearest-neighbor atoms with respect to the binding atom. For example, metal atoms in a bulk metal crystal are usually characterized by a large number of nearest neighbors, 8 or 12, yielding metallic binding. At surfaces, the changed chemical binding due to different coordination, compared to that in the bulk, is closely connected with local geometry that can be expressed by relaxation and reconstruction. Furthermore, atoms or molecules can adsorb at specific sites of crystalline substrates, where the adsorption geometry is essential to an understanding of local binding behavior.electronic properties at surfaces of single crystals can differ substantially from those of the corresponding bulk. For example, the existence of a surface can induce additional electronic states, surface states, that have been found in experiments and studied theoretically some time ago [3]. Here, the detailed surface geometry determines both the existence and the energetic behavior of the states. Further, electronic interband transitions in silicon nanowires and nanodots are found to cause photoluminescence that does not occur in silicon bulk crystals [4]. The difference is explained by both the spatial confinement of the nanoparticles and the changed geometric properties of their atom arrangement. Finally, it has been claimed from experiment that semiconducting bulk silicon shows metallicity at its (7 × 7) reconstructed (1 1 1) surface [5], and metallicity is also found in theoretical studies on silicon nanowires [6].magnetism of crystalline bulk material and its surfaces depends on the crystal structure and local coordination. For example, vanadium sesquioxide (V2O3) in its monoclinic crystal structure at low temperatures is antiferromagnetic, whereas its high-temperature phase is described by a trigonal corundum lattice and is paramagnetic [7]. Vanadium crystals with a body-centered cubic lattice are found to be paramagnetic in their bulk volume but ferromagnetic at their surfaces [8]. Other examples are thin iron films grown on top of copper single crystal surfaces where, as a function of film thickness, their crystal geometry changes and, as a consequence, so do their magnetic properties [9].anisotropic electrical conductivity is often connected with dense atom packing along specific directions inside crystals. An example is given by trigonal LiCoO2 crystals that form the most common lithium storage material for rechargeable batteries. Here, the electrical conductivity is greatly enhanced along densely packed Co and Li planes while it is much smaller perpendicular to the planes [10].catalytic surface reactions depend crucially on geometric properties of the surfaces of crystalline catalyst materials [11, 12] and are needed for understanding the heterogeneous catalysis at an atomic scale. The atomic surface geometry determines possible adsorption and reaction sites for molecules, which can support specific catalytic reactions but also can exclude others (structure–reactivity relationship [11]). For example, catalytic CO oxidation happens at single crystal surfaces of platinum with different efficiency depending on the surface orientation [13], where the surface geometry determines the type and density of reactive sites.

In addition to bulk crystals and their surfaces, crystalline nanoparticles [14, 15] have become a new exciting field of research. This includes nanotubes [16], nanowires [14], or compact particles of finite size, such as atom clusters [17], fullerenes [18], or quantum dots [19], which show novel physical and chemical properties deviating from those of corresponding bulk material. Examples are carbon nanotubes providing substrate material to yield new active catalysts [20] or silicon nanowires whose visible photoluminescence is determined by their size [21]. Furthermore, nanosize quantum dots at semiconductor surfaces are found to yield quite powerful light emitting diodes (LEDs) of technological relevance [19].

These nanosystems are described as atom aggregates of finite size in one or more dimensions, where their local geometric arrangement can still be close to that of extended bulk crystals. Likewise, their spatial confinement with corresponding surfaces and interfaces can be considered analogous to that appearing at bulk crystal surfaces. Therefore, surface crystallography, initially developed to describe geometric properties at single crystal surfaces, also forms a sound basis for characterizing geometry of nanoparticle surfaces. This is particularly interesting since the relative number of atoms positioned at nanoparticle surfaces compared to those of their inner volume is always larger than that of extended macroscopic single crystals. Thus, atoms at nanoparticle surfaces are expected to play a more important role in determining physical properties than corresponding atoms at single crystal surfaces. In addition, nanoparticles can possess symmetry and geometric properties that do not appear in single crystals or at their surfaces. Examples are curved nanoparticle surfaces that originate from bending single crystal sections, where in this book nanotubes will be discussed as examples.

In many experimental and theoretical studies, real crystalline systems are, for the sake of simplicity, approximately described by ideal single crystals with a well-defined atomic composition and an unperturbed three-dimensional periodicity. In addition, surfaces of the single crystals are assumed to be bulk-terminated and of unperturbed two-dimensional periodicity. With this approximation in mind, a rigorous mathematical description of all geometric parameters becomes possible and is one of the basic subjects of classical crystallography. As an illustration, Figure 1.1 shows the geometry of a section of an ideal single crystal of magnesium oxide (MgO) with its perfect three-dimensional periodic arrangement of atoms. Here, sections of ideal planar surfaces, originating from bulk truncation, become visible and demonstrate the variety of surface types for the same crystal depending on the crystal cut.

Figure 1.1 Section of an MgO crystal (NaCl lattice). The atoms are shown as colored balls and labeled accordingly. The section is enclosed by nonpolar (0 0 1), (−1 1 0) and by polar (1 1 1) oriented surfaces.

In this book, we will discuss basic elements and mathematical methods used in crystallography to evaluate geometric parameters of single crystals with particular emphasis on their surfaces. We start with ideal bulk crystals of three-dimensional periodicity, where classical bulk crystallography provides a quantitative description. Then, we introduce ideal two-dimensional surfaces as a result of bulk truncation along specific directions including high-density, vicinal, stepped, kinked, and chiral surfaces. We give a detailed account of their two-dimensional symmetry behavior following the crystallographic classification scheme of Bravais lattices and two-dimensional space groups. Next, we discuss in detail the deviation of atom geometry at surfaces due to changed surface binding compared to the bulk. This is usually described by surface relaxation and reconstruction, where we consider different schemes. After that, we mention crystallographic aspects of commensurate and incommensurate adsorbate systems as special cases of surface reconstruction, where the different notations used in the literature will also be described. The discussion of surface structure will be completed by an overview of the surfaces that have been analyzed quantitatively at an atomic level in scattering, diffraction, imaging, or spectroscopic experiments. Finally, we describe theoretical aspects and structural details of nanotubes of different element composition as special cases of rolled sections of crystal monolayers. These nanotubes are examples of a larger class of crystalline materials, nanoparticles, and demonstrate that crystallographic methods can also be applied to these systems in order to account for their geometric properties. The book concludes with appendices providing details of the mathematical methods used in different chapters.

The theoretical concepts treated in this book will be illustrated by example applications for further understanding, which include results from measured real single crystal surfaces that are documented in the NIST Surface Structure Database (SSD) [22–24] or its earlier version SCIS (Surface Crystallographic Information Service) [25]. In addition, each chapter of the book concludes with a set of exercises. These exercises are of varying difficulty, ranging from simple problems to small research projects, and are meant to stimulate questions and answers about the different subjects. Some of the exercises may require a visualization tool for crystals, such as Balsac [26], or Survis, the visualization part of the SSDIN package [27] or the like.

For the theoretical treatment of some geometric properties of ideal single crystals, we will apply number theoretical methods, dealing with relations between integer numbers. While this approach is not commonly used in textbooks on surface science or crystallography, it can considerably simplify the formal treatment. Examples are solutions of linear and quadratic Diophantine equations that facilitate the discussion of netplanes or of atom neighbor shells in crystals. Therefore, number theoretical methods will be introduced briefly as required, and further details are provided in Appendix C.

A few illustrations are included as stereo pictures for an enhanced three-dimensional impression. These pictures may be viewed by either using optical stereo glasses (available separately) or by cross-eyed viewing without glasses. In the latter case, viewing for an extended time may overstrain the eyes and should be avoided.

Obviously, the present book cannot cover all aspects of the field and may, in some cases, be quite brief. Furthermore, the selection of topics, as well as their presentation, is, to some degree, determined by the author's personal preferences. However, the interested reader may consult the extensive crystallographic literature, for example, Refs. [28–32], or the solid-state physics literature, for example, Refs. [1, 2], to explore additional details.