《表面物理与表面分析2》由会员分享，可在线阅读，更多相关《表面物理与表面分析2（80页珍藏版）》请在金锄头文库上搜索。
1、Chapter 2 SURFACE ATOMIC STRUCTURE,Xinju Yang, Surface Physics Lab. Physics Dept., Fudan University,Surface Physics and Surface Analysis,Crystallography Ideal Surfaces Surface Relaxation and Reconstruction Surface Defects,Outline,I. Crystallography,Crystallography deals basically with the question:
2、“Where are the atoms in solids?”,Condensed matter can be classified as either crystalline or amorphous.,Amorphous,Crystalline,Single Crystalline,Poly- Crystalline,Amorphous silicon,Many solids are made of crystallites that are microscopic - but contain 1020 atoms!,The focus of this chapter is on the
3、 description of periodic solids (crystalline), which represent the major proportion of condensed matter.,Sheet steel,Crystal Structure (3D) Crystal Surface (2D) - Periodicity & Symmetry - Miller Indices - Surface Notation - Reciprocal lattice,Including:,Lattice point: 3D array of points repeating pe
4、riodically in all three dimensions and providing the framework of the crystal structure.,A crystal can be described by two entities, the lattice and the basis.,3D Crystallography,Basis: simplest chemical unit presents at every lattice point.,Note: the basis can be single atom, group of atom, ion, mo
5、lecule, ect.,Crystal Lattice + Basis,Periodicity of Lattice,- primitive vectors,Simplest possible unit of the structure, but contains all information of the structure.,Repeating of unit cell macroscopic crystal structure.,Unit cell,Note: the primitive vectors are not unique, different vectors can de
6、fine the same lattice.,Atomic arrangement looks identical at and ,- translational vector,h, k, l - integers,Lattice: the set of points for all values of h, k, l .,-Bravais lattices,3D unit cell,For most cases, the 3D unit cell is a parallelepiped with three sets of parallel faces.,7 crystal systems
7、14 Bravais Lattices,3D unit cells,Primitive Unit cell,Primitive unit cell: smallest, containing one basis,Unit cell: the simplest and most symmetric, containing one or several basises.,Periodicity & symmetry,Periodicity,Not unique,Wigner-Seitz cell,Smallest and symmetric,Metal: fcc, bcc, hcp; Semico
8、nductor: diamond Compound: complex (NaCl, CsCl, ZnS).,Symmetrical operations,Typical structures,- n-fold rotation - Mirror & point reflections - Glide and screw,Body-Centered Cubic (bcc),Atoms are square packed !,Cubic,Face-Centered Cubic (fcc) Hexagonal Close Packed (hcp),Atoms are closed-packed!,B
9、,A,fcc: ABCABC,hcp: ABABAB,2D Crystallography,Periodicity of Lattice,The entire crystal surface can be constructed from repeated translations for all values of h, k.,2D Lattice,Note: In 2D, only lattices with 2, 3, 4 and 6-fold rotational symmetry possible.,2D Unit cell,2D unit cell: parallelogram,A
10、lso the selection of unit cell is not unique, and it can contain one or several bases.,2D unit cell 5 Bravais Lattices,正方,长方/矩形,有心长方/矩形,六角,斜方,2D Primitive Unit cell,A primitive unit cell contains minimum number of lattice points (usually one) to satisfy translation operator.,The choice is not unique
11、!,Wigner-Seitz method for finding primitive unit cell: Connect one lattice point to nearest neighbors; Bisect connecting lines and draw a line perpendicular to connecting line; Area enclosed by all perpendicular lines will be a primitive unit cell.,Wigner-Seitz Cell is most compact, highest symmetry
12、 cell possible.,Surface Symmetry,Rotation symmetry means the lattice is invariant by a rotation operation around an axis with an angle of 2 /n.,Rotation Reflection Glide,Point group,- Space group,To fulfill the requirement of lattice periodicity, n can take the values of 1, 2, 3, 4, and 6 only.,Rota
13、tion Symmetry, = 360, 180 n =1, 2, = 360, 180, 90 n =1, 2, 4, = 360, 180 n =1, 2,In the rotation operation, one point is fixed., = 360, 180 n =1, 2, = 360, 180, 120, 60 n =1, 2, 3, 6,Reflection Symmetry,The reflection symmetry means the lattice is invariant by a reflection operation with respect to
14、a lattice line. In the reflection operation, one line of the lattices is fixed.,No refection symmetry,1m 2mm 4mm,1m 2mm,1m 2mm,3m 6mm,Rotation Reflection,Glide Symmetry,Mirror reflection + Translation, 17 Space group,Miller Indices ( h k l ),We need a method to notate the surface, which is known as
15、Miller Indices. The orientation of a surface or a crystal plane (Miller Indices) are defined by considering how the plane (or indeed any parallel plane) intersects the main crystallographic axes of the solid.,Step 1 : Find intercepts on the x, y and z axes. Intercepts : 3a , 2b, 1c Step 2 : Take rec
16、iprocals. The reciprocals are: (a/3a, b/2b, c/1c), i. e. (1/3,1/2,1) Step 3 : Reduce to smallest integers. Miller Indices : (2,3,6),So the surface/plane illustrated is the (236) plane.,Example:,Intercepts : a , , Reciprocals: (1, 0, 0) Miller Indices : (100),Intercepts : a , a, Reciprocals: (1, 1, 0) Miller Indices : (110),Common Planes (Cubic System),Intercepts : 1/2a, a, Reciprocals: (2
