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: “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 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 periodically 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, molecule, 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 define 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 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; Semiconductor: 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,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,Also 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!,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 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.,Rotation 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 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 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 reciprocals. 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