表面物理与表面分析2.ppt

1、Chapter 2SURFACE 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 periodi

4、cally 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, molecul

5、e, 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

6、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 Br

7、avais 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; Semiconduct

8、or: 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:

9、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

10、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

11、-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 po

12、ssible.,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 Sym

13、metry, = 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, 60n =1, 2, 3, 6,Reflection Symmetry,The reflection symmetry means the lattice is invariant by a reflection operation with respect to a lattice

14、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 Ind

15、ices. 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.

16、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 I

17、ndices : (110),Common Planes (Cubic System),Intercepts : 1/2a, a, Reciprocals: (2,1,0) Miller Indices : (210),Intercepts : a, a, a Reciprocals: (1,1,1) Miller Indices : (111),Notes for Miller indices,If any of the intercepts are negative, the Miller indices are denoted, for example: (00 -1) is inste

18、ad by .,Miller indices are usually multiplied or divided by an integer to simplify them, for example: (200) is transformed to (100) by divided by 2 .,(100), ( 00) , (200), (300) are parallel,100,111,(111), (222), (333) are parallel (100), (010), (001) are orthogonal and in some crystal systems may b

19、e identical,In the hcp crystal system, four Miller indices are used by convention (only three are independent),Crystallographic directions,Vectors should pass through the origin (but can be translated); The length of the vector projected onto the axes is determined in terms of a, b, and c; These num

20、bers are reduced to the smallest integer values.,Crystallographic direction is defined as:,Vector is 0.5a 1b 0c Multiply by 2 Gives 120,Some crystal planes and directions in a cubic crystal, and their Miller indices.,( h k l ) plane,h k l direction,In cubic systems only, the h k l direction is perpe

21、ndicular to the ( h k l ) plane.,Surface Notation,.,It is very common that the surface unit cell is not the same as that of the bulk. This phenomenon is known as surface reconstruction. There are varieties of different periodicities for the surface reconstruction, thus we need a form of notations to

22、 describe the different surface reconstructions. Two notations are usually used, one is Woods notation, and the other is matrix notation.,Wood Notation,Wood notation: 22,Simplest and most frequently used method for describing a surface structure. If surface unit vectors (as , bs) have the relation w

23、ith the substrate unit vectors (a, b) as: as = m a , bs= n b Thus the notation for this surface is (mn).,as = 2 a bs = 2 b,If the surface unit cell is rotated with respect to the underlying lattice by an angle of degrees, the notation becomes (m n) R (anticlockwise). If the surface unit cell is best

24、 described using a centered rather than a primitive cell, this is indicated as c (mn). The full notation of a surface can be written as:M (h k l) (mn) R, (for clean surfaces)or M (h k l) (mn) R A, (for adsorbed surfaces)where M is the chemical symbol of the bulk crystal, (h k l) are the Miller index

25、 of its surface, A is the symbol of the adsorbed atoms.,Ni(100) - 22 - O,Examples:,Oxygen on Ni(100),CO on Ni(100),fcc (100) (22),fcc(100) c(22),Problems?,fcc (100),or ( 2 2)R45,fcc (110) (22),fcc (110) c (22),fcc (110),fcc(111) (22),fcc(111) ( 3 3)R30,fcc (111),Matrix Notation,In matrix notation, t

26、he surface basis vectors as and bs are the linear combinations of the substrate basis vectors a and b:,A much more general system of describing surface structures which can be applied to all ordered surface structures.,So the above equation can be expressed as,Mij are four coefficients which form a

27、matrix M:,M is now used as the notation of the surface.,Examples,Matrix notation:,Matrix notation is:,Stepped Surface,E - element s - sign of step structure m - width of terrace hkl - miller index of terrace n - height of step hkl - miller index of step,Notation (755) = Pt (s) - 7 (111) (100) ,E = P

28、t m = 7 h k l : 111 n =1 hk l : 100,Example:,Surface Notation,(2) Stepped SurfaceTerrace StepE (s) - m ( h k l ) n ( hkl ),Wood notationE ( h k l )( mn) R E ( h k l ) (mn) R - A,Matrix notation,(1) Flat Surface,Reciprocal space is also called Fourier space, k-space, or momentum space in contrast to

29、real space or direct space. The concept of the reciprocal lattice was devised to tabulate two important properties of crystal planes: their slopes and their interplanar distances. The reciprocal space lattice is a set of imaginary points, with the direction normal to the real space planes and the ab

30、solute value of the vector is equal to the reciprocal of the real interplanar distance.,Reciprocal Lattice,Reciprocal lattice vector:,Bulk (3D),For surface unit cell, the periodicity in c dimension is lost, hence only two Miller indices, h and k are needed.,Surface (2D),is the unit vector normal to

31、the surface,Reciprocal lattice vector:,a = (a, 0) a* = (2 /a, 0) b = (0, b) b* = (0, 2 /b) Real-space Reciprocal space Position k-position length 1/length,Square,Rectangle,Oblique,Bravais lattices,Centered Rectangle,Hexagonal,(a) No reconstruction,(b) 22 reconstruction,Examples,Exercise,Real space,R

32、eciprocal lattice?,The ideal crystal surface is a simple termination plane of the crystal bulk and possesses perfect two dimensional periodicity. It is a plane passing through an infinite crystal and separating the two parts of it to infinity. The important point in the definition of an “ideal surfa

33、ce” is that it forbids any changes on the surface. Positions of the atoms and the electron density inside the semi-infinite crystal remain the same as in the original infinite crystal,II. Ideal Surface Structure,fcc metals,(100),Square lattice, 4-fold rotational symmetry,(110),Rectangular lattice 2-

34、fold rotational symmetry,(111),Hexagonal lattice 3-fold rotational symmetry,fcc (100),fcc (110),fcc (111),bcc Metals,(100),(111),(110),bcc (100),bcc (110),bcc (111),hcp Metals,hcp(0001),The Miller Indices used to describe the orientation of hcp surface planes has four numbers. The notation is based

35、upon three axes at 120 in the close-packed plane, and one axis (c -axis) perpendicular to these planes.,The elementary cubes consist of two face-centered cubic lattices. In the diamond lattice all the atoms in the two elementary cubes are atoms from the same chemical element.,Diamond lattice,Semicon

36、ductor,The elementary cubes also consist of two face-centered cubic lattices, which are occupied by different atomic species, for example by Zn-ions and by S-ions of opposite charge.,Zinc blende lattice,Si, Ge: Diamond structure,Si (100), (110) and (111) surfaces:,NaCl(100),Compound materials,ZnS (1

37、10),CsCl (100),Ni3Al (111),Ni3Al(100),NiAl alloy,High miller index planes,High index surfaces are those for which one or more of the Miller Indices are relatively large numbers. The most commonly studied surfaces of this type are vicinal surfaces which are cut at a relatively small angle to one of the low index surfaces.,fcc(10.8.7),fcc(775),Thank you!,