Title: Ch1. Crystal Structure
1Solid State Physics
Ch1. Crystal Structure
Prof. J. Joo (jjoo_at_korea.ac.kr) Department of
Physics, Korea University http//smartpolymer.kore
a.ac.kr
Electronic Materials Research Lab in Physics,
http//smartpolymer.korea.ac.kr
21-1 Crystal
- Crystal periodic arrays of atoms (??? ??? ??)
- cf. non-crystal disorder or amorphous material
- (??? ??? ??? ??)
- infinite repetition of identical blocks
- to check through experimental
method - X-ray scattering (or X-ray diffraction)
- Structure of all crystals
- described in terms of
- Lattice Basis
?? ?? ?? ??? ?(point)?? ???? ???? geometrical
pattern
Lattice point ??? ?? group
31-2 Lattice Translation Vectors
- ??? ??? r ?? r ?? ??? ? ??? ??
41-3 Primitive Lattice Cell
- Minimum volume cell
- A type of cell or unit cell
- of atoms in a primitive cell (or primitive
basis) is always the same for a given structure - One lattice point identical atoms per primitive
cell - The basis associated with a primitive cell
primitive basis
- Wigner-Seitz cell (primitive cell ? ??? ??? ??)
?? all nearby lattice point
(not the nearest) normal midpoints
51-4 Symmetry of Crystals
- Translational property lattice translation
vector - Rotation and reflection point operation
- Rotation (about a particular axis)
- Reflection lattice point ?? ???? ??? ??
reflection - sh reflection in a horizontal plane (? to a
principal axis) - sv reflection in a vertical plane
(containing the principal axis) - Inversion operation r r
Ref. Space Groups for Solid State
Scientists 2nd Ed. By G.Burns A.M.Glazer
not satisfy translation symmetry (Ch1, Fig5??)
6Continued.. (reference)
71-5 Fundamental Types of Lattices
- 2- Dimensional Lattice Types
- 5 Bravais lattices
- square lattice
- hexagonal lattice
- rectangular lattice
- centered rectangular lattice
- oblique lattice Fig.3(a)
- 3- Dimensional Lattice Types
- 7 system 14 different lattice
types
Fig.7
8Continued.. (reference)
91-6 Index System for Crystal Planes
- Crystal plane ? ??? ???? ?? ??
- Find the intercepts on the axis in terms of
a1,a2,a3 - Take the reciprocals of these numbers and then
reduce to three integers having the same ratio,
usually the smallest three integers - The result in parenthesis ( h k l )
- index of
the plane
? Negative indices ( h k l ) e.g.)
( -1 , 0 , 0 ) ( 1 , 0 , 0 )
101-7 Simple Crystal Structures
- Sodium Chloride (NaCl) Structure
- Cl
- Na
- lattice fcc
- basis 2-basis (Na
Cl-) - e.g.) LiH, MgO, MnO, KBr,
- Cesium Chloride (CsCl) Structure
- Cl
- Cs
- gtgt simple cubic lattice with one
body-centered - different atom
- e.g.) BeCu, AlNi, AgMg,
11Continued..
- Hexagonal Close-packed Structure (hcp)
- maximize the packing fraction
- packing ratio 0.74 (the same as the fcc
structure) - 12 nearest neighbors (fcc ? ??)
12Continued..
- Diamond Structure
- fcc lattice with the basis(2) at
identical atoms - conventional unit cell
- 8 atoms (no way to choose the primitive cell)
- cf) 4? ?? C, Si, Ge, Sn(tin), Pb(lead),
- Cubic Zinc Sulfide Structure
- fcc lattice with the basis(2) at different
atoms - Zn
- S
131.8 Direct Imaging of Atomic Structure
- STM (Scanning Tunneling Microscopy)
- ?? Table Table 3. Crystal Structure of the
Element - Table 4. Density and Atomic Concentration
- ?? ???? 3? (1? ?)
fine metal tip
fine surface of a crystal