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Ch1. Crystal Structure

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Title: Ch1. Crystal Structure


1
Solid 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
2
1-1 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
3
1-2 Lattice Translation Vectors
  • ??? ??? r ?? r ?? ??? ? ??? ??
  • Basis ? ??

4
1-3 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
5
1-4 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??)
6
Continued.. (reference)
7
1-5 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
8
Continued.. (reference)
9
1-6 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 )
10
1-7 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,

11
Continued..
  • Hexagonal Close-packed Structure (hcp)
  • maximize the packing fraction
  • packing ratio 0.74 (the same as the fcc
    structure)
  • 12 nearest neighbors (fcc ? ??)

12
Continued..
  • 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

13
1.8 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
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