Ch1. Crystal Structure

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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
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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
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1-2 Lattice Translation Vectors

• ??? ??? r ?? r ?? ??? ? ??? ??

• Basis ? ??

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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
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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??)
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Continued.. (reference)
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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
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Continued.. (reference)
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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 )
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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,

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Continued..

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

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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

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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