Crystalline Solids

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Lecture 2.1

• Crystalline Solids

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Crystalline Solids

• Poly-crystalline solids - Grains
• Mono-crystalline solids- Whiskers, Wafers

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Crystal Lattices
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Crystal Systems gt14 Bravais Lattices
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Bravais lattice (abc)

• Lattice is constructed of repeated unit cells
• Lattice Point - 1/3a,1/2b,1/4c
• Crystallographic Direction (vector from 0,0,0 to
  xyz) which is defined by
• uvw smallest set of integers having the same
  ratio as xyz
• bar over number minus number

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Close Packed Structures

• Cubic, BCC, FCC, HCC are the focus of this
  course
• Determining distances and volume fractions in
  Cubic Structures

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Miller indices for a plane (hkl)
Family of Miller Planes hkl
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EXAMPLE- Miller Index

• intercepts on a,bc axes3,12, respectively
• reciprocals 1/3,1/11/2, respectively
• smallest set of integers with same common ratio
  2,63
• Miller indexes of Plane, (hkl)(263)
• also called reciprocal space plane

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Family of Planes 110
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Measuring Structure with X-rays

• Generate X-ray radiation
• X-ray Diffraction (?????90)
• ao cubic lattice parameter

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X-Ray Generation

• Electron Scattering
• Broad Band X-rays
• Electron Kickout
• K,L,M shell electron
• Replace with higher electron
• Transition gives X-rays
• one wave length
• K?,K?, L?, L?

K?
K?
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X-ray GenerationEnergy Level Diagrams
-0.85 eV
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-1.51 eV
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L?
L?
K?
L
-3.40 eV
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K?
K
-13.6 eV
1
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X-ray Camera-1

• Single Crystal Camera
• Broad Band X-rays
• all ? in source
• only Bragg (diffracting) wavelengths reflect

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SiGe Crystal
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X-ray Camera-2 (film strip)

• X-rays of Single ?
• All (hkl) planes are exposed at all angles at all
  times
• Diffraction of Bragg planes

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Electron Diffraction
Focused Electrons

• Electrons of different energy
• Transmission through sample
• CCD detector

Thinned Sample
CCD Detector
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Seeing Crystal Structure with and Atomic Force
Microscope

• Electron Microscope
• Atomic Force Microscope
• Scanning Tunneling Microscope

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Diffracting Planes
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Changing Crystal Structure Allotropic Phase
Change HCP-gtFCC-gtBCC-gtSC

• Ca(fcc) --(447ºC)-gt Ca(bcc)
• Co(hcp) --(427ºC)--gt Co(fcc)
• Fe(bcc) --(912ºC)--gtFe(fcc) --(1394ºC)--gtFe(hcp)
• Na(bcc) --(-233ºC)--gt Na(hcp)
• Ti(hcp) --(883ºC)--gtTi(bcc)
• Zr(hcp) --(872ºC)--gt Zr(bcc)

Decreasing density with increasing temperature!
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Defects in Crystal Structure

• Vacancy, Interstitial, Impurity
• Schottky Defect
• Frenkel Defect
• Dislocations edge dislocation, line, screw
• Grain Boundary

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Effect of Structure on Mechanical Properties

• Elasticity
• Plastic Deformation