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Lecture 2.1

Lecture 2.1. Crystalline Solids. Crystalline Solids. Poly-crystalline solids - Grains Mono-crystalline solids- Whiskers, Wafers. Crystal Lattices. Crystal Systems =>14 Bravais Lattices. Bravais lattice (abc). Lattice is constructed of repeated unit cells Lattice Point - 1/3a,1/2b,1/4c

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Lecture 2.1

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  1. Lecture 2.1 Crystalline Solids

  2. Crystalline Solids • Poly-crystalline solids - Grains • Mono-crystalline solids- Whiskers, Wafers

  3. Crystal Lattices

  4. Crystal Systems =>14 Bravais Lattices

  5. 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

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

  7. Miller indices for a plane (hkl) Family of Miller Planes {hkl}

  8. EXAMPLE- Miller Index • intercepts on a,b&c axes=3,1&2, respectively • reciprocals = 1/3,1/1&1/2, respectively • smallest set of integers with same common ratio = 2,6&3 • Miller indexes of Plane, (hkl)=(263) • also called “reciprocal space plane”

  9. Family of Planes {110}

  10. Measuring Structure with X-rays • Generate X-ray radiation • X-ray Diffraction (=90) • ao= cubic lattice parameter

  11. 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

  12. X-ray GenerationEnergy Level Diagrams -0.85 eV 4 -1.51 eV 3 L L K L -3.40 eV 2 K K -13.6 eV 1

  13. X-ray Camera-1 • Single Crystal Camera • Broad Band X-rays • all  in source • only Bragg (diffracting) wavelengths reflect

  14. SiGe Crystal

  15. 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

  16. Electron Diffraction Focused Electrons • Electrons of different energy • Transmission through sample • CCD detector Thinned Sample CCD Detector

  17. Seeing Crystal Structure with and Atomic Force Microscope • Electron Microscope • Atomic Force Microscope • Scanning Tunneling Microscope

  18. Diffracting Planes

  19. Changing Crystal Structure – Allotropic Phase Change HCP->FCC->BCC->SC • Ca(fcc) --(447ºC)-> Ca(bcc) • Co(hcp) --(427ºC)--> Co(fcc) • Fe(bcc) --(912ºC)-->Fe(fcc) --(1394ºC)-->Fe(hcp) • Na(bcc) --(-233ºC)--> Na(hcp) • Ti(hcp) --(883ºC)-->Ti(bcc) • Zr(hcp) --(872ºC)--> Zr(bcc) Decreasing density with increasing temperature!

  20. Defects in Crystal Structure • Vacancy, Interstitial, Impurity • Schottky Defect • Frenkel Defect • Dislocations – edge dislocation, line, screw • Grain Boundary

  21. Effect of Structure on Mechanical Properties • Elasticity • Plastic Deformation

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