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 Electron Kickout K,K, L, L
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 Generation Energy Level Diagrams4
-1.51 eV 3 L L K L
-3.40 eV 2 K K
-13.6 eV 1

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

15. SiGe Crystal

16. 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

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

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

19. Diffracting Planes

20. 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!

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

27. Effect of Structure on Mechanical Properties
Elasticity
Plastic Deformation