Transcript Lecture2.1.ppt

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
 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
Close Packed Structures
Cubic, BCC, FCC, HCC
are the focus of this course
 Determining distances and volume
fractions in Cubic Structures

Miller indices for a plane (hkl)
Family of Miller Planes {hkl}
EXAMPLE- Miller Index
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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”
Family of Planes {110}
Measuring Structure with X-rays

Generate X-ray radiation

X-ray Diffraction (=90)
wave length
– ao= cubic lattice parameter
n  2d hkl sin(  )  2
1
2
2
2
h
k
l


a 2 b2 c 2
sin(  )  2
ao
h k l
2
2
2
sin(  )
X-Ray Generation

Electron Scattering
– Broad Band X-rays

Electron Kickout
– K,L,M shell electron
– Replace with higher
electron
– Transition gives Xrays
• one wave length

K,K, L, L
K
e-
X-Rays
K
Applied
Voltage
wave length
X-ray Generation
Energy Level Diagrams
-0.85 eV
-1.51 eV
4
3
K
2
K
1
L
L
L
-3.40 eV
 Z 2 Z 2  hc
En  13.6eV  2  2  
 nb na  
K
-13.6 eV
X-ray Camera-1

Single Crystal
Camera
– Broad Band X-rays
– all  in source
– only Bragg
(diffracting)
wavelengths reflect
Single
Crystal
Broad
Band
X-rays
Film
SiGe Crystal
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

Strip of Film
in Circle
X-rays
Capillary w
PolycrystalS
ample
Rotated
Electron Diffraction
Focused
Electrons

Electrons of
different energy
 Transmission
through sample
 CCD detector
Thinned
Sample
CCD Detector
Seeing Crystal Structure with and
Atomic Force Microscope
Electron
Microscope
 Atomic Force
Microscope
 Scanning
Tunneling
Microscope

Diffracting Planes
Changing Crystal Structure –
Allotropic Phase Change
HCP->FCC->BCC->SC
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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!
Defects in Crystal Structure
Vacancy, Interstitial, Impurity
 Schottky Defect
 Frenkel Defect
 Dislocations – edge dislocation, line,
screw
 Grain Boundary

Effect of Structure on
Mechanical Properties
Elasticity
 Plastic Deformation
