Lecture 2.1Lecture 2.1

Crystalline Solids

Crystalline SolidsCrystalline Solids

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

Crystal LatticesCrystal Lattices

Crystal Systems =>14 Bravais LatticesCrystal Systems =>14 Bravais Lattices

Bravais lattice (abc) Bravais lattice (abc)

Lattice is constructed of repeated unit cells

Lattice Point - 1/3a,1/2b,1/4cCrystallographic 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 StructuresClose Packed Structures

Cubic, BCC, FCC, HCC are the focus of this course

Determining distances and volume fractions in Cubic Structures

Miller indices for a Miller indices for a planeplane (hkl) (hkl)

Family of Miller Planes {hkl}

EXAMPLE- Miller Index 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”

Family of Planes {110}Family of Planes {110}

Measuring Structure with X-raysMeasuring Structure with X-rays

Generate X-ray radiation

X-ray Diffraction (=90)– ao= cubic lattice parameter

)sin(2)sin(1

2)sin(2222

2

2

2

2

2

2

lkh

a

cl

bk

ah

dn ohkl

wave length

X-Ray GenerationX-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

wave length

e-

X-Rays

Applied Voltage

K

K

X-ray GenerationX-ray GenerationEnergy Level DiagramsEnergy Level Diagrams

1 K

2

34

-13.6 eV

-3.40 eV

-1.51 eV

L

-0.85 eV

K

K L L

hc

n

Z

n

ZeVE

ab

n

2

2

2

2

6.13

X-ray Camera-1X-ray Camera-1

Single Crystal Camera– Broad Band X-rays– all in source– only Bragg

(diffracting) wavelengths reflect

Film

Single Crystal

Broad Band X-rays

SiGe Crystal

X-ray Camera-2 (film strip)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

X-rays

Capillary w PolycrystalSample Rotated

Strip of Film in Circle

Electron DiffractionElectron Diffraction

Electrons of different energy

Transmission through sample

CCD detector

Focused Electrons

ThinnedSample

CCD Detector

Seeing Crystal Structure with and Seeing Crystal Structure with and Atomic Force MicroscopeAtomic Force Microscope

Electron Microscope

Atomic Force Microscope

Scanning Tunneling Microscope

Diffracting PlanesDiffracting Planes

Changing Crystal Structure – Changing Crystal Structure – Allotropic Phase Change Allotropic Phase Change HCP->FCC->BCC->SCHCP->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!

Defects in Crystal StructureDefects in Crystal Structure

Vacancy, Interstitial, ImpuritySchottky DefectFrenkel DefectDislocations – edge dislocation, line,

screwGrain Boundary

Effect of Structure on Effect of Structure on Mechanical PropertiesMechanical PropertiesElasticityPlastic Deformation