Lecture 2.1 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 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) –a o = cubic lattice parameter

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 KK

X-ray Generation Energy Level Diagrams 1 K eV eV eV L eV KK KK LL LL

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

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

Electron Diffraction Electrons of different energy Transmission through sample CCD detector Focused Electrons 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 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