SAED Patterns of Single Crystal, Polycrystalline and Amorphous Samples b c 020 110 200 r1 r2

Electron Diffraction Geometry for e-diffraction  e- Bragg’s Law: l = 2dsin l=0.037Å (at 100kV) =0.26o if d=4Å dhkl Specimen foil l = 2d L 2 r/L=sin2 as   0 r/L = 2 r/L = l/d or r = lLx r T D Reciprocal lattice http://www.matter.org.uk/diffraction/electron/electron_diffraction.htm Due to short wavelength, diffraction angle in TEM is very small. Diffraction angle in diagram is exaggerated. Value of dhkl can be obtained by measuring rhkl. 1 d L -camera length r -distance between T and D spots 1/d -reciprocal of interplanar distance(Å-1) SAED –selected area electron diffraction hkl [hkl] SAED pattern

Ewald’s Sphere Ewald’s sphere is built for interpreting diffraction lkl=1/ Ewald circle C incident beam diffracted beam 2 kd H ki g G 130 http://www.matter.org.uk/diffraction/geometry/ewald_sphere_construction_2d.htm http://www.matter.org.uk/diffraction/geometry/ewald_sphere_construction_3D.htm http://www.matter.org.uk/diffraction/geometry/ewald_sphere_diffraction_patterns.htm - Compare XRD (long wavelength) with SAED (short wavelength) To build the Ewald sphere 1. k has a magnitude of 1/ and points in the direction of the electron wave, 2. Construct a circle with radius 1/, i.e., lkl, which passes through 0, 3. The Ewald circle intersects the lattice point at G. CG-C0=0G or kd-ki=g Laue equation Wherever a reciprocal lattice point touches the circle, e.g., at G, Bragg's Law is obeyed and a diffracted beam will occur. At H, no diffraction.

Convergent Beam Electron Diffraction (CBED) CBED uses a conver- gent beam of elec- trons to limit area of specimen which con- tributes to diffraction pattern. Each spot in SAED then becomes a disc within which variations in intensity can be seen. CBED patterns contain a wealth of information about symmetry and thickness of specimen. Big advantage of CBED is that the information is generated from small regions beyond reach of other techniques. http://www.matter.org.uk/diffraction/electron/cbed.htm

SAED vs CBED SAED CBED Parallel beam Convergent beam sample objective Spatial resolution >0.5m Spatial resolution beam size Convergence angle sample objective lens spots disks T D T D SAED CBED

CBED-example 1

CBED-example 2 HOLZ HOLZ - High Order Laue Zone

Applications of CBED Phase identification Symmetry determination-point and space group Phase fingerprinting Thickness measurement Strain and lattice parameter measurement Structure factor determination

Symmetry Deviations

Phase Identification in BaAl2Si2O8 Hexagonal Orthorhombic Hexagonal 6mm 6mm 2mm 800oC 200oC 400oC <0001>

Phase Fingerprinting By CBED Orthorhombic AFE Cubic PE [001] CBED patterns of an antiferroelectric PbZrO3 single crystal specimen at (a) 20oC, (b) 280oC, (c)220oC. (d) [001] CBED pattern of a rhombohedral ferroelectric Pb(ZrTi)O3 Specimen at 20oC. Rhombohedral FE Rhombohedral FE

Symmetry and Lattice Parameter Determination EDS CBED A BF A B 010 Nb A B 001 B [100] SAED 0.2m A B A [111] EDS can identify difference in chemical composition between the core and shell regions. Using CBED HOLZ line pattern accuracy of lattice parameter measurement is ~0.1%. [143] CBED-HOLZ B Lattice parameters Experimental simulated