Electron diffraction Selected area diffraction SAD in TEM

Electron diffraction Selected area diffraction (SAD) in TEM Electron back scatter diffraction (EBSD) in SEM 9/2 -10 MENA 3100

Bragg’s law tells you at which angle θB to expect maximum diffracted intensity for a particular family of crystal planes. For large crystals, all other angles give zero intensity. The Ewald Sphere Cu Kalpha X-ray: = 150 pm Electrons at 200 k. V: = 2. 5 pm ko k The observed diffraction pattern is the part of the reciprocal lattice that is intersected by the Ewald sphere g 9/2 -10 MENA 3100

Intensity distribution and Laue zones Ewald sphere (Reflecting sphere) ko First order Laue zone 2θ k g Zero order Laue zone 9/2 -10 MENA 3100 The intensity distribution around each reciprocal lattice point is spread out in the form of spikes directed normal to the specimen

Multiple scattering Incident beam • Multiple scattering (diffraction) leads to oscillations in the diffracted intensity with increasing thickness of the sample – Forbidden reflection may be observed – Kinematical intensities with XRD Transmitted Diffracted beam Multiple diffracted beam 9/2 -10 MENA 3100

Simplified ray diagram Parallel incoming electron beam 3, 8 Å Si Sample 1, 1 nm Objective lense Diffraction plane Objective aperture (back focal plane) Image plane 9/2 -10 MENA 3100 Selected area aperture

Apertures Condenser aperture Objective aperture Selected area aperture 9/2 -10 MENA 3100

Diffraction with large SAD aperture, ring and spot patterns Poly crystalline sample Four epitaxial phases Similar to XRD from polycrystalline samples. 9/2 -10 The orientation relationship between the phases can be determined with ED. MENA 3100

Camera constant R=L tan 2θB ~ 2 LsinθB 2 dsinθB =λ ↓ R=Lλ/d Camera constant: K=λL Film plate 9/2 -10 MENA 3100

Indexing diffraction patterns The g vector to a reflection is normal to the corresponding (h k l) plane and Ig. I=1/dnh nk nl (h 2 k 2 l 2) - Measure Ri and the angles between the reflections - Calculate di , i=1, 2, 3 - Compare with tabulated/theoretical calculated d-values of possible phases - Compare Ri/Rj with tabulated values for cubic structure. - g 1, hkl+ g 2, hkl=g 3, hkl (vector sum must be ok) - Perpendicular vectors: gi ● gj = 0 Orientations of corresponding planes in the real space 9/2 -10 (=K/Ri) Zone axis: gi x gj =[HKL]z All indexed g must satisfy: g ● [HKL]z=0 MENA 3100

Example: Study of unknown phase in a Bi. Fe. O 3 thin film Metal organic compound on Pt Bi. Fe. O 3 Heat treatment at 350 o. C (10 min) to remove organic parts. Pt Ti. O 2 Lim Process repeated three times before final heat treatment at 500 -700 o. C (20 min). (intermetallic phase grown) Si. O 2 Si 200 nm Goal: Bi. Fe. O 3 with space grupe: R 3 C and celle dimentions: a= 5. 588 Å c=13. 867 Å 9/2 -10 MENA 3100

Determination of the Bravais-lattice of an unknown crystalline phase Tilting series around common axis 27 o 15 o 50 nm 10 o 0 o 9/2 -10 MENA 3100

Determination of the Bravais-lattice of an unknown crystalline phase Tilting series around a dens row of reflections in the reciprocal space 0 o 50 nm 19 o Positions of the reflections in the reciprocal space 25 o 40 o 52 o 9/2 -10 MENA 3100

Bravais-lattice and cell parameters 011 111 001 c 101 b 010 a 110 [100] [011] [101] d=Lλ/R 100 6. 04 Å From the tilt series we find that the unknown phase has a primitive orthorhombic Bravias-lattice with cell parameters: a= 6, 04 Å, b= 7. 94 Å og c=8. 66 Å 7. 94 Å 9/2 -10 6 8. 6 Å α= β= γ= 90 o MENA 3100

Chemical analysis by use of EDS and EELS Ukjent fase Bi. Fe 2 O 5 Bi. Fe. O 3 O-K Fe - L 2, 3 Bi. Fe. O 3 Ukjent fase 500 e. V forskyvning, 1 e. V pr. kanal 9/2 -10 MENA 3100

Published structure A. G. Tutov og V. N. Markin The x-ray structural analysis of the antiferromagnetic Bi 2 Fe 4 O 9 and the isotypical combinations Bi 2 Ga 4 O 9 and Bi 2 Al 4 O 9 Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy (1970), 6, 2014 -2017. Romgruppe: Pbam nr. 55, Bi Fe Fe O O 4 g 4 h 4 f 4 g 8 i 4 h 2 b celleparametre: 7, 94 Å, 8, 44 Å, 6. 01Å x 0, 176 0, 349 0 0, 14 0, 385 0, 133 0 y 0, 175 0, 333 0, 5 0, 435 0, 207 0, 427 0 z 0 0, 5 0, 244 0 0, 242 0, 5 Celle parameters found with electron diffraction (a= 6, 04 Å, b= 7. 94 Å and c=8. 66 Å) fits reasonably well with the previously published data for the Bi 2 Fe 4 O 9 phase. The disagreement in the c-axis may be due to the fact that we have been studying a thin film grown on a crystalline substrate and is not a bulk sample. The conditions for reflections from the space group Pbam is in agreement with observations done with electron diffraction. Conclusion: The unknown phase has been identified as Bi 2 Fe 4 O 9 with space group Pbam with cell parameters a= 6, 04 Å, b= 7. 94 Å and c=8. 66 Å. 9/2 -10 MENA 3100

Kikuchi pattern Inelastically scattered electrons give rise to diffuse background in the ED pattern. θB 2θB Kikuchi lines are due to: -Inelastic+ elastic scattering event -lattice parameter -accelerating voltage Objective lens Diffraction plane Excess line Deficient line 1/d -Burgers vector 9/2 -10 Excess θB -Angular distribution of inelastic scattered electrons falls of rapidly with angle. I=Iocos 2α Used for determination of: -crystal orientation Deficient MENA 3100 http: //www. doitpoms. ac. uk/index. html http: //www. doitpoms. ac. uk/tlplib/diffraction-patterns/kikuchi. php

Electron Back Scattered Diffraction (EBSD) Orientation Image Microscopy (OIM) in a SEM • EBSD – Geometry similar to Kikuchi diffraction in TEM – Information from nm regions • OIM – Gives the distribution of crystal orientation for grains intersected by the sample section that can be presented in various ways. (+/- 0. 5 o) – Involves • collection a large sets of EBSD data • Bin the crystallographic data from each pixel (stereographic triangle) – Colour codes – Localized preferred orientation and residual stress etc. 9/2 -10 MENA 3100

Orientation map example CD-200 Nordiff EBSD Camera Step=0. 2 micron 9/2 -10 MENA 3100

Overlaid maps 9/2 -10 MENA 3100

Electron back scattered diffraction (EBSD) Principal system components Sample tilted at 70° from the horizontal, a phosphor screen, a sensitive CCD video camera, a vacuum interface for mounting the phosphor and camera in an SEM port. Electronic hardware that controls the SEM, including the beam position, stage, focus, and magnification. A computer to control EBSD experiments, analyse the EBSD pattern and process and display the results. http: //www. ebsd. com/ebsd-explained/anim 2. htm http: //www. ebsd. com/ebsd-explained/simulationapplet. htm 9/2 -10 MENA 3100

Microscope operating conditions Probe current Increased probe current – shorter camera integration time – increased beam size Accelerating voltage Increased accelerating voltage – reduced λ - reduced width of the Kikuchi bands – brighter pattern - shorter integration time – higher penetration depth Changing the accelerating voltage may require adjustment to the Hough transform filter size to ensure the Kikuchi bands are detected correctly 20 k. V 10 k. V Effect of changing accelerating voltage on diffraction patterns from nickel 9/2 -10 MENA 3100 30 k. V

Microscope operating conditions Working distance and magnification Because the sample is tilted, the SEM working distance will change as the beam position moves up or down the sample, and the image will go out of focus. Image without tilt or dynamic focus compensation 9/2 -10 Image with tilt compensation and no dynamic focus compensation MENA 3100 Image with tilt and dynamic focus compensation. The working distance is 14. 98 mm at the top and 15. 11 mm at the bottom of the image

Microscope operating conditions EBSD systems can compensate automatically for shifts in the pattern centre by calibrating at two working distances and interpolating for intermediate working distance values. It is important to know the range of working distances for which the EBSD system will remain accurately calibrated. With a tilted sample, the pattern centre position will depend on the sample working distance. The yellow cross shows the pattern centre with working distance 10, 18 and 22 mm 9/2 -10 MENA 3100

Band Intensity The mechanisms giving rise to the Kikuchi band intensities and profile shapes are complex. As an approximation, the intensity of a Kikuchi band for the plane (hkl) is given by: where fi(θ) is the atomic scattering factor for electrons and (xi yi zi) are the fractional coordinates in the unit cell for atom i. An observed diffraction pattern should be compared with a simulation to ensure only planes that produce visible Kikuchi bands are used when solving the diffraction pattern. Diffraction pattern from the orthorhombic ceramic mullite (3 Al 2 O 3 2 Si. O 2) collected at 10 k. V accelerating voltage. 9/2 -10 Solution overlaid on the diffraction pattern giving the crystal orientation as {370}<7 -34> Simulated diffraction pattern showing all Kikuchi bands with intensity greater than 10% of the most intense band. MENA 3100 Simulation of crystal orientation giving the solution shown.

Background removal The background can be measured by scanning the beam over many grains in the sample to average out the diffraction information. The background can be removed by subtraction from, or division into, the original pattern. Background Original pattern Background subtraction Background division http: //www. ebsd. com/ebsd-explained/undertakingexperiments 3. htm 9/2 -10 MENA 3100