Electron diffraction Selected area diffraction (SAD) in TEM Electron back scatter diffraction (EBSD) in SEM 9/2-10 MENA3100

Bragg’s law The Ewald Sphere Cu Kalpha X-ray:  = 150 pm 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 ko k g Cu Kalpha X-ray:  = 150 pm Electrons at 200 kV:  = 2.5 pm Hva er forskjell i tetabragg for røntgen og elelktroner for samme d-verdi i en krystall? Elektroner vekselvirker sterkere enn røntgen, mer dynamisk spredning (kinematiske intensiteter med røntgen). The observed diffraction pattern is the part of the reciprocal lattice that is intersected by the Ewald sphere 9/2-10 MENA3100

Intensity distribution and Laue zones 2θ ko k g Intensity distribution and Laue zones Ewald sphere (Reflecting sphere) The intensity distribution around each reciprocal lattice point is spread out in the form of spikes directed normal to the specimen First order Laue zone Zero order Laue zone 9/2-10 MENA3100

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 Multiple diffracted beam Transmitted beam Diffracted beam 9/2-10 MENA3100

Simplified ray diagram Parallel incoming electron beam 1,1 nm 3,8 Å Sample Objective lense Diffraction plane (back focal plane) Objective aperture Parallel incoming electron beam and a selection aperture in the image plane. Diffraction from a single crystal in a polycrystalline sample if the aperture is small enough/crystal large enough. Orientation relationships between grains or different phases can be determined. ~2% accuracy of lattice parameters Convergent electron beam better Selected area aperture Image plane 9/2-10 MENA3100

Apertures Condenser aperture Objective aperture Selected area aperture Intermediate and projector lenses. Tilting of sample, beam tilt. Recording on film or CCD camera. 9/2-10 MENA3100

Diffraction with large SAD aperture, ring and spot patterns Poly crystalline sample Four epitaxial phases Similar to XRD from polycrystalline samples. The orientation relationship between the phases can be determined with ED. 9/2-10 MENA3100

Camera constant Film plate R=L tan2θB ~ 2LsinθB 2dsinθB =λ ↓ R=Lλ/d K=λL 9/2-10 MENA3100

Indexing diffraction patterns The g vector to a reflection is normal to the corresponding (h k l) plane and IgI=1/dnh nk nl Measure Ri and the angles between the reflections - Calculate di , i=1,2,3 (=K/Ri) Compare with tabulated/theoretical calculated d-values of possible phases Compare Ri/Rj with tabulated values for cubic structure. g1,hkl+ g2,hkl=g3,hkl (vector sum must be ok) Perpendicular vectors: gi ● gj = 0 Zone axis: gi x gj =[HKL]z All indexed g must satisfy: g ● [HKL]z=0 (h2k2l2) Orientations of corresponding planes in the real space 9/2-10 MENA3100

Example: Study of unknown phase in a BiFeO3 thin film 200 nm Si SiO2 TiO2 Pt BiFeO3 Lim Metal organic compound on Pt Heat treatment at 350oC (10 min) to remove organic parts. Process repeated three times before final heat treatment at 500-700 oC (20 min) . (intermetallic phase grown) Goal: BiFeO3 with space grupe: R3C and celle dimentions: a= 5.588 Å c=13.867 Å 9/2-10 MENA3100

Determination of the Bravais-lattice of an unknown crystalline phase 50 nm Tilting series around common axis 9/2-10 MENA3100

Determination of the Bravais-lattice of an unknown crystalline phase Tilting series around a dens row of reflections in the reciprocal space 50 nm Positions of the reflections in the reciprocal space 9/2-10 MENA3100

Bravais-lattice and cell parameters 100 110 111 010 011 001 101 [011] [100] [101] d = L λ / R 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 α= β= γ= 90o 6.04 Å 7.94 Å 8.66 Å 9/2-10 MENA3100

Chemical analysis by use of EDS and EELS Ukjent fase BiFeO3 BiFe2O5 Ukjent fase BiFeO3 Fe - L2,3 O - K 500 eV forskyvning, 1 eV pr. kanal 9/2-10 MENA3100

Published structure 9/2-10 MENA3100 A.G. Tutov og V.N. Markin The x-ray structural analysis of the antiferromagnetic Bi2Fe4O9 and the isotypical combinations Bi2Ga4O9 and Bi2Al4O9 Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy (1970), 6, 2014-2017. Romgruppe: Pbam nr. 55, celleparametre: 7,94 Å, 8,44 Å, 6.01Å x y z Bi 4g 0,176 0,175 0 Fe 4h 0,349 0,333 0,5 Fe 4f 0 0,5 0,244 O 4g 0,14 0,435 0 O 8i 0,385 0,207 0,242 O 4h 0,133 0,427 0,5 O 2b 0 0 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 Bi2Fe4O9 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 Bi2Fe4O9 with space group Pbam with cell parameters a= 6,04 Å, b= 7.94 Å and c=8.66 Å. 9/2-10 MENA3100

Kikuchi pattern Excess line Deficient 1/d 2θB θB Diffraction plane Objective lens 1/d Inelastically scattered electrons give rise to diffuse background in the ED pattern. Angular distribution of inelastic scattered electrons falls of rapidly with angle. I=Iocos2α Kikuchi lines are due to: Inelastic+ elastic scattering event Deficient Excess Used for determination of: crystal orientation -lattice parameter -accelerating voltage -Burgers vector Tegn opp Kikuchi mønster for et tenkt SAD mønster (feks. [100] proj) http://www.doitpoms.ac.uk/index.html http://www.doitpoms.ac.uk/tlplib/diffraction-patterns/kikuchi.php 9/2-10 MENA3100

Electron Back Scattered Diffraction (EBSD) Orientation Image Microscopy (OIM) in a SEM 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. (+/- 0.5o) 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. Presenting the results both quantitatively and in an image format. The first step is to define a grid of test pixels across the region of interest. The total number of pixel in the image grid is critical, since it determines, with the dwell-time per pixel, the time required to collect data. 9/2-10 MENA3100

Orientation map example CD-200 Nordiff EBSD Camera Step=0.2micron 9/2-10 MENA3100

Overlaid maps 9/2-10 MENA3100

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/anim2.htm http://www.ebsd.com/ebsd-explained/simulationapplet.htm 9/2-10 MENA3100

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   It is very important to understand the effect of varying the microscope operating conditions on the diffraction pattern. Increased probe size Must be balanced with the spatial resolution required Also, because more energy is being deposited on the phosphor screen, this will result in a brighter pattern which requires a shorter integration time (Figure 4). Higher accelerating voltages may be required to penetrate conducting layers, and lower accelerating voltages for restraining the beam to thin layers, or for charging samples. Note that there is an effect on the bandwidth, sharpness and contrast Experimental setup It is important to balance the requirements of total experiment time, orientation accuracy and spatial resolution when designing an EBSD experiment. The orientation measurement accuracy is typically ±0.5°. Spatial resolution The electrons contributing to the diffraction pattern originate within nanometres of the sample surface. Spatial resolution depend on the electron beam diameter i.e. type of electron source and probe current.   Typical beam diameters at 0.1 nA probe current and 20 kV accelerating voltage are 2 nm for a FEG source and 30 nm for a tungsten source. Pressure EBSD patterns can also be collected from samples at low vacuum in environmental SEMs. This can be useful with specimens which may otherwise charge, such as ceramic or geological materials. 10 kV 20 kV 30 kV Effect of changing accelerating voltage on diffraction patterns from nickel 9/2-10 MENA3100

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 Image with tilt compensation and no dynamic focus compensation 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 9/2-10 MENA3100

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. With a tilted sample, the pattern centre position will depend on the sample working distance. Middle: The top and bottom of the field of view may have a different working distance and hence pattern centre positions. Right: If the sample is moved, the working distance and hence pattern centre position will change. The yellow cross shows the pattern centre with working distance 10mm The pattern centre moves down the screen as the working disance increases to 18mm  The pattern centre moves down the screen as the working disance increases to 22mm The yellow cross shows the pattern centre with working distance 10, 18 and 22 mm 9/2-10 MENA3100

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. This is especially important when working with materials with more than one atom type. Diffraction pattern from the orthorhombic ceramic mullite (3Al2O3 2SiO2) collected at 10 kV accelerating voltage. 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. Simulation of crystal orientation giving the solution shown. 9/2-10 MENA3100

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. Electrons of all energies scattered from the sample form a background to the diffraction pattern. The background intensity can be removed to improve the visibility of the Kikuchi bands Original pattern Background subtraction Background division Background http://www.ebsd.com/ebsd-explained/undertakingexperiments3.htm 9/2-10 MENA3100