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Transmissions electron microscopy

Transmissions electron microscopy. Basic principles Sample preparation Imaging aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase). Basic principles, first TEM. Electrons are deflected by both electrostatic and magnetic fields

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Transmissions electron microscopy

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  1. Transmissions electron microscopy Basic principles Sample preparation Imaging aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase) MENA3100 V08

  2. Basic principles, first TEM Electrons are deflected by both electrostatic and magnetic fields Force from an electrostatic field (in the gun) F= -e E Force from amagnetic field (in the lenses) F= -e (v x B) Wave length: λ= h/(2meV)0.5 (NB non rel. expr.) λ= h/(2m0eV(1+eV)/2m0c2)0.5(relativistic expression) 200kV: λ= 0.00251 nm (v/c= 0.6953, m/m0= 1.3914) • The first electron microscope built by Knoll • and Ruska in 1933, b) The first commercial • electron Microscope built by Siemens in 1939. Nobel prize lecture: http://ernst.ruska.de/daten_e/library/documents/999.nobellecture/lecture.html MENA3100 V08

  3. Basic TEM Electron gun Electron source: ●Tungsten, W ● LaB6 ● FEG Cold trap Sample position • Vacuum requirements: • Avoid scattering from residual gas in • the column. • - Thermal and chemical stability of the • gun during operation. • - Reduce beam-induced contamination • of the sample. • LaB6: 10-7 torr • FEG: 10-10 torr MENA3100 V08

  4. The lenses in a TEM Filament Anode The diffraction limit on resolution is given by the Raleigh criterion: δd=0.61λ/μsinα, μ=1, sinα~ α 1. and 2. condenser lenses Sample Objective lens Compared to the lenses in an optical microscope they are very poor! The point resolution in a TEM is limited by the aberrations of the lenses. Intermediate lenses Projector lens • Spherical • Chromatic • Astigmatism MENA3100 V08

  5. Spherical aberration coefficient r2 r1 α Disk of least confusion Spherical aberrations Cs corrected TEMs are now available ds = 0.5MCsα3 M: magnification Cs :Spherical aberration coefficient α: angular aperture/ angular deviation from optical axis 2000FX: Cs= 2.3 mm 2010F: Cs= 0.5 nm The diffraction and the spherical aberration limits on resolution have an opposite dependence on the angular aperture of the objective. MENA3100 V08

  6. v - Δv v Chromatic aberration Disk of least confusion Chromatic aberration coefficient: dc = Ccα ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5 Cc: Chromatic aberration coefficient α: angular divergence of the beam U: acceleration voltage I: Current in the windings of the objective lens E: Energy of the electrons 2000FX: Cc= 2.2 mm 2010F: Cc= 1.0 mm Thermally emitted electrons: ΔE/E=KT/eV Force from amagnetic field: F= -e (v x B) MENA3100 V08

  7. Technical data of different sources http://dissertations.ub.rug.nl/FILES/faculties/science/1999/h.b.groen/c1.pdf H.B. Groen et al., Phil. Mag. A, 79, p 2083, 1999 MENA3100 V08

  8. Lens astigmatism Loss of axial asymmetry x y-focus y x-focus Lens aberrations This astigmatism can not be prevented, but it can be corrected! MENA3100 V08

  9. Crushing Cutting saw, diamond pen, ultrasonic drill, FIB Mechanical thinning Grinding, dimpling Electrochemical thinning Ion milling Coating Replica methods Sample preparation for TEM Plane view or cross section sample? Is your material brittle or ductile? Is it a conductor or insulator? Is it a multi layered material? MENA3100 V08

  10. Top view TEM sample preparation: Thin films Grind down/ dimple Cut out cylinder Ione beam thinning Grind down and glue on Cu-rings Cut out a cylinder and glue it in a Cu-tube Cut out slices • Cross section Glue the interface of interest face to face together with support material or • Focused Ion Beam (FIB) Cut a slice of the cylinder and grind it down / dimple Cut off excess material Ione beam thinning MENA3100 V08

  11. BiFeO3 Pt TiO2 Glue SiO2 Si 200 nm Imaging / microscopy TEM - High resolution (HREM) - Bright field (BF) - Dark field (DF) - Shadow imaging (SAD+DF+BF) STEM - Z-contrast (HAADF) - Elemental mapping (EDS and EELS) GIF - Energy filtering Holography MENA3100 V08

  12. 3,8 Å 1,1 nm Simplified ray diagram Parallel incoming electron beam Si Sample Objective lense Diffraction plane (back focal plane) Objective aperture Selected area aperture Image plane MENA3100 V08

  13. Apertures Condenser aperture Objective aperture Selected area aperture MENA3100 V08

  14. Use of apertures Condenser aperture: Limits the number of electrons hitting the sample (reducing the intensity), Reducing the diameter of the discs in the convergent electron diffraction pattern. Selected area aperture: Allows only electrons going through an area on the sample that is limited by the SAD aperture to contribute to the diffraction pattern (SAD pattern). Objective aperture: Allows certain reflections to contribute to the image. Increases the contrast in the image. Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), High resolution Images (several reflections from a zone axis). MENA3100 V08

  15. 50 nm Objective aperture: Contrast enhancement Ag and Pb Si hole glue (light elements) A small aperture allows only electrons in the central spot in the back focal plane to contribute to the image. All electrons contributes to the image. Intensity: Thickness and density dependence Mass-thickness contrast Diffraction contrast (Amplitude contrast) One grain seen along a low index zone axis. MENA3100 V08

  16. Objective aperture BF image Weak-beam DF image Diffraction contrast: Bright field (BF), dark field (DF) and weak-beam (WB) Dissociation of pure screw dislocation In Ni3Al, Meng and Preston, J. Mater. Scicence, 35, p. 821-828, 2000. MENA3100 V08

  17. sample Obj. lens Obj. aperture BF image DF image DF image Bending contours MENA3100 V08

  18. g 000 Ig=1- Io t Thickness fringes/contours e In the two-beam situation the intensity of the diffracted and direct beam is periodic with thickness (Ig=1- Io) Sample (side view) Sample (top view) Hole Ig=(πt/ξg)2(sin2(πtseff)/(πtseff)2)) t = distance ”traveled” by the diffracted beam. ξg = extinction distance Positions with max Intensity in Ig MENA3100 V08

  19. BF image DF image Thickness fringes, bright and dark field images Sample Sample MENA3100 V08

  20. HREM image 2 nm Phase contrast: HREM and Moire’ fringes Long-Wei Yin et al., Materials Letters, 52, p.187-191 A Moiré pattern is an interference pattern created, for example, when two grids are overlaid at an angle, or when they have slightly different mesh sizes (rotational and parallel Moire’ patterns). Interference pattern http://www.mathematik.com/Moire/ 200-400 kV TEMs are most commonly used for HREM MENA3100 V08

  21. Moire’ fringe spacing Parallel Moire’ spacing dmoire’= 1 / IΔgI = 1 / Ig1-g2I = d1d2/Id1-d2I Rotational Moire’ spacing dmoire’= 1 / IΔgI = 1 / Ig1-g2I ~1/gβ = d/β Parallel and rotational Moire’ spacing dmoire’= d1d2/((d1-d2)2 + d1d2β2)0.5 g1 g2 Δg g1 Δg β g2 MENA3100 V08

  22. Simulating HREM imagesContrast transfer function (CTF) • CTF (Contrast Transfer Function) is the function which modulates the amplitudes and phases of the electron diffraction pattern formed in the back focal plane of the objective lens. It can be represented as: • k = u • The curve depend on: • Cs (the quality of objective lens)l (wave-length defined by accelerating voltage)Df (the defocus value)u (spatial frequency) In order to take into account the effect of the objective lens when calculating HREM images, the wave function Ψ(u) in reciprocal space has to be multiplied by a transfer function T(u). In general we have: Ψ(r)= Σ Ψ(u) T(u) exp (2πiu.r) T(u)= A(u) exp(iχ), A(u): aperture function 1 or 0 Χ(u)= πΔfλu2+1/2πCsλ3u4 : coherent transfer function MENA3100 V08

  23. Simulating HREM imagesContrast transfer function (CTF) Effect of the envelope functions can be represented as: where Ec is the temporal coherency envelope (caused by chromatic aberrations, focal and energy spread,instabilities in the high tension and objective lens current), and Ea is spatial coherency envelope (caused by the finite incident beam convergence). http://www.maxsidorov.com/ctfexplorer/webhelp/background.htm MENA3100 V08

  24. Contrast transfer function (CTF) Contrast transfer functions and damping envelopes of the JEOL 2010F at optimum defocus (analytical model). The highly coherent electron source used in the 2010F, a FEG, is apparent from the many oscillations in the CTF of the 2010F http://dissertations.ub.rug.nl/FILES/faculties/science/2004/s.mogck/c2.pdf MENA3100 V08

  25. Scherzer defocus Δ f= - (Csλ)1/2 Δ f= -1.2(Csλ)1/2 Scherzer condition Extended Scherzer condition http://www.maxsidorov.com/ctfexplorer/webhelp/effect_of_defocus.htm MENA3100 V08

  26. HREM simulations One possible model for which the simulated HREM images match rectangular region I HREM simulation along [0 0 1] based on the above structures. The numbers before and after the slash symbol “/” represent the defocus and thickness (nm), respectively ”The assessment of GPB2/S′′ structures in Al–Cu–Mg alloys ” Wang and Starink, Mater. Sci. and Eng. A, 386, p 156-163, 2004. MENA3100 V08

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