1. A.E. GunnæsMENA3100 V10 Transmissions electron microscopy Sample preparation Basic principles Imaging aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase)

2. A.E. GunnæsMENA3100 V10 Sample preparation for TEM Crushing Cutting –saw, diamond pen, ultrasonic drill, FIB Mechanical thinning –Grinding, dimpling Electrochemical thinning Ion milling Coating Replica methods FIB Plane view or cross section sample? Is your material brittle or ductile? Is it a conductor or insulator? Is it a multi layered material?

3. A.E. GunnæsMENA3100 V10 Grind down/ dimple TEM sample preparation: Thin films Top view Cross section or Cut out a cylinder and glue it in a Cu-tube Grind down and glue on Cu-rings Cut a slice of the cylinder and grind it down / dimple Ione beam thinning Cut out cylinder Ione beam thinning Cut out slices Glue the interface of interest face to face together with support material Cut off excess material Focused Ion Beam (FIB)

4. A.E. GunnæsMENA3100 V10 Basic principles, first TEM Wave length: λ= h/(2meV) 0.5 (NB non rel. expr.) λ= h/(2m 0 eV(1+eV)/2m 0 c 2 ) 0.5 (relativistic expression) 200kV: λ= 0.00251 nm (v/c= 0.6953, m/m 0 = 1.3914) Electrons are deflected by both electrostatic and magnetic fields Force from an electrostatic field (in the gun) F= -e E Force from a magnetic field (in the lenses) F= -e (v x B) Nobel prize lecture: http://ernst.ruska.de/daten_e/library/documents/999.nobellecture/lecture.html a)The first electron microscope built by Knoll and Ruska in 1933, b) The first commercial electron Microscope built by Siemens in 1939.

5. A.E. GunnæsMENA3100 V10 Basic TEM Electron source: ●Tungsten, W ● LaB 6 ● FEG Electron gun

6. A.E. GunnæsMENA3100 V10 Electron guns Thermionic gun Field emission gun (FEG)

7. A.E. GunnæsMENA3100 V10 Technical data of different sources TungstenLaB 6 Cold FEG SchottkyHeated FEG Brightness (A/m2/sr) (0.3-2)10 9 10 11 -10 14 Temperature (K) 2500-30001400-20003001800 Work function (eV) 4.62.74.62.84.6 Source size (μm) 20-5010-20<0.01 Energy spread (eV) 3.01.50.30.80.5 H.B. Groen et al., Phil. Mag. A, 79, p 2083, 1999 http://dissertations.ub.rug.nl/FILES/faculties/science/1999/h.b.groen/c1.pdf Monochromator: Energy spread less than 0.15 ev

8. A.E. GunnæsMENA3100 V10 Basic TEM Electron gun 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. LaB 6 : 10 -7 torr FEG: 10 -10 torr Electron source: ●Tungsten, W ● LaB 6 ● FEG Cold trap Sample position

9. A.E. GunnæsMENA3100 V10 The lenses in a TEM Sample Filament Anode 1. and 2. condenser lenses Objective lens Intermediate lenses Projector 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. The diffraction limit on resolution is given by the Raleigh criterion: δ d =0.61λ/μsinα, μ=1, sinα~ α -Spherical - Chromatic -Astigmatism

10. A.E. GunnæsMENA3100 V10 Spherical aberrations Spherical aberration coefficient d s = 0.5MC s α 3 M: magnification C s :Spherical aberration coefficient α: angular aperture/ angular deviation from optical axis 2000FX: C s = 2.3 mm 2010F: C s = 0.5 nm r1r1 r2r2 Disk of least confusion α C s corrected TEMs are now available The diffraction and the spherical aberration limits on resolution have an opposite dependence on the angular aperture of the objective.

11. A.E. GunnæsMENA3100 V10 Aberrations in a nutshell Core of the M100 galaxy seen through Hubble (source: NASA) Before C s correction After C s correction Q.M. Ramasse

12. A.E. GunnæsMENA3100 V10 Resolution limit YearResolution 1940s ~10nm 1950s ~0.5-2nm 1960s 0.3nm (transmission) ~15-20nm (scanning) 1970s 0.2nm (transmission) 7nm (standard scanning) 1980s 0.15nm (transmission) 5nm (scanning at 1kV) 1990s 0.1nm (transmission) 3nm (scanning at 1kV) 2000s <0.1 nm (Cs correctors) http://www.sfc.fr/Material/hrst.mit.edu/hrs/materials/public/ElecMicr.htm

13. A.E. GunnæsMENA3100 V10 Chromatic aberration v v - Δ v d c = C c α ((ΔU/U) 2 + (2ΔI/I) 2 + (ΔE/E) 2 ) 0.5 C c : 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: C c = 2.2 mm 2010F: C c = 1.0 mm Chromatic aberration coefficient: Thermally emitted electrons: ΔE/E=KT/eV Force from a magnetic field: F= -e (v x B) Disk of least confusion

14. A.E. GunnæsMENA3100 V10 Lens aberrations Lens astigmatism Loss of axial asymmetry y-focus x-focus y x This astigmatism can not be prevented, but it can be corrected!

15. A.E. GunnæsMENA3100 V10 Operating modes Convergent beamParallel beam Can be scanned (STEM mode) Specimen Imaging mode or Diffraction mode Spectroscopy and mapping (EDS and EELS)

16. A.E. GunnæsMENA3100 V10 Image or diffraction mode 1. and 2. condenser lenses Objective lens Intermediate lenses Projector lens Spesimen Filament Anode Diffraction plane Image plane Objective aperture Selected area aperture Image or diffraction pattern STEM detectors (BF and HAADF) Bi-prism Viewing screen

17. A.E. GunnæsMENA3100 V10 Advanced nanotool JEOL 2010F FEGTEM Ultra high resolution version with analytical possibilities

18. A.E. GunnæsMENA3100 V10 Imaging / microscopy 200 nm Si SiO 2 TiO 2 Pt BiFeO 3 Glue 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

19. A.E. GunnæsMENA3100 V10 Simplified ray diagram Objective lense Diffraction plane (back focal plane) Image plane Sample Parallel incoming electron beam Si 1,1 nm 3,8 Å Objective aperture Selected area aperture

20. A.E. GunnæsMENA3100 V10 Apertures Selected area aperture Condenser aperture Objective aperture

21. A.E. GunnæsMENA3100 V10 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).

22. A.E. GunnæsMENA3100 V10 Objective aperture: Contrast enhancement All electrons contributes to the image. A small aperture allows only electrons in the central spot in the back focal plane to contribute to the image. Intensity: Thickness and density dependence Mass-thickness contrast Si Ag and Pb glue (light elements) hole 50 nm One grain seen along a low index zone axis. Diffraction contrast (Amplitude contrast)

23. A.E. GunnæsMENA3100 V10 Diffraction contrast: Bright field (BF), dark field (DF) and weak-beam (WB) BF image Objective aperture DF imageWeak-beam Dissociation of pure screw dislocation In Ni 3 Al, Meng and Preston, J. Mater. Scicence, 35, p. 821-828, 2000.

24. A.E. GunnæsMENA3100 V10 Bending contours BF image DF image Obj. aperture Obj. lens sample

25. A.E. GunnæsMENA3100 V10 Thickness fringes/contours Sample (side view) e 000 g t I g =1- I o In the two-beam situation the intensity of the diffracted and direct beam is periodic with thickness (I g =1- I o ) I g =(πt/ξ g ) 2 (sin 2 (πts eff )/(πts eff ) 2 )) t = distance ”traveled” by the diffracted beam. ξ g = extinction distance Sample (top view) Hole Positions with max Intensity in I g

26. A.E. GunnæsMENA3100 V10 Thickness fringes, bright and dark field images Sample DF image BF image

27. A.E. GunnæsMENA3100 V10 Phase contrast: HREM and Moire’ fringes 2 nm http://www.mathematik.com/Moire/ 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). HREM image Long-Wei Yin et al., Materials Letters, 52, p.187-191 200-400 kV TEMs are most commonly used for HREM Interference pattern

28. A.E. GunnæsMENA3100 V10 Moire’ fringe spacing Parallel Moire’ spacing d moire’ = 1 / IΔgI = 1 / Ig 1 -g 2 I = d 1 d 2 /Id 1 -d 2 I Rotational Moire’ spacing d moire’ = 1 / IΔgI = 1 / Ig 1 -g 2 I ~1/gβ = d/β Parallel and rotational Moire’ spacing d moire’ = d 1 d 2 /((d 1 -d 2 ) 2 + d 1 d 2 β 2 ) 0.5 β g1g1 g2g2 ΔgΔg g1g1 g2g2 ΔgΔg

29. A.E. GunnæsMENA3100 V10 Simulating HREM images Contrast 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) (wave-length defined by accelerating voltage)  f (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)= πΔfλu 2 +1/2πCsλ 3 u 4 : coherent transfer function

30. A.E. GunnæsMENA3100 V10 Simulating HREM images Contrast 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).spatial coherency http://www.maxsidorov.com/ctfexplorer/webhelp/background.htm

31. A.E. GunnæsMENA3100 V10 Scherzer defocus http://www.maxsidorov.com/ctfexplorer/webhelp/effect_of_defocus.htm Δ f = - (C s λ) 1/2 Δ f = -1.2(C s λ) 1/2 Scherzer condition Extended Scherzer condition

32. A.E. GunnæsMENA3100 V10 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.

33. A.E. GunnæsMENA3100 V10 HAADF image of an icosahedral FePt particle (false colors): thanks to the small probe size, it is possible to probe precisely the chemical structure of samples at the atomic level, revealing here a small crystalline layer of iron oxide surrounding the outermost shell of the particle. Combined HAADF and EELS

34. A.E. GunnæsMENA3100 V10 Energy filtering A. Thøgersen et al., Collaboration with Prof. T. Finnstad, UiO, S. Diplas, SINTEF and UniS, UK and NIMS, Japan