A.E. GunnæsMENA3100 V08 Transmissions electron microscopy Basic principles Sample preparation Imaging aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase)

A.E. GunnæsMENA3100 V08 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= nm (v/c= , m/m 0 = ) 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: a)The first electron microscope built by Knoll and Ruska in 1933, b) The first commercial electron Microscope built by Siemens in 1939.

A.E. GunnæsMENA3100 V08 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 : torr FEG: torr Cold trap Electron source: ●Tungsten, W ● LaB 6 ● FEG Sample position

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 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.

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 Technical data of different sources TungstenLaB 6 Cold FEG SchottkyHeated FEG Brightness (A/m2/sr) (0.3-2) Temperature (K) Work function (eV) Source size (μm) <0.01 Energy spread (eV) H.B. Groen et al., Phil. Mag. A, 79, p 2083,

A.E. GunnæsMENA3100 V08 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!

A.E. GunnæsMENA3100 V08 Sample preparation for TEM Crushing Cutting –saw, diamond pen, ultrasonic drill, FIB Mechanical thinning –Grinding, dimpling Electrochemical thinning Ion milling Coating Replica methods Plane view or cross section sample? Is your material brittle or ductile? Is it a conductor or insulator? Is it a multi layered material?

A.E. GunnæsMENA3100 V08 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)

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 Apertures Selected area aperture Condenser aperture Objective aperture

A.E. GunnæsMENA3100 V08 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).

A.E. GunnæsMENA3100 V08 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)

A.E. GunnæsMENA3100 V08 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 , 2000.

A.E. GunnæsMENA3100 V08 Bending contours BF image DF image Obj. aperture Obj. lens sample

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 Thickness fringes, bright and dark field images Sample DF image BF image

A.E. GunnæsMENA3100 V08 Phase contrast: HREM and Moire’ fringes 2 nm 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 kV TEMs are most commonly used for HREM Interference pattern

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 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

A.E. GunnæsMENA3100 V08 Scherzer defocus Δ f = - (C s λ) 1/2 Δ f = -1.2(C s λ) 1/2 Scherzer condition Extended Scherzer condition

A.E. GunnæsMENA3100 V08 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 , 2004.