1. Image formation: contrast arises from interference of the electron wave with itself.

1. High Resolution Electron Microscopy 1. Image formation: contrast arises from interference of the electron wave with itself. 2. Phase contrast imaging: When the sample is thin enough and the amplitude variations do not contribute to the images. (Weak phase object approximation).

2. Why HREM: 1). High resolution electron microscopy can resolve object details smaller than 1 nm (10-9 m). 2). It can be used to image the interior structure of the specimen (comparing to atomic resolution scanning tunneling microscopy, only at the surface). 3). Comparing to atomic resolution provided by X-ray diffraction (averaging information), HREM can provide information on the local structure. 4). Direct imaging of atom arrangements, in particular the structural defects, interface, dislocations.

3. HREM vs CTEM (Conventional TEM) CTEM contrast is mostly diffraction contrast Different specimen regions generate Bragg reflections of different intensity. The contrast forms by either Bragg reflections or transmitted beam do not contribute to the image. Thus the atomic resolution can not be realized.

4. (r) - electron (r) - potential q(r) - exit-wave function sample Fourier transform Objective lens transfer function I(H)=|Q(H)|2 Q(H)T(H) Q(H) Backfocal Plane Inverse Fourier transform I(r)=|(r)|2 I(r) (r) image Plane Wave functions for elastically-scattered, forward electrons From potential (r) to exit-wave function q(r) : 1). Weak Phase Object (single scattering): q(r) = 1 - i(r), where =/U. 2). Phase Object: q(r) = exp[i(r)]. 3). Dynamic Scattering: Multislice method Bloch-wave method.

5. (r) - electron (r) - potential q(r) - exit-wave function sample Fourier transform Objective lens transfer function I(H)=|Q(H)|2 Q(H)T(H) Q(H) Backfocal Plane Inverse Fourier transform I(r)=|(r)|2 I(r) (r) image Plane Phase contrast transfer function: T(H)=sin(Cs3H4/2+fH2). Cs: Spherical aberration constant. f: defocus value. Phase contrast transfer function calculated at f=-61 nm with Cs=1.0 mm.

6. What is phase contrast transfer function? The exit wave now passes through the imaging system of the microscope where it undergoes further phase change and interferes as the image wave in the imaging plane.However, the recorded image is NOT a direct representation of the samples crystallographic structure. For instance, high intensity might or might not indicate the presence of an atom column in that precise location. The relationship between the exit wave and the image wave is a highly nonlinear one and is a function of the aberrations of the microscope. It is described by the contrast transfer function.

7. (r) - electron (r) - potential q(r) - exit-wave function sample Fourier transform Objective lens transfer function I(H)=|Q(H)|2 Q(H)T(H) Q(H) atoms Backfocal Plane Inverse Fourier transform I(r)=|(r)|2 I(r) Sample thickness (r) image Plane Wave functions for elastically-scattered, forward electrons High-Resolution Electron Microscopy: • For a weak phase object, the observable image intensity is: • I=1 - 2(r)  FFT[T(H)]. • represents convolution. This shows a pure phase-contrast image. Illustration of electron wave passing through under phase object approximation. The phase changes (contrast) is imaged.

8. High resolution image contrast depends strongly on defocus, astigmatism, beam tilt, crystal tilt, etc. All of these cause the lattice fringes to become stronger or weaker or move. A structure image is when the lattice image is a good representation of the crystal structure, with heavy atoms as dark spots. To get a structure image: The specimen must be thin The crystal must be on axis The beam must be on axis No Astigmatism The microscope must be at the correct focus (Scherzer focus) The lattice spacing must be within the resolution limit of the microscope For microscope: 1). Illumination has a high degree of coherence (small source, small spread of the wavelength). 2). Mechanics and electronics should be sufficiently stable 3). Electron lenses should have small aberrations. 4). Remove objective aperture (or use a large one).

9. More on Contrast Transfer Function: T(H)<0 implies “positive” constrast: atom columns appear dark (in the print, not the negative!). T(H)>0 implies “negative” contrast: atom columns appear bright. • T(H) = 0 implies no transfer of the respective spatial frequency at all! Example: hypothetical crystal with four different sets of planes parallel to the viewing direction – plane spacing: d1 > d2 > d3 > d4 – corresponding spatial frequencies: 1/d1 < 1/d2 < 1/d3 < 1/d4. – the planes with spacing d1 appear with positive contrast – the planes with spacing d2 appear with negative contrast – the planes with spacing d3 do not appear at all – it is difficult to predict the contrast of the planes with spacing d4. We can avoid these problems by introducing an objective aperture. T(H) H d3 d2 d1

10. HREM image and focus settings: Choosing the optimum defocus is crucial to fully exploit the capabilities of an electron microscope in HREM mode. However, there is no simple answer as to which one is the best. In Gaussian focus one sets the defocus to zero, the sample is in focus. With other focus values, the CTF now becomes a function that oscillates quickly with Csu4. What this means is that for certain diffracted beams with a given spatial frequency u the contribution to contrast in the recorded image will be reversed, thus making interpretationof the image difficult.

11. Scherzer defocus • In Scherzer defocus, one aims to choose the right defocus value Δf one flattens χ(u) and creates a wide band where low spatial frequencies u are transferred into image intensity with a similar phase. In 1949, Scherzer found that the optimum defocus depends on microscope properties like the spherical aberration Cs and the accelerating voltage (through λ) in the following way: •                                                                    , • where the factor 1.2 defines the extended Scherzer defocus. For example, when Cs=0.6 and an accelerating voltage is 300keV result in ΔfScherzer = -41,25 nm. • The point resolution point resolution of a microscope is defined as the spatial frequency ures where the CTF crosses the X-axis for the first time. At Scherzer defocus this value is maximized.

12. Simulation of exit wave and recorded images for GaN[0001].

13. High Resolution Electron Microscopy images simulation – influence of thickness of defocus

14. High-Resolution Electron Microscopy: Interfaces Columnar grain boundaries in SrTiO3 film are associated with {111} planar defects in the SrRuO3 layer. Two atomic structural models of the antiphase boundaries in the (-110) plane, with a crystallographic shear vector R=a/2[001] (a) and R=a/2[-1-11] (b). a/3[-112] a/6[-221] + a/2[001]

15. High-Resolution Electron Microscopy: Carbon nanotube Discovery of the carbon nanotube S. Iijima, Nature 354, 56 (1991). This paper has been cited by more than 5000 times!

16. Shape Determination of Au Nanoparticles

17. High-Resolution Electron Microscopy: Stacking fault and nanotwins A HREM image of SrRuO3 crystal along the [110] direction shows an isolated {111} intrinsic stacking fault. The dislocation at the end of the fault is identified as a Shockley partial dislocation Burgers vectors of a/3<112>. A HREM image of a {111} nanotwin, which have a wider thickness of the ‘fault planes’.

18. High-Resolution Electron Microscopy: Interfaces a=0.3905 nm Misfit=0.64% a=0.3982 nm HREM image the coherent SrTiO3/SrRuO3 interface.

19. High-Resolution Electron Microscopy: Interfaces Misfit=3.6% a=0.3982 nm a=0.3790 nm A dissociated [-110] superdislocation: [-110] a/2[-11-1] + a/2[-111], accompanied by an antiphase boundary. a/2[-11-1] a/3[-11-1] + a/6[-11-1], with {111} stacking fault. a/2[-111] a/3[-111] + a/6[-111], with {111} stacking fault. HREM image the SrRuO3/LaAlO3 interface. Misfit dislocations are generated release the large misfit.

20. Electron Beam irradiation damage for carbon nanotubular structures Electron beam damage and safety: the high energy electron beam can cause damage to the specimens. The combination of high-kV beams with the intense electron sources that are available means that the TEM can destroy almost any specimen.

21. (r) - electron (r) - potential q(r) - exit-wave function sample Fourier transform Objective lens transfer function I(H)=|Q(H)|2 Q(H)T(H) Q(H) Backfocal Plane Inverse Fourier transform I(r)=|(r)|2 I(r) (r) image Plane Super Resolution Scheme I: Exit-wave Reconstructions by through focus series HREM images In order to obtain exit-wave function q(r) which has higher resolution, we need: 1). Find phase for I(r) so as to obtain (r). 2). Find exact defocus value and lens aberration coefficients so as to deconvolute the phase transfer function.

22. Super Resolution Scheme I: Exit-wave Reconstructions by through focus series HREM images 1). Record a series of HREM images with known focus steps. 2). Use “paraboloid method” to solve phase and get the first estimation of the exit-wave function. (Linear information of an image is within the parabola.) 3). The estimated exit-wave function can be iteratively refined by maximum likehood fitting. (comparison of experimental images and calculated one from the estimated exit-wave function). Schematic representation of the through focus exit wave reconstruction. Zandbergen and Van Dyck 2000, Micro. Res. Tech. 49, 301.

23. Phase Image Cs = 1.2 mm, Df = -137 nm C.L. Jia, R. Rosenfeld, A. Thust and K. Urban, Phil. Mag. Lett.79, 99 (1999).

24. 1/4.17=0.24 nm 1/7.4=0.135 nm Super Resolution Scheme II: Aberration Correction Cs=1.0 mm Cs=0 mm Philips CM200FEG ST with Cs-corrector at Juelich Germany Up: Phase contrast transfer function with Cs=1.0 mm (f=-61 nm). Down: Phase contrast transfer function with Cs=0 mm (f=-7 nm). r  r = 2Cs 3

25. Super Resolution Scheme II: Aberration Correction “Seeing is Believing” Direct imaging of light O atoms at resolution of 0.138 nm. C.L. Jia, M. Lentzen and K. Urban, Science 299, 870 (2003).

26. High Resolution Electron Microscopy for Biological Sample ?? Resolution of Biomolecules or Cells achieved by TEM is limited mainly by Radiation damage Neutze, et al. Nature 406, 752 (2000). X-ray Beam intensity: 3.8×106 photons/A2 A femtosecond is one millionth of a nanosecond or 10 -15 of a second.

27. Resolution of Biomolecules or Cells achieved by TEM is limited by Radiation damage Negative staining: low resolution surface shape can be imaged at resolution ~2 nm, distorted 3D structure. Low Dose Cryo-TEM: sample stored in vitreous ice. For a single biomolecule, contrast is low and signal/noise ratio is pretty low.

28. The more molecules in the beam, the higher signal/noise ratio Signal/noise ~ (number of molecules)2 Illustration of periodic pattern of motifs in a crystal. Crystallization: 2D or 3D crystal. single-particle reconstruction: Theribosome structure determined to 1 nm resolution by TEM (tomographic cryomicroscopy) by J. Frank.