Dislocation networks in graphite

Dislocation networks in graphite

High Resolution Microscop With Reference to Lattice Fringe Imaging in a TEM

f f r Real space Specimen Reciprocal space hr Point spread function Diffraction pattern Back focal plane F u Hu Contrast transfer function g g r Image Gu Fourier transform

2 4 3 2 u C u f u s r h r f r g u F u H u G Point spread function Convolution in real space gives multiplication in reciprocal space Contrast transfer function Aperture function Envelope function Aberration function u B u E A u u H Propert of lens s C u f f u ] ep[ u i u B Specimen transmission function Phase distortion function

High resolution implies abilit to see two closel spaced features in the sample real r space as distinct This corresponds to high spatial frequencies large distances from the optic ais in the diffraction pattern reciprocal u space Ras which pass through the lens at such large distances are bent through a larger angle b the objective lens Due to an imperfect lens spherical aberration these ras are not focused at the same point b the lens Point in the sample disc in the image spreading of a point in the image Objective lens magnifies the image but confuses the detail hence the resolution is limited Each point in the final image has contributions from man points in the specimen no linear relation between the specimen and the image Is a linear relationship possible?

i e A f f specimen function phase function of Vz Vz specimen potential V t projected potential Interaction constant =/E Phase Object approimation i e f Weak Phase Object appro. 1 V f t d Vz Specimen Phase change = fv t V i t e f WPOA For a ver thin specimen the amplitude of the transmitted wave function will be linearl related to the projected potential Specimen and approimations ] [ V i t e f dz z V V t V V E d t t Including absorption

mee h 2 In vacuum 2 ' z V E me h In the specimen dz dz d 2 2 ' Phase change dz z V E d dz z V d dz z V V t V V E d t t Interaction constant =/E tends to a constant value as V increases energ of electron proportional to E & 1 variables tend to compensate 2 3 4 1 1! 2! 3! 4! e

POA holds good onl for thin specimens If specimen is ver thin {V t << 1} WPOA In WPOA {f = 1 i V t } the amplitude of the transmitted wave will be linearl related to the projected potential of the specimen

g r f r h r WPOA [1 Vt ] h [1 Vt ] [ Cos i Sin ] I = * Neglecting 2 I [12 V ] Sin t Onl imaginar part of Bu contributes to intensit B u ep[ i u] B u 2Sin[ u]

Objective lens transfer function T u A u E u 2Sin[ u] Approimatel T u 2A u Sin[ u] T Or effective u T u E chromatic E spatial coherence Incoherent illumination Tu = Hu Tu ve +ve phase contrast atoms would appear dark In WPOA Tu is sometimes called CTF Envelope is like a virtual aperture at the back focal plane

v T u 2A u Sin[ u] +2 C s = 1 mm E 0 = 200 kev f = 58 nm Tu = 2 Sin 2 4 6 2.5Å 2 u nm 1

1 Scherzer defocus and Information Limits 4 2 fscherzer Cs 3 Tu = 2 Sin T effective u C s = 2.2 mm E 0 = 200 kev f = -100 nm T u 2A u Sin[ u] T effective u nm 1 u T u E u nm 1 chromatic E Damping envelope spatial coherence Scherzer 1 3 4 4 s u =1.51 C r Scherzer = 0.66 C 1 3 4 4 s Instrumental resolution limit can use nearl intuitive arguments to interpret the contrast Information limit

IMAGE SIMULATION a b Computer simulation a and electron micrograph b of a Cu Cubeoctahedron consisting of seven shells 1415 atoms in [001] orientation. Structures of nanoclusters b high-resolution transmission electron microscop b J. Urban Volume 10 p.161 in Encclopedia of Nanoscience and Nanotechnolog Ed.: Hari Singh Nalva American Scientific Publishers Stevenson Ranch 2004.

Defocus dependenc of lattice images of a Si crstal 200 kv t = 6 nm. Thickness changes from 20 nm a to 90 nm l in steps of 10 nm. High-Resolution Electron Microscop for Materials Science b Daisuke Shindo and Kenji Hiraga Springer-Verlag Toko 1998. Thickness dependenc of lattice images of a Si crstal 200 kv f = 65 nm. Thickness changes from 1nm a to 86 nm r in steps of 5 nm. High-Resolution Electron Microscop for Materials Science b Daisuke Shindo and Kenji Hiraga Springer-Verlag Toko 1998.

HRTEM- some tips In lattice fringe imaging mode: Things which look like atoms are not atoms! Use image simulation to confirm what ou see Do not interpret details below the resolution limit of the microscope

ADVANCES Spherical aberration correctors for illumination as well as imaging lens sstems Electron beam monochromators reducing the energ spread of the electron beam to < 0.1 ev High-energ resolution spectrometers Sub-eV mandoline filter for EELS Imaging energ filters Advanced specimen holders for in-situ eperiments High-sensitivit and high-dnamic-range detectors for images diffraction patterns electron energ loss spectra EELS and energ dispersive X-ra spectra EDXS Advanced methods Focal series reconstruction Electron Holograph In-focus Fresnel reconstruction It is possible to record phase contrast images with point resolutions of well below 0.1 nm or alternativel scan electron probes of size < 0.1 nm across the specimen recording high-angle scattering or high-energ resolution spectra from areas as small as a single atomic column.

ELECTRON HOLOGRAPHY a b High-resolution a amplitude and b phase images of the aberration-corrected object wave reconstructed from an electron hologram of [110] Si obtained at 300 kv on a CM 30 FEG TEM. The characteristic Si dumbbell structure is visible onl after aberration correction. A. Orchowski et al. Phs. Rev. Lett. 74 399 1995.

FRESNEL RECONSTRUCTION RT A 2.3 nm RT HT Cooled to RT A 20 HTnm B 2.5 nm B Cooled to RT 20 nm C 3.2 nm 20 nm C -40-20 0 20 40 Distance Å Eit face wave reconstructed profiles of the imaginar part of the inner potential using zero-defocus Fresnel fringe images

NANOSTRUCTURES IMAGE GALLERY

NANOTUBES HRTEM image of a BN multi-walled nanotube inner shell distance of ~ 0.33 nm. D. Golberg et al. J. of Appl. Phs. 86 2364 1999. a b c HRTEM micrographs of MWNT: a 5-walled diameter = 6.7 nm; b 2-walled diamter = 5.5 nm; c seven-walled diameter = 6.5 nm hollow diameter = 2.2 nm. S. Iijima Nature 354 p.56 1991.

NANOLAYERS a b Cross section of TiN/NbN nanolaered coatings: a Conventional TEM micrograph with SAD patterns b HRTEM of {200} lattice fringes. M. Shinn et al. J. Mater. Res. 7 901 1992.

NANOPARTICLES [001] [110] High-resolution micrograph of Si 3 N 4 TiN composite prepared b CVD. High-Resolution Electron Microscop for Materials Science b Daisuke Shindo and Kenji Hiraga Springer-Verlag Toko 1998. a b Gas atomized Al-Si powders: a HREM b SEM c BFI. High-Resolution Electron Microscop for Materials Science b Daisuke Shindo and Kenji Hiraga Springer-Verlag Toko 1998. c [110] Al

NANOTWINS Twin Plane HREM of ZrO2 showing formation of nanotwins. High-Resolution Electron Microscop for Materials Science b Daisuke Shindo and Kenji Hiraga Springer-Verlag Toko 1998. [0 11]

NANOpolCRYSTALLINE MATERIAL HREM image of nanocrstalline Pd G.J. Thomas et al. Scripta Metall. Mater. 24 201 1990.

MOIRÉ FRINGES HRTEM image of a Kr nanocluster on a Mg substrate showing Moiré fringes. The lattice parameter of Kr can be calculated from the Moiré fringe spacing: [1/d fringes = 1/d MgO 1/d Kr ] Encclopedia of Nanoscience and Nanotechnolog Ed.: Hari Singh Nalva American Scientific Publishers Stevenson Ranch 2004.

Intergranular Glass Film High-Angle Annular Dark Field Imaging Incident convergent beam θ 1 > 50 mrad off ais θ 2 >10-50 mrad θ 3 < 10 mrad Specimen θ 1 HAADF detector θ 3 θ 2 BF detector ADF detector HAADF-STEM images of the interface between the IGF and the prismatic surface of an -Si 3 N 4 grain. N. Shibata S.J. Penncook T.R. Gosnell G.S. Painter W.A. Shelton P.F. Becher Observation of rare-earth segregation in silicon nitride ceramics at subnanometre dimensions Nature 428 2004 730-33.