Signals from a thin sample

Transcription

1 Signals from a thin sample Auger electrons Backscattered electrons BSE Incident beam secondary electrons SE Characteristic X-rays visible light nm absorbed electrons Specimen electron-hole pairs elastically scattered electrons direct beam Bremsstrahlung X-rays inelastically scattered electrons MSE Interaction of high energetic electrons with matter biological samples, polymers crystalline structure, defect analysis, high-resolution TEM chemical analysis, spectroscopy MSE

2 Interaction -> contrast EDS, element maps Thin section of mouse brain: mass contrast of stained membrane structures (G.Knott) STEM-DF Dark field image of differently ordered domains: Diffraction contrast High-resolution image: Image contrast due to interference between transmitted and diffracted beam Element distribution maps Of Nb3Sn superconductor MSE Two basic operation modes Diffraction <-> Image Diffraction Mode Image Mode MSE

3 (K,Nb)TaO3 Nano-rods TEM holey Carbon film SEM MSE dark field image Diffraction pattern Shape, lattice parameters, defects, lattice planes (K,Nb)O3 Nano-rods Bright field image High-resolution image MSE

4 Diffraction theory Introduction to electron diffraction Elastic scattering theory Basic crystallography & symmetry Electron diffraction theory Intensity in the electron diffraction pattern Thanks to Dr. Duncan Alexander for slides MSE Why use electron diffraction? Diffraction: constructive and destructive interference of waves wavelength of fast moving electrons much smaller than spacing of atomic planes => diffraction from atomic planes (e.g. 200 kv e -, λ = nm) electrons interact very strongly with matter => strong diffraction intensity (can take patterns in seconds, unlike X-ray diffraction) spatially-localized information ( 200 nm for selected-area diffraction; 2 nm possible with convergent-beam electron diffraction) close relationship to diffraction contrast in imaging orientation information immediate in the TEM! ( diffraction from only selected set of of planes in in one pattern -- e.g. only 2D 2D information) ( limited accuracy of of measurement -- e.g. 2-3%) ( intensity of of reflections difficult to to interpret because of of dynamical effects) MSE

5 Image formation BaTiO3 nanocrystals (Psaltis lab) MSE Area selection BaTiO3 nanocrystals (Psaltis lab) Insert selected area aperture to choose region of interest MSE

6 Take selected-area diffraction pattern Press D for diffraction on microscope console - alter strength of intermediate lens and focus diffraction pattern on to screen Find cubic BaTiO3 aligned on [0 0 1] zone axis MSE Scatter range of electrons, neutrons and X-rays (99% of intensity lost) MSE

7 electron, neutron X-ray scattering wave X-rays Electrons Neutrons (1) Neutrons (2) Wavelength 0.07nm 0.15nm ~0.1nm Source Scattering at Differentiation of X-ray tubes synchrotrons e guns (SEM/TEM) Nuclear reactors Electron cloud Potential distribution (electrons & nucleus) Nuclear scattering (nucleus) Magnetic spin (outer electrons) Lattice parameters Unit cell Lattice parameters, Orientations LP, isotopes Oxidation states Sample size 0.1mm 0.1um m m Scattering power: n : X-ray : e = 1 : 10 : 10 4 MSE Scattering theory - Atomic scattering factor Consider coherent elastic scattering of electrons from atom Atomic scattering factor for electrons Differential elastic scattering cross section: The Mott-Bethe formula is used to calculate electron form factors from X-ray form factors (f x ) MSE

8 Scattering theory - Huygen s principle Periodic array of scattering centres (atoms) Plane electron wave generates secondary wavelets Secondary wavelets interfere => strong direct beam and multiple orders of diffracted beams from constructive interference Atoms closer together => scattering angles greater => Reciprocity! MSE Basic crystallography Crystals: translational periodicity & symmetry Repetition of translated structure to infinity MSE

9 Crystallography: the unit cell Unit cell is the smallest repeating unit of the crystal lattice Has a lattice point on each corner (and perhaps more elsewhere) Defined by lattice parameters a, b, c along axes x, y, z and angles between crystallographic axes: α = b^c; β = a^c; γ = a^b MSE The seven crystal systems 7 possible unit cell shapes with different symmetries that can be repeated by translation in 3 dimensions => 7 crystal systems each defined by symmetry Triclinic Monoclinic Orthorhombic Tetragonal Rhombohedral Hexagonal Cubic Diagrams from MSE

10 14 Bravais lattices Combinations of crystal systems and lattice point centring that describe all possible crystals - Equivalent system/centring combinations eliminated => 14 (not 7 x 4 = 28) possibilities Diagrams from MSE Diffraction theory - Bragg law Path difference between reflection from planes distance dhkl apart = 2dhklsinθ 2dhklsinθ = λ/2 λ => - constructive -Bragg destructive law: interference nλ = 2dhklsinθ Electron diffraction: λ ~ nm therefore: λ << dhkl => small angle approximation: nλ 2dhklθ Reciprocity: scattering angle θ ~ dhkl -1 MSE

11 Bragg s law 2 sin d hkl = n d hkl = n sin Difference in path d Distance between lattice planes Elastic diffraction k = k k k Periodic arrangement of lattice planes: g : reciprocal lattice vector g = k-k MSE The reciprocal lattice In diffraction we are working in reciprocal space ; useful to transform the crystal lattice in to a reciprocal lattice that represents the crystal in reciprocal space: Real lattice rn = n1a + n2b + n3c vector: Reciprocal lattice r* = m1a* + m2b* + m3c* vector: where: a*.b = a*.c = b*.c = b*.a = c*.a = c*.b = 0 i.e. a*.a = b*.b = c*.c = 1 a* = (b ^ c)/vc VC: volume of unit cell For scattering from plane (h k l) the diffraction vector: ghkl = ha* + kb* + lc* Plane spacing: MSE

12 Ewald sphere A vector in reciprocal space: g hkl = h a * + k b * + l c * diffraction if : k I k D = g and k I = k D Bragg and elastic scattering reciprocal space real space Bragg: d hkl = /2 sin = 1/ g k I a* b* ki: incident beam wave vector Reciprocal space: sphere radius 1/λ represents possible scattering wave vectors intersecting reciprocal space Electron diffraction: radius of sphere very large compared to reciprocal lattice => sphere circumference almost flat MSE Ewald sphere A vector in reciprocal space: g hkl = h a * + k b * + l c * diffraction if : k I k D = g and k I = k D Bragg and elastic scattering reciprocal space k D real space k I a* b* ki: incident beam wave vector kd: diffracted wave vector Reciprocal space: sphere radius 1/λ represents possible scattering wave vectors intersecting reciprocal space Electron diffraction: radius of sphere very large compared to reciprocal lattice => sphere circumference almost flat MSE

13 Laue Zones Ewald plans réflecteu E k g k' Zones de Laue d'ordre O H MSE Laue zones J.-P. Morniroli MSE

14 Ewald Sphere : Laue Zones (ZOLZ+FOLZ) ZOLZ 6-fold Source: P.A. Buffat FOLZ 3-fold =2.0mrad s=0.2 MSE Ewald Sphere: Laue Zones (ZOLZ+FOLZ) tilted sample ZOLZ 6-fold FOLZ 3-fold =2.0mrad s=0.2 MSE

15 Symmetry information Zone axis SADPs have symmetry closely related to symmetry of crystal lattice Example: FCC aluminium [0 0 1] [1 1 0] [1 1 1] 4-fold rotation axis 2-fold rotation axis 6-fold rotation axis - but [1 1 1] actually 3-fold axis Need third dimension for true symmetry! MSE Twinning in diffraction Example: Co-Ni-Al shape memory FCC twins observed on [1 1 0] zone axis (1 1 1) close-packed twin planes overlap in SADP Images provided by Barbora Bartová, CIME MSE

16 Epitaxy and orientation relationships SADP excellent tool for studying orientation relationships across interfaces Example: Mn-doped ZnO on sapphire Sapphire substrate Sapphire + film Zone axes: [1-1 0]ZnO // [0-1 0]sapphire Planes: c-planezno // c-planesapphire MSE Ring diffraction patterns If selected area aperture selects numerous, randomly-oriented nanocrystals, SADP consists of rings sampling all possible diffracting planes - like powder X-ray diffraction Example: needles of contaminant cubic MnZnO3 - which XRD failed to observe! MSE

17 Ring diffraction patterns Larger crystals => more spotty patterns Example: ZnO nanocrystals ~20 nm in diameter MSE X-ray diffraction XRD MSE

18 Laue Method MSE Debeye-Scherrer MSE

19 X-ray tube MSE Diffractometer MSE

20 MSE MSE

21 MSE MSE

22 References Transmission Electron Microscopy, Williams & Carter, Plenum Press Transmission Electron Microscopy: Physics of Image Formation and Microanalysis (Springer Series in Optical Sciences), Reimer, Springer Publishing Electron diffraction in the electron microscope, J. W. Edington, Macmillan Publishers Ltd Large-Angle Convergent-Beam Electron Diffraction Applications to Crystal Defects, Morniroli, Taylor & Francis Publishing JEMS Electron Microscopy Software Java version Web-based Electron Microscopy APplication Software (WebEMAPS) access to crystal structure file database Can download CIF file and import to JEMS MSE Electron Microscopy 1. Introduction, types of microscopes, some examples 2. Electron guns, Electron optics, Detectors 3. SEM, interaction volume, contrasts 4. Electron diffraction, X-ray diffraction 5. TEM, contrast, image formation MSE

23 dark field image Diffraction pattern Shape, lattice parameters, defects, lattice planes (K,Nb)O3 Nano-rods Bright field image High-resolution image MSE Image formation BaTiO3 nanocrystals (Psaltis lab) MSE

24 Bright Field Imaging Diffraction Contrast Au (nano-) particles on C film MSE Bright Field / Dark Field MSE

25 Bend Contours /Bragg Contours Bragg conditions change across the bent sample MSE Twin lamellae in PbTiO 3 MSE

26 Ni based Superalloy BF image DF image MSE Dynamical scattering For interpretation of intensities in diffraction pattern, single scattering would be ideal - i.e. kinematical scattering However, in electron diffraction there is often multiple elastic scattering: i.e. dynamical behaviour This dynamical scattering has a high probability because a Bragg-scattered beam is at the perfect angle to be Bragg-scattered again (and again...) As a result, scattering of different beams is not independent from each other MSE

27 Thickness Fringes extinction contours Wedge shaped crystal GaAs/Al x Ga 1-x As MSE TEM dark field image g=(200)dyn HRTEM zone axis [001] HRTEM zone axis [001] MSE

28 the TEM in high-resolution mode A high-resolution image is an interference image of the transmitted and the diffracted beams! Diffracted electrons: coherent elastic scattering (the electrons have seen the crystal lattice ) The quality of the image depends on the optical system that makes the beams interfere Bright Field High-Resolution MSE High resolution The image should resemble the atomic structure of the sample! Atoms? Thin samples: atom columns: sample orientation (beam // atom columns) Contrast varies with sample thickness and defocus! Comparison with simulation necessary! MSE

29 High-resolution TEM K. Ishizuka (1980) Contrast Transfer of Crystal Images in TEM, Ultramicroscopy 5,pages L. Reimer (1993) Transmission Electron Microscopy, Springer Verlag, Berlin. J.C.H. Spence (1988), Experimental High Resolution Electron Microscopy, Oxford University Press, New York. Pb Ti O Ti Pb MSE Scherzer-defocus: black-atom contrast MSE

30 White-atom contrast Hg CuO 2 Hg MSE the TEM in high-resolution mode A high-resolution image is an interference image of the transmitted and the diffracted beams! Diffracted electrons: coherent elastic scattering (the electrons have seen the crystal lattice ) The quality of the image depends on the optical system that makes the beams interfere Bright Field High-Resolution MSE

31 High resolution The image should resemble the atomic structure of the sample! Atoms? Thin samples: atom columns: sample orientation (beam // atom columns) Contrast varies with sample thickness and defocus! Comparison with simulation necessary! MSE