Signals from a thin sample Auger electrons Backscattered electrons BSE Incident beam secondary electrons SE Characteristic X-rays visible light 1-100 nm absorbed electrons Specimen electron-hole pairs elastically scattered electrons direct beam Bremsstrahlung X-rays inelastically scattered electrons MSE-621 2013 97 Interaction of high energetic electrons with matter biological samples, polymers crystalline structure, defect analysis, high-resolution TEM chemical analysis, spectroscopy MSE-621 2013 98
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-621 2013 99 Two basic operation modes Diffraction <-> Image Diffraction Mode Image Mode MSE-621 2013 100
(K,Nb)TaO3 Nano-rods TEM holey Carbon film SEM MSE-621 2013 101 dark field image Diffraction pattern Shape, lattice parameters, defects, lattice planes (K,Nb)O3 Nano-rods Bright field image High-resolution image MSE-621 2013 102
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-621 2013 103 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 = 0.0025 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-621 2013 104
Image formation BaTiO3 nanocrystals (Psaltis lab) MSE-621 2013 105 Area selection BaTiO3 nanocrystals (Psaltis lab) Insert selected area aperture to choose region of interest MSE-621 2013 106
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-621 2013 107 Scatter range of electrons, neutrons and X-rays (99% of intensity lost) MSE-621 2013 108
electron, neutron X-ray scattering wave X-rays Electrons Neutrons (1) Neutrons (2) Wavelength 0.07nm 0.15nm 2pm @300keV ~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-621 2013 109 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-621 2013 110
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-621 2013 111 Basic crystallography Crystals: translational periodicity & symmetry Repetition of translated structure to infinity MSE-621 2013 112
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-621 2013 113 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 www.wikipedia.org MSE-621 2013 114
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 www.wikipedia.org MSE-621 2013 115 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 ~ 0.001 nm therefore: λ << dhkl => small angle approximation: nλ 2dhklθ Reciprocity: scattering angle θ ~ dhkl -1 MSE-621 2013 116
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-621 2013 117 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-621 2013 118
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-621 2013 119 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-621 2013 120
Laue Zones Ewald plans réflecteu E k g k' Zones de Laue d'ordre 3 2 1 0 O H MSE-621 2013 121 Laue zones J.-P. Morniroli MSE-621 2013 122
Ewald Sphere : Laue Zones (ZOLZ+FOLZ) ZOLZ 6-fold Source: P.A. Buffat FOLZ 3-fold =2.0mrad s=0.2 MSE-621 2013 123 Ewald Sphere: Laue Zones (ZOLZ+FOLZ) tilted sample ZOLZ 6-fold FOLZ 3-fold =2.0mrad s=0.2 MSE-621 2013 124
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-621 2013 125 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-621 2013 126
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-621 2013 127 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-621 2013 128
Ring diffraction patterns Larger crystals => more spotty patterns Example: ZnO nanocrystals ~20 nm in diameter MSE-621 2013 129 X-ray diffraction XRD MSE-621 2013 130
Laue Method MSE-621 2013 131 Debeye-Scherrer MSE-621 2013 132
X-ray tube MSE-621 2013 133 Diffractometer MSE-621 2013 134
MSE-621 2013 135 MSE-621 2013 136
MSE-621 2013 137 MSE-621 2013 138
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 http://escher.epfl.ch/ecrystallography http://www.doitpoms.ac.uk JEMS Electron Microscopy Software Java version http://cimewww.epfl.ch/people/stadelmann/jemswebsite/jems.html Web-based Electron Microscopy APplication Software (WebEMAPS) http://emaps.mrl.uiuc.edu/ http://crystals.ethz.ch/icsd - access to crystal structure file database Can download CIF file and import to JEMS MSE-621 2013 139 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-621 2013 140
dark field image Diffraction pattern Shape, lattice parameters, defects, lattice planes (K,Nb)O3 Nano-rods Bright field image High-resolution image MSE-621 2013 141 Image formation BaTiO3 nanocrystals (Psaltis lab) MSE-621 2013 142
Bright Field Imaging Diffraction Contrast Au (nano-) particles on C film MSE-621 2013 143 Bright Field / Dark Field MSE-621 2013 144
Bend Contours /Bragg Contours Bragg conditions change across the bent sample MSE-621 2013 145 Twin lamellae in PbTiO 3 MSE-621 2013 146
Ni based Superalloy BF image DF image MSE-621 2013 147 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-621 2013 148
Thickness Fringes extinction contours Wedge shaped crystal GaAs/Al x Ga 1-x As MSE-621 2013 149 TEM dark field image g=(200)dyn HRTEM zone axis [001] HRTEM zone axis [001] MSE-621 2013 150
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-621 2013 151 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-621 2013 152
High-resolution TEM K. Ishizuka (1980) Contrast Transfer of Crystal Images in TEM, Ultramicroscopy 5,pages 55-65. 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-621 2013 153 Scherzer-defocus: black-atom contrast MSE-621 2013 154
White-atom contrast Hg CuO 2 Hg MSE-621 2013 155 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-621 2013 156
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-621 2013 157