Principles & Practice of Electron Diffraction

Principles & Practice of Electron Diffraction Duncan Alexander EPFL-CIME 1 Contents Introduction to electron diffraction Elastic scattering theory Basic crystallography & symmetry Electron diffraction theory Intensity in the electron diffraction pattern Selected-area diffraction phenomena Convergent beam electron diffraction Recording & analysing selected-area diffraction patterns Quantitative electron diffraction References 2

Introduction to electron diffraction 3 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 planes in one pattern - e.g. only 2D information) ("" limited accuracy of measurement - e.g. 2-3%) ("" intensity of reflections difficult to interpret because of dynamical effects) 4

Optical axis Image formation Electron source Condenser lens Specimen Objective lens Back focal plane/ diffraction plane Intermediate image 1 Selected area aperture Intermediate lens Projector lens BaTiO3 nanocrystals (Psaltis lab) Insert selected area aperture to choose region of interest Image 5 Take selected-area diffraction pattern Optical axis Electron source Condenser lens Specimen Objective lens Back focal plane/ diffraction plane Intermediate image 1 Selected area aperture Intermediate lens Projector lens Image Diffraction 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 6

Elastic scattering theory 7 Scattering theory - Atomic scattering factor Consider coherent elastic scattering of electrons from atom Differential elastic scattering cross section: Atomic scattering factor 8

Scattering theory - Huygen s principle Periodic array of scattering centres (atoms) Plane electron wave generates secondary wavelets k 0 k D1 k D2 Atoms closer together => scattering angles greater k 0 k D2 k 0 Secondary wavelets interfere => strong direct beam and multiple orders of diffracted beams from constructive interference => Reciprocity! k D1 9 Basic crystallography & symmetry 10

Crystals: translational periodicity & symmetry Repetition of translated structure to infinity 11 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 12

Building a crystal structure Use example of CuZn brass Choose the unit cell - for CuZn: primitive cubic (lattice point on each corner) Choose the motif - Cu: 0, 0, 0; Zn:!,!,! Structure = lattice +motif => Start applying motif to each lattice point z Motif: y Cu Zn x z y x 13 Building a crystal structure Use example of CuZn brass Choose the unit cell - for CuZn: primitive cubic (lattice point on each corner) Choose the motif - Cu: 0, 0, 0; Zn:!,!,! Structure = lattice +motif => Start applying motif to each lattice point Extend lattice further in to space z Motif: z y Cu Zn x z y y y y y x x x x 14

As well as having translational symmetry, nearly all crystals obey other symmetries - i.e. can reflect or rotate crystal and obtain exactly the same structure Symmetry elements: Mirror planes: Introduction to symmetry Rotation axes: Centre of symmetry or inversion centre: Inversion axes: combination of rotation axis with centre of symmetry 15 Introduction to symmetry Example - Tetragonal lattice: a = b c; α = β = γ = 90 Anatase TiO2 (body-centred lattice) view down [0 0 1] (z-axis): Identify mirror planes Identify rotation axis: 4-fold = defining symmetry of tetragonal lattice! y Mirror plane y Tetrad: 4-fold rotation axis z x x O Ti 16

More defining symmetry elements Cubic crystal system: a = b = c; α = β = γ = 90 View down body diagonal (i.e. [1 1 1] axis) Choose Primitive cell (lattice point on each corner) Identify rotation axis: 3-fold (triad) Defining symmetry of cube: four 3-fold rotation axes (not 4-fold rotation axes!) z x y 17 (Cubic α-al(fe,mn)si: example of primitive cubic with no 4-fold axis) 18

More defining symmetry elements Hexagonal crystal system: a = b c; α = β = 90, γ = 120 Primitive cell, lattice points on each corner; view down z-axis - i.e.[1 0 0] Draw 2 x 2 unit cells Identify rotation axis: 6-fold (hexad) - defining symmetry of hexagonal lattice z a y a a z 120 120 120 a y x 19 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 20

Four possible lattice centerings P: Primitive - lattice points on cell corners I: Body-centred - additional lattice point at cell centre F: Face-centred - one additional lattice point at centre of each face A/B/C: Centred on a single face - one additional lattice point centred on A, B or C face Diagrams from www.wikipedia.org 21 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 22

14 Bravais lattices 23 Crystallography - lattice vectors A lattice vector is a vector joining any two lattice points Written as linear combination of unit cell vectors a, b, c: t = Ua + Vb + Wc Also written as: t = [U V W] Examples: z z z y y y x x [1 0 0] [0 3 2] [1 2 1] x Important in diffraction because we look down the lattice vectors ( zone axes ) 24

Crystallography - lattice planes Lattice plane is a plane which passes through any 3 lattice points which are not in a straight line Lattice planes are described using Miller indices (h k l) where the first plane away from the origin intersects the x, y, z axes at distances: a/h on the x axis b/k on the y axis c/l on the z axis 25 Crystallography - lattice planes Sets of planes intersecting the unit cell - examples: z y z x (1 0 0) y z x (0 2 2) y x (1 1 1) 26

Lattice planes and symmetry Lattice planes in a crystal related by the crystal symmetry For example, in cubic lattices the 3-fold rotation axis on the [1 1 1] body diagonal relates the planes (1 0 0), (0 1 0), (0 0 1): z x y Set of planes {1 0 0} = (1 0 0), (0 1 0), (0 0 1), (-1 0 0), (0-1 0), (0 0-1) 27 Weiss Zone Law If the lattice vector [U V W] lies in the plane (h k l) then: hu + kv + lw = 0 Electron diffraction: Electron beam oriented parallel to lattice vector called the zone axis Diffracting planes must be parallel to electron beam - therefore they obey the Weiss Zone law* (*at least for zero-order Laue zone) 28

θ Electron diffraction theory 29 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 + = θ d d hkl Electron diffraction: λ ~ 0.001 nm therefore: λ dhkl => small angle approximation: nλ 2dhklθ Reciprocity: scattering angle θ dhkl -1 30

Diffraction theory - 2-beam condition θ θ θ θ θ k I θ θ θ θ θ θ θ θ k D k I g 0 0 0 d hkl G 2-beam condition: strong scattering from single set of planes 31 Electron beam parallel to low-index crystal orientation [U V W] = zone axis Crystal viewed down zone axis is like diffraction grating with planes parallel to e-beam In diffraction pattern obtain spots perpendicular to plane orientation Example: primitive cubic with e-beam parallel to [0 0 1] zone axis 2 x 2 unit cells z Multi-beam scattering condition y -1 0 0 0-1 0 0 0 0 0 1 0 1 0 0 1 1 0 2 0 0 2 2 0 x 3 0 0 Note reciprocal relationship: smaller plane spacing => larger indices (h k l) & greater scattering angle on diffraction pattern from (0 0 0) direct beam Also note Weiss Zone Law obeyed in indexing (hu + kv + lw = 0) 32

Scattering from non-orthogonal crystals With scattering from the cubic crystal we can note that the diffracted beam for plane (1 0 0) is parallel to the lattice vector [1 0 0]; makes life easy However, not true in non-orthogonal systems - e.g. hexagonal: z a y (1 0 0) planes a 120 120 x [1 0 0] g 1 0 0 => care must be taken in reciprocal space! 33 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 vector: Reciprocal lattice rn = n1a + n2b + n3c r* = m1a* + m2b* + m3c* vector: where: a*.b = a*.c = b*.c = b*.a = c*.a = c*.b = 0 a*.a = b*.b = c*.c = 1 i.e. 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: 34

Fourier transforms for understanding reciprocal space Fourier transform: identifies frequency components of an object - e.g. frequency components of wave forms Each lattice plane has a frequency in the crystal lattice given by its plane spacing - this frequency information is contained in its diffraction spot The diffraction spot is part of the reciprocal lattice and, indeed the reciprocal lattice is the Fourier transform of the real lattice Can use this to understand diffraction patterns and reciprocal space more easily 35 The Ewald sphere ki: incident beam wave vector kd: diffracted wave vector radius = 1/λ k I C k D 0 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 36

Ewald sphere in 2-beam condition θ k I 2θ k I k D θ θ k D 0 0 0 g hkl G k I g 0 0 0 G 2-beam condition with one strong Bragg reflection corresponds to Ewald sphere intersecting one reciprocal lattice point 37 Ewald sphere and multi-beam scattering Assume reciprocal lattice points are infinitely small With crystal oriented on zone axis, Ewald sphere may not intersect reciprocal lattice points k I k D However, we see strong diffraction from many planes in this condition Because reciprocal lattice points have size and shape! 0 0 0 38

Fourier transforms and reciprocal lattice Real lattice is not infinite, but is bound disc of material with diameter of selected area aperture and thickness of specimen - i.e. thin disc of material X FT FT X Relrod = 2 lengths scales in reciprocal space! 39 Ewald sphere intersects Relrods k I k D 0 0 0 40

Relrod shape Shape (e.g. thickness) of sample is like a top-hat function Therefore shape of Relrod is: sin(x)/x Can compare to single-slit diffraction pattern with intensity: 41 Relrod shape 42

Intensity in the electron diffraction pattern 43 Excitation error Tilted slightly off Bragg condition, intensity of diffraction spot much lower Introduce new vector s - the excitation error that measures deviation from exact Bragg condition 44

Excitation error 45 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 46

Dynamical scattering for 2-beam condition For a 2-beam condition (i.e. strong scattering at ϴB) it can be derived that: where: and ξg is the extinction distance for the Bragg reflection: Further: i.e. the intensities of the direct and diffracted beams are complementary, and in anti-phase, to each other. Both are periodic in t and seff If the excitation distance s = 0 (i.e. perfect Bragg condition), then: 47 Extinction and thickness fringes Dynamical scattering in the dark-field image => Intensity zero for thicknesses t = nξg (integer n) See effect as dark thickness fringes on wedge-shaped sample: Composition changes in quantum wells => extinction at different thickness compared to substrate 48

Dynamical scattering for 2-beam 2-beam condition: direct and diffracted beam intensities beams π/2 out of phase: Model with absorption using JEMS: Bright-field image showing modulation with absorption: 49 2-beam: kinematical vs dynamical Kinematical (weak interactions) Dynamical (strong interactions) 50

Weak beam; kinematical approximation Before we saw for 2-beam condition: where: Weak-beam imaging: make s large (~0.2 nm -1 ) Now Ig is effectively independent of ξg - kinematical conditions! => dark-field image intensity easier to interpret 51 Structure factor Amplitude of a diffracted beam: ri: position of each atom => ri: = xi a + yi b + zi c K = g: K = h a * + k b * + l c * Define structure factor: Intensity of reflection: Note fi is a function of s and (h k l) 52

Forbidden reflections Consider FCC lattice with lattice point coordinates: 0,0,0;!,!,0;!,0,!; 0,!,! Calculate structure factor for (0 1 0) plane (assume single atom motif): z => y x 53 Cu3Au - like FCC Au but with Cu atoms on face-centred sites. What happens to SADP if we gradually increase Z of Cu sites until that of Au (to obtain FCC Au)? z Forbidden reflections Diffraction pattern on [0 0 1] zone axis: y x Au Cu Patterns simulated using JEMS 54

Cu3Au - like FCC Au but with Cu atoms on face-centred sites. What happens to SADP if we gradually increase Z of Cu sites until that of Au (to obtain FCC Au)? z Forbidden reflections Diffraction pattern on [0 0 1] zone axis: y x Au Cu Patterns simulated using JEMS 55 Extinction rules Face-centred cubic: reflections with mixed odd, even h, k, l absent: Body-centred cubic: reflections with h + k + l = odd absent: Reciprocal lattice of FCC is BCC and vice-versa 56

Selected-area diffraction phenomena 57 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! 58

Twinning in diffraction Example: FCC twins Stacking of close-packed {1 1 1} planes reversed at twin boundary: A B C A B C A B C A B C # A B C A B C B A C B A C View on [1 1 0] zone axis: {1 1 1} planes: A B 1-1 -1 1-1 -1 B 1-1 1 A 0 0 2 59 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 60

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 61 Crystallographically-oriented precipitates Co-Ni-Al shape memory alloy, austenitic with Co-rich precipitates Bright-field image Dark-field image!"#$%#&'#%()*+,&-./0 1 &2 '3)#.),2'+4'!"#"$"%!&'(%51167!8 9956617 -:;:/: <'=>11>1?!8 99=116? -:;:/: 8,@ '3)#.),2'+4'!"#"$"%!&'(%51167!8 9956617 -:;:/: <%=>111?!8 99=116? -:;:/: Images provided by Barbora Bartová, CIME 62

Double diffraction Special type of multiple elastic scattering: diffracted beam travelling through a crystal is rediffracted Example 1: rediffraction in different crystal - NiO being reduced to Ni in-situ in TEM Epitaxial relationship between the two FCC structures (NiO: a = 0.42 nm Ni: a = 0.37 nm) Formation of satellite spots around Bragg reflections Images by Quentin Jeangros, EPFL 63 Double diffraction Example 1: NiO being reduced to Ni in-situ in TEM movie 64

Double diffraction Example 1I: rediffraction in the same crystal; appearance of forbidden reflections Example of silicon; from symmetry of the structure {2 0 0} reflections should be absent However, normally see them because of double diffraction Simulate diffraction pattern on [1 1 0] zone axis: 65 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! Note: if scattering sufficiently kinematical, can compare intensities with those of X-ray PDF files 66

Ring diffraction patterns Larger crystals => more spotty patterns Example: ZnO nanocrystals ~20 nm in diameter 67 Ring diffraction patterns Texture - i.e. preferential orientation - is seen as arcs of greater intensity in the diffraction rings Example: hydrozincite Zn5(CO3)2(OH)6 recrystallised to ZnO crystals 1-2 nm in diameter 68

Amorphous diffraction pattern Crystals: short-range order and long-range order Amorphous materials: no long-range order, but do have short-range order (roughly uniform interatomic distances as atoms pack around each other) Short-range order produces diffuse rings in diffraction pattern Example: Vitrified germanium (M. H. Bhat et al. Nature 448 787 (2007) 69 Kikuchi lines Inelastic scattering event scatters electrons in all directions inside crystal Some scattered electrons in correct orientation for Bragg scattering => cone of scattering Cones have very large diameters => intersect diffraction plane as ~straight lines 70

Kikuchi lines Position of the Kikuchi line pairs of (excess and deficient) very sensitive to specimen orientation Can use to identify excitation vector; in particular s = 0 when diffracted beam coincides exactly with excess Kikuchi line (and direct beam with deficient Kikuchi line) Lower-index lattice planes => narrower pairs of lines 71 Kikuchi lines - road map to reciprocal space Kikuchi lines traverse reciprocal space, converging on zone axes - use them to navigate reciprocal space as you tilt the specimen! Examples: Si simulations using JEMS Si [1 1 0] Si [1 1 0] tilted off zone axis Si [2 2 3] Obviously Kikuchi lines can be useful, but can be hard to see (e.g. from insufficient thickness, diffuse lines from crystal bending, strain). Need an alternative method... 72

Convergent beam electron diffraction 73 Convergent beam electron diffraction Instead of parallel illumination with selected-area aperture, CBED uses highly converged illumination to select a much smaller specimen region Small illuminated area => no thickness and orientation variations There is dynamical scattering, but it is useful! Can obtain disc and line patterns packed with information: 74

Convergent beam electron diffraction 75 Convergent beam electron diffraction 76

Convergent beam electron diffraction 77 Convergent beam electron diffraction Kikuchi from: inelastic scattering convergent beam Kikuchi lines much less diffuse for CBED => use CBED to orientate sample! 78

Convergent beam electron diffraction practical example ZnO thin-film sample; Conditions: convergent beam, large condenser aperture, diffraction mode 79 Convergent beam electron diffraction practical example ZnO thin-film sample; Conditions: convergent beam, large condenser aperture, diffraction mode [1 1 0] zone axis 80

Recording & analysing selected-area diffraction patterns 81 Recording SADPs Orientate your specimen by tilting - focus the beam on specimen in image mode, select diffraction mode and use Kikuchi lines to navigate reciprocal space - or instead use contrast in image mode e.g. multi-beam zone axis corresponds to strong diffraction contrast in the image In image mode, insert chosen selected-area aperture; spread illumination fully (or near fully) overfocus to obtain parallel beam Select diffraction mode; focus diffraction spots using diffraction focus Choose recording media: - if CCD camera, insert beam stopper to cut out central, bright beam to avoid detector saturation (unless you have very strong scattering to diffracted beams) - if plate negatives, consider using 2 exposures: one short to record structure near central, bright beam; one long (e.g. 60 s) to capture weak diffracted beams 82

Recording media: image plates vs CCD camera! no saturation damage! high dynamic range and sensitivity! linear dynamic range! large field of view " time consuming loading, scanning! immediate digital image! linear dynamic range " small field of view " care to avoid oversaturatation " reduced dynamic range 83 Calibrating your diffraction pattern Plate negatives CCD camera Record SADP from a known standard - e.g. NiOx ring pattern λl = dhklrhkl λ: e - wavelength (Å) L: camera length (mm) dhkl: plane spacing (Å) Rhkl: spot spacing on negative (mm) (D/2)C = dhkl -1 D: diameter of ring (pixels) C: calibration (nm -1 per pixel) dhkl -1 : reciprocal plane spacing (nm -1 ) 84

Optical axis Calibrating rotation Unless Electron you source are using rotation-corrected TEM (e.g. JEOL 2200FS), you must calibrate rotation between image and diffraction pattern if you want to correlate orientation with image Condenser lens Specimen Objective lens Back focal plane/ diffraction plane Use specimen with clear shape orientation Defocus diffraction pattern (diffraction focus/ intermediate lens) to image pattern above BFP Diffraction spots now discs; in each disc there is an image (BF in direct beam, DF in diffracted beams Intermediate image 1 Selected area aperture Intermediate lens Projector lens BF image (GaAs nanowire) Defocus SADP 85 Diffraction Analysing your diffraction pattern Calculate planes spacings for lower index reflections (measure across a number and average) Measure angles between planes Compare plane spacings e.g. with XRD data for expected crystals Identify possible zone axes using Weiss Zone Law Simulate patterns e.g. using JEMS; overlay simulation on recorded data 86

Indexing planes example 87 Indexing planes example 88

Indexing planes example 89 Quantitative electron diffraction 90

Disadvantages of conventional SADP " lose higher symmetry information (projection effect; 2D information; intensities not kinematical) " dynamical intensity hard to interpret " poor measurement accuracy of lattice parameters (2-3%) Can solve with:! higher order Laue zones: 3D information! advanced CBED: higher order symmetry, accurate lattice parameter measurements, interpretable dynamical intensity! electron precession: kinematical zone axis patterns => full symmetry/point group, space group determination; strain measurements; polarity of non-centrosymmetric crystals; thickness determination;... 91 Higher-order Laue Zones ZOLZ: hu + kv + lw = 0 FOLZ: hu + kv + lw = 1 SOLZ: hu + kv + lw = 2... 92

Higher-order Laue Zones 93 Advanced CBED Patterns from dynamical scattering in direct and diffraction discs allow determination of: - polarity of non-centrosymmetric crystals - sample thickness JEMS simulation: GaN [1-1 0 0] zone axis Simulation vs experiment: t = 100 nm t = 150 nm t = 200 nm t = 250 nm T. Mitate et al. Phys. Stat. Sol. (a) 192, 383 (2002) 000-2 0000 0002 94

HOLZ lines in CBED Positions of Kikuchi HOLZ lines in direct CBED beam very sensitive to lattice parameters => use for lattice parameter determination with e.g. 0.1% accuracy, strain measurement 95 HOLZ lines in CBED Because HOLZ lines contain 3D information, they also show true symmetry e.g. three-fold {111} symmetry for cubic - unlike apparent six-fold axis in SADP or from ZOLZ Kikuchi lines 96

HOLZ lines in CBED Energy-filtered imaging mandatory for good quality CBED pattern - e.g. Si [1 0 0] below taken with new JEOL 2200FS Unfiltered Filtered Images by Anas Mouti, CIME 97 Precession electron diffraction Tilt beam off zone axis, rotate => hollow-cone illumination Descan to reconstruct pointual diffraction spots => spot pattern with moving beam 98

Precession electron diffraction Because beam tilted off strong multi-beam axis, much less dynamical scattering => Multi-beam zone axis diffraction with kinematical intensity Precession pattern shows higher order symmetry lost in conventional SADP Precession pattern also much less sensitive to specimen tilt - can try on the CM20 in CIME! Images from www.nanomegas.com 99 Large angle CBED (LACBED) Bragg and HOLZ lines superimposed on defocus image - use for: - Burgers vector analysis: splitting of lines by dislocations - orientation relationships: lines continuous/discontinuous across interfaces -... 100

Nano-area electron diffraction Image the condenser aperture using a third condenser lens => nanometer-sized beam with parallel illumination Zuo et al. Microscopy Research and Technique 64 347 (2004) 101 Nano-area electron diffraction Method developed for nano-objects where no dynamical scattering problem but phase is required - therefore need coherent illumination that you do not obtain with CBED Electron diffraction pattern from single double-walled carbon nanotube - can determine chirality 102

Phase/orientation mapping NanoMEGAS ASTAR: phase and orientation mapping in TEM similar to EBSD in SEM but e.g. much higher spatial resolution (~5 nm possible) Record diffraction patterns as electron probe moved across sample Analyse diffraction patterns by template matching i.e. correlate to ~2000 patterns simulated at different orientations Combine with precession and can achieve angular resolution of < 1 Orientation map for nanocrystalline Cu: Phase map showing local martensitic structure of steel at stacking faults: Images from NanoMEGAS company literature 103 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 104