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Duncan Alexander: Principles & Practice of Electron Diffraction November 2010, EPFL

Principles & Practice of Electron Diffraction

1

Duncan AlexanderEPFL-CIME


Contents

2

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


Introduction to electron diffraction

3


Diffraction: constructive and destructive interference of waves

! electrons interact very strongly with matter => strong diffraction intensity (can take patterns in seconds, unlike X-ray diffraction)

" diffraction from only selected set of planes in one pattern - e.g. only 2D information

! 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)

! spatially-localized information(≳ 200 nm for selected-area diffraction; 2 nm possible with convergent-beam electron diffraction)

! orientation information

! close relationship to diffraction contrast in imaging

! immediate in the TEM!

" limited accuracy of measurement - e.g. 2-3%

" intensity of reflections difficult to interpret because of dynamical effects

Why use electron diffraction?

4

(" 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)


Insert selected area aperture to choose region of interest

Optical axis

Electron source

Condenser lens

Specimen

Objective lens

Back focal plane/di!raction plane

Intermediate lens

Projector lens

Image

Intermediate image 1

Optical axis

Electron source

Condenser lens

Specimen

Objective lens


Intermediate lens

Projector lens

Image


Selected areaaperture

BaTiO3 nanocrystals (Psaltis lab)

Image formation

5


Press “D” for diffraction on microscope console - alter strength of intermediate lens and focus

diffraction pattern on to screen

Optical axis

Electron source

Condenser lens

Specimen

Objective lens


Intermediate lens

Projector lens

Image



Optical axis

Electron source

Condenser lens

Specimen

Objective lens


Intermediate lens

Projector lens

Di!raction



Find cubic BaTiO3 aligned on [0 0 1] zone axis

Take selected-area diffraction pattern

6


Elastic scattering theory

7


Consider coherent elastic scattering of electrons from atom

Differential elastic scatteringcross section:

Atomic scattering factor

Scattering theory - Atomic scattering factor

8


Atoms closer together => scattering angles greater

=> Reciprocity!

Periodic array of scattering centres (atoms)

k0k0k0k0k0k0k0k0k0

k0

k0

kD1

k0

kD2

k0

kD2k0kD1

Plane electron wave generates secondary wavelets

Secondary wavelets interfere => strong direct beam and multiple orders of diffracted beams from constructive interference

Scattering theory - Huygen’s principle

9


Basic crystallography & symmetry

10


Repetition of translated structure to infinity

Crystals: translational periodicity & symmetry

11


Unit cell is the smallest repeating unit of the crystal latticeHas a lattice point on each corner (and perhaps more elsewhere)

Defined by lattice parameters a, b, c along axes x, y, zand angles between crystallographic axes: α = b^c; β = a^c; γ = a^b

Crystallography: the unit cell

12


Use example of CuZn brassChoose the unit cell - for CuZn: primitive cubic (lattice point on each corner)

x

y

z

Choose the motif - Cu: 0, 0, 0; Zn: !,!,!

x

y

z

Motif:Cu

Znx

y

z

Structure = lattice +motif => Start applying motif to each lattice point

x

y

z

Motif:Cu

Znx

y

z

x

y

z

Motif:Cu

Znx

y

z

Building a crystal structure

13


x

y

z

Motif:Cu

Znx

y

z

Use example of CuZn brassChoose 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

x

y

z

Cu

Zn

x

y

z

Cu

Zn

x

y

z

Cu

Zn

y

x

y

zCu

Zn

y

y

x

y

zCu

Zn

y

y

y

x

y

zCu

Zn

y

y

y

y

Building a crystal structure

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:

Rotation axes:

Inversion axes: combination of rotation axis with centre of symmetry

Centre of symmetry orinversion centre:

Introduction to symmetry

15


Example - Tetragonal lattice: a = b ≠ c; α = β = γ = 90°

Anatase TiO2 (body-centred lattice) view down [0 0 1] (z-axis):

x

y

z

O

Ti

x

y

z

O

Ti

Identify mirror planes

x

y

z

O

Ti

x

y

z

O

Ti

x

y

z

O

Ti

x

y

z

O

Ti

x

y

z

O

Ti

x

y

z

O

Ti

Tetrad:4-fold rotationaxis

Mirror plane

Identify rotation axis: 4-fold = defining symmetry of tetragonal lattice!

Introduction to symmetry

16


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!)

x y

z

x y

z

x y

z

More defining symmetry elements

17


(Cubic α-Al(Fe,Mn)Si: example of primitive cubic with no 4-fold axis)

18


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]

x

yz

120

a

a

Draw 2 x 2 unit cells

Identify rotation axis: 6-fold (hexad) - defining symmetry of hexagonal lattice

x

yz

120

a

a

x

yz

120

a

a

More defining symmetry elements

19


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

The seven crystal systems

20


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 latticepoint centred on A, B or C face


Four possible lattice centerings

21


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


14 Bravais lattices

22


14 Bravais lattices

23


A lattice vector is a vector joining any two lattice pointsWritten as linear combination of unit cell vectors a, b, c:

t = Ua + Vb + WcAlso written as: t = [U V W]

Examples:z

x

y

z

x

y

z

x

y

[1 0 0] [0 3 2] [1 2 1]

Important in diffraction because we “look” down the lattice vectors (“zone axes”)

Crystallography - lattice vectors

24


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 axisb/k on the y axisc/l on the z axis

Crystallography - lattice planes

25


Sets of planes intersecting the unit cell - examples:

x

z

y

x

z

y

x

z

y

(1 0 0)

(0 2 2)

(1 1 1)

Crystallography - lattice planes

26


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 diagonalrelates the planes (1 0 0), (0 1 0), (0 0 1):

x y

z

x y

z

x y

z

x y

z

x y

z

Set of planes {1 0 0} = (1 0 0), (0 1 0), (0 0 1), (-1 0 0), (0 -1 0), (0 0 -1)

Lattice planes and symmetry

27


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)

Weiss Zone Law

28


Electron diffraction theory

29


Path difference between reflection from planes distance dhkl apart = 2dhklsinθ

Electron diffraction: λ ~ 0.001 nmtherefore: λ ≪ dhkl

=> small angle approximation: nλ ≈ 2dhklθReciprocity: scattering angle θ ∝ dhkl

-1

dhkld!

hkld! !

hkld! !

hkld! !

hkld! !

+ =

hkld! !

+ =

hkl

2dhklsinθ = λ/2 - destructive interference2dhklsinθ = λ - constructive interference=> Bragg law:nλ = 2dhklsinθ

Diffraction theory - Bragg law

30


d

!

!

hkl

!

!

!

!!

k I

!

!!

k I

k D

k I!

!

0 0 0 Gg

!

k I

k D

k I

2-beam condition: strong scattering from single set of planes

Diffraction theory - 2-beam condition

31


x

yz

x

yz

0 0 00 0 0

1 0 0

x

yz

0 0 0

1 0 0

0 1 0

x

yz

0 0 0

1 0 0

0 1 0

1 1 0

x

yz

0 0 0

1 0 0

0 1 0

1 1 0

2 0 0

x

yz

0 0 0

1 0 0

0 1 0

1 1 0

2 0 0 2 2 0

x

yz

Electron beam parallel to low-index crystal orientation [U V W] = zone axisCrystal “viewed down” zone axis is like diffraction grating with planes parallel to e-beam

In diffraction pattern obtain spots perpendicular to plane orientationExample: primitive cubic with e-beam parallel to [0 0 1] zone axis

Note reciprocal relationship: smaller plane spacing => larger indices (h k l)& greater scattering angle on diffraction pattern from (0 0 0) direct beam

2 x 2 unit cells

0 0 0

1 0 0

0 1 0

1 1 0

2 0 0 2 2 0

3 0 0

0 0 0

1 0 0

0 1 0

1 1 0

2 0 0 2 2 0

3 0 0

-1 0 0

0 -1 0

Also note Weiss Zone Law obeyed in indexing (hU + kV + lW = 0)

Multi-beam scattering condition

32


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:

x

yz

120

a

a

(1 0 0) planes

yz

120

a

a

[1 0 0]

(1 0 0) planes

yz

120

a

a

[1 0 0] g1 0 0

(1 0 0) planes

=> care must be taken in reciprocal space!

Scattering from non-orthogonal crystals

33


For scattering from plane (h k l) the diffraction vector: ghkl = ha* + kb* + lc*

rn = n1a + n2b + n3cReal lattice

vector:

In diffraction we are working in “reciprocal space”; useful to transform the crystal lattice in toa “reciprocal lattice” that represents the crystal in reciprocal space:

r* = m1a* + m2b* + m3c*Reciprocal lattice

vector:

a*.b = a*.c = b*.c = b*.a = c*.a = c*.b = 0

a*.a = b*.b = c*.c = 1

a* = (b ^ c)/VC

where:

i.e. VC: volume of unit cell

Plane spacing:

The reciprocal lattice

34


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 latticeis the Fourier transform of the real lattice

Can use this to understand diffraction patterns and reciprocal space more easily

Fourier transforms for understanding reciprocal space

35


radius = 1/!

0

kIkD

C

Reciprocal space: sphere radius 1/λ represents possible scattering wave vectors intersecting reciprocal space

kI: incident beam wave vector

kD: diffracted wave vector

Electron diffraction: radius of sphere very large compared to reciprocal lattice=> sphere circumference almost flat

The Ewald sphere

36


kIkD

ghkl

kk

G0 0 0

2!

!

!

0 0 0 Gg

!

k I

k D

k I

2-beam condition with one strong Bragg reflection corresponds to Ewald sphereintersecting one reciprocal lattice point

Ewald sphere in 2-beam condition

37


0 0 0

kIkDkk

With crystal oriented on zone axis, Ewald sphere may not

intersect reciprocal lattice points

However, we see strong diffractionfrom many planes in this condition

Assume reciprocal lattice pointsare infinitely small

Because reciprocal lattice pointshave size and shape!

Ewald sphere and multi-beam scattering

38


Real lattice is not infinite, but is bound disc of material with diameter ofselected area aperture and thickness of specimen - i.e. thin disc of material

X

FT FT

X “Relrod”

= 2 lengths scales inreciprocal space!

Fourier transforms and reciprocal lattice

39


0 0 0

kIkDkk

0 0 0

kIkDkk

Ewald sphere intersects Relrods

40


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:

Relrod shape

41


Relrod shape

42


Intensity in the electron diffraction pattern

43


Tilted slightly off Bragg condition, intensity of diffraction spot much lower

Introduce new vector s - “the excitation error” that measures deviation fromexact Bragg condition

Excitation error

44


Excitation error

45


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 beamis at the perfect angle to be Bragg-scattered

again (and again...)

As a result, scattering of different beams is not independent from each other

Dynamical scattering

46


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:

If the excitation distance s = 0 (i.e. perfect Bragg condition), then:

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

Dynamical scattering for 2-beam condition

47

Duncan Alexander: Principles & Practice of Electron Diffraction November 2010, EPFL 48

Dynamical scattering in the dark-field image –

=> Intensity zero for thicknesses t = nξg (integer n)

Composition changes in quantum wells=> extinction at different thickness compared to substrate

See effect as dark “thickness fringes” on wedge-shaped sample:

Extinction and thickness fringes


Dynamical scattering for 2-beam

49

2-beam condition: direct and diffracted beam intensities beams π/2 out of phase:

Bright-field image showing modulation

with absorption:

Model with absorption using JEMS:


2-beam: kinematical vs dynamical

50

Kinematical (weak interactions) Dynamical (strong interactions)


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

Weak beam; kinematical approximation

51

where:

Before we saw for 2-beam condition:


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:

Structure factor

52

Note fi is a function of s and (h k l)


Consider FCC lattice with lattice point coordinates:0,0,0; !,!,0; !,0,!; 0,!,!

x

z

y

Calculate structure factor for (0 1 0) plane (assume single atom motif):

x

z

y

=>

x

z

y

x

z

y

Forbidden reflections

53


x

z

y

Au

Cu

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)?

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

Patterns simulated using JEMS

Diffraction pattern on [0 0 1] zone axis:

x

z

y


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)?

x

z

y

Au

CuPatterns simulated using JEMS

Diffraction pattern on [0 0 1] zone axis:

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y

x

z

y


55


Reciprocal lattice of FCC is BCC and vice-versa

Extinction rules

56

Face-centred cubic: reflections with mixed odd, even h, k, l absent:

Body-centred cubic: reflections with h + k + l = odd absent:


Selected-area diffraction phenomena

57


Symmetry information

58

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 axisNeed third dimension for true symmetry!


Twinning in diffraction

59

Example: FCC twinsStacking 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

Example: FCC twinsStacking of close-packed {1 1 1} planes reversed at twin boundary:

A B C A B C A B C A B C

View on [1 1 0] zone axis:

{1 1 1} planes:

1 -1 1

0 0 2

1 -1 -1

{1 1 1} planes:{1 1 1} planes:

1 -1 1A

1 -1 -1B

A B


Twinning in diffraction

60

Example: Co-Ni-Al shape memory FCC twins observed on [1 1 0] zone axis

Images provided by Barbora Bartová, CIME

(1 1 1) close-packed twin planes overlap in SADP


Epitaxy and orientation relationships

61

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


Crystallographically-oriented precipitates

62

Images provided by Barbora Bartová, CIME

Bright-field image Dark-field image

!"#$%#&'#%()*+,&-./01&2'3)#.),2'+4'!"#"$"%!&'(%51167!89956617-:;:/:<'=>11>1?!899=116?-:;:/:8,@'3)#.),2'+4'!"#"$"%!&'(%51167!89956617-:;:/:<%=>111?!899=116?-:;:/:

Co-Ni-Al shape memory alloy, austenitic with Co-rich precipitates


Double diffraction

63

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


Double diffraction

64

Example 1: NiO being reduced to Ni in-situ in TEM movie


Double diffraction

65

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 patternon [1 1 0] zone axis:


Ring diffraction patterns

66

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



67

Larger crystals => more “spotty” patterns

Example: ZnO nanocrystals ~20 nm in diameter



68

Example: hydrozincite Zn5(CO3)2(OH)6 recrystallised to ZnO crystals 1-2 nm in diameter

“Texture” - i.e. preferential orientation - is seen as arcs of greater intensityin the diffraction rings


Amorphous diffraction pattern

69

Crystals: short-range order and long-range order

Vitrified germanium (M. H. Bhat et al. Nature 448 787 (2007)

Example:

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


Inelastic scattering event scatters electrons in all directions inside crystal

Cones have very large diameters => intersect diffraction plane as ~straight lines

Kikuchi lines

70

Some scattered electrons in correct orientation for Bragg scattering => cone of scattering


Kikuchi lines

71

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 coincidesexactly with excess Kikuchi line (and direct beam with deficient Kikuchi line)

Lower-index lattice planes => narrower pairs of lines


Kikuchi lines - “road map” to reciprocal space

72

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...



73


Instead of parallel illumination with selected-area aperture, CBED useshighly converged illumination to select a much smaller specimen region


74

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:



75



76



77



78

Kikuchi from: inelastic scattering convergent beam

“Kikuchi” lines much lessdiffuse for CBED

=> use CBED to orientatesample!


Convergent beam electron diffraction– practical example

79

ZnO thin-film sample;Conditions: convergent beam, large condenser aperture, diffraction mode


Convergent beam electron diffraction– practical example

80

ZnO thin-film sample;Conditions: convergent beam, large condenser aperture, diffraction mode

[1 1 0] zone axis


Recording & analysing selected-area

diffraction patterns

81


Recording SADPs

82

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


! no saturation damage! high dynamic range! large field of view

" need to develop, scan negative" intensities not linear

Recording media:plate negatives vs CCD camera

83

! immediate digital image! linear dynamic range" small field of view

" care to avoid oversaturatation" reduced dynamic range


Calibrating your diffraction pattern

84

Plate negatives

λL = dhklRhkl

λ: e- wavelength (Å)L: “camera length” (mm)

dhkl: plane spacing (Å)Rhkl: spot spacing on negative (mm)

CCD camera

(D/2)C = dhkl-1

D: diameter of ring (pixels)C: calibration (nm-1 per pixel)

dhkl-1: reciprocal plane spacing (nm-1)

Record SADP from a known standard -e.g. NiOx ring pattern


Calibrating rotation

85

Unless you are using rotation-corrected TEM (e.g. JEOL 2200FS), you must calibrate rotationbetween image and diffraction pattern if you want to correlate orientation with image

Optical axis

Electron source

Condenser lens

Specimen

Objective lens


Intermediate lens

Projector lens

Di!raction



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

BF image (GaAs nanowire) Defocus SADP


Analysing your diffraction pattern

86

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

Simulate patterns e.g. using JEMS;overlay simulation on recorded data

Identify possible zone axes using Weiss Zone Law


Indexing planes example

87



88



89


Quantitative electron diffraction

90


Disadvantages of conventional SADP

91

" 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; ...


Higher-order Laue Zones

92

ZOLZ: hU + kV + lW = 0FOLZ: hU + kV + lW = 1SOLZ: hU + kV + lW = 2

...


Higher-order Laue Zones

93


Advanced CBED

94

Patterns from dynamical scattering in direct and diffraction discs allow determination of:- polarity of non-centrosymmetric crystals

- sample thickness

T. Mitate et al. Phys. Stat. Sol. (a)192, 383 (2002)

Simulation vs experiment:JEMS simulation: GaN [1 -1 0 0] zone axis

t = 100 nm

t = 150 nm

t = 200 nm

t = 250 nm

000-2 0000 0002


HOLZ lines in CBED

95

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


HOLZ lines in CBED

96

Because HOLZ lines contain 3D information, they also show true symmetrye.g. three-fold {111} symmetry for cubic

- unlike apparent six-fold axis in SADP or from ZOLZ Kikuchi lines


HOLZ lines in CBED

97

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


Precession electron diffraction

98

Tilt beam off zone axis, rotate => hollow-cone illumination

“Descan” to reconstruct “pointual” diffraction spots => spot pattern with moving beam


Precession electron diffraction

99

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


Large angle CBED (LACBED)

100

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- ...


Nano-area electron diffraction

101

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)


Nano-area electron diffraction

102

Electron diffraction pattern from single double-walled carbon nanotube- can determine chirality

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


Phase/orientation mapping

103

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


“Transmission Electron Microscopy”, Williams & Carter, Plenum Press

http://www.doitpoms.ac.uk

“Transmission Electron Microscopy: Physics of Image Formation and Microanalysis (Springer Series in Optical Sciences)”, Reimer, Springer Publishing

“Large-Angle Convergent-Beam Electron Diffraction Applications to Crystal Defects”, Morniroli, Taylor & Francis Publishing

References

104

http://crystals.ethz.ch/icsd - access to crystal structure file databaseCan download CIF file and import to JEMS

Web-based Electron Microscopy APplication Software (WebEMAPS)http://emaps.mrl.uiuc.edu/

JEMS Electron Microscopy Software Java versionhttp://cimewww.epfl.ch/people/stadelmann/jemsWebSite/jems.html

“Electron diffraction in the electron microscope”, J. W. Edington, Macmillan Publishers Ltd

http://escher.epfl.ch/eCrystallography

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