Electron Microscopy - Wikis09-10]_DOWNLOAD/4 tem i.… · Electron Microscopy 4. TEM Basics:...

$: Electron Microscopy - Wikis09-10]_DOWNLOAD/4 tem i.… · Electron Microscopy 4. TEM Basics: interactions, basic modes, sample preparation, Diffraction: elastic scattering theory,$
Autumn 2009 Experimental Methods in Physics Marco Cantoni

Electron Microscopy

4. TEM

Basics: interactions, basic modes,sample preparation,

Diffraction: elastic scattering theory, reciprocal space, diffraction pattern,

Laue zonesDiffraction phenomena

Image formation: contrasts,


Types of electron microscopes

TransmissionElectron Microscope

ScanningElectron Microscope

Slide Projector

TV

What you see is what the

detector sees !!!

Scanning beamScanning beam


Typical TEM

EPFL: Philips CM300EPFL: Philips CM300

300300’’000V000V


Signals from a thin sample

Specimen

Inc

ide

nt b

ea

m

Auger electrons

Backscattered electronsBSE

secondary electronsSE Characteristic

X-rays

visible light

“absorbed” electrons electron-hole pairs

elastically scatteredelectrons

inelasticallyscattered electrons

BremsstrahlungX-rays

11--100 nm100 nm


Interaction of high energetic electrons with matter

biological samples,polymers

crystalline structure,defect analysis,high-resolution TEM

chemical analysis,spectroscopy


Interaction -> contrastE

DS

, e

lem

ent

map

sE

DS

, e

lem

ent

map

s

STEMSTEM--DFDF

Thin section of mouse brain: mass contrast of stained membrane structures(G.Knott)

Dark field image of differently ordered domains:Diffraction contrast

High-resolution image:Image contrast due to interference between transmitted and diffracted beam

Element distribution mapsOf Nb3Sn superconductor


Two basic operation modesDiffraction <-> Image

Diffraction Mode Image Mode


Projector lens system, TEM

mode DIFFRACTION mode IMAGE

• TEM:• Intermediate and

projector lenses– Projection of the

back focal plane to the screen“diffraction”mode

– Projection of the image plane to the screen“image” mode(haute resolution)


Not to forgetNot to forget…….!.!the specimen preparationthe specimen preparation

electron transparency: sample thickness < 100nmelectron transparency: sample thickness < 100nmstandard sample holders: disc shaped samples with 3mm diameterstandard sample holders: disc shaped samples with 3mm diameter

3mm3mm


CrossCross--section section --preparationpreparation• Mechanical polishing down to a thickness of 30 mm

• Ion milling (4kV Ar ions) until perforation

Si-wafer

Si-wafer

thin film

thin film

glue line

-gluing face-to-face-cutting a slice-polishing down to 30mm-copper washer for mechanical stability

1 – 1.5days


PlanePlane--view preparation (also bulk)view preparation (also bulk)

• cutting a disk of 3mm(ultrasonic cutter)

• polishing down to 30mm(copper washer for mechanical stability)

• Ion milling until perforation

1 day

Thick film of PZT (Pt bottom electrode)

PZTPt

SiO2 Si


Lucky if you have powders !

preparation time: 15-30Min.

Cupper grid coveredwith carbon film

Optical microscopereflected light

Optical microscopetransmitted light


preparation time: 15-30Min.

SEM

TEM

holey Carbon film(K,Nb)TaO3Nano-rods


Shape, lattice parameters, defects, lattice planes

(K,Nb)O3Nano-rods

Bright field image

dark field image

Diffraction pattern

High-resolution image


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


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?

( 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

BaTiO3 nanocrystals (Psaltis lab)

Image formation


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

Take selected-area diffraction pattern


Consider coherent elastic scattering of electrons from atom

Differential elastic scatteringcross section:

Atomic scattering factor

Scattering theory - Atomic scattering factor


Atoms closer together => scattering angles greater

=> Reciprocity!

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

Scattering theory - Huygen’s principle


Repetition of translated structure to infinity

Basic crystallographyCrystals: translational periodicity & symmetry


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


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: ½,½,½Structure = lattice +motif => Start applying motif to each lattice point

Building a crystal structure


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: ½,½,½Structure = lattice +motif => Start applying motif to each lattice point

Extend lattice further in to space

Building a crystal structure


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


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


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


14 Bravais lattices


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:

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

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

Crystallography - lattice vectors


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


Sets of planes intersecting the unit cell - examples:

(1 0 0)

(0 2 2)

(1 1 1)

Crystallography - lattice planes

a/h on the x axisb/k on the y axisc/l on the z axis


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):

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


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

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

Diffraction theory - Bragg law


Loi de Bragg

• 2 sinθ dhkl = n λ distance

entre

plan atomiquesd

ondeentrante

onde

sorta

nte

θλ

θdifférence dechemin parcouru

“1”

“2”

“1”

“2”

dhkl = n λ/2 sinθ

kk’

g = k-k’

Diffraction élastique

|k| = |k’|

arrangement périodique d’atomes dans l’espace (réelle):g : vecteur dans l’espace réciproque


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

Diffraction theory - 2-beam condition


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

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

Multi-beam scattering condition


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


Ewald Sphere

• A vector in reciprocal space:• ghkl = h a* + k b* + l c*

• diffraction if : k0 – k’ = g and |k| =|k’|Bragg and elastic scattering

Bragg: dhkl = λ/2 sinθ = 1/ |g|

Construction of EWALD sphere:Intersection of two geometric locations:Reciprocal space AND Ewald sphere


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

Ewald sphereElastic scattering:

|k| = |k’|


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

Ewald sphere in 2-beam condition


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 scattering


Laue Zones

O H

E

k k'

g

Zonesde Laued'ordre

32

10

Ewald

θ θ

plan

s ré

flec

teu


• Laue zones

J.-P. Morniroli


Ewald Sphere : Laue Zones (ZOLZ+FOLZ)

α=2.0mrads=0.2

ZOLZ6-fold

FOLZ3-fold

Source: P.A. Buffat


Ewald Sphere: Laue Zones (ZOLZ+FOLZ) tilted sample

α=2.0mrads=0.2

ZOLZ6-fold

FOLZ3-fold


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

Dynamical scattering


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:

Intensity in the electron diffraction patternStructure factor


Consider FCC lattice with lattice point coordinates:0,0,0; ½,½,0; ½,0,½; 0,½,½

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

=>

Forbidden reflections


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)?

Patterns simulated using JEMS

Diffraction pattern on [0 0 1] zone axis:



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)?

Patterns simulated using JEMS

Diffraction pattern on [0 0 1] zone axis:



Reciprocal lattice of FCC is BCC and vice-versa

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

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


Selected-area diffraction phenomena


Symmetry informationZone 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 diffractionExample: 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 relationshipsSADP 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


Ring diffraction patternsIf 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!


Ring diffraction patternsLarger crystals => more “spotty” patterns

Example: ZnO nanocrystals ~20 nm in diameter


Inelastic scattering event scatters electrons in all directions inside crystal

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

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


Kikuchi lines

Position of the Kikuchi line pairs of (excess and deficient) verysensitive to specimen orientation

Lower-index lattice planes => narrower pairs of lines


Convergent beam electron diffraction


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

Convergent beam electron diffraction

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:


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

http://www.doitpoms.ac.uk

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

Publishing

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

References

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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