Introduction to Transmission Electron Microscopy (Physical ...microscopy.anu.edu.au/files/CAM introduction to TEM...24/04/2018 1 Introduction to Transmission Electron Microscopy (Physical

24/04/2018

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Introduction to Transmission Electron Microscopy

(Physical Sciences)

Centre for Advanced Microscopy

Program

9:00 – 10:15 Lecture 1 – Basics of TEM

10:15 – 10:30 Morning tea

10:30 – 11:45 Lecture 2 – Diffraction

11:45 – 12:00 Practice 1 – Indexing diffraction patterns

12:00 – 12:30 Demonstration 1 – Basics of TEM operation

12:30 – 13:30 Lunch

13:30 – 14:45 Lecture 3 - Imaging

14:45 – 15:00 Afternoon tea

15:00 – 15:30 Demonstration 2 – Collection of diffraction patterns and images

15:30 – 16:00 EDX, STEM

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• Transmission Electron Microscopy and Diffractometry of Materials. Brent Fultz and James Howe

• Transmission Electron Microscopy: A Textbook for Materials Science David B. Williams and C. Barry Carter

• Transmission Electron Microscopy: Physics of Image Formation. L. Reimer H. Kohl

• Introduction to Conventional Transmission Electron Microscopy. Marc de Graef

• Scanning Transmission Electron Microscopy: Imaging and Analysis. S. J. Penycock and P. Nellist

• Essential software: Digital micrograph, ImageJ

• Other useful software: JEMS (available in CAM), Crystal Maker, CRISP

• Contact: [email protected]

• For initial sessions and training in the TEM, please contact:

– [email protected] or [email protected]

Notes

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Part 1The basics of TEM


E-learning room

Introduction

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What is a microscope?

A. An instrument used for viewing verysmall objects, such as mineral samplesor animal or plant cells, typicallymagnified several hundred times.

Light microscope vs TEM

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What do we know about electrons?

What do we know about electrons:

Amber = elektron ()

Negatively charged particles => We can apply an electric field to accelerate it!

Electron Duality

Behave as waves => Diffraction patterns when passing by crystals

Behave as particles => Excitation of inner shell electrons => x-ray chemical analysis


Electron DualityWave characteristics of the electron gives rise to coherent scattering (diffraction)

Particle characteristics gives rise to characteristic X-rays

Reproduced from: Transmission Electron Microscopy: A Textbook for Materials ScienceDavid B. Williams and C. Barry Carter

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de Broglie wavelength

Wave characteristics =>

CLASSICAL

RELATIVISTIC

Planck’s constant

Wavelength

Why electrons?

Resolution

Light microscopy vs electron microscopy

Wavelength of the radiation

Collection angleNumerical aperture

Rayleigh criterion


Ex.: Green light (~500 nm) ~ 300 nm

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Why electrons?

Wavelength of the radiation

Collection angleNumerical aperture

Rayleigh criterion

Ex.: Green light (~500 nm) ~ 300 nm (100 kV) = 3.7x10-3 nm (200 kV) = 2.5x10-3 nm (300 kV) = 2.0x10-3 nm

Resolution

Light microscopy vs electron microscopy

Wavelength as a function of the acceleration voltage

Wavelength five orders of magnitude smaller than visible light!!!

Reproduced from: Brent Fultz · James Howe Transmission Electron Microscopy and Diffractometry of Materials

Why electrons?

Resolution


Increasing aperture size

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Resolution vs Magnification

A B C

“A” has same Mag than “C”“B” has same Res than “C”

d

D

Mag = D/d

What else can we “see”?

Incident high kV beam

Secondary electrons (SE)

Characteristic X-rays

Visible light

Electron-hole pairs

‘Absorbed’ electrons

Backscattered electrons (BE)

Auger electrons

Elastically scattered electrons

Direct beam

Inelastically scattered electrons

Bremsstrahlung X-rays

specimen

Multitude of signals resulting from the electron matter interaction

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What else can we “see”?

Incident high kV beam

Secondary electrons (SE)

Characteristic X-rays

Visible light

Electron-hole pairs

‘Absorbed’ electrons

Backscattered electrons (BE)

Auger electrons

Elastically scattered electrons

Direct beam

Inelastically scattered electrons

Bremsstrahlung X-rays

specimen

Multitude of signals resulting from the electron matter interaction

Techniques

• Crystallographic information:

–Electron diffraction

• Selected area diffraction (SAD)

• Convergent beam electron diffraction (CBED)

–Imaging

• Dark field / Bright field imaging

• High resolution (transmission) electron microscopy (HRTEM or HREM)

• Chemical analysis:

–X-rays

• Energy dispersive X-ray spectroscopy (EDS or EDX)

–Electrons

• Electron energy loss spectroscopy (EELS)

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Instrumentation

Basic requirements:

- Intermediate voltages (200, 300, 400 keV)- Brilliant source: LaB6, FEG, W hairpin

Possible extras:

- Scanning transmission electron microscope (STEM)- Energy dispersive X-ray detector (EDS)- Electron energy loss spectometer (EELS)- X-ray and EELS mapping software- Cold stage, heating stage, tensile stage, bias stage, etc.- SE & BSE detectors

Essential extras:

- Diffraction and image simulation software- Image processing software

TEM scheme

Gun assembly

Condenser system

Objective system

Projector system

Viewing/recording system

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TEM scheme

Gun assembly

Condenser system

Objective system

Projector system

Viewing/recording system

Illumination

Image formation

Magnification

Jeol 2100F

TEM instrument

Gun chamber

High voltage cable

Goniometer

Viewing chamber

Condenser aperture

Left side control panel

Cold trap

Right side control panel

Objective aperture

Selected area aperture

FEI CM300

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Right control panel

Spot size

Magnification

Diffraction/ImageBeam shift

Focus reset FocusBeam deflectors

Filament knob

Left control panel

CCD control

Tilt controlFine/coarse

BrightnessNegative exposure control

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Electron guns

Diameter do

Emission current icDivergence semi-angle 0

Brightness

Temporal coherence

Spatial coherence


Electron guns

Thermionic emission

Diameter do

Emission current icDivergence semi-angle 0

LaB6 crystal


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Electron guns

Thermionic emission

Diameter do

Emission current icDivergence semi-angle 0Transmission Electron Microscopy: A Textbook for Materials Science

David B. Williams and C. Barry Carter

Electron guns

Cold FEG (W tip)

Transmission Electron Microscopy: A Textbook for Materials ScienceDavid B. Williams and C. Barry Carter

Reproduced: Transmission Electron Microscopy: Physics of Image FormationL. Reimer H. Kohl

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Electron guns


Lenses

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Magnetic lenses

Electro-magnetic lenses



Magnetic lenses

Brent Fultz · James Howe Transmission Electron Microscopy and Diffractometry of Materials

Lorentz force

Cylindrical coordinates

Convergent lens that produces a rotation to the image.

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Magnetic lenses

e-

A

A

A

A

A

A

Electron entering the lens field Electron spiralling in the field Conventional optical ray diagram

Focus and magnification

Remember: Electro-magnetic lens behave like convergent lenses

do df di

o

i

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Focus and magnification

Remember: Electro-magnetic lens behave like convergent lenses

df

Object

Back focal plane(power spectrum of the object – Fourier Transform)

Aberrations

Spherical aberration Cs


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Aberrations

Spherical aberration Cs Chromatic aberration Cc


#1 Condenser lens system

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Condenser lens system• Core functions:

– Probe size

– Convergence angle

– Brightness

• Different modes of operation:– Parallel illumination

– Focused beam

– Translating and tilting the beam

• Components:– C1, C2, C3 lens

– Condenser aperture

– Condenser stigmator

Focus


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C1 role (spot size)


<1

Demagnification of the source

C2 role (brightness)


CO or c/oCondenser-objective system

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C2 operation


Most microscopes employ a condenser mini-lens system.

(S)TEM

C2 operation


“Parallel” beam achieved in both under- and over-focus.

Which one should I chose to operate the microscope?

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C2 operation

R

R

Parallel illumination should be achieved in over focus condition

Convergence angle ()


Spatial coherence

Misaligned aperture Aligned aperture

At the microscope

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Scanning coils

y

x



Condenser astigmatism

Perfect lenses Real lenses Small compensating field

Result

At the microscope

Focusing the beam (C2)results in a elliptical view ofthe source. Astigmatismpresent.


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More on astigmatism

The difference in the focus point between the two axis leads to the ellipsoidal shape of the electron beam.

#2 Post-specimen lenses

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Eucentric height• Z position corresponding to the

eucentric plane (reference plane towhich the calibrations arereproducible). Hence the sampleshould be kept at this height for bestperformance.

– (Eucentric plane is perpendicular tothe optic axis).

• Sample does not move laterally whentilted.

• Best position for analysis.

• At this position if the objective is infocus, then the objective-lens current isat a standard value. Therefore it ispossible to use the same lens-currentvalue independent of sample.

– It is the object plane.

Object plane

Change strength of

objective lens

Change the height z of the

sample

Eucentric height

1) Adjust the eucentric current using “standard focus”.

2) Adjust the right of the sample until minimum contrast is achieved.

Object plane

Change strength of

objective lens

Change the height z of the

sample

“standard focus”

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Diffraction and image modes

Image mode

Back focal plane

Objective aperture

Selected area diffraction aperture (SAD)

Intermediate lens

Projector lens

Image

Object

Objective lens

From diffraction to image mode: change in the strength of the intermediate lens

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Diffraction mode

Back focal plane

Objective aperture

Selected area diffraction aperture (SAD)

Intermediate lens

Projector lens

DP

Object

Objective lens

Diffraction mode

Intermediate lens

Projector lens

Objective lens

Diff

ract

ion

patte

rn

L = 880 mm

L = 245 mm

L = 420 mm

CM 300

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Diffraction mode

Intermediate lens

Projector lens

Objective lens

Diff

ract

ion

patte

rn

Hitachi H7100

Image mode

Intermediate lens

Projector lens

Objective lens

Imag

es

SiSiO2

Si

M = 5900x

M = 115kx M = 195kx

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Bright and Dark field


Bright Field “Dirty” Dark Field Centred Dark Field

Bright field


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“Dirt” dark field


Centred dark field


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Centred dark field

Brent Fultz · James Howe Transmission Electron Microscopy and Diffractometry of Materials

Weak beam

Aligning aperturesSelected area aperture (sits in the image plane, hence it is aligned in real space)

Aligned Misaligned

Objective aperture (sits in the back focal plane, hence it is aligned in reciprocal space)

Aligned Misaligned

Even distribution of intensities

Even distribution of intensities

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Optics in TEM

• TEM is primarily a scattering technique

– In materials with long range order this mean that diffraction patterns will be generated.

• The main steps in a TEM experiment are:

– Locate the region of interest

– Adjust the eucentric height

– Isolate the feature of interest with the SAD aperture.

– Switch to diffraction mode.

– Tilt the sample.

– Select which diffracted beams will contribute to the image formation.

– Back to image mode.


Summary

• Electron scattering as a imaging tool

• Electron sources

• The TEM construction

• Basic TEM operation

• Lenses– Pre-specimen

• Condenser system control of electron beam illumination on the sample

– Post-specimen• Intermediate lenses Image / Diffraction modes

• Projector lenses Magnification

• Image / Diffraction mode

• Bright field imaging

• “Dirt” and Centred dark field modes

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Part 2Diffraction


E-learning room

Scattering

Ψ .

Ψ.

Δ


First Born approximation

Scattering center

Δ2

. ′

Scattering factor is the Fourier Transform of the scattering potential.

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Scattering


Coherent forward scattering

In a crystal

Ψ.

Δ Ψ Δ .

Distance between source and detection unknown and notactually relevant. Only relative intensities will be measured.


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When do we get diffraction spots?

Ψ Δ ∝ .

Lattice translations

Reproduced from: Brent Fultz · James Howe Transmission Electron Microscopy and Diffractometry of MaterialsLaue condition

When do we get diffraction spots?

Plane

θB

d

Coherent illumination Source

See intensity only when angle θ is such thatpath difference, 2d sin θ = nλBragg’s Law, θB = Bragg angle

λ

θ

I

0

θBθB

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k0

k

k0

k

k0

k

k k

|k0| = |k| = k

∆ 2 sin

Diffractionk = g (Laue condition)

= B

2

Hence,

∆ 2 sin or 2 sin1

21sin

By comparison

2 sin

and

Shape factor and structure factor

Shape factor

Structure factor

Crystal = lattice + basis

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Structure factor rules (extinction conditions)

Example:

Simple cubic

One atom basis

(0 0 0)

F(hkl) = Σi fie2πiK·ri

F(hkl) = f e2πi(0)

Structure FactorCalculations

No extinction condition

Extinction conditions

Example:

000 100

010 110P

020

200

220

I

[001] ZA, Cubic unit cell

P

210

120

Primitive unit cell

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Example:

Body centred cubic

Two lattice points per unit cell

(0 0 0) and ( ½ ½ ½)


F(hkl) = f e2πi(0) + f e2πi( ½ h + ½ k + ½ l)

F(hkl) = f (1 + eπi( h + k + l) )

F(hkl) = 0 when h + k + l is odd

F(hkl) = 2f when h + k+ l is even

(N.B: eiθ = cos θ + i sin θ)



I

Example:

000

110

020

200

220


I

Body centred unit cell

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Example:

Body centred cubic

Two lattice points per unit cell

(0 0 0) and ( ½ ½ ½)


F(hkl) = f 1e2πi(0) + f2 e2πi( ½ h + ½ k + ½ l)

F(hkl) ≈ 0 when h + k + l is odd

F(hkl) = f1+f2 when h + k+ l is even

(N.B: eiθ = cos θ + i sin θ)



Example:

000 100

010 110P

020

200

220

I


210

120

I

Body centred unit cell

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http://www.seas.upenn.edu/~chem101/sschem/solidstatechem.html

Lets look at the shape factor

Rectangular prism

Lets focus in the x direction

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Lets focus in the x direction 1 + + + +⋯ + Geometric series

Ψ∗Ψ ΨIntensity is the square product of the amplitude

Diffraction peaks broadened by the shape factor



Diffraction peaks broadened by the shape factor


Nx = 12Ny = 6

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Crystal real shape

Diffraction intensities

Other shape factors

Simple cubic (large crystal)

Simple cubic (thin disc)

Ewald sphere

Laue condition

Diffraction occurs whenever the Ewald sphere touches a point in the reciprocal space.

The origin of the Ewaldsphere lies at the base ofthe undiffracted beam k0


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Ewald sphereSample tilting tilting of the reciprocal space

Effects of the Ewald sphere curvature

3D information through the higher order Laue zones

Due to “striking” caused by the shape factor the diffraction spots appear dislocated


λ/d = r/L

Crystalline sample

L (camera length, mm)

d (d-spacing, Å)

2θ

r (reciprocal d-spacing, Å-1)

tan2θ = r/L2θ = r/L

From Bragg equation 2θ = λ/d

Diffraction

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d = L λ r-1

Crystalline sample

L (camera length, mm)

d (d-spacing, Å)

2θ = r/L

2θ = λ/d

Camera constant(Å mm)

r (reciprocal d-spacing, Å-1)

Diffraction

Indexing a diffraction pattern

J. Wong-Leung, Dep. of Electronic Materials Eng. - ANU

3.07

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1.08

1.08

1.53

1.083.07

1.533.07

2.84

2.01



1.08

1.53

2.84

2.01

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The diffraction pattern cannot beuniquely defined due to its symmetry.

Once a set of reflections indexed theothers must be indexed consistently.

To find the zone-axis two approachesare possible since this vector isperpendicular to the ones in this plane

#1 Dot product = 0

#2 Cross product.

Powder diffraction (polycrystalline materials)

In implanted Si0.1Ge0.9 implanted region polycrystalline

Unimplanted regions remain single crystal Ruixing (Andy) Feng - EME

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Powder diffraction (polycrystalline materials)

Reproduced: Transmission Electron Microscopy: Physics of Image FormationL. Reimer H. Kohl

Summary

• Diffraction is a result of coherent scattering

• Structure factor extinction conditions

• Shape factor size effects

• Bragg’s Law and Laue conditions are equivalent statements

• Ewald sphere is a geometrical construct from Laue conditions which facilitates understanding of the diffraction in a TEM

– 3D information can be obtained from higher order Laue zones

• Polycrystalline samples lead to the formation of ring patterns

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PracticeIndexing diffraction patterns


E-learning room

Diffraction pattern analysis


2.18

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1.39

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Part 3Imaging


E-learning room

Contrast


∆

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Contrast mechanisms in TEM

Mass thickness contrast

• Formed by incoherent scattering

• Visible without the objective aperture

I

Contrast mechanisms in TEM

Diffraction contrast

I

• Formed by coherent scattering

• Arises from crystals satisfying Bragg’s condition

• Greatly enhanced inserting the objective aperture

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Phase contrast-Fresnel Fringes

Intensity profileReproduced: Transmission Electron Microscopy: Physics of Image FormationL. Reimer H. Kohl

Phase contrast-Fresnel Fringes

Fresnel Fringes

In focus:

No dephasingadded by theOL.

Under focus:

= 90º

Over focus:

= - 90º

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Shape factor

Deviation vector

Shape factor only depends on the deviation

How does the deviation vector affects the shape factor?

Diffraction contrast

Deviation vector and the Ewald sphere

The s vector points from the Ewald sphere toward the reciprocal points

s > 0 if points ups < 0 if points down

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Kikuchi lines

Forward peaked incoherent scattering

Incoherent scattering plus coherent (diffraction) Kikuchi lines

Kicuchi lines

Roads through the reciprocal space helps to tilt the sample towards the desired zone-axis


Kikuchi lines and the deviation



Position of the Kikuchi line in relation to the diffraction spot changes with s

Setting up a two beam condition

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Centred dark field vs Weak beam

• Tilting the sample means tilting the entire reciprocal space.

• Tilting the beam means tilting the Ewald sphere.

Procedure:

• Tilt the sample achieve a good two beamcondition (only the direct beam and +gare visible.

• As you tilt the sample the diffractionintensities change but the diffraction spotsdo not move!

• Now move the vector –g to the centre inorder to have this vector excited.


What is the effect of tilting the beam

K0K0

-g0

+g+g

-g0

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Weak beam

Two beam Centred dark field Weak beam diffraction


Phase-amplitude diagram


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Thickness fringes (Two-beam)

1


Thickness fringes


Two beam condition:Total intensity divided between the direct beam the the diffracted one

Extinction coefficient

For s = 0, period of the thickness fringes is

(dynamical)

For s >> 0, shorter periods(kinetical)

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Bending countours

Excites the pair +g and -g


Dislocation strain fields


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High Resolution TEM

High resolution imaging (phase contrast)

Objectives:

• Know that High Resolution (HR) TEM microscopy is only possible for very thin crystals within the limits in which the Weak Phase Object Approximation is valid.

• Realize HR images can only be obtained if great care in tilting to a zone axis and aligning the aperture is taken.

• Learn that the Contrast Transfer Function can be used to describe the imaging characteristics of the microscope.

• Understand that contrast in HR images cannot be directly assessed without image simulation.

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HRTEM

In “high-resolution” transmission electron microscopy (HRTEM or HREM) thephase of the diffracted electron wave is preserved and interferes constructively ordestructively with the phase of the transmitted wave. This technique of “phase-contrast imaging” is used to form images of columns of atoms.

• Electrons that pass between atoms traverse the crystal withminimum change in Intensity.

• Electrons that pass through the columns of atoms undergo largechanges in its intensity and its exit phase changes.

• The information preserved in phase of the waveinterfering produces the phase contrast.

• A objective aperture large enough to allow for boththe direct beam and the g vectors is a requirement

HRTEM

Sb2S3 crystal

• High resolution is not looking at atoms.

• It is a result of phase contrast from theinterference of electrons with columns of atoms.

• The resulting intensity 2D intensity distributionreflects the atomic arrangement in the sampleand therefore rendering atomic resolution.

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Contrast transfer function (CTF)

, , ⨂ ,

2 sin

Aperture function

Envelope function

It is the function that describes how the microscope transfers information

It is the function that describes how the microscope transfers information

CTF

Aperture functionSpherical aberration

DefocusVector of the reciprocal space

Ideal T(u)

Resolution limit

Contrast transfer function (CTF)

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Contrast Transfer Function

Contrast inversion


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Through focus and thickness series


Effect of OA at Scherzer defocus


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Resolution


Amplitude vs Phase contrast


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FFT and CTFf = 0 f = - 500 nm f = 500 nm

Astigmatism

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Summary

• The optimum focus condition for HR is not at ‘optical’ focus but in anunderfocus condition known as the Scherzer (de)focus.

• The contrast in HR images is strongly dependent on defocus (just a click ortwo on the TEM panel!).

• Atoms are neither black or white in HR images. Atoms in a thin crystal modifythe phase of the electron wave in ways that may fortuitously result in a‘structure’ image where atomic columns have darker contrast.

• Through-focus and through-thickness series can be used to monitor changes inphase contrast

Summary

• Bright field (BF) and dark field (DF) imaging are less demanding than high resolution (HR) microscopy .

• BF and DF microscopy are based on excluding scattered electrons.

• HR microscopy is based on including as many beams as feasible and examining the amplitude variation due to phase shifting.

• HR images can sometimes be interpreted in terms of atomic scale potentials.

• All imaging modes require pre-alignment of the specimen in diffraction mode.

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Part 4EDS and STEM


E-learning room

Energy dispersive X-ray spectroscopy

Particle characteristics gives rise to characteristic X-rays


Energy levels are characteristic of each element henceallowing for chemical information to be obtained.

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In EDS spectrum, the x-ray peaks from different elements have intensities that depend on:

1) The path and energy of the high-energy electron passing through the sample;

2) The ionization cross-sections of the elements;3) The fluorescence yields;4) The probabilities that the emitted x-rays are seen by the detector;


15 kV, Bulk 200 kV, 100 nm thick film

C

Pb

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Accurate quantitative measurements require the knowledge of the following parameters:

1) Probe diameter; complicated calculation (or measuring directly with camera)

0.61 1

4Δ

1) Current; Faraday cup2) Convergence angle; Using diffraction

Thin film limit

KAB (Cliff-Lorimer factor) is a constant for a specificenergy-detector configuration and is independentof sample thickness and composition.

Scanning TEM

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Scanning Transmission Electron Microscopy

Reciprocity



Reproduced from: Transmission Electron Microscopy: A Textbook for Materials Science. David B. Williams and C. Barry Carter

0.61 1

4Δ

Reproduced: Transmission Electron Microscopy: Physics of Image FormationL. Reimer H. Kohl.

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Ronchigram

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What is the right aperture

Ronchigram no Cs

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Ronchigram no Cs

Ronchigram no Cs

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Ronchgram Cs > 0

STEM + EDS = Chemical maps

Documents

Introduction to Transmission Electron Microscopy (Physical ...microscopy.anu.edu.au/files/CAM introduction to TEM...24/04/2018 1 Introduction to Transmission Electron Microscopy (Physical