Application of Forward Modeling to Indexing of Electron Dif - PowerPoint Presentation

Slide1

Application of Forward Modeling to Indexing of Electron Diffraction patterns

August 18th, 2015Carnegie Mellon University, Pittsburgh

MURI Meeting, 2015Saransh SinghMarc De GraefSlide2

2

Outline

Introduction to

Forward Models in Electron

Scattering

Electron

Channeling Patterns (ECP)

Electron

Back Scatter Diffraction (EBSD)

Precession

Electron Diffraction (PED)

Dictionary Approach for Indexing of Diffraction Patterns

Results and

ConclusionsSlide3

3

Introduction: Bragg’s law in reciprocal space

Length of the scattered wave vector is invariant (elastic scattering)

This represents a change in momentum, but not the energy

Exact diffraction condition satisfied when the

Ewald

sphere intersects any reciprocal lattice point

Introduction to Conventional Transmission Electron

Microscopy,

Marc

De

Graef

, Cambridge University Press

Introduction to Conventional Transmission Electron

Microscopy,

Marc

De

Graef

, Cambridge University Press

For electrons, which interact strongly with matter, the Bragg’s law need not be satisfied exactly

The intensity of a reflection decreases as the excitation error increasesSlide4

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Geometry of Diffraction Modalities: Electron Channeling Patterns

Sample

Annular Integrating Detector

Electron SourceSlide5

5

Geometry of Diffraction Modalities: Electron Backscatter Diffraction

Sample

Electron Source

Position Sensitive DetectorSlide6

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Geometry of Diffraction Modalities: Conventional TEM

Sample

Electron Source

CCD CameraSlide7

Scan

De-scan

Specimen

Conventional Diffraction Pattern

Precession…

Precession Diffraction Pattern

(Ga,In)

2

SnO

5

Intensities

412Å crystal thickness

Non-

precessed

Precessed

(Diffracted amplitudes)

By C.S.

Own

http://

www.numis.northwestern.edu

/Research/Current/

precession.shtmlSlide8

8

Introduction: Dynamical Electron Scattering for Perfect Crystal

Energy of incident electron

Complex potential

Real

part: scattering (elastic)

Complex

part: absorption (inelastic)

Ansatz:

Column vector of unknowns

Structure matrix

Scattering matrix

outgo

ing state

Incom

ing stateSlide9

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Introduction: Electron Channeling Patterns

Two types of backscattered electrons: BSE1 and BSE2

BSE1

contain dynamical scattering Information

BSE2

are the background intensity

BSE1/BSE2 ~ 10

-

3

The energy of the backscattered electron is almost the same as the incident electron

BSE1

BSE2

Sample

Annular Integrating Detector

Electron SourceSlide10

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Introduction: Depth Integrated Intensity for Electron Channeling Patterns

For the backscatter geometry, we need to calculate the probability that an

electron with a certain k vector is backscattered.

Since the electron can be backscattered at any depth, we need to compute the average value

w.r.t

. depth.

The squared modulus of the

wavefunction

gives the probability that an electron is present at a particular depth.

: Probability that electron with

wavevector

k is scattered

Z:

Atomic number

DW

: Debye-Waller factor (thermal vibrations)

z

0

:

Depth of integration

λ

(z

)

: Depth dependent weight factor

|

ψ

(

r

i

)

|

2

: Probability of finding atom at position

r

iSlide11

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Introduction: Depth Integrated Intensity for Electron Backscatter Diffraction

Sample

Electron Source

Position Sensitive Detector

The backscattered intensity in an EBSD geometry comprises of signal both from the BSE1 and BSE2 electrons.

The

backscattered intensity in a given pixel will depend on the location of the pixel.

The expression for depth integrated intensity is very similar to the ECP, except that for EBSD, the expression is calculated for electrons of all energy.

: Probability that electron with

wavevector

k is scattered

Z:

Atomic number

DW

: Debye-Waller factor (thermal vibrations)

z

0

:

Depth of integration

λ

(z

)

: Depth dependent weight factor

|

ψ

(

r

i

)

|

2

: Probability of finding atom at position

r

iSlide12

12

Introduction: Intensity for Precession Electron Diffraction

Sample

Electron Source

CCD Camera

For a PED pattern, the intensity for a reflection by a

g

vector is equal to the modulus square of the Fourier coefficient of that reflection.

The final pattern is just the sum of patterns formed by the individual incident

k

vectors.

Note that for indexing PED patterns, we can usually get away with just a kinematical simulation and not the full dynamical simulationSlide13

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Introduction: Dictionary Approach to Indexing Diffraction Modalities

For any diffraction modality, the orientation space is sampled uniformly and a set of patterns are calculated for these orientations.

The experimental patterns

are indexed by matching them with the dictionary patterns using a normalized dot product approach.

A dot product of 1 represents the same pattern and a -1 represents the worst possible match.Slide14

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Indexing of EBSD Patterns: IN100

Commercial Software

Dictionary ApproachSlide15

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Indexing of EBSD Patterns: Nickel

Dictionary

CommercialSlide16

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Indexing of PED Patterns: 50% Cold Rolled Copper

Experimental

Dictionary

Fuse

Finer Dictionary

Coarser

DictionarySlide17

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Conclusion

Forward models combined with

an image matching tool

can (normalized dot products in our case) serve as a unified method to index

e

lectron

d

iffraction

m

odalities.

D

ictionary approach is more reliable and robust than the existing algorithm.

The downside is that the computation time is longer.Slide18

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Future work

Using the dictionary approach to index material systems having low symmetry, pseudo symmetry and

overlappingpatterns

.

Automating the detector parameter fitting routine using an open source optimization routine.Slide19

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Spherically Bent Thin FoilSlide20

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Monte Carlo Trajectory Simulations

The current used in a typical EBSD experiment is of the order of 1

nA.

1

nA

~ 6.24 x

10

9

electrons.

Therefore, for reliable statistics, the number of electrons to be simulated has to be of the order of 10

9

.

Slide21

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Simulation: Dynamical Electron Scattering in presence of Defects

In presence of a defect, the translational symmetry

of the lattice is broken.

This modifies the lattice potential, which in turn affects the electron scattering process.

The modification depends on the displacement field of the defect.

Marc De

Graef

, Introduction to Conventional Transmission Electron Microscopy, Cambridge

University Press, 2003

512 nm

512 nm

(1 -1 0)

outgo

ing state

Incom

ing stateSlide22

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Acknowledgements

Air Force

O

ffice of Scientific Research,

AFOSR MURI grant FA9550

-12-1-

0458

Current and former research group members: Patrick Callahan, Amy Wang,

Lily

Nguyen,

Shan

Hua

, Mike Chapman,

Prabhat

KC, Ryan Harrison,

Isha

Kashyap

.