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Electron diffraction

Selected area diffraction (SAD) in TEM

Electron back scatter diffraction (EBSD) in SEM

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Bragg’s law ndhkl )sin(2

Bragg’s law tells you at which angle θB to expect maximum diffracted intensity for a particular family of crystal planes. For large crystals, all other angles give zero intensity.

1kko

kkko

The Ewald Sphere

The observed diffraction pattern is the part of the reciprocal lattice that is intersected by the Ewald sphere

kok

g

Cu Kalpha X-ray: = 150 pmElectrons at 200 kV: = 2.5 pm

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2θko k

g

The intensity distributionaround each reciprocal lattice point is spread out in the form of spikes directednormal to the specimen

Ewald sphere(Reflecting sphere)

Intensity distribution and Laue zones

Zero order Laue zone

First order Laue zone

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Multiple scattering

• Multiple scattering (diffraction) leads to oscillations in the diffracted intensity with increasing thickness of the sample

– Forbidden reflection may be observed

– Kinematical intensities with XRD

Incident beam

Diffracted beam Multiplediffracted beam

Transmitted beam

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Simplified ray diagram

Objective lense

Diffraction plane(back focal plane)

Image plane

Sample

Parallel incoming electron beamSi

a

b

cP

ow

derC

ell 2.0

1,1 nm3

,8 Å

Objective aperture

Selected area aperture

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Apertures

Selected area aperture

Condenser aperture

Objective aperture

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Diffraction with large SAD aperture, ring and spot patterns

Poly crystalline sample Four epitaxial phases

Similar to XRD from polycrystalline samples. The orientation relationship between the phases can be determined with ED.

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Camera constant

R=L tan2θB ~ 2LsinθB

2dsinθB =λ ↓ R=Lλ/d

Camera constant: K=λL

Film plate

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Indexing diffraction patterns

The g vector to a reflection is normal to the corresponding (h k l) plane and IgI=1/dnh nk nl

- Measure Ri and the angles between the reflections

- Calculate di , i=1,2,3 (=K/Ri)

- Compare with tabulated/theoretical calculated d-values of possible phases

- Compare Ri/Rj with tabulated values for cubic structure.

- g1,hkl+ g2,hkl=g3,hkl (vector sum must be ok)

- Perpendicular vectors: gi ● gj = 0

- Zone axis: gi x gj =[HKL]z

- All indexed g must satisfy: g ● [HKL]z=0

(h2k2l2)

Orientations of correspondingplanes in the real space

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Example: Study of unknown phase in a BiFeO3 thin film

200 nm

Si

SiO2

TiO2

Pt

BiFeO3

Lim

ab

c

BiBi

Fe

O O

Fe

Fe

Bi

O

Bi

Bi

O

Fe

O

O

Bi

O

Fe

Bi

Fe

O

Bi

O

Bi

O

Fe

O

Fe

O

Bi

Bi

O

Fe

O

Bi

Bi

O O

Bi

O

Fe

Fe

O

Fe

BiBi

PowderCell 2.0

Goal:

BiFeO3 with space grupe: R3Cand celle dimentions: a= 5.588 Å c=13.867 Å

Metal organic compound on Pt

Heat treatment at 350oC (10 min) to remove organic parts.

Process repeated three times before final heat treatment at 500-700 oC (20 min) . (intermetallic phase grown)

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Determination of the Bravais-lattice of an unknown crystalline phase

Tilting series around common axis

0o

10o

15o

27o

50 nm

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50 nm

Tilting series around a dens row of reflections in the reciprocal space

0o

19o

25o

40o

52o

Positions of the reflections in the reciprocal space

Determination of the Bravais-lattice of an unknown crystalline phase

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Bravais-lattice and cell parameters

From the tilt series we find that the unknown phase has a primitive orthorhombic Bravias-lattice with cell parameters:

a= 6,04 Å, b= 7.94 Å og c=8.66 Å

α= β= γ= 90o

6.0

4 Å

7.94 Å8.66 Å

a

bc

100

110

111

010

011

001 101

[011] [100] [101]

d = L λ / R

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Chemical analysis by use of EDS and EELS

Ukjent faseBiFeO3 BiFe2O5

1_1evprc.PICT

-0 200 400 600 800 10005

10

15

20

25

30

35

40

Energy Loss (eV)

CC

D c

ount

s x

100

0

Nr_2_1evprc.PICT

-0 200 400 600 800 1000

-0

2

4

6

8

10

12

14

Energy Loss (eV)

CC

D c

ount

s x

100

0

Ukjent faseBiFeO3

Fe - L2,3

O - K

500 eV forskyvning, 1 eV pr. kanal

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Published structure

A.G. Tutov og V.N. MarkinThe x-ray structural analysis of the antiferromagnetic Bi2Fe4O9 and the isotypical combinations Bi2Ga4O9 and Bi2Al4O9

Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy (1970), 6, 2014-2017.

Romgruppe: Pbam nr. 55, celleparametre: 7,94 Å, 8,44 Å, 6.01Å

x y zBi 4g 0,176 0,175 0Fe 4h 0,349 0,333 0,5Fe 4f 0 0,5 0,244O 4g 0,14 0,435 0O 8i 0,385 0,207 0,242O 4h 0,133 0,427 0,5O 2b 0 0 0,5

ab

c

O

Bi

Fe

O

Fe

Bi

O

Fe O

O

O

Fe

Fe

O O

O

O

Fe

Bi

O

O

Bi

O

Bi

O

O

Bi

Fe

O

O

O O

Fe

Fe

O

O

O Fe

O

Bi

Fe

O

Fe

Bi

O

PowderCell 2 .0

Celle parameters found with electron diffraction (a= 6,04 Å, b= 7.94 Å and c=8.66 Å) fits reasonably well with the previously published data for the Bi2Fe4O9 phase. The disagreement in the c-axis may be due to the fact that we have been studying a thin film grown on a crystalline substrate and is not a bulk sample. The conditions for reflections from the space group Pbam is in agreement with observations done with electron diffraction.

Conclusion: The unknown phase has been identified as Bi2Fe4O9 with space group Pbam with cell parameters a= 6,04 Å, b= 7.94 Å and c=8.66 Å.

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Kikuchi pattern

http://www.doitpoms.ac.uk/index.htmlhttp://www.doitpoms.ac.uk/tlplib/diffraction-patterns/kikuchi.php

ExcessDeficient

Used for determination of:-crystal orientation

-lattice parameter

-accelerating voltage

-Burgers vector

Excess line

Deficient line

2θB

θB

θB

Diffraction plane

Objective lens

1/d

Inelastically scattered electronsgive rise to diffuse background in the ED pattern.

-Angular distribution of inelastic scattered electrons falls of rapidly with angle. I=Iocos2α

Kikuchi lines are due to:-Inelastic+ elastic scattering event

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• EBSD– Geometry similar to Kikuchi diffraction in TEM

– Information from nm regions

• OIM– Gives the distribution of crystal orientation for grains intersected by the

sample section that can be presented in various ways. (+/- 0.5o)

– Involves • collection a large sets of EBSD data • Bin the crystallographic data from

each pixel (stereographic triangle)

– Colour codes

– Localized preferred orientation

and residual stress etc.

Electron Back Scattered Diffraction (EBSD)Orientation Image Microscopy (OIM)

in a SEM

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Orientation map example

Step=0.2micron

CD-200 Nordiff EBSD Camera

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Overlaid maps

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http://www.ebsd.com/ebsd-explained/simulationapplet.htm

Electron back scattered diffraction (EBSD)

http://www.ebsd.com/ebsd-explained/anim2.htm

Principal system componentsSample tilted at 70° from the horizontal, a phosphor screen,a sensitive CCD video camera, a vacuum interface for mounting the phosphor and camera in an SEM port. Electronic hardware that controls the SEM, including the beam position, stage, focus,and magnification. A computer to control EBSD experiments, analyse the EBSD pattern and process and display the results.  

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Probe current Increased probe current – shorter camera integration time

– increased beam size 

Accelerating voltage  Increased accelerating voltage – reduced λ - reduced width of the Kikuchi bands

– brighter pattern - shorter integration time

– higher penetration depth

Changing the accelerating voltage may require adjustment to the Hough transform filter size to

ensure the Kikuchi bands are detected correctly  

Microscope operating conditions

Effect of changing accelerating voltage on diffraction patterns from nickel

10 kV 20 kV 30 kV

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Working distance and magnification Because the sample is tilted, the SEM working distance will change as the beam position moves up or down the sample, and the image will go out of focus.

 

Microscope operating conditions

Image with tilt and dynamic focus compensation. The working distance is 14.98 mm at the top and 15.11 mm at the bottom of the image

Image with tilt compensation and no dynamic focus compensation

Image without tilt or dynamic focus

compensation

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Microscope operating conditionsEBSD systems can compensate automatically for shifts in the pattern centre by calibrating at two working distances and interpolating for intermediate working distance values. It is important to know the range of working distances for which the EBSD system will remain accurately calibrated.  

With a tilted sample, the pattern centre position will depend on the sample working distance.

The yellow cross shows the pattern centre with working distance 10, 18 and 22 mm

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Band Intensity The mechanisms giving rise to the Kikuchi band intensities and profile shapes are complex. As an approximation, the intensity of a Kikuchi band for the plane (hkl) is given by:   22

)(2sin)()(2cos)(

iii

iiiii

iihkl lzkyhxflzkyhxfI

 

where fi(θ)  is the atomic scattering factor for electrons and (x i yi zi)  are the fractional coordinates in

the unit cell for atom i. An observed diffraction pattern should be compared with a simulation to ensure only planes that produce visible Kikuchi bands are used when solving the diffraction pattern.  

Simulation of crystal orientation giving the

solution shown.

Simulated diffraction pattern showing all Kikuchi bands with intensity greater than 10% of the most intense band.

Solution overlaid on the diffraction pattern giving the crystal orientation as {370}<7-34>

Diffraction pattern from the orthorhombic ceramic mullite (3Al2O3 2SiO2) collected at 10 kV accelerating voltage.

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The background can be measured by scanning the beam over many grains in the sample to average out the diffraction information.

The background can be removed by subtraction from, or division into, the original pattern.

Background removal

Background division Background subtraction Original pattern

http://www.ebsd.com/ebsd-explained/undertakingexperiments3.htm

Background