8. Electron Diffraction - Electron Microscopy and Diffraction

8/9/2019 8. Electron Diffraction - Electron Microscopy and Diffraction

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Electron MicroscopyElectron Microscopyand Diffractionand Diffraction

8. Electron difraction8. Electron difraction

Do Minh Nghiep

Materials Science Center

Part of the figures, texts are quoted from internet resources. All the copyrights belong to the original authors.

All the references made here are for educational purpose only.


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ContentContent Diffraction in crystals

Diffraction lawDiffraction patterns

Electron diffraction in TEM Application


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DiffractionDiffractionin crystalsin crystals


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Diffraction the spreading out of waves as they encounter a barrierDiffraction the spreading out of waves as they encounter a barrier

What is diffraction?What is diffraction?


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William Henry Bragg:William Henry Bragg:1862 19421862 1942

Nobel Prize in Physics: 1915Nobel Prize in Physics: 1915

Like an X-ray an electron beam has itsown wavelength which is inverselyproportional to its energy: E = h =hc/

Diffraction in crystalsDiffraction in crystals

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Braggs law reminds us that for any given wavelength it will be diffractedby a crystal if it strikes the crystal at precisely the correct angle .

Vulf-Braggs diffractionVulf-Braggs diffraction


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If a known wavelength is used and the Braggsangle can be measured or inferred then the d-spacing of a crystal of unknown composition can becalculated.

Diffraction lawDiffraction law

sin2nd =


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Diffraction lawDiffraction law

For a given wavelength there is a specific angle (Braggs angle) at whichdiffraction will occur. Braggs angle is determined by the d-spacing(interplanar spacing) of the crystal and the order of diffraction (n = 1, 2, 3.).

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This is the principle behind X-ray diffraction (XRD) in which an X-ray ofknown wavelength is focussed onto a crystal that can be aligned until a

diffraction pattern is created. A blanker on the optical access blocksthe transmitted wavelengths.

X-ray diffractionX-ray diffraction

Diffraction

pattern

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An XRD pattern ofAn XRD pattern ofsilicon single crystalsilicon single crystalisis discrete spots.

Diffraction patternDiffraction pattern

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Diffraction patternDiffraction pattern

If a polycrystal diffracted the resultant pattern will be a set ofdistinct concentric rings, not discrete spots.

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PowderPowder

methodmethod X-ray source:

Xray tube Debye chamber:

powder sample,film windedaround sample

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ElectronElectrondiffractiondiffraction

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If a monochromatic e-beamof known strikes a crystalat the appropriate Braggsangle a number of thediffracted electrons will beforward scattered.

Like the transmittedelectrons these diffracted

electrons will have nearlytheir same energy, but willhave been significantlyaltered from their trajectory.

Electron diffractionElectron diffraction

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ED in TEMED in TEM

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The transmitted electrons will

be brought to convergence inthe back focal plane of theobjective lens at point Y.

Likewise the diffracted

electrons will also be broughtto convergence in the backfocal plane of the lens but ata different spot X.


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Normally an aperture isplaced in the back focal

plane of the objective lensto stop widely scatteredelectrons from reachingthe viewing screen.

But in the case ofdiffraction it is these samescattered electrons thatcontain the informationabout the diffraction event.

ED in TEMED in TEM

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ED in TEMED in TEM

To operate the TEM in

diffraction mode theobjective aperture isremoved from the beam

path and the scope isadjusted to focus an image

of the back focal plane ofthe objective lens, not the

image plane.

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ED in TEMED in TEM

This is most easily

accomplished byadjusting the

strength of theobjective lens so that

an image of the backfocal plane isprojected onto theviewing screen.

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BackBackfocalfocal

planeplane


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ED patternED pattern

The result is an electron diffraction (ED) pattern. The pattern oneobtains is completely dependent on the d-spacing and composition of

the crystal that is being analyzed.

ED spots

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ED pattern ofED pattern of

single crystalsingle crystal

An ED from a single crystal will result in a series of diffraction spotsarranged in concentric rings around the central bright spot which is

comprised of transmitted electrons.

Diffraction spots

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polycrystalpolycrystal

If an ED is made of field of many crystals, some of which are orientedat the Braggs angle while others are not, a pattern with well defined

concentric rings, but not spots, will result.

Diffraction rings

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amorphousamorphousmaterialmaterial

If an ED is made of anamorphous structure (i.e. no

crystalline formation) then onesimply gets a central bright

spot comprised of transmittedelectrons and a single ring ofrandomly forward scattered

electrons.

ED diffusion ring

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Sample position by tiltSample position by tilt

holder to Braggs angleholder to Braggs angle

So that individual crystals can be oriented to the appropriate Braggsangle one uses a double tilt specimen holder, which allows for

positioning in X, Y, and Z directions.

Sample

holder

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CalculationCalculation

of d-spacingof d-spacingP - photographic planeL - distance of specimen from PT - forward transmitted beam

O - point where T strikes PS - Bragg diffracted beamG - point where S strikes PR - distance from O to G

Calculation d from ED imageCalculation d from ED image: R / L = tan2 and from Braggs law weknow that 2d.sin = .Thus R / L 2 2 / 2d which simplifies to R = .L / d. If we canmeasure R and both and L are constants then d can be calculated.

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The R values for differentorder diffraction eventscan be measured directly

from a diffraction pattern,but it is crucial that it notbe enlarged or reduced.

It should always becompared to a pattern ofa crystal with a known d-spacing, so that the valuefor the camera length L isaccurate.

Exact R and L values requiredExact R and L values required

Index of ED spots

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ApplicationApplication

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Microstructure + structureMicrostructure + structure

Crysotile is a monocyclic crystal that tends toform a hollow tube. This results in a distinctive

diffraction pattern with smeared spots.Hollow

tube

TEM of

Crysotile fiber

Diffraction of CrysotileDiffraction of Crysotile

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Mg3Si2O5(OH)4

and compositionand composition

Magnesium 26,31 % MgSilicon 20,27 % SiHydrogen 1,45 % HOxygen 51,96 % O

TEM of

Crysotile fiber

Diffraction of CrysotileDiffraction of Crysotile

EDS hologram of

Mg3Si2O5(OH)4

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http://webmineral.com/chem/Chem-Mg.shtmlhttp://webmineral.com/chem/Chem-Si.shtmlhttp://webmineral.com/chem/Chem-H.shtmlhttp://webmineral.com/chem/Chem-O.shtmlhttp://webmineral.com/chem/Chem-O.shtmlhttp://webmineral.com/chem/Chem-H.shtmlhttp://webmineral.com/chem/Chem-Si.shtmlhttp://webmineral.com/chem/Chem-Mg.shtml


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SAED pattern of a crystal

SA Aperture

VirtualAperture

Specimen

Lower ObjectiveLens

Back Focal Plan

Selected Area ElectronSelected Area Electron

Diffraction (SAED)Diffraction (SAED)

SAED use parallel illumination andlimits the sample volume by anaperture in the image plane of thelower objective lens.

a*

b*

D

( ) ( )

=

==

B

B

dSin

L

D

2

;2tantan

L

D

d

1

D

KK+g

L

Camera length

Ewald Sphere

Lattice plane havespacing of d


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ELECTRON DIFFRACTION PATTERNSELECTRON DIFFRACTION PATTERNS

MOSAIC SINGLE

CRYSTAL

PLATELIKE TEXTURE POLYCRYSTA

L


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Electron backscatter diffraction (EBSD) is a technique for determiningcrystallographic information of submicron regions of flat polished samples. Ithas made possible studies of microtextures, phase identification (ofpolymorphs), grain boundary distribution, and deformation microstructures.

EBSD is also known by the names backscatter Kikuchi diffraction BKD, orelectron backscatter pattern EBSP. The phenomenon has been known since1928 by Kikuchi, who noted remarkable lines resulting from electron diffractionthru a thin mica crystal. Two research groups (in UK) started working on EBSD~1973, and it has only been commercially available since 1994.

In many cases it replaces more time-consuming/difficult TEM or XRD, or

possibly electron channeling studies, with the benefit of SEMs point by pointhigh spatial resolution (


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Kikuchi recognized the importance of a divergent electronbeam being diffracted - how the spreading of the incidentbeam (by inelastic scattering in upper surface of sample)

Orientation mapping (OIM, orientation imaging microscopy) Phase identification by step-by-step deduction of pattern

point group symmetry, though some problems; othertechnique is to determine approx value of unit cell volume

from measured lattice spacing and interplanar angles,together with EDS, searching a database for possiblematches, then match angles

EBSDEBSD


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The sample is tilted steeply (70, so beam is 20 tosample) which enhances the number of BSEs able toundergo diffraction and escape the surface. The HVelectrons are scattered by the electrons of the atomsin the top unit cells of the material, scattering fromelectrons in crystallographic planes producingintersecting bands imaged by film or a phosphorscreen immediately adjacent.

The pattern and bands provide information about thecrystal structure:

Symmetry of crystal lattice

Width and intensity of bands are a measure of theplane spacing (and unit volume)

Angles between bands are related to the anglesbetween planes in the lattice.

EBSDEBSD


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Specimen prep important: surface must

have damaged layer (esp from coarsepolishing) removed, e.g. with colloidal silica(which is also chemical etching action);

carbon coat must be very very thin ( 10 )

Specimen preparationSpecimen preparation


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SummarySummary

Electron diffraction is a technique which allows

users to determine the atomic arrangement ofcrystals. When combined with other analyticaltechniques such as EDS it can aid in theidentification of unknown crystals and/or determine

the d-spacing of newly described crystals.

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