Exercise:Indexing of the electron

diffraction patterns

Louisa Meshi

Formation of electron diffraction and HRTEM image

Ewald sphere construction:

Bragg’s conditions are satisfied when the Ewald sphere cuts a reciprocal lattice point specified by the indices of the reflecting plane.

sin= = =g/21/ 1/

1/dhkl * 1/2

=/2dhkl

Bragg’s lawghkl

O

Phkl

Origin of the reciprocal lattice

2

specimen

1/

Points of reciprocal lattice

(hkl) plane

For diffraction in electron microscope:

The single crystal electron diffraction pattern is a series of spots equivalent to a magnified view of a planar section through the reciprocal lattice normal to the incident

beam.

specimen

Ewald sphere (1/>>g)

1/

CameraLength (L)

r

L r =

1\ g ;

rdhkl=L, L - camera constant

r

Types of electron diffraction patterns:

• Ring pattern – from polysrystalline – from polysrystalline specimen. Major use:specimen. Major use:

• Identification of the phases;Identification of the phases;• Analysis of texture;Analysis of texture;• Determination of the camera constant LDetermination of the camera constant L..

• Spot pattern – from single-crystal – from single-crystal regionregion of of the specimen. Major use: the specimen. Major use:

• The foil orientation can be determined;The foil orientation can be determined;• Identification of phases;Identification of phases;• The orientation relationship between structures can The orientation relationship between structures can

be determined.be determined.

Ring pattern:The reciprocal lattice becomes a series of sphere concentric with the origin of the reciprocal lattice. beam

O

hkl sphereD

The main steps of indexing ring patterns:The main steps of indexing ring patterns:1)1) Measuring ring diameters DMeasuring ring diameters D11, D, D22, D, D33 ……. …….

2)2) Calculation of the dCalculation of the dhklhkl (using the expression: rd (using the expression: rdhklhkl=L=L))

3)3) Use some structure database to index each ring.Use some structure database to index each ring.

Spot patternAll diffraction spots are obtained from planes belonging to one zone.

O

g1 g2

g3

Crystalbeam

Ewaldsphere

Reciprocal lattice plane

h1k1l1

h2k2l2

beam

Zone of reflecting planesB – is a zone axis

B

h1k1l1

h2k2l2

Schematic representation of diffraction pattern:

Real diffraction pattern:

Indexing the SAED pattern (spot pattern):

1)1) Choose a parallelogram with Choose a parallelogram with smallest Rsmallest R11, R, R22, R, R33..

2)2) Measure distances RMeasure distances R11, R, R22, R, R33 and and angles angles 11, , 22..

3)3) Calculate dCalculate d11,d,d22,d,d33 (using the rule (using the rule rd=Lrd=L).).

4)4) Correlate the measured d-values Correlate the measured d-values with dwith dhklhkl taken from the list of taken from the list of standard interplanar distances for standard interplanar distances for the given structure and ascribe hthe given structure and ascribe h11kk11ll11 and hand h22kk22ll22 and h and h33kk33ll33 indices for the indices for the chosen three spots.chosen three spots.

5)5) Check the condition that hCheck the condition that h11+h+h22=h=h33; ; kk11+k+k22=k=k33; l; l11+l+l22=l=l33..

6)6) Compare the measured angles (both Compare the measured angles (both 11 and and 22) with the calculated angles. ) with the calculated angles.

h1k1l1

h2k2l2

h3k3l3

1

2

R3R1

R2

Zone axis of theED pattern = (h1k1l1) (h2k2l2)

Practice time:

• In the tutorial of the school you will find In the tutorial of the school you will find three electron diffraction patterns.three electron diffraction patterns.

• These patterns are taken from Cu and These patterns are taken from Cu and Al. (Crystallographic data and LAl. (Crystallographic data and L of the of the microscope - are given). microscope - are given).

• Index the SAED patterns and calculate Index the SAED patterns and calculate the Zone Axis (ZA).the Zone Axis (ZA).