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Exercise: Indexing of the electron diffraction patterns. Louisa Meshi. Formation of electron diffraction and HRTEM image . (hkl) plane. 1/ d hkl * 1/2. g/2. specimen. sin = = =. 1/ . 1/ . 2 . = /2d hkl. 1/ . g hkl. P hkl. Bragg’s law. O.

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ewald sphere construction

(hkl) plane

1/dhkl * 1/2

g/2

specimen

sin= = =

1/

1/

2

=/2dhkl

1/

ghkl

Phkl

Bragg’s law

O

Points of reciprocal lattice

Origin of the reciprocal lattice

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.

for diffraction in electron microscope

specimen

1/

Ewald sphere

(1/>>g)

Camera

Length

(L)

=

L r

r

1\ g ;

rdhkl=L, L - camera constant

r

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.

types of electron diffraction patterns
Types of electron diffraction patterns:
  • Ring pattern – from polysrystalline specimen. Major use:
      • Identification of the phases;
      • Analysis of texture;
      • Determination of the camera constant L.
  • Spot pattern – from single-crystal region of the specimen. Major use:
      • The foil orientation can be determined;
      • Identification of phases;
      • The orientation relationship between structures can be determined.
ring pattern

beam

O

hkl sphere

D

Ring pattern:

The reciprocal lattice becomes a series of sphere concentric with the origin of the reciprocal lattice.

  • The main steps of indexing ring patterns:
  • Measuring ring diameters D1, D2, D3 …….
  • Calculation of the dhkl (using the expression: rdhkl=L)
  • Use some structure database to index each ring.
spot pattern

h1k1l1

h2k2l2

Spot pattern

beam

Schematic representation of diffraction pattern:

beam

All diffraction spots are obtained from planes belonging to one zone.

Crystal

h1k1l1

Ewald

sphere

h2k2l2

g1

g2

O

g3

Reciprocal lattice plane

Real diffraction pattern:

B

Zone of reflecting planes

B – is a zone axis

indexing the saed pattern spot pattern

h1k1l1

h3k3l3

2

R3

1

R1

R2

h2k2l2

Zone axis of the

ED pattern =

(h1k1l1) (h2k2l2)

Indexing the SAED pattern (spot pattern):
  • Choose a parallelogram with smallest R1, R2, R3.
  • Measure distances R1, R2, R3 and angles 1, 2.
  • Calculate d1,d2,d3 (using the rule rd=L).
  • Correlate the measured d-values with dhkl taken from the list of standard interplanar distances for the given structure and ascribe h1k1l1 and h2k2l2 and h3k3l3 indices for the chosen three spots.
  • Check the condition that h1+h2=h3; k1+k2=k3; l1+l2=l3.
  • Compare the measured angles (both 1 and 2) with the calculated angles.
practice time
Practice time:
  • In the tutorial of the school you will find three electron diffraction patterns.
  • These patterns are taken from Cu and Al. (Crystallographic data and L of the microscope - are given).
  • Index the SAED patterns and calculate the Zone Axis (ZA).