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Formation of the diffraction pattern in the
transmision electron microscope
based on: J-P. Morniroli: Large-angle convergent-beam
diffraction (LACBED), 2002 Société Française des
Microscopies, Paris.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Selected area (electron) diffraction
SAED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Diffraction pattern produced by a parallel incident beam: e.g.
SAED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
θB=λ/2dhkl
→Dhkl dhkl=L λ
Camera constant C=Lλ
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED patternSAED →the diffracted area of the specimen is selected with the selected-area aperture
(located in the image plane of the objective lens).
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
An hkl diffracted beam is produced when an hkl node of the reciprocal lattice is exactly located on
the Ewald sphere.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
Very small wavelenngth λ of the electron
beam makes the radius R=1/ λ of the Ewald
sphere very large (compared to the moduli
ghkl of the reciprocal lattice vector).
Specimens for electron microscopy are thin
foils → the nodes of the reciprocal lattice are
extended along the direction of least
specimen thickness.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
A diffracted beam can be
produced even if the set of (hkl)
lattice planes is not at the exact
Bragg orientation.
s – excitation error
s – an expression of the misorientation ΔΘ=Θi-ΘB of
the set of (hkl) lattice planes with respect to the exact
Bragg orientation.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
A misorientation of the incident beam with
respect to the optic axis leads to a shift of
the „whole” diffraction pattern in the back
focal plane of the objective lens.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
General case:
Several sets of lattice planes
can simultaneously be at the
Bragg orientation (exactly or
approximately).
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
SAED pattern
Special case: [uvw] zone axis pattern (ZAP)
A very useful case occurs when a high symmetry [uvw]
lattice of crystal is set paralel to the incydent electron
beam.
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SAED pattern
J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
The whole pattern composed of the Zero-
Order Laue Zone (ZOLZ) and of all High-
Order Laue Zones (HOLZs) gives three-
dimensional information about the reciprocal
lattice since is generated by several layers of
the reciprocal lattice.
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J-P. Morniroli: Large-angle convergent -
beam diffraction (LACBED), 2002 Société
Française des Microscopies, Paris.
SAED pattern
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J-P. Morniroli: Large-angle convergent -
beam diffraction (LACBED), 2002 Société
Française des Microscopies, Paris.
Convergent Beam Electron Diffraction
CBED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
Diffraction pattern produced by a convergent incident beam: CBED
pattern
The convergence angle α is of the same order as the Bragg angle θB.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
The CBED pattern can be regarded as the collection of spot patterns that
would result from parallel incident beams having all possible orientations
within the convergent incident beam.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
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CBED pattern
J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
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CBED pattern
J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
s – excitation error
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
The set of (hkl) lattice planes is not
exactly at the Bragg orientation
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
CBED pattern
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CBED pattern
J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
The diameter of the transmitted and
diffracted disks is related to the
convergence angle α of the incident
beam.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Large-angle convergent beam
electron diffractionLACBED pattern – Kossel patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
Advantage of a large convergence angle → the large transmitted disk
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
The disks overlap when the
convergense angle α is larger than
the Bragg angle θB (since the
distance between the centre of the
two disks is D=2fθB and their
diameter is Ф=2fα).
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
All the incident rays on the ABE
surface give a bright hkl excess line
located in the hkl diffracted disk, and
a dark hkl deficiency line in the
transmited disk. I the same way, the
incident rays located in the CDE
plane produce a –h-k-l deficiency line
located in the transmitted disk.
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED pattern – Kossel patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
The ilumunation conditions are the same as those used for the Kossel method, i.e.
the incident beam has a large convergence and is focused on the object plane of the
objective lens. The main difference concerns the specimen, which is now raised (or
lovered) by a distance Δh from its normal position in the object plane (M. Tanaka, R.
Saito, K. Ueno and Y. Harada: Large angle CBED, Journal of Electron Microscopy,
A31 (1980) 408).
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
LACBED patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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J-P. Morniroli: Large-angle convergent -beam diffraction (LACBED), 2002 Société Française des Microscopies, Paris.
Kikuchi patterns
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