electron diffraction analisys-1

7/31/2019 Electron Diffraction Analisys-1

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Di!raction Patterns

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Examples of Diffraction Patterns


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Camera Length

magnification of a

diffraction pattern?

camera length L

distance between ob-

ject and screen (with-

out imaging lenses)

with imaging lenses:

effective L

L =R

2

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Determination of Lattice Plane Spacingsand Indexing of Diffraction Patterns

Bragg condition for TEM ( 1): = 2d(hi)

L = R/2 implies

L = Rd(hi)

indexing of an unknown diffraction pattern

(general method):

measure R for the fundamental reflections

calculate the corresponding plane spacings d(hi)

index the reflections with hi

mind symmetry-related extinctions (F(hi) = 0)


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Indexing of Diffraction Patterns

in a good approximation, the reflecting planes lie parallel

to the primary beam

primary beam corresponds to the zone axis of the reflecting

planes

addition rule:

if a zone includes the planes (hi) and (ki), it also

includes the planes (hi+ ki)

for the diffraction pattern of a single crystal this implies:

after indexing two non-collinear fundamental reflections,the indices of the entire pattern follow from vector addition

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Indexing of Diffraction Patterns:Principle


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Example of Indexing: Ag111

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Effect of Beam Convergence


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Effect of Beam Convergence

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Contribution of Inelastic Scattering

conventional high-energy electron diffraction: elastic scat-

tering

but in thick enough specimen: also inelastic scattering

inelastically scattered electrons:

travel in all directions

distribution peaks in for-

ward direction

grey background around

central spot


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Bragg Reflection of InelasticallyScattered Electrons

inelastically scattered electrons can subsequently be

diffracted

but only if they are now traveling at the Bragg angle, B to

a set (hi) of lattice planes

consider (hi) inclined by angle (hi) versus primary beam

Bragg reflection can occur with twosets of inelastically scat-

tered electrons at + = (hi) + B and = B

result: intensity changes in the background

Iinel[] > Iinel excess

Iinel[] < Iinel deficiency

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Bragg Reflection of InelasticallyScattered Electrons


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Kikuchi Lines

diffraction of inelastically-scattered electrons:

in all directions for which [(hi)]=

B

recall derivation of Laue equations:

diffracted electrons will form a cone, not a beam

intersection of cones with viewing plane:

hyperbola, not spots!

usually:

camera length (magnification) radius of curvature

only small sections visible straight lines

Kikuchi lines

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Kikuchi Lines


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Examples of Kikuchi Lines

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Features of Kikuchi Lines

Kikuchi lines belong to particular lattice planes hiaaai

can be indexed

spacing hiaaaiii, distance of diffraction spot from center

mirror line in the center between excess and deficiency line

trace of planes (extension to infinity)

specimen tilt lines rotate as if attached to specimen

position sensitive to small specimen tilts

adjust crystal orientation and excitation error

accuracy: 0.1

compare accuracy using spot intensities: 2


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Kikuchi Lines Excitation Error

= 2dhiB trace of (hi) ex-

actly between direct beam and

diffracted beam spot

excitation error s > 0

(hi) tilted too much

Kikuchi lines farther

from direct beam

excitation error s < 0

(hi) tilted too little

Kikuchi lines closer to di-

rect beam

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Kikuchi Lines Excitation Error


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Reflecting Planes Primary Beam

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Zone Axis Kikuchi Line Patterns


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Example of Zone Axis Kikuchi LinePatterns

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Tilt Sensitivity of Kikuchi Lines

example: Ag 110, 200kV, effect of1 tilt

electron diffraction analisys-1

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