TEM - kikuchi lines
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Transcript of TEM - kikuchi lines
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CHEM 793, 2008 Fall
Chapter 3
Basic Crystallography and Electron Diffraction from Crystals
Lecture 15
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Announcement
Midterm Exam: Oct. 22, Wednesday, 2:30 4:30
Close note, and bring your calculator
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Outline
Kikuchi Line and its indexing
Double diffraction
CBED pattern (convergent beam electron diffraction)
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Conventional high energy electron diffractionrelies on elastic scattering. However, in a thickenough specimen, inelastic scattering will alsotake place. Inelastically scattered electrons travelin all directions but their distribution peaks in aforward direction, as shown in Figure (a). Notethat in reality, the scattering is occurring in 3dimensions.
More electrons are scattered forward thansideways. This contributes a grey backgroundaround the central spot of the diffraction pattern,as shown in Figure (b).
Kikuchi Line
(a)
(b)
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(1). Electrons which have been inelasticallyscattered can subsequently be diffracted, but onlyif they are now traveling at the Bragg angle, B to
a set of planes, {hkl}.(2). Two sets of electrons will be able to do this -those at (+ B ) and those at (- B), as seen in Fig.(a).(3). This diffraction results in intensity changes in
the background. Because there are moreelectrons at A than B (since electrons passingthrough A are closer to the incident direction
than those through B) one bright line isdeveloped (the excess line) together with one
dark line (the deficit line).(4). Because the electrons are inelasticallyscattered in all directions, the diffracted electronswill form a cone, called Kossel cone, not abeam. Hence we observe Kikuchi lines - not
Kikuchi spots,as seen in Fig. (b).(5) The spacing of the pair of Kikuchi lines is thesame as the spacing of the diffracted spots fromthe same plane. However, the position of thelines is very sensitively controlled by the
orientation of the specimen and Kikuchi lines areoften used to set the orientation of a crystal in theTEM to an accuracy of 0.01 degrees.
(a)
(b)
Incident electrons
2 B
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(6) Kikuchi (1928) described this phenomenon
before the development of the TEM; It can occurin any crystalline specimen.(7). Kikuchi lines are useful for precisedetermination of specimen in a TEM. When we tiltthe specimen, we tilt its reciprocal lattice. Tilts of
the reciprocal lattice with respect to a stationaryEwald Sphere do not cause any substantialchanges in the positions of the diffraction spots,but the individual spots grow of fade in intensity.(8). The positions the Kikuchi lines are extremely
sensitive to the tilt of the specimen. During a tilt,the Kikuchi lines moves as if they are affixed tothe bottom of the crystal. With a long cameralength typical for diffraction work, there issignificant movement of the Kikuchi lines on the
viewing screen.
(a)
(b)
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This simulation shows Kikuchi lines moving in relation to thediffracted spots when the crystal is tilted through small angles.
Tilt angle 10Tilt angle 20
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Kikuchi line images
Some Kikuchi linemicrographs for silicon areshown.
(a)The Kikuchi lines passstraight through thetransmitted and diffractedspots. The diffractingplanes are thereforetilted at exactly the Braggangle to the optic axis
The ideal specimenthickness will be such thatwe can see both the spotpattern and the Kikuchi lines
as seen in Fig. (a). This isone of the few situationswhen thinner is notnecessarily better. In most
cases, the specimen is thethinner and the better
(a)
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(b) The crystal has now been
titled slightly away from theBragg angle, so that the Kikuchilines no longer pass throughthe transmitted and diffracted
spots
(b)
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(c). The crystal is tiltedso that more that oneset of planes arediffracting. Each set ofdiffracting planes hasits own pair of Kikuchilines
(c)
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Indexing Kikuchi Lines
The separation between the two Kikuchi lines is the same as the separation
between the (hkl) diffraction spot.
(a) Only Diffraction Spot Pattern (b) Diffraction Spot Pattern with Kikuchi Lines
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Indexing Kikuchi Lines
The separation between the two Kikuchilines is the same as the separationbetween the (hkl) diffraction spot and the(000) spot.
Diffraction Spot Pattern with Kikuchi Lines
We can index the Kikuchi lines bymeasuring their separations in much the
same ways as we index diffraction spots.Consider two different pairs of Kikuchilines from the planes( h1k1l1) and (h2k2l2). The separationsbetween their pairs of excess and deficitlines, p1 and p2, are in the ratio:
2
2
2
2
2
2
2
1
2
1
2
1
2
1
lkh
lkh
p
p
++
++
=
8
32
Figure shows ratios of32 and 8 forindexed (440) and (220)
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Indexing Kikuchi Lines
Diffraction Spot Pattern with Kikuchi Lines
The angles between intersecting Kikuchi
line pairs are the same as the anglesbetween their corresponding diffractionspots, at least so long as the Kikuchi lineare not too far from the center of the viewscreen. These angles are helpful for
indexing Kikuchi lines in the same waythat the angles between pairs ofdiffraction spots are useful for indexingdiffraction patterns. For example theangle, , between the (220) and (400)Kikuchi line in left figure is:
o45
]400[
16
1]220[
8
1arccos
=
=
8
32
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Indexing Kikuchi Lines and constructing Kikuchi lines
Diffraction Spot Pattern with KikuchiLines
For a crystal oriented precisely on a zone axis, we can generate an indexed Kikuchi linepattern from its indexed diffraction. Each (hkl) Kikuchi line is drawn perpendicularly to the line
between the (000) and (hkl) diffraction spots, bisecting this line. The procedure is shown infigure.
Kikuchi line, (400),bisectsthe line between (000)and (400)
Kikuchi line, (-400), bisects,the line between (000) and(-400)
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Specimen Orientation and Deviation parameter (s)The positions the Kikuchi lines are extremely sensitive to the tilt of the specimen. During a tilt,the Kikuchi lines moves as if they are affixed to the bottom of the crystal. With a long cameralength typical for diffraction work, there is significant movement of the Kikuchi lines on theviewing screen. The Kikuchi lines can be used to determine the sign and magnitude of thedeviation parameter, s, which quantifies how accurately the Laue condition is satisfied.
Crystalrotate
x
Kikuchi lines(D and E line)
2
0g
(000)
g(hkl)
r
Perfectorientation, s=0
Ewald Sphere
CameraLength L
Kossel Conesand diffractedbeams
s=0
D
E
(a)
S>0
2
2
g
r
x
r
x
k
gs ==
Deviation Parameter, s:
x is the distance between the diffraction spots and its
corresponding bright Kikuchi line (E-line)
r is the distance between the (000) and (hkl) diffraction spots.
is the wavelength
the unit of s is -1 or nm-1
K
S
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The sign of s
s points from the Ewald sphere to thereciprocal lattice point.
For Kikuchi line, s=0, when the Kikuchi
line runs exactly through itscorresponding diffraction spots.
s0 if the excess line lies outside its
corresponding diffraction spot g. In thiscase the reciprocal lattice point lies insidethe Ewald sphere
g
k
k
s
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K
k=g+s
g
k
k
s