TEM - kikuchi lines

7/29/2019 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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CHEM 793, 2008 Fall

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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CHEM 793, 2008 Fall

(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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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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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

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TEM - kikuchi lines