transmission electron microscopy - specify indexing of kikuchi.pdf

8/14/2019 Transmission Electron Microscopy - specify indexing of kikuchi.pdf

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Transmission ElectronMicroscopy (TEM)

EE 80603/CBE 80603


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Kikuchi DiffractionIf the specimen has optimum thickness

not too thin , to allow incoherent diffusivescattering - initially being scattered by theatoms in the crystal they lose all memory ofdirection, but can be scattered again by Bragdiffraction. not too thick , otherwise inelastic scatteringdominates and there is no Brag diffraction

we can see paired arrays of lines in SADPs,known as Kikuchi patterns

Ideal thickness when we can see both the spotpatterns and the Kikuchi lines

An ideal DP containing both well-defined spots andclearly visible pairs of bright and dark Kikuchi lines

Simple spot patterns are produced in the thinnest regions of the foil, up to roughly 0.1 m (100 nm)depending on the atomic number and accelerating voltage. Inelastic scattering, with small energy loss,becomes more probable with increasing thickness t.


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Kikuchi lines and Brag Scattering

Since typical energy losses are small (~20 eV) compared to E0

(100-400 KeV or DE/E~0.01%) the diffusely scattered electronscan be assumed to have the same as incident beam When first formed most of the diffusely scattered electronstravel close to the direction of the incident beam. While the electrons shown (A) as diverging from a point, infact, they are scattered at different points through out thespecimen thickness.

Some of these electrons travel at the Brag angle, qB, to the hkl plane andthen be Bragg diffracted (Figure B). Since diffracted electrons are travellingin all directions the diffracted beam lies on one of two cones (C).

In another words: Any electron with q i = qB lies on a cone of directionsqB from (hkl) and diffracts into a direction on the same cone.The cone of diffracted inelastic electrons intersects the screen or film planein an hyperbola. But, since qB is so small, the cone is nearly flat, and itsintersection is indistinguishable from a straight line.


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Since there is a range of incident k-vectors (ratherthan a single k-vector), which be Bragg diffracted, weconstruct the cones, considering all the vectorsoriented at angle qB to the hkl plane: these are calledKossel cones . In general, there is a pair of Kosselcones for g, another pair for 2g and so on.


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Since the screen/detector is flat and nearly normalto the incident beam, Kossel cones appear asparabola. For the region close to the optic axis these

parabolas appear a s two parallel lines: Kikuchi band


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The scattered beam which was initially closest to theoptic axis and therefore the more intense is fartheraway from the axis after being Bragg diffracted. Thisbeam gives the excess (bright) line and the other onethe deficient (dark) line. Thus if you find the brightline its partner should be closer to O and dark. Thepair is separated by 2 q

B .

Considering only diffraction from the top of (hkl), electrons areadded to directions they diffract into, which would produce awhite line in the diffraction pattern. The diffuse background dueto inelastic scattering is higher on this line, and the cone and lineare called the excess cone and excess line.

Since inelastic electrons incident at qB from the top of (hkl)diffract, they are lost from this direction. This would cause adeficit of intensity in diffuse scattering for directions on thedefect cone, and a dark defect Kikuchi line.


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Kikuchi lines and Brag ScatteringThe cones are rigidly fixed to the plane hkl and thusto the crystal. We can draw a line half way between

the two Kickuchi lines to represent the trace of the plane (hkl).

Since the Kikuchi cones each make an angle qB with their (hkl) plane,and are nearly flat, it follows that:

1) The hkl Kikuchi lines are both parallel to the trace (intersection) of(hkl) on the diffraction pattern (SADP) at virtually equal distances from it.

2)The spacing between the hkl lines is R = l L / dhkl, which is the same asthe distance of the hkl spot from 000 (The TB), because the anglebetween the cones is 2 qB, the same as that between TB and DB.

3)Looking at the SADP, the hkl Kikuchi lines are normal to ghkl.

As we tilt the specimen, all Kikuchi lines move in the same direction onthe screen, i.e. the entire Kikuchi pattern translates as a unit, withoutchanging its geometry. This follows from the fact that the lines representcones which are always qB from their (hkl);as we tilt the planes, the cones tilt.

The spot pattern does not move as we tilt.(Remember that the rel-rods are vertical, so their intersection with theEwald sphere is essentially unchanged by tilting.)


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Uses of Kikuchi PatternsThree important applications are:1)Obtaining two-beam diffraction conditions(i.e. the exact Bragg condition for a single (hkl) plane),by tilting so that dark/white lines pass through TB/DBspots.2)Tilting to a new orientation; e.g. if we are close to 112and want to tilt to a 111 or 110 zone axis.3)Accurate orientation determination,

by solution of Kikuchi pattern.


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Two-Beam Conditions The best conditions for imaging the internal defects in a crystal, particularly dislocations, are obtained whenwe have only two strong beams, the TB plus one strong DB. Calculations of image contrast are also simpler

for two-beam conditions. E.g., if we have two strong DBs at once (two RL points on the Ewald sphere),we will usually see two parallel images of any given dislocation line.

If the tilt axis happens to lie in (hkl) (parallel to it), tilting moves the lines in the direction normal to them (parallel to g):

Any other tilt axis moves the lines in an oblique direction (unless the axis is normal to the lines):


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Exact Bragg ConditionThe exact Bragg condition occurs when an RL point lies exactly on the Ewald sphere. When this happens, the darkand white Kikuchi cones pass exactly through the TB and DB spots respectively. This must be true, since we know

the Kikuchi cones are each q degrees from (hkl), and (hkl) bisects g, as above.

This condition is easily recognized in the diffraction pattern; the Kikuchi lines pass through the TB and DB spots.The Kikuchi line spacing is the same as the length of g, and the lines are normal to g.The trace (intersection) of (hkl) in the diffraction pattern is midway between the Kikuchi lines:

Most TEMs have a double-tilt specimen holder with two orthogonal tilt axes.By combined tilting about both axes, the Kikuchi pattern can be moved in any direction needed tobring the Kikuchi lines to the exact Bragg condition above.


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Deviation parameter sImage contrast is very sensitive to exactly how close the RL point is to the Ewald sphere.s is the vector from the RL point to the sphere, along the rel-rod.s is defined as positive when it points down (~ parallel to the IB), i.e. when the RL pointis inside the Ewald sphere. This corresponds to having the white Kikuchi line just outsidethe hkl spot:

To see that the RL point is inside the sphere for the above diffraction pattern, consider tilting the specimen so that g moves the RL point at its endpoint from the exact Bragg condition (with the RL point on the sphere), into the sphere.At the exact Bragg condition the dark and white lines are at the endpoints of ko and k respectively, and (hkl) bisectsg and is (of course) normal to it. ko and k are each q degrees from (hkl).

After tilting the specimen e degrees counterclockwise, g, (hkl) and the Kikuchi lines have tilted e degreescounterclockwise. The Kikuchi lines remain at q degrees either side of (hkl); the dashed lines indicate the Kikuchi cones.We can see that the white line has moved outside of the diffraction spot, as in the diffraction pattern shown above.


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Specimen Orientation and Deviation Parameter

s points from the Ewald sphere to the reciprocal lattice point. For Kikuchi line, s=0, when theKikuchi line runs exactly through itscorresponding diffraction spots. s0 if the excess line lies outside its corresponding diffraction spotg. In this case the reciprocal lattice point lies inside the Ewald sphere


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Specimen Orientation and Deviation Parameter


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Specimen Orientation and Deviation ParameterThe 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 .


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Specimen Orientation and Deviation ParameterThe positions the Kikuchi lines are extremely sensitive to the tilt ofthe specimen. During a tilt, the Kikuchi lines moves as if they areaffixed to the bottom of the crystal. With a long camera length

typical for diffraction work, there is significant movement of theKikuchi lines on the viewing screen. The Kikuchi lines can be used todetermine the sign and magnitude of the deviation parameter, s,which quantifies how accurately the Laue condition is satisfied .

where d=/ g/ -1. The x and R are measuredon the image.

and set h e

and or

x is the distance between the diffractionspots and its corresponding bright Kikuchi line R is the distance between the (000) and (hkl)diffraction spots. is the wavelength the unit of s is -1 or nm -1


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Indexing Kikuchi Lines

DPs without (A)and with (B) Kikuchi Bands

A B


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Indexing Kikuchi LinesThe separation between the two Kikuchi

lines is the same as the separationbetween the (hkl) diffraction spot and the(000) spot.

We can index the Kikuchi lines bymeasuring their separations in much thesame ways as we index diffraction spots.Consider two different pairs of Kikuchilines from the planes ( h 1k1l1) and (h 2k2l2).The separations between their pairs ofexcess and deficit lines, p1 and p2,are in the ratio:

For example, figure shows ratio of

32 and 8for indexed (440) and (220) planes


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Indexing Kikuchi LinesThe angles between intersecting Kikuchiline 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 forindexing 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:


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Constructing Kikuchi LinesFor 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 .

Kikuchi line, (-400), bisects, theline between (000) and (-400)

Kikuchi line, (400), bisects, theline between (000) and (400)

Diffraction Spot Pattern with Kikuchi Lines


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Kikuchi MapsAs we tilt the sample, the diffraction spots fade orgrow in intensity, always at the same positions.

The Kikuchi lines move with the tilt, as if they were fixed to the crystal planes of sample. If we know which Kikuchi lines are on the screen, we can use the Kikuchi lines as roads todrive the tilt from one spot pattern (crystal zoneaxis) to another. This is extremely useful fororienting specimensalong particular crystallographic axes.

Based on Kikuchi lines, we can easilyfind thezone axis (How?).

As seen above figure, we can extend the Kikuchi line to create a second pattern from one Kikuchi pattern. E.g. knowing the [001] pattern we can construct the [101] pattern since a pair of lines is common to both, i.e. (020) lines have zone axes [101] and [001] pole. So we draw (020) lines from the [001] pole 45 to the [101] pole. Although the angle between the [001]and [101] pole is 45 , we draw the (020) lines as parallel and straight because we are always looking ata small segment of the Kikuchi pattern. To find [101] pole pattern in operation, we just need to keep (020) lines visible while tilting specimen 45 about [001]


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Kikuchi Maps

Experimental Kikuchi Map for fcc crystal and index Kikuchi lines in the schematic map.Maps for other cubic materials are available in handbook, or refer to J. W. Edington PracticalElectron Microscopy in Materials Science, 1976, Van Nostrand Reinhold Company.


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Symmetrical OrientationWhen the beam is along the zone axis, the RL points on the zone plane are below the Ewald sphere,

so s < 0 for both g. In the SADP, the Kikuchi lines are equal distances either side of the TB spot.

You will see in the lab that since both diffracted beams have s < 0, the image of a relatively thick region ofthe specimen will be very dark.

Symmetric Kikuchi orientation

Random orientation, thick areaGoodhew & Humphreys

The Kikuchi pattern above is typical of a thick foil region; diffraction spots are not seen partly because therel-rods are too short to pierce the Ewald sphere. All we see is the Kikuchi pattern, which is strong becauseinelastic scattering intensity increases with thickness. The specimen is in a random, non-symmetric orientation.A-A and B-B are white/dark pairs of lines; other examples can also be seen.C1, C2 and C3 are 1 st , 2nd and 3 rd order white lines from the same (hkl), and C1 and C2 are the corresponding1st and 2 nd order black lines.


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transmission electron microscopy - specify indexing of kikuchi.pdf

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