Home
Analyzing Kossel-Moellenstedt fringes
Figure 1 is plotted with parameters from the current crystal, accelerating voltage, etc. It is
recommended to use the proper crystal. By default zone axis [001] is set and microscope parameters from the selected
microscope are employed.

Figure 1 The K-M fringes analysis window (current opended crystal file).
Follow these steps to analyze the K-M fringes pattern:
- Open the K-M window (Fig. 1).
- Load the K-M pattern (Fig. 2).
- Adjust diffraction conditions (Fig. 4).
- Set the K-M profile (Fig. 5).
Top
Load the K-M pattern
The K-M fringes pattern is loaded as a background image (Fig. 2). It is still necessary the
experimental zone axis [uvw], CLC (hkl) with the K-M pattern.

Figure 2 Loading the K-M fringes.
Top
Setting the diffraction conditions
A low magnification SAED pattern taken under the diffraction conditions of the CBED K-M fringes is
usually necessary to determine [uvw] zone axis indices and (hkl) CLC indices. Figuring out the [uvw] and (hkl) indices
can be done using Kikuchi lines and/or HOLZ lines.
An other possibility is to load the SAED into the diffraction pattern window and
manually align the calculated pattern onto the experimental SAED. Adjusting precisely the beam half-convergence,
camera length, deviation, accelerating voltage, and the acceptance angle is important for accurate fitting of the K-M
fringes with calculated ones. diffraction conditions.

Figure 2 Loading the K-M disks.
Introducing the measured [uvw] and (hkl) indices, camera length and beam convergence is shown in the good match
shown in (Fig. 3). Note that the Keeper stores all these parameters
(often not too easy to figure out) and allows to load them in the K-M analysis.
 |
 |
Figure 3a Keeper [uvw] zone axis indices. |
Figure 3b Keeper (hkl) CLC indices. |
 |
 |
Figure 3a Keeper accelerating voltage, camera length, beam-convergence, deviation. |
Figure 3b Alignment of K-M pattern and calculated one. |
Top
Getting the profile through the CBED disks
A mouse click identifies the reflections, (000) left and (200) right, at Bragg diffraction conditions.
To get a profile of the K-M fringes select the Profile mask (Figures 4a,
4d) and drag the profle on the K-M pattern using the yellow squares (Fig. 4b).
The profile center must remain exactly between the reflections (green cross). When done the profile accross the (000) disk is blue
and accross the (200) disk red.
 |
 |
Figure 4a Activated profile. |
Figure 4b Aligned profile. |
 |
 |
Figure 4c (000) disk blue, (200) disk red. |
Figure 4d Alignment of the disks and profile. |
The profile does not have to aligned with the disks nor does it have to cover the whole disks
(Figures 5a, 5b). Every point of the profile contains
the diffraction conditions to do a complete dynamical calculation. But the wider the profile the more
accurate the thickness determination.
 |
 |
Figure 5a Tilted profile. |
Figure 5b Tilted shorter profile. |
Top
2-Beams profile fitting
With the profile shown on Fig. 4c proceed with its fitting with a dynamically calculated
profile (Bloch-wave) by clicking the
process tool button. In case it is not enabled, reselect the Profile mask.

Figure 6 2-beams dynamical calculation profile (green) fitted to the profile disk (200) red.
A 2-beams dynamical fit is shown of Figure 6. The fit is using the 2-beams dynaminal formula and is
only using (200) disk profile. A 157 nm crystal thickness is obtained. The fit can be further improved by checking the
Deviation and (000) center. This is modifying the diffraction conditions using a Levenberg-Marquardt fitting.
The final residual is 0.076 (Fig. 7).

Figure 7 Levenberg-Marquardt fitting of deviation and (000) center.
Top
Many Beams profile fitting
The fitting controls are distributed in 2-panes:
- Many beams Bloch-wave calculation using many reflections.
- Two beams Analytic formula.
 |
 |
Figure 8a 2-Beams controls.
| Figure 8b 2-Beams fitted.
|
 |
 |
Figure 9a Many-Beams controls.
| Figure 9b Many-Beams before fit.
|
The many-beams fitting can adjust supplementary parameters. Examples are:
(000) center adjustment (Figures 10a, 10b).
Debye-Waller temperature factor center adjustment (Figures 12a, 12b).
(000) and (200) structure factors (Figures 12a, 12b)
 |
 |
Figure 10a First fit without (000) center adjustment.
| Figure 10b Second fit with (000) center adjustment.
|
 |
 |
Figure 11a Checking the Debye-Waller fit.
| Figure 11b Third fit with Debye-Waller adjustement.
|
 |
 |
Figure 12a Adjusting (000) and (200) structure factors.
| Figure 12b Residual is now 0.02.
|
Top
Many-Beams Parameters before the fits
I N I T I A L P A R A M E T E R S
Acc. Volt. 100.00000
Dilation 0.98761
Fog 0.00000
Scale 1.00000
Thickness 157.21496
clc_x 0.00000
clc_y 0.00000
CLC (1.0162, 4.0115, -12.0346)
ooo_x 0.00000
ooo_y 0.00000
OOO (0.0000,0.0000,0.0000)
---------------------------------------------------------
atom [0] Al 0.00000 0.00000 0.00000 0.00500 1.00000 0.03400
atom [1] Al 0.50000 0.50000 0.00000 0.00500 1.00000 0.03400
atom [2] Al 0.00000 0.50000 0.50000 0.00500 1.00000 0.03400
atom [3] Al 0.50000 0.00000 0.50000 0.00500 1.00000 0.03400
---------------------------------------------------------
(Vr, Vi) (0, 0, 0) 0.00000 (20.26200, 0.86143)
(Vr, Vi) (2, 0, 0) 0.00074 (5.90540, 0.19101)
(Vr, Vi) (-7, 1, -3) 0.07954 (0.61792, 0.04835)
(Vr, Vi) (4, 0, 0) -0.08941 (2.16122, 0.11282)
(Vr, Vi) (-2, 0, 0) -0.09162 (5.90540, 0.19101)
(Vr, Vi) (6, 0, 0) -0.27054 (1.07624, 0.07320)
(Vr, Vi) (-4, 0, 0) -0.27423 (2.16122, 0.11282)
Many-Beams Parameters After the fits
F I N A L P A R A M E T E R S
Acc. Volt. 100.00000
Dilation 1.00644
Fog 0.00000
Scale 14.28545
Thickness 149.84101
clc_x 0.00000
clc_y 0.00000
CLC (0.9866, 3.9953, -11.9860)
ooo_x 0.00000
ooo_y 0.00000
OOO (0.0000,0.0000,0.0000)
---------------------------------------------------------
atom [0] Al 0.00000 0.00000 0.00000 0.00548 1.00000 0.03400
atom [1] Al 0.50000 0.50000 0.00000 0.00548 1.00000 0.03400
atom [2] Al 0.00000 0.50000 0.50000 0.00548 1.00000 0.03400
atom [3] Al 0.50000 0.00000 0.50000 0.00548 1.00000 0.03400
---------------------------------------------------------
(Vr, Vi) (0, 0, 0) 0.00000 (19.98091, 1.21811) (-0.28109, 0.34865)
(Vr, Vi) (2, 0, 0) 0.00074 (5.90540, 0.19101) (0.01742, -0.00614)
(Vr, Vi) (-7, 1, -3) 0.07954 (0.61792, 0.04835) (0.02634, 0.00083)
(Vr, Vi) (4, 0, 0) -0.08941 (2.16122, 0.11282) (0.02538, -0.00320)
(Vr, Vi) (-2, 0, 0) -0.09162 (5.90540, 0.19101) (0.01742, -0.00614)
(Vr, Vi) (6, 0, 0) -0.27054 (1.07624, 0.07320) (0.02823, -0.00061)
(Vr, Vi) (-4, 0, 0) -0.27423 (2.16122, 0.11282) (0.02538, -0.00320)