DEF4: Simulation of plane wave topographs of dislocations
DEF4: Simulation of plane wave topographs of dislocations 
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DEF4, version 3.0, is a simulation program devoted to the simulation of plane wave topographs of dislocations. When the incident wave along the entrance surface of the crystal can be considered as a spherical wave (Kato approximation [1]) i.e. in the case of section topographs, it must not be used. Consider DEFW instead.
DEF4 runs on any modern workstation. It needs less than 1 Mbyte of memory and a moderate time of computation. The result is an image written as non formatted Fortran file. To display it as an image it is usually necessary to convert these data into raw floating point numbers acceptable by most visualisation programs such as Triton or any visualization program written in C language. A program named convert is available for this purpose.
All explanations are given for a Unix machine.
It is recommanded to run DEF4 in batch mode. In most cases the computation needs from a few minutes up to a few tens of minutes without any dialogue, thus it is unnecessary to use an interactive display. All data are edited in a file called topoX.tmp. The name of the file containing the computed image is given in the script file used to start the computation.
A basic script looks like:
# use Korne shell
#
#!/bin/ksh
#
#
# If the image file exists, it must be deleted before starting
# the computation, otherwise the program will stop.
#
#
rm -f image.img
#
# Now we start the program.
# All lines before EOF are data for DEF4. It is limited to the
# name of the image file since all other data are given in a file
# named topoX.tmp, which name cannot be changed
#
def4 <<EOF
image.img
EOF
These lines must be written in a file named def4.bat, for instance. Make it executable, using the command: "chmod 700 def4.bat" and submit it as a batch. How to submit a batch depends on your system. Ask your supervisor to know how to do this. You may also run interactively this job by typing the name of the file: "def4.bat".
In this part you will find a brief comment about the data described later in details.
You need:
The elastic stiffnesses are 3 to up 21 independant values - their number depends on the crystallographic symetry of the crystal. You will have to write half the tensor, i.e. you must know which components are null. See for instance [4].
All explanations refer to set of axes described below. You must know:
Note that the Kih are complex numbers and that you must calculate, for each reflection, both the real and imaginary parts. The ratio of the imaginary and real part depend on the choice of the origin in the unit cell. These data are often negative. The program computes the extinction distance and the width at half the maximum of the rocking curve (See the example below) The extinction distance and the width of the rocking curve are a good means to check the consistency of your data.
You must know, from an experimental topograph:
The dimensions of the computed image are computed, as well as the number of pixels along a line or a column, from the knowledge of the width of the incident beam, the thickness of the crystal, the Bragg and the asymetry angle. The width of the image is the width of the beam in the film, for an incidence plane. It corresponds to a line in the image. The height of the image is the vertical dimension. More explanations are given in the section set of axes.
Other data are:
At first look it seems difficult to choose all these data. A simple means to check their consistency is the following: run first the program with the characters: "test" or "TEST" as first characters for the title. The program will write all the output as shown below but it will not run the integration. Thus you will be able to check your data, to verify if the size of the image is reasonnable (most image browsers will not accept more than 512x512pixels), the validity of the diffraction parameters (look at the extinction distance and at the width at half maximum of the rocking curve) and all other data.
The program also estimates the computation time which is related to the numbers of nodes in the integration. It gives a number which has to be calibrated for your computer. For instance, I found that 166.7 corresponds to 4mn19s when using an IBM RS6000/390 and to 8mn27s when using an IBM RS6000/560. A method to perform this calibration is to run first the program giving a large amount of time, to note this time value together with the time needed for the computation. It will be then easy to estimate the time for other computations since it is proportionnal to the time coefficient.
The program uses a set of axes called experimental axes or macroscopic axes. The
macroscopic axes are oriented as follow:
- axis x lies along the entrance surface, oriented from right to left. It is the
projection of the transmitted direction s0 along the surface.
- axis z is the normale to the entrance surface, towards the inside of the crystal.
- axis y is perpendicular to the plane of incidence, in the plane of the surface. The
origin is in the first computed line of the image which means that all lines in the image
correspond to negative y values.
Note that the origin is on the left side of the incident beam along the surface.
The dislocation orientation may be given either in this set of axes or in the crystallographic axes.
As explained before it is assumed that the film is perpendicular to the difracted beam. Steps are choosen to represent the image in the film, not along the exit surface of the crystal.
The diffraction equations [3] are a set of partial derivative hyperbolic equations which are integrated using a finite elements method [2]. The integration network, in a plane of incidence, is determined as follow.
In a plane of incidence, the crystal is divided into slabs of equal thickness ELEM. A set of characteristics parallel to the diffracted and reflected directions is drawn. It may be shown [2] that the amplitude at point A may be computed from the knowledge of the amplitudes at points B and C. Lengthy tests have shown that ELEM should always be smaller than 2 microns, thus the computation step BC, along the exit surface, (which is written in the output in the section "network of integration") is always much smaller than the desired resolution in the image. This is why one samples one over KPERFO computed points along the exit surface for the image file.
This is an example of data file. The numbers on the left, starting at 01, do not belong to the file. They are written to clarify the explanations.
01 Example for DEF4 IMP=1
02 5.43 5.43 5.43 lengths of the unit vector of the crystal cell
03 90 90 90 angles for the unit cell (cubic in this example)
04 1 -1 -1 normale to the entrance surface
05 -2 -2 0 diffraction vector
06 -0.3 1 2.11 1 orientation of the dislocation. 1 means macroaxes.
07 0.5 0.5 0. Burgers vector
08 16.6 7.96 7.96 0 0 0
16.6 7.96 0 0 0
16.6 0 0 0
6.4 0 0
6.4 0
6.4 Elastic constants cij (cubic in this example)
09 0.70926 wave length
10 10.667 Bragg angle (positive value)
11 -10.667 Asymetry angle (- theta for symetric reflection)
12 -1.993e-06 -1.57e-08 KIhm dielectric components -h values
13 -1.993e-06 -1.57e-08 KIhp idem h values (real and imaginary parts)
14 100 Height of the image
15 -1.E-06 KI0r dielectric components (real part 000 reflection)
16 -32.17 0. 200. A point along the dislocation in the choosen set of axes.
17 0.00142 absorbtion per micron
18 4 3 reduction factor for output and interpollation between lines
19 200 Thickness of crystal
20 1.0 Thickness of integration slab
21 0. 50. delta theta (radians) and width of slit (microns)
Each section refers to the line number in the preceeding part. All input are to be written in free format.
The following example is the contents of to the file def4.log, automatically created when running DEF4, and corresponds to the data shown before.
Programm DEF4 (Rev.3.0) Plane wave topograph
---------------------------------------------
Example for DEF4 IMP=1
Diffraction data
----------------
wave length .709260 Angstroms
Theta 10.667 Deg.
Psi zero -10.667 Deg.
Mu .001420 per micron
Khi H minus R -1.9930 10(-6), Khi H minus I -.0157 10(-6)
Khi H plus R -1.9930 10(-6), Khi H plus I -.0157 10(-6)
Khi H 0 R -1.0000 10(-6), Khi H 0 I -.0160 10(-6)
Delta theta (radians): .00000E+00
Slit width (microns) : 50.000
rocking curve half width 2.260 seconds
extinction distance 34.972 microns
defect data
-----------
Parameters of the crystal
A = 5.430 angstroms
B = 5.430 angstroms
C = 5.430 angstroms
angles 90.000 90.000 90.000
Burgers vector .500 .500 .000
Dislocation (macro axes) -.300 1.000 2.110
Normale to the surface 1.000 -1.000 -1.000
Diffraction vector -2.000 -2.000 .000
Position of the core (microns) -32.170 .000 200.000
Elastic stiffnesses
16.600
7.960 16.600
7.960 7.960 16.600
.000 .000 .000 6.400
.000 .000 .000 .000 6.400
.000 .000 .000 .000 .000 6.400
network of integration
----------------------
slab thickness (microns): 1.000
computation step (microns): .377
number of nodes per line: 333
Characteristics of the image
----------------------------
Thickness of simulated crystal 200.00 microns
width of simulated image 125.44 microns
height of image 103.66 microns
vertical calculated step 4.44 microns
horizontal representation step 1.48 microns
vertical representation step 1.48 microns
number of calculated planes 24
number of lines in image 70
Time estimation
---------------
time coefficient: .39960E+01
number of points per plane 84
Please note the indication of a version number. It is important to note it in case of error before reporting the problem. The results are presented in different sections as follow:
The name of the file containing the image is not in the data file topoX.tmp. It is part of the script used to run the program or may be input from the keyboard. See the section How to run DEF4.
The image file is written without format:
This file contains some additional informations added by the Fortran subroutines for non formatted write. Thus it cannot be read directly by a visualisation routine written in C language. The program CONVERT is a utility to translate these data in asuitable form.
convert is a utility program to convert the various image formats used in simulation programs. It is self explanatory.
CONVERT allows to:
DEF4 and CONVERT sources are available in the directory pub/topo, when logging as anonymous at ftp.lmcp.jussieu.fr directory pub/sincris-top/software/dynamical_theory.
Read first 00readme which contains some additional explanations.
To install the program:
Please send your comments and your suggestions to Yves Epelboin, Yves.Epelboin@lmcp.jussieu.fr .
Last update28/06/98 Y.E.
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