Indexing example

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Example K2Cr2O7

At first, set up the file k2cr2o7.sav as follows: 
VERZERR=rd7ff31
VAL[1]=k2cr2o7
Vmax=1.5
Vmin=0.1
PARAM[1]=EPS1
OUTPUTMASK=k2cr2o7-$
TITELMASK=k2cr2o7-teil-$
Minlattice=Cubic
Maxlattice=Triclinic
Then, you must call TEIL with the command 
teil k2cr2o7
at the DOS or WIN32 or OS/2 command screen prompt. It generates some lines of output on the sreen: 
BGMN and related programs Copyright (C) J. Bergmann Dresden 1991-2002
BGMN is a registered trademark of J. Bergmann
Version 3.4.8
This program may not be used after Mar 2003
RU=9
there were designed 26 partial angular ranges
Significantly, it adds a lot of lines to k2cr2o7.sav. This file now looks like 
VERZERR=rd7ff31
VAL[1]=k2cr2o7
Vmax=1.5
Vmin=0.1
PARAM[1]=EPS1
OUTPUTMASK=k2cr2o7-$
TITELMASK=k2cr2o7-teil-$
Minlattice=Cubic
Maxlattice=Triclinic
%teil has computed the following angular ranges: Teil 1
WMIN[1]==1.0000000193910020E+001
WMIN2[1]==1.0000000000000000E+001
WMAX2[1]==1.3929930686950680E+001
WMAX[1]==1.4289999749257440E+001
VAL[1,1]=k2cr2o7
OUTPUT[1]=k2cr2o7-1
TITEL[1]=k2cr2o7-teil-1
% Teil 2
WMIN[2]==1.3569999890062170E+001
WMIN2[2]==1.3929930686950680E+001
WMAX2[2]==1.5714461326599120E+001
WMAX[2]==1.6659999299444910E+001
VAL[2,1]=k2cr2o7
OUTPUT[2]=k2cr2o7-2
TITEL[2]=k2cr2o7-teil-2
 .
 .  (etc)
 .
% Teil 26
WMIN[26]==7.2820003746537340E+001
WMIN2[26]==7.5215393066406250E+001
WMAX2[26]==7.9000002704233040E+001
WMAX[26]==7.9000002704233040E+001
VAL[26,1]=k2cr2o7
OUTPUT[26]=k2cr2o7-26
TITEL[26]=k2cr2o7-teil-26
%these constants have been notated by TEIL for internal use
VALZAHL==1.0000000000000000E+000
TEILZAHL==2.6000000000000000E+001
In following, you must call EFLECH with the command line 
eflech k2cr2o7
It will generate the files k2cr2o7-1.par...k2cr2o7-26.par, which contain all peak parameters plus inverse curvature matrices. There will be some output like 
BGMN and related programs Copyright (C) J. Bergmann Dresden 1991-2002
BGMN is a registered trademark of J. Bergmann
Version 3.4.8
This program may not be used after Mar 2003
using default value ABSCHNEID=2.500
computation with minimal error EPSILON=8.00E-002
    (relative intensity error)
Evaluation of 1th range with 144 measuring points
unable to read peak parameter start values from file k2cr2o7-1.par
starting iteration.............. Q=3336.49        
using fast startup peak scanning
N zweiTheta=13.4444  HWB=0.0462  Q=419.89         
N zweiTheta=13.0061  HWB=0.0461  Q=130.37         
terminating fast startup peak scanning
 . 
 .  (angular ranges 2...25)
 . 
Evaluation of 26th range with 207 measuring points
unable to read peak parameter start values from file k2cr2o7-26.par
starting iteration.............. Q=388.58         
using fast startup peak scanning
N zweiTheta=77.8572  HWB=0.0589  Q=247.15         
terminating fast startup peak scanning
closing iteration............... Q=247.15
After this step, you may call INDEX with the command line 
index k2cr2o7
The results are given on the screen, it looks like 
BGMN and related programs Copyright (C) J. Bergmann Dresden 1991-1998
BGMN is a registered trademark of J. Bergmann
Version 3.4.8
This program may not be used after Mar 2003
Cubic
*** using 43 pre-scan peaks, WMAX=55.28, ignore=2/7%
+----+----+----+----+----+----+----+----+
Hexagonal
*** using 43 pre-scan peaks, WMAX=55.28, ignore=1/5%
+----+----+----+----+----+----+----+----+
Q         V       ignore A      B      C      ALPHA   BETA    GAMMA
 52.89%   1.368 P  1/ 0% 0.6933 0.6933 3.2870  90.000  90.000 120.000
Tetragonal
*** using 43 pre-scan peaks, WMAX=55.28, ignore=1/5%
+----+----+----+----+----+----+----+----+
Orthorhombic
*** using 43 pre-scan peaks, WMAX=55.28, ignore=1/4%
+----+----+----+----+----+----+----+----+
Q         V       ignore A      B      C      ALPHA   BETA    GAMMA
 71.22%   0.375 P  1/ 0% 0.1673 1.4623 1.5337  90.000  90.000  90.000
 71.07%   0.379 P  1/ 0% 0.1689 1.4626 1.5341  90.000  90.000  90.000
 71.01%   0.385 P  1/ 0% 0.1714 1.4626 1.5340  90.000  90.000  90.000
 52.79%   0.804 A  1/ 0% 0.6598 0.8799 1.3843  90.000  90.000  90.000
 50.69%   0.972 C  1/ 0% 0.6633 0.9829 1.4907  90.000  90.000  90.000
 49.86%   1.202 B  1/ 0% 0.6212 0.7778 2.4871  90.000  90.000  90.000
 44.26%   0.780 P  1/ 0% 0.3474 1.4641 1.5345  90.000  90.000  90.000
 39.46%   1.619 B  1/ 0% 0.3598 1.5361 2.9286  90.000  90.000  90.000
 37.18%   1.123 P  1/ 0% 0.5007 1.4627 1.5336  90.000  90.000  90.000
 31.49%   1.363 P  1/ 0% 0.3919 1.3431 2.5888  90.000  90.000  90.000
Monoclinic
*** using 27 pre-scan peaks, WMAX=39.24, ignore=0/0%
+----+----+----+----+----+----+----+----+
Q         V       A      B      C      ALPHA   BETA    GAMMA
 21.90%   1.257 P 1.8917 0.2387 2.7854  90.000  92.304  90.000
 20.33%   1.305 P 1.8923 0.2479 2.7853  90.000  92.309  90.000
Triclinic
*** using 25 pre-scan peaks, WMAX=36.86, ignore=0/0%
+----+----+----+----+----+----+----+----+
Q         V       A      B      C      ALPHA   BETA    GAMMA
 27.29%   0.470 P 0.5445 0.7404 1.2301  96.756  97.383 104.500
 24.67%   0.647 P 0.6895 0.9653 1.0704 107.632 103.602  96.256
 23.15%   0.658 P 0.5214 0.6994 1.8496  95.063  90.826 101.498
 13.55%   0.727 P 0.7384 0.7469 1.3405  96.214  98.094  90.830
  7.51%   1.454 P 0.7466 1.3406 1.4769  98.142  90.762  96.144
As explained, INDEX selects the maximum ignore values using some advanced algorithms. Especially, these values depend on the maximum unit cell volumen as set in the control file (was 1.5 nm3 in this case). Large volumina hide INDEX from using other ignore values than zero. And the maximum ignore values depend from lattice symmetry. In this case, INDEX decides to use zero ignore values down from the monoclinic system.

In this case, the true solution is that of the last but one line 

A=0.7384 
B=0.7469 
C=1.3405  
ALPHA=96.214  
BETA=98.094  
GAMMA=90.830
This may be confirmed by a LeBail-Fit using BGMN. The last line only doubles the unit cell. This gives an even better solution, in this case.

In complicated cases (large alignment errors makes classical indexing impossible), you may also use the entries 

PARAM[1]=EPS1...
PARAM[2]=EPS2...
etc. for INDEX. INDEX will search for the best alignment correction while searching for best indexing. Of course, this complicates indexing. All EPSx are implemented, but no more than EPS1 (plus EPS2 for sufficient large upper angular limit) are recommended.

For the final decision about truth of indexing, I recommend using BGMN in the LeBail mode: It will refine the line's position plus widths, the latter depending on some minor number real structure paramters.

Even the lattice base (P/A/B/C/I/F/R) as given by INDEX is a recommendation, only. For example, for cassiterite (SnO2), INDEX finds a body-centered base I. Looking at the structure, it becomes clear: The heavy Sn atoms fullfill the special reflection condition of body centering. Only the light O atoms contribute to the non-body-centered reflection intensities, and by ignoring two reflections of only one per cent summed (u-like) intensity INDEX decides for body-centering.
On the other hand, by chosing low ignore values, a non-primitve cell may be marked as primitive for some spurious lines accidentally corresponding to the primitve cell.

For particular, if there are strong different line widths, a LeBail refinement with B1=ANISO and/or k2=ANISO4 will give strong anisotropic results and a good fit only for the true index solution. Since level 3.4, the LeBail mode was much improved in computing time. Tt was fastened up by a factor above ten. So, patterns with 2500 lines and 10000 points may be LeBail-refined in some hours.