examples

dirax (version 1.17 2018011700) started on celesta at 26-Apr-2018 02:40:30

   Albert J.M. Duisenberg, Indexing in Single-Crystal Diffractometry with an Obstinate List of Reflections
   J. Appl. Cryst. (1992). 25,92-96.

                    C O N D I T I O N S    F O R    U S E
                    =====================================
a. You may not copy DirAx neither the auxiliary files except for use by yourself or for use in your laboratory, institute,
   office and the like.
b. You may not hand over DirAx in any form to third parties without provable permission from the author.
c. You use DirAx at your own responsibility completely.

   Albert J.M. Duisenberg, Antoine M.M. Schreurs
   BIJVOET Centre for Biomolecular Research
   Laboratory for Crystal and Structural Chemistry
   Utrecht University since A.D. MDCXXXVI
   Padualaan 8, NL-3584 CH UTRECHT
   The Netherlands
   Electronic MAIL addres: a.m.m.schreurs@uu.nl


example 0

This is a straightforward model run for a single lattice. (In fact too easy for DirAx.)
First load the data
Dirax> example 0
ex00 - This is a straightforward model run for a single lattice.
 (In fact too easy for DirAx.)

  go              ! run with defaults
  lo              ! accept proposed ACL and show H indices
  ro              ! show cell and [R] and [D] matrices
  write           ! write file ex00.out for print-out

25 reflections from file ../ex00.drx.

Dirax> go
2496 triplets
2497 final triplets
2470 triplet vectors
Squishd: 2470 t vectors ==> 1841 t vectors
Sorting 1841 t vectors...
Reducing 1841 t vectors ==> 794 t vectors
Acl nH     a      b      c  alpha   beta  gamma Volume S Indexstatus
 25 25 6.530 41.209  6.671  89.99 101.53  90.00   1759   HHHHHHHHHHHHHHHHHHHHHHHHH
 13 13 6.530  6.671 10.431  88.22  80.99  78.48    440 Q HnHHnnHnHnHnnHHnHnHHnnnHH
  9  9 6.530  6.671  8.410  97.33  97.10 101.54    352 ? nHHnnnnnnHnnHHnHnnnnHnnHH
  8  8 5.893  6.519  6.529 116.29 113.09  95.59    195   nnnnHnnnHHHnnnnHHnHnHnnnn
  7  7 4.930  5.173  6.530  91.48 104.10  97.39    160 ? HnnnnnnHnnnHHnnnnnnnnHnHH
Solutions limited by voltest

 25 25 6.530 41.209  6.671  89.99 101.53  90.00   1759   HHHHHHHHHHHHHHHHHHHHHHHHH
selected ACL 25

Here you see 5 possible solutions. The solutions are identified by the Acl number in the first column. The second column, marked nH, gives the number of fitting reflections. In the last column, marked Indexstatus, the 'fitting' of all the reflections is displayed (H=fit, n=nonfit). The question marks in solutions 9 and 7 indicate some warning. More about this later. The last line of the output shows the selected solution. The number of fitting reflections for solution 25 is 25.

Make a list of reflections
Dirax> lo
  nr      H       K      L  1/err Netint    dth    dom    dch
H  1: -0.000  16.000  1.000 89222  130.8 -0.000  0.000 -0.001
H  2:  2.000  -2.999  1.000 22257  112.3  0.001  0.004  0.005
H  3:  0.000 -15.999  1.000 14128  141.7 -0.002  0.007 -0.003
H  4:  0.000 -12.002  1.000 26055  194.5  0.001  0.001 -0.004
H  5: -1.000  -5.001  2.001  6088   99.2  0.007  0.001  0.008
H  6: -1.000  -4.001  2.000 28893   82.0  0.000  0.001 -0.006
H  7: -1.000   5.001  2.000 15205   87.8 -0.002 -0.006 -0.006
H  8:  0.000 -16.998  1.000 21468  144.1 -0.002  0.003  0.001
H  9: -1.000   8.997  1.000 11459  173.0 -0.003 -0.001  0.009
H 10:  1.000   8.000  1.000 34788   69.6  0.001 -0.001  0.004
H 11:  2.000  -2.000  1.999  8707  141.3 -0.005 -0.002 -0.002
H 12:  1.000   4.002  1.001  7712   43.4  0.006  0.005  0.003
H 13: -1.000  -4.998  1.000  9341  334.6 -0.005  0.000  0.002
H 14: -0.999   4.998  1.000  9969  332.7 -0.004 -0.003  0.002
H 15: -1.000   9.001 -0.000 12965  148.9  0.000 -0.013 -0.010
H 16: -1.000  -4.002 -0.000 14342  330.6  0.003  0.003 -0.007
H 17: -1.000   5.004 -0.000  8953  197.6  0.003 -0.024 -0.011
H 18:  1.000  -4.001 -0.000 15313  371.0  0.002  0.003 -0.012
H 19:  1.000  -5.001 -0.000 14639  178.5  0.003  0.006  0.001
H 20: -1.000   1.000  1.001  8373 1537.2  0.005  0.001  0.010
H 21: -1.000  -0.000  1.000 21259 1100.8  0.002  0.003 -0.003
H 22:  1.000  -2.000  2.000 17439   62.5 -0.003 -0.000 -0.002
H 23: -1.000   2.000 -0.000 12613  304.3 -0.002 -0.008 -0.019
H 24: -1.000   1.001 -0.000 19954  579.3  0.002 -0.006 -0.008
H 25:  1.000  -1.001 -0.000 17506  532.3  0.002 -0.006 -0.012
1/error for H: from 6088 to 89222.

Show the cell parameters
Dirax> ro
cell for ex00                                   Niggli values
a, b, c :   6.5298  41.2087   6.6705          42.6379  1698.1539    44.4957
al,be,ga:   89.993  101.527   89.997           0.0337    -8.7038     0.0162
  volume: 1758.721
Nrefls=25 Nfit=25 NNonfit=0
                R                                        D
   0.1377718  -0.0098145  -0.0096078        5.9577661   2.6083508   0.5826150
   0.0587051   0.0221645  -0.0120556      -16.6646996  37.6393433   1.9291350
   0.0447371   0.0011326   0.1522207       -1.6269770  -1.0466336   6.3838272
Determinant:  0.5685949E-03                             1758.721

The question marks in the Acl solution list mark some warning. In this example, you could select a different solution:
Dirax> acl
Acl nH     a      b      c  alpha   beta  gamma Volume S Indexstatus
 25 25 6.530 41.209  6.671  89.99 101.53  90.00   1759   HHHHHHHHHHHHHHHHHHHHHHHHH
 13 13 6.530  6.671 10.431  88.22  80.99  78.48    440 Q HnHHnnHnHnHnnHHnHnHHnnnHH
  9  9 6.530  6.671  8.410  97.33  97.10 101.54    352 ? nHHnnnnnnHnnHHnHnnnnHnnHH
  8  8 5.893  6.519  6.529 116.29 113.09  95.59    195   nnnnHnnnHHHnnnnHHnHnHnnnn
  7  7 4.930  5.173  6.530  91.48 104.10  97.39    160 ? HnnnnnnHnnnHHnnnnnnnnHnHH
Solutions limited by voltest

 25 25 6.530 41.209  6.671  89.99 101.53  90.00   1759   HHHHHHHHHHHHHHHHHHHHHHHHH

acl/auto [25] 9
selected ACL 9
ACL 9                                           Niggli values
a, b, c :   6.5299   6.6711   8.4100          42.6399    44.5038    70.7283
al,be,ga:   97.329   97.101  101.543          -7.1574    -6.7886    -8.7169
  volume: 351.7956
Nrefls=25 Nfit=9 NNonfit=16
WARNING ALL |K| indices zero or one

Solutions with question marks are not selected as default solution.

Example 1

fragmented crystal


Dirax> example 1
ex01 - Data from a fragmented crystal. First run with default parameters
and accept proposed solution. Inspect the hkl list and note that more
reflections could be made fitting with a wider IndexFit: change
value to 6 and select the default solution.

  list             ! show input data
  go               ! run with defaults
  lo               ! note that some refl's might fit with...
  indexfit 6       ! ...a more relaxed fitting criterion
  acl              ! display solutions with new parameters
  auto             ! select solution with most H refl's
  lch invert       ! interchange n <--> H
  go               ! go again with n-refl's only, for other lattice

The alien reflections do not form one lattice and cannot be
identified properly.

25 reflections from file ../ex01.drx.

Dirax> list
Wavelength:0.7093
nr    Theta     PhiB   ChiB   Inet    C(1)    C(2)   C(3)
 1 H 16.200 -106.450 34.880  257.0  0.6189 -0.1827 0.4499
 2 H 17.910  -51.980 30.500  259.4  0.5886  0.4602 0.4401
 3 H 17.970 -106.300 31.120  230.8  0.7148 -0.2090 0.4496
 4 H 12.410 -132.040 22.530  540.0  0.4157 -0.3748 0.2322
 5 H 12.490  -93.650 23.450  849.4  0.5583 -0.0356 0.2427
 6 H 12.440 -118.740 22.950  598.0  0.4904 -0.2689 0.2368
 7 H 12.850 -106.230 22.990  404.9  0.5543 -0.1613 0.2449
 8 H 12.910  -81.410 22.880  631.2  0.5739  0.0867 0.2449
 9 H 12.640   28.000 35.600  346.0 -0.2355  0.4430 0.3592
10 H 15.930    0.770 49.660  192.7 -0.0067  0.5009 0.5899
11 H 11.330    5.320 20.160  496.6 -0.0482  0.5178 0.1909
12 H 10.930   -2.920 21.260  417.5  0.0254  0.4976 0.1939
13 H 10.900   -4.000 21.730  249.6  0.0346  0.4941 0.1974
14 H 11.290   57.530 41.760  556.1 -0.3474  0.2211 0.3677
15 H 10.680   74.740 42.170  671.7 -0.3736  0.1019 0.3508
16 H 11.210  -26.170 48.060 1197.4  0.1616  0.3288 0.4077
17 H 15.980   87.850 45.290  372.2 -0.5457  0.0205 0.5517
18 H 16.270   74.560 25.500  414.5 -0.6873  0.1898 0.3401
19 H 12.610  121.210 34.830  407.3 -0.4322 -0.2618 0.3516
20 H 10.980   88.100 16.740 2209.4 -0.5140  0.0171 0.1547
21 H 11.330 -177.850 21.130  735.3  0.0194 -0.5163 0.1997
22 H  9.790  129.140 50.900  778.5 -0.2345 -0.1909 0.3721
23 H  8.430  128.970 68.160 1672.1 -0.1196 -0.0967 0.3837
24 H 13.140  145.400 65.470  538.3 -0.1511 -0.2191 0.5831
25 H 14.060 -160.310 63.210  197.4  0.1040 -0.2907 0.6115

Dirax> go
2496 triplets
2497 final triplets
2497 triplet vectors
Squishd: 2497 t vectors ==> 989 t vectors
Sorting 989 t vectors...
Reducing 989 t vectors ==> 912 t vectors
Acl nH     a     b      c  alpha   beta  gamma Volume S Indexstatus
 12  3 1.607 1.667  2.035  81.97  66.77  69.35      5 ? nnnnnnnnnnnHnnnnnHnnnnnHn
 11 11 8.192 5.062 12.007  90.03 101.16  89.92    488   HHnnnnHHnHnHnHnHHnnHnnnHn
  9  4 5.025 6.984  8.176 113.69  92.00 110.11    242 ? HnnnnnHnnnnnnnnnHnnHnnnnn
  7  3 1.831 1.897  1.988  72.79  86.03  89.51      7 ? HnnnnnnnnnnnnHnnnnnnnnnHn
  6  3 2.184 2.634  3.460  67.97  81.18  71.87     18 ? nnHnHnnnnnnnnnnHnnnnnnnnn
Solutions limited by voltest

 11 11 8.192 5.062 12.007  90.03 101.16  89.92    488   HHnnnnHHnHnHnHnHHnnHnnnHn
selected ACL 11

not so good: only 11 out of 25 reflections fit. Let's have a look at all reflections.
Dirax> lo
   nr      H      K      L  1/err Netint    dth    dom    dch
H   1:  0.001 -2.008  8.003   615  257.0  0.022 -0.012  0.090
H   2: -4.995 -2.005  6.993   816  259.4 -0.007  0.005  0.078
Nn  3: -0.007 -1.966  9.172    63  230.8
Nn  4:  1.994 -0.983  5.557    26  540.0
Nn  5: -0.999 -0.995  6.931   169  849.4
Nn  6:  0.992 -0.981  6.348    34  598.0
H   7:  0.000 -1.002  7.010  1082  404.9  0.019 -0.005  0.001
H   8: -1.998 -1.006  6.998   757  631.2  0.003 -0.017  0.118
Nn  9: -3.001 -1.931 -2.898    62  346.0
H  10: -3.997 -3.005 -0.001   942  192.7  0.011  0.014  0.068
Nn 11: -3.992 -1.010 -0.903   115  496.6
H  12: -3.999 -0.994 -0.002   783  417.5 -0.012  0.009 -0.121
Nn 13: -3.992 -1.008  0.114   100  249.6
H  14: -1.003 -2.008 -4.003   600  556.1  0.030 -0.024  0.084
Nn 15: -0.004 -1.928 -4.214    43  671.7
H  16: -2.998 -2.009  1.999   588 1197.4  0.022  0.012  0.138
H  17:  1.001 -3.007 -5.989   590  372.2  0.009  0.028  0.118
Nn 18:  0.008 -2.006 -8.052   223  414.5
Nn 19:  2.993 -1.936 -4.549    25  407.3
H  20:  1.001 -0.991 -5.995   534 2209.4 -0.021  0.030 -0.166
Nn 21:  4.002 -0.973  0.940   135  735.3
Nn 22:  1.988 -1.963 -2.243    45  778.5
Nn 23:  0.987 -1.980 -0.954   178 1672.1
H  24:  2.000 -2.992 -1.014   527  538.3 -0.028 -0.090 -0.082
Nn 25:  1.989 -3.028  2.128    83  197.4
1/error for H: from 527 to 1082. n: from 25 to 223.

A reflection is considered to be fitting if 1/err > levelfit/indexfit.
levelfit=1000 and indexfit=2, so reflections with 1/err > 500 are fitting. We could increase indexfit to 6 and thus add reflections 5 and 23 to the 'fitting' list.
Dirax> indexfit 6
acl is the command to redisplay the solutionslist
Dirax> acl
Acl nH     a     b      c  alpha   beta gamma Volume S Indexstatus
 12 13 8.196 5.057 12.010  89.91 101.15 90.05    488   HHnnHnHHnHnHnHnHHHnHnnnHn
 11 13 8.199 5.061 11.995  89.97 101.24 90.03    488   HHnnnnHHnHnHnHnHHHnHnnHHn
  8  3 2.179 4.666  8.002  95.93  92.59 93.56     81 ? HnnnHnHnnnnnnnnnnnnnnnnnn
  7  7 5.064 8.205 11.872  85.52  79.15 89.86    483   HnnnnHnnnHHnHHnnnnnnnnnHn
  6  3 2.184 2.634  3.460  67.97  81.18 71.87     18 ? nnHnHnnnnnnnnnnHnnnnnnnnn
  5  3 1.998 2.126  2.187 117.76 107.92 95.34      8 ? nnnnHnnnnnnnnnnHnnnnHnnnn
Solutions limited by voltest

 12 13 8.196 5.057 12.010  89.91 101.15 90.05    488   HHnnHnHHnHnHnHnHHHnHnnnHn

acl waits for an answer. Use auto to accept the proposed solution.
acl/auto [12] auto
selected ACL 12
ACL 12                                          Niggli values
a, b, c :   8.1957   5.0567  12.0097          67.1701    25.5704   144.2319
al,be,ga:   89.909  101.152   90.051           0.0965   -19.0368    -0.0368
  volume: 488.3245
Nrefls=25 Nfit=13 NNonfit=12

Still not a good result.
Now search for a solution with the non-fitting reflections: Use lch to manipulate the fitting/nonfitting status of the reflections.
Dirax> lch invert
Nfit:12       123456789 123456789 12345
Nonfit:13     nnHHnHnnHnHnHnHnnnHnHHHnH

And try again with the previous noinfitting reflections
Dirax> go
12 H_reflections selected out of 25
286 triplets
286 final triplets
286 triplet vectors
Squishd: 286 t vectors ==> 50 t vectors
Sorting 50 t vectors...
Reducing 50 t vectors ==> 50 t vectors
Acl nH     a      b      c alpha  beta gamma Volume S Indexstatus
  7  7 8.191 16.128 46.010 88.17 85.56 75.56   5868   nnHHHHnnHnnnnnHnnnnnHnnnn
  6  5 8.216 14.896 33.064 83.66 88.14 81.85   3981   nnHnnnnnnnnnHHnnnnnnnHHnn
  5  4 5.323  8.222 15.765 99.38 91.66 91.80    680 ? nnHnnHnnHnHnnnnnnnnnnnnnn
Solutions limited by voltest

  7  7 8.191 16.128 46.010 88.17 85.56 75.56   5868   nnHHHHnnHnnnnnHnnnnnHnnnn
selected ACL 7

The alien reflections do not form their own lattice.
We give up.

Example 2

Area detector data for a small protein


Dirax> example 2
resetting indexfit 2.0
ex02 - Area detector data for a small protein, note narrow phiB region.
Set Dmax to 160. The crystal is known to be tetragonal, so there IS
something wrong with the data(conversion)!

  dmax              ! display current dmax
  160               ! dmax set larger than usual
  go
  lo                ! list H and n refls

You might try the default dmax = 80 and see what happens.

26 reflections from file ../ex02.drx.

This is a small protein. So we are expecting larger cell dimensions. First increase dmax
Dirax> dmax
dmax[80.0] 160
Dirax> go
2700 triplets
2701 final triplets
2701 triplet vectors
Squishd: 2701 t vectors ==> 2130 t vectors
Sorting 2130 t vectors...
Reducing 2130 t vectors ==> 2059 t vectors
Acl nH      a      b      c alpha  beta  gamma Volume S Indexstatus
 26 23 38.258 76.762 79.773 89.60 87.90  87.72 233927   HHHHHHHHnHHnHHHHHHHHHnHHHH
 14 12 38.344 60.167 65.920 74.64 88.61  85.42 146180 Q HnnHnHnnnHnnHnHnHHnHHnHnnH
 13  4 19.456 24.502 32.822 93.63 96.58 106.10  14860 ? HnHnnnnnnnnnHnnnnnnnHnnnnn
 12 13 38.203 70.554 76.699 81.18 87.59  82.14 202321   nHHHHnnHnnnnHnnHHnnnHnHHHH
 11 10 38.220 58.440 60.888 89.10 73.24  71.88 123348 ? nHnnnnnnnnnnHHHHnHnnHnHnHH
 10  4 36.430 38.403 67.439 80.17 76.25  76.18  88338 ? nnnHnnnHnHnnnnnHnnnnnnnnnn
  8  3  9.195  9.455  9.895 65.80 87.95  80.25    773 ? nnnHnHnnnnnnnnnnnnnnnHnnnn
  7  3 12.901 14.629 17.831 88.78 84.05  71.95   3182 ? nnnnnnnnnnnnnnHnnnnHnnnnnH
  5  3  7.266  7.673 13.480 89.22 86.13  68.46    697 ? nnHnnnnnnnnnnnnnnHnnnnHnnn
Solutions limited by voltest

 26 23 38.258 76.762 79.773 89.60 87.90  87.72 233927   HHHHHHHHnHHnHHHHHHHHHnHHHH
selected ACL 26

The proposed solution looks promissing. We expect a tetragonal lattice, so b and c should be equal and the angles should all be 90°
There is something wrong with the data or with the conversion from area detector impacts to c-vectors.
Dirax> lo
   nr      H       K       L  1/err   Netint    dth    dom    dch
H   1:  0.018  -3.920  -6.898   592 149320.0 -0.071  0.078 -0.296
H   2: -3.007 -15.016 -10.999  3572   3248.0  0.009 -0.001  0.043
H   3: -4.005 -23.990 -13.973  2551  15750.0 -0.011 -0.001  0.048
H   4: -0.992  -5.952  -6.925   883 186641.0 -0.050  0.044  0.069
H   5: -6.001 -14.976   0.016  2691 109012.0 -0.010 -0.028  0.065
H   6: -4.993 -22.034 -10.074   955   2150.0  0.029 -0.007 -0.142
H   7: -4.007 -26.938 -14.907   696   6786.0 -0.055  0.003  0.117
H   8: -7.001 -26.025  -5.047  1493   1945.0  0.017 -0.019 -0.081
Nn  9: -8.996 -26.868   6.145   401   7987.0
H  10: -6.004 -29.055  -9.979  1289   5220.0  0.028  0.051  0.044
H  11: -4.985 -24.000 -11.057  1207   1431.0  0.006 -0.004 -0.130
Nn 12: -0.973 -25.803 -20.824   293   5325.0
H  13: -6.010 -13.005   3.055  1337 242389.0  0.016  0.033  0.160
H  14: -4.002 -15.028  -8.040  1602  64597.0  0.023 -0.009 -0.082
H  15: -3.000  -5.005   2.042  1886  43748.0  0.008  0.137  0.237
H  16: -4.002  -7.017   3.029  2301  62740.0  0.013  0.098  0.085
H  17: -4.002  -8.031   0.994  2428  13368.0  0.014  0.072 -0.079
H  18: -7.002 -22.972  -3.025  2074   2283.0 -0.011 -0.061 -0.032
H  19: -5.987  -9.964  11.019  1619 227825.0 -0.014  0.041  0.116
H  20: -5.001 -13.007  -2.015  4751  29292.0  0.005 -0.010 -0.049
H  21: -6.000 -19.999  -5.052  1538  19254.0  0.005 -0.055 -0.107
Nn 22: -1.992 -25.846 -18.846   361   6561.0
H  23: -8.004 -27.971  -0.975  1986   1847.0 -0.013 -0.016  0.057
H  24: -7.994 -30.033  -2.022  1857   4676.0  0.015  0.023 -0.051
H  25: -2.998 -13.009  -9.020  3586  28443.0  0.009  0.001 -0.050
H  26: -6.999 -15.959   5.043  1332  30408.0 -0.012 -0.003  0.143
1/error for H: from 592 to 4751. n: from 293 to 401.

Examine reflection 4: 1/err > 500, so this reflection fits the lattice, although L is not a perfect integer at first sight.

Example 3

incommensurate crystal


Dirax> example 3
resetting dmax 80.0
ex03 - Data from an incommensurate crystal from dr. J.L. de Boer,
Groningen. As usual these are very accurate data (from SET4 procedure on
CAD4). We know that problems might be ahead so we set LevelFit to 1/3000
(more severe criterion) to discriminate interfering reflections.
Note that super solutions are found with (almost) all reflections fitting.
We know however (aha!) that the correct volume is about 100 so we select
the appropriate ACL. In the hkl list you see that not fitting reflections
are at discrete distances from main lattice points.

  go                ! run with defaults
  acl 25            ! first accept solution with most fitting reflections
  acl auto          ! now select 'best' solution (*)
  lon               ! list satellite refl's
  qvtest            ! search qvector
  sethklm           ! add qvector
  lo                ! list reflections (x)
(*) Note that for this solution alpha = gamma = 90 and a = c,
    so it is worth trying it. (Moreover the cell volume was expected
    to be about 100, aha!)
(x) Note the extremely small errors (1/err): SET4 data from
    dr Jan L. de Boer, Groningen, NL.
25 reflections from file ../ex03.drx.

Dirax> go
2496 triplets
2497 final triplets
2479 triplet vectors
Squishd: 2479 t vectors ==> 1844 t vectors
Sorting 1844 t vectors...
Reducing 1844 t vectors ==> 881 t vectors
Acl nH     a      b      c alpha   beta gamma Volume S Indexstatus
 25 25 4.413 20.713 25.766 90.76  94.87 96.11   2333 ? HHHHHHHHHHHHHHHHHHHHHHHHH
 24 24 4.413 18.116 20.714 99.18  96.12 96.92   1609 ? HHHHHHHHHHHHHHnHHHHHHHHHH
 21 25 4.413 18.109 20.713 99.22  96.11 96.86   1609 ? HHHHHHHHHHHHHHHHHHHHHHHHH
 16 16 4.219  5.069  4.219 89.95 116.94 90.01     80 Q nHHHHHHHnnHHHHnHnHnHnnHHn
 11 11 3.827  4.414  5.440 68.71  82.90 70.02     80 ? HnHnHHHHnnnHHnnnnnnHHHnnn
  9  9 2.350  3.760  5.177 89.89  78.25 89.36     45 ? nHnHHnnHnHnHnnnHnHnnnnHnn
Solutions limited by voltest

 16 16 4.219  5.069  4.219 89.95 116.94 90.01     80 Q nHHHHHHHnnHHHHnHnHnHnnHHn
selected ACL 16

Dirax> acl 25
selected ACL 25
ACL 25                                          Niggli values
a, b, c :   4.4129  20.7133  25.7664          19.4736   429.0388   663.9090
al,be,ga:   90.756   94.866   96.115          -7.0424    -9.6442    -9.7368
  volume: 2332.763
Nrefls=25 Nfit=25 NNonfit=0
WARNING ALL |H| indices zero or one

Aha, a warning. All h indices zero or one.
Now let's inspect the proposed solution: the only one without a question mark.
Dirax> acl auto
selected ACL 16
ACL 16                                          Niggli values
a, b, c :   4.2187   5.0686   4.2195          17.7978    25.6911    17.8038
al,be,ga:   89.951  116.941   90.012           0.0181    -8.0650    -0.0043
  volume: 80.43401
Nrefls=25 Nfit=16 NNonfit=9

Dirax> lon
   nr      H     K      L  1/err Netint dth dom dch
Nn  1: -0.203 1.447  1.203    10  453.0
Nn  9: -1.205 1.447  0.205    10  190.0
Nn 10:  0.795 2.447 -1.796    10  222.0
Nn 15:  0.408 3.104  0.593     9   84.0
Nn 17:  0.204 2.553  0.796    10  502.0
Nn 19: -1.204 2.446  0.204    10  294.0
Nn 21:  1.796 2.448 -0.797    10  312.0
Nn 22: -0.204 2.450  1.205     9  342.0
Nn 25:  0.204 1.552  0.796    10  373.0
1/error for H: from 1451 to 19195. n: from 9 to 10.

Dirax> qvtest
9 nonfitting reflections Searching qvectors of maximum order 1
 qv nhit qvector                     fom
  1    8 -0.2040  0.4475  0.2040  0.8889
selected qvector 1
qvector -0.20403 0.44748 0.20405 qvfom=0.89 8 extra reflections.
(Use qvector to change the qvector)

The program proposes to add one qvector (-0.2, 0.45, 0.2). With this vector 8 more reflections are added to the fitting list. Let's accept this solution:
Dirax> sethklm
qvector= -0.2 0.45 0.2 maximum order=1
Refl  fh      fk      fl       H       K       L    order
   1 -0.2032  1.4472  1.2027  0.0008  0.9997  0.9987    1
   9 -1.2045  1.4472  0.2047 -1.0005  0.9997  0.0006    1
  10  0.7955  2.4470 -1.7958  0.9995  1.9995 -1.9999    1
  17  0.2039  2.5534  0.7959 -0.0001  3.0009  0.9999   -1
  19 -1.2039  2.4460  0.2042 -0.9999  1.9985  0.0002    1
  21  1.7956  2.4483 -0.7966  1.9996  2.0008 -1.0007    1
  22 -0.2038  2.4496  1.2048  0.0002  2.0021  1.0008    1
  25  0.2039  1.5520  0.7957 -0.0001  1.9994  0.9997   -1
8 extra fitting reflections added

The first set of columns marked fh,fk and fl contain the same information as before. But now a column order is added. 1 means: add the qvector to the lattice point. -1 means subtract the qvector from the lattice point. The observed reflections are the result of this +/-qvector, so if we reverse the operation the lattice points will show. This is reflected in the columns marked H,K and L.
Dirax> lo
   nr      H     K      L   M 1/err  Netint    dth    dom    dch
H   1:  0.001 1.000  0.999  1  3218   453.0 -0.006  0.021  0.005
H   2:  0.999 1.000  0.000  0  4176 -1640.0 -0.003 -0.030  0.007
H   3: -1.000 0.999  1.000  0  5388 23326.0 -0.003 -0.020 -0.003
H   4:  0.999 1.999  0.000  0  4133  5737.0 -0.005 -0.004 -0.004
H   5: -0.000 1.999  0.000  0  4704   367.0 -0.004 -0.008  0.001
H   6:  1.000 2.000 -1.000  0  6079 21154.0 -0.000 -0.014 -0.014
H   7:  0.999 0.999 -0.999  0  2815  1097.0 -0.007  0.017 -0.003
H   8: -0.000 2.998  0.000  0  2950 13612.0 -0.007 -0.008  0.001
H   9: -1.001 1.000  0.001  1  8569   190.0  0.001 -0.004 -0.012
H  10:  0.999 1.999 -2.000  1 13178   222.0 -0.000  0.004  0.005
H  11:  1.001 2.000 -2.000  0  4941   164.0  0.001 -0.003 -0.018
H  12:  0.001 3.003 -0.001  0  1421 12328.0  0.013  0.029  0.001
H  13: -1.000 3.001  1.000  0  4541   277.0  0.003  0.013  0.004
H  14:  0.000 3.000  1.000  0 18445  8874.0 -0.000  0.000 -0.005
Nn 15:  0.408 3.104  0.593  0     9    84.0
H  16:  1.000 2.999 -0.000  0  4218   116.0 -0.004  0.006 -0.011
H  17: -0.000 3.001  1.000 -1  8361   502.0  0.002 -0.002  0.007
H  18: -1.001 2.000  0.000  0  3129 18910.0  0.005 -0.020  0.007
H  19: -1.000 1.998  0.000  1  4411   294.0 -0.005 -0.006  0.002
H  20: -2.000 1.999  2.001  0  5125  3649.0 -0.001 -0.010 -0.013
H  21:  2.000 2.001 -1.001  1  5009   312.0  0.001  0.003  0.017
H  22:  0.000 2.002  1.001  1  2332   342.0  0.009  0.005 -0.004
H  23:  1.001 2.001 -0.000  0  3940  5947.0  0.005  0.006 -0.004
H  24: -0.000 2.000  1.000  0  7767 21696.0 -0.001 -0.012 -0.006
H  25: -0.000 1.999  1.000 -1  5169   373.0 -0.004 -0.008 -0.006
1/error for H: from 1421 to 18445. n: 9.

The values in 1/err are excellent. Only one reflection (nr 15) does not fit this solution.

Example 4

One axis much longer than the others


Dirax> example 4
ex04 - One axis much longer than the others (more than 80 A), a classic
indexing problem. Set Dmax to 120 (200 will work too, not critical if
large enough).

  dmax 120            ! increase dmax
  go                  ! for the rest use defaults
  lo                  ! inspect list

25 reflections from file ../ex04.drx.

Dirax> dmax 120
Dirax> go
2496 triplets
2497 final triplets
2493 triplet vectors
Squishd: 2493 t vectors ==> 1244 t vectors
Sorting 1244 t vectors...
Reducing 1244 t vectors ==> 1018 t vectors
Acl nH      a      b      c  alpha  beta gamma Volume S Indexstatus
 24 24 11.147 22.553 98.327  90.02 90.03 90.06  24720   HHHHHHHnHHHHHHHHHHHHHHHHH
 18 19  5.564 22.574 98.324  90.04 89.92 89.96  12350 ? HHHHHHHnHnnnnHHHHnHHHHHHH
 15 13  5.567 22.579 50.548 102.89 93.13 90.05   6183 ? HnnHnHHnHnnnnnHnHnHHHnHHH
 13 14  5.565 22.587 49.211  90.04 93.11 89.90   6177 ? nHHnHHnnHnnnnHHHHnHnHHHnH
  9  8  5.564 18.069 22.285  67.11 87.58 87.03   2061 ? nHnnHHnnnnnnnnnnHnHnnHHnH
  7  4 11.149 20.255 31.607  91.97 99.13 99.12   6945 ? nnHnnnnnnnHnnnnnnnnHnnnHn
Solutions limited by voltest

 24 24 11.147 22.553 98.327  90.02 90.03 90.06  24720   HHHHHHHnHHHHHHHHHHHHHHHHH
selected ACL 24

Dirax> lo
   nr      H      K       L  1/err Netint    dth    dom    dch
H   1:  0.004 -3.010 -21.058  1225    0.0  0.033 -0.001  0.078
H   2: -0.001 -2.996 -23.996  4845    0.0 -0.005  0.023 -0.026
H   3:  0.001 -3.026 -22.141   543    0.0  0.082 -0.053  0.021
H   4: -0.001 -2.993 -22.981  2667    0.0 -0.014  0.030 -0.031
H   5:  0.003 -4.994 -15.994  2413    0.0 -0.011  0.034  0.059
H   6:  0.000 -3.990 -25.954  1557    0.0 -0.029  0.019  0.004
H   7: -0.003 -0.998 -28.975  2570    0.0 -0.012  0.000 -0.055
Nn  8:  0.009 -0.878 -31.034   183    0.0
H   9: -0.003  0.002 -21.969  2425    0.0 -0.014  0.008 -0.067
H  10:  1.000 -3.996  17.984  4054    0.0 -0.010 -0.004  0.020
H  11:  0.999 -4.000  16.991  9058    0.0 -0.004  0.011 -0.005
H  12:  1.001 -4.999  10.997  9187    0.0 -0.000  0.003  0.023
H  13:  0.995 -5.011  10.025  1373    0.0  0.016 -0.009 -0.139
H  14:  2.001  1.001 -18.976  3637    0.0 -0.004  0.031  0.047
H  15:  2.000  0.004 -20.991  4651    0.0 -0.004  0.040 -0.002
H  16:  2.000  1.001 -22.965  2760    0.0 -0.013  0.024  0.034
H  17:  1.998  0.003 -22.982  3244    0.0 -0.012  0.028 -0.014
H  18:  1.002 -2.998  27.003  5771    0.0  0.001 -0.020  0.023
H  19: -2.003 -2.000  19.000  4304    0.0  0.007  0.007 -0.035
H  20: -2.002 -3.002  16.011  4804    0.0  0.009 -0.003 -0.008
H  21: -2.001 -3.994  11.046  1847    0.0  0.003 -0.111 -0.007
H  22: -2.000 -3.001  17.013  7049    0.0  0.003 -0.015  0.020
H  23: -2.001 -4.001   9.009  6856    0.0  0.006 -0.013 -0.004
H  24: -1.997 -5.000   0.011  3841    0.0 -0.007 -0.019  0.036
H  25: -2.000 -3.995  14.995  4351    0.0 -0.008 -0.021 -0.019
1/error for H: from 543 to 9187. n: 183.


Example 5

twinned crystal


Dirax> example 5
resetting dmax 80.0
ex05 - Data from a twinned crystal. Default parameters. A super solution
is found for all reflections, which is common with real twins.
Note: It it not possible to give general rules for this sort of problems.
The super cell COULD be correct (and IS geometrically!) but you have to
consider crystallographical aspects. Here we select ACL 18 because this
looks promising.  Write results to file ex05.out1.
Continue with 'n' (not fitting) reflections only. Now the other lattice
is found. Write to file ex05.out2 and compare with .out1 later.
Normally with so few 'n' reflections a sub-lattice is found rather then a
congruent lattice. Then you have to search further selectively.

  go                 ! run with defaults
  acl 18             ! overrule super lattice solution ACL 25
  go                 ! go again with H-refl's only, for 1st lattice
  cell               ! cell etc. for 1st lattice
  store a            ! save this solution
  write ex05.out1    ! write file for print-out
  lch
  invert             ! H -> n and n -> H
  go                 ! again with N-refls only, for other lattice
  loh                ! list H refls for 2nd lattice
  cell               ! cell etc. for 2nd lattice
  store b            ! save this solution
  write ex05.out2    ! write file for print-out
  compare a b        ! compare the two solutions
  .                  ! accept proposed solution
  end

The super lattice is geometrically correct, but we know better.
The lattices with V=833.7 can be transformed to monoclinic C.
NOTE: as usually some reflections fit into both twin lattices.

25 reflections from file ../ex05.drx.

Dirax> go
2496 triplets
2497 final triplets
2463 triplet vectors
Squishd: 2463 t vectors ==> 1751 t vectors
Sorting 1751 t vectors...
Reducing 1751 t vectors ==> 984 t vectors
Acl nH     a      b      c  alpha   beta  gamma Volume S Indexstatus
 25 25 9.642 15.090 75.029  95.77  93.65  89.98  10839   HHHHHHHHHHHHHHHHHHHHHHHHH
 21 21 9.642 15.090 68.772  90.00  91.97  89.97  10000 Q HHHHHHHHnHnHHHHHHnnHHHHHH
 20 20 9.642 15.090 45.886  90.00  91.96  89.98   6672 Q HnHHHHnnHHHHHHHHHnnHHHHHH
 18 18 9.641  9.824  9.827 100.33 105.39 105.35    834   HnHHHHnnnHnHHHHHHnnHHHHHH
  7  5 2.345  2.962  7.634  89.12  81.20  84.20     52 ? nnnnHnnnnnnnnnHHnnnnnHnHn
Solutions limited by voltest

 25 25 9.642 15.090 75.029  95.77  93.65  89.98  10839   HHHHHHHHHHHHHHHHHHHHHHHHH
selected ACL 25

We are ignoring the supercell. Select the solution with a small volume, and still 18 'fitting' reflections.
Dirax> acl 18
selected ACL 18
ACL 18                                          Niggli values
a, b, c :   9.6414   9.8240   9.8275          92.9573    96.5113    96.5792
al,be,ga:  100.326  105.385  105.349         -17.3060   -25.1381   -25.0722
  volume: 833.7263
Nrefls=25 Nfit=18 NNonfit=7

One more run, but now starting with the 18 'H' reflections.
Dirax> go
18 H_reflections selected out of 25
969 triplets
969 final triplets
948 triplet vectors
Squishd: 948 t vectors ==> 858 t vectors
Sorting 858 t vectors...
Reducing 858 t vectors ==> 401 t vectors
Acl nH     a     b     c  alpha   beta  gamma Volume S Indexstatus
 18 18 9.641 9.824 9.827 100.33 105.39 105.35    834   HnHHHHnnnHnHHHHHHnnHHHHHH
Solutions limited by voltest

 18 18 9.641 9.824 9.827 100.33 105.39 105.35    834   HnHHHHnnnHnHHHHHHnnHHHHHH
selected ACL 18

Dirax> cell
cell for ex05                                   Niggli values
a, b, c :   9.6414   9.8240   9.8275          92.9573    96.5113    96.5792
al,be,ga:  100.326  105.385  105.349         -17.3060   -25.1381   -25.0722
  volume: 833.7263
Nrefls=25 Nfit=18 NNonfit=7
Nfit:18       123456789 123456789 12345
Nonfit:7      HnHHHHnnnHnHHHHHHnnHHHHHH
                R                                        D
   0.0563984   0.0278408   0.1075332        1.8414379   3.7727258   8.6794577
   0.0112999  -0.0992265  -0.0093282       -0.5880539  -9.6983547   1.4516902
   0.0983373   0.0372244  -0.0187596        8.4859133   0.5322431  -4.9280000
Determinant:  0.1199434E-02                             833.7263

save this solution for later use.
Dirax> store a
Now look for another solution with the nonfits only.
Set H to N and N to H
Dirax> lch
Nfit:18       123456789 123456789 12345
Nonfit:7      HnHHHHnnnHnHHHHHHnnHHHHHH

invert/status invert
Nfit:7        123456789 123456789 12345
Nonfit:18     nHnnnnHHHnHnnnnnnHHnnnnnn

And try with the previously nonfitting reflections
Dirax> go
7 H_reflections selected out of 25
48 triplets
49 final triplets
49 triplet vectors
Squishd: 49 t vectors ==> 25 t vectors
Sorting 25 t vectors...
Reducing 25 t vectors ==> 23 t vectors
Acl nH     a     b     c  alpha   beta  gamma Volume S Indexstatus
  7 10 9.643 9.821 9.826 100.35 105.36 105.34    834 Q nHnnnnHHHnHnnnnnnHHnnHHHn
Solutions limited by voltest

  7 10 9.643 9.821 9.826 100.35 105.36 105.34    834 Q nHnnnnHHHnHnnnnnnHHnnHHHn
selected ACL 7

Another solution, with same volume as the previous one. Interesting.
a further inspection of the reflection indices and errors
Dirax> loh
  nr      H      K      L  1/err Netint    dth    dom    dch
H  2: -2.001  1.999  1.999  4375 4588.8 -0.005  0.010  0.033
H  7: -2.000  1.000  3.000 16437  626.4  0.001  0.003 -0.009
H  8: -4.000  3.000 -0.000 88324 1099.0 -0.000 -0.001 -0.001
H  9: -2.999  0.999 -1.000  7130 1513.3 -0.006  0.005  0.002
H 11: -3.000  0.001 -1.001 11779 2270.6  0.002 -0.009 -0.005
H 18: -1.001 -3.001  1.000  9842 1292.2  0.004 -0.004  0.003
H 19: -1.001 -1.997  4.001  2976 2679.0 -0.001  0.043  0.012
H 22:  0.001 -3.002  2.999  3926 9553.0  0.005 -0.031 -0.013
H 23:  0.001 -1.001  3.000  6065 3950.3  0.001 -0.021 -0.020
H 24:  0.000 -2.000  2.000 18951 9643.8 -0.002  0.005 -0.003
1/error for H: from 2976 to 88324. n: from 12 to 73.

More details on the cell parameters:
Dirax> cell
cell for ex05                                   Niggli values
a, b, c :   9.6433   9.8214   9.8260          92.9941    96.4592    96.5506
al,be,ga:  100.352  105.358  105.339         -17.3420   -25.0964   -25.0544
  volume: 833.6285
Nrefls=25 Nfit=10 NNonfit=15
Nfit:10       123456789 123456789 12345
Nonfit:15     nHnnnnHHHnHnnnnnnHHnnHHHn
                R                                        D
   0.0167104   0.1075829   0.0279482       -1.8428528  -3.7753263  -8.6801424
  -0.0698617  -0.0092616  -0.0991917        9.4740200   2.5771527  -0.2458956
  -0.0883677  -0.0188123   0.0372087        0.4133405  -7.6631231   6.1364737
Determinant:  0.1199575E-02                             833.6285

save this solution also.
Dirax> store b
Now compare both solutions
Dirax> compare a b
Correlation=-0.76
            a       b       c      alpha    beta   gamma    volume
Save A :   9.641   9.824   9.827  100.33  105.39  105.35      833.7
HnHHHHnnnHnHHHHHHnnHHHHHH
Save B :   9.643   9.821   9.826  100.35  105.36  105.34      833.6
nHnnnnHHHnHnnnnnnHHnnHHHn
Volume ratio = 1.0 Trying 216 solutions
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.954 -0.1913 -0.3914 -0.9001 -11.00  2.97  2.97 (  0.27)  -1.00  0.00 -0.00 (  0.02)   0.150
 2  179.991  0.7760 -0.6218  0.1055  -0.00  1.00  1.00 (  0.03)   7.02 12.99 13.00 (  0.07)   0.130 U
Selected Solution 2
            a       b       c      alpha    beta   gamma    volume
Save A :   9.641   9.824   9.827  100.33  105.39  105.35      833.7 <
Save B :   9.643   9.821   9.826  100.35  105.36  105.34      833.6 <
H'= -1.000*H +0.000*K -0.000*L
K'= +0.539*H -0.001*K +0.999*L
L'= +0.540*H +1.000*K +0.001*L
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 2  179.991  0.7760 -0.6218  0.1055  -0.00  1.00  1.00 (  0.03)   7.02 12.99 13.00 (  0.07)   0.130 U<
abaaaabbbabaaaaaabbaa***a
a=15 b=7 0=0 *=3

As mentioned before, two axes (b and c) are almost equal, and also two angles (beta and gamma). Later, these solutions can be converted to a C-centered lattice with cell parameters a=12.5888 b=15.0898 c=9.6414 alpha=90 beta=114.436 gamma=90 and a volume of 1667.45ų

Example 6

Inaccurate data


Dirax> example 6 go
removing A B
ex06 - Inaccurate data. Start with default run and note that all solutions
imply only a few fitting reflections. Raise IndexFit to 9 (for
example). Now the best solution fits more or less 24 reflections.

  loh                ! only a few fitting reflections
  lon                ! note that many refl's could be made fitting...
  indexfit 9         ! ...with less severe IndexFit
  acl                ! calculate solutions with new IndexFit
  auto               ! select default solution
  lo                 ! note errors: about 10 times as large as normal

Reflection nr 10 is a real outsider.

25 reflections from file ../ex06.drx.
2496 triplets
2497 final triplets
2497 triplet vectors
Squishd: 2497 t vectors ==> 983 t vectors
Sorting 983 t vectors...
Reducing 983 t vectors ==> 849 t vectors
Acl nH     a     b      c  alpha  beta  gamma Volume S Indexstatus
 15  4 4.007 5.955  8.636 102.22 91.32  91.46    201 ? nnnnnnHnnnnnHnnnHnnnnHnnn
 12  6 3.902 6.041 16.980  82.19 87.74  85.61    395 ? nnnHHHHnHnnnnHnnnnnnnnnnn
 11  4 2.454 3.173 16.870  92.86 91.14  94.30    131 ? nnHnnnnnnnnnnHHHnnnnnnnnn
 10  4 3.893 6.043 17.067  82.15 88.38  85.61    397 ? nnnnnnnnnnnnnHnnHHnnnnnHn
  8  3 1.981 2.796  6.062  96.57 92.46 110.69     31 ? nnnnnnHHnnnnnnnnnnnnnHnnn
  5  3 1.641 3.798  4.572  74.68 82.03  85.96     27 ? nnnnnnHnnnnnHnnnnnHnnnnnn
Solutions limited by voltest

 12  6 3.902 6.041 16.980  82.19 87.74  85.61    395 ? nnnHHHHnHnnnnHnnnnnnnnnnn
selected ACL 12
WARNING: only one K+L is not even. Nr:5
WARNING: only one L+H is not even. Nr:6

Examine fitting reflections
Dirax> loh
  nr      H      K      L  1/err Netint    dth    dom    dch
H  4: -0.001  2.001  5.995  2292 1015.7 -0.001 -0.046 -0.029
H  5: -0.000  2.999  3.998  7628 5119.2 -0.002 -0.006 -0.003
H  6: -0.000  1.000  8.999  9148 1258.5 -0.002  0.005 -0.002
H  7:  1.001  1.000  5.008  1811 1418.6  0.010  0.038 -0.008
H  9:  2.000 -1.998 -2.003  2933 4119.0 -0.003  0.026  0.011
H 14:  0.999 -1.003 -1.001  1939 2789.5  0.002 -0.022 -0.089
1/error for H: from 1811 to 9148. n: from 32 to 448.
WARNING: only one K+L is not even. Nr:5
WARNING: only one L+H is not even. Nr:6

Examine nonfitting reflections
Dirax> lon
   nr      H      K      L  1/err  Netint dth dom dch
Nn  1:  2.017 -0.008 10.012   217   211.3
Nn  2:  2.030  1.996  9.061   116   591.9
Nn  3:  1.009 -1.011 12.972   292   300.5
Nn  8:  0.992  0.003  5.004   448  2161.2
Nn 10:  1.904 -0.053 -6.331    32   247.9
Nn 11:  0.980 -2.000  1.993   191  1510.9
Nn 12: -0.045 -2.005 -6.016    86  1080.8
Nn 13: -0.033 -1.012 -2.999   116 20068.3
Nn 15: -0.024 -3.001  4.958   151   727.0
Nn 16: -0.047 -3.001 -4.030    83  3348.8
Nn 17:  1.992  1.003 -6.919   191   823.1
Nn 18:  1.011  3.999 -0.902   157  1547.0
Nn 19:  2.016  2.998 -1.892   131  1370.0
Nn 20:  1.027  5.001  4.141    94   180.5
Nn 21:  1.011  4.013 -4.023   259   705.3
Nn 22:  0.975  0.002 -7.955   141  1037.6
Nn 23:  0.987  2.009 -5.049   205  1463.7
Nn 24:  1.001  4.019 -6.862   119   608.7
Nn 25: -0.045 -1.006 -6.022    87  4830.3
1/error for H: from 1811 to 9148. n: from 32 to 448.

Try to fit more
Dirax> indexfit 9
Dirax> acl
Acl nH     a     b      c  alpha  beta gamma Volume S Indexstatus
 15 24 3.906 6.034 16.993  82.41 88.47 86.12    396   HHHHHHHHHnHHHHHHHHHHHHHHH
  7 10 3.901 6.027 11.037 102.12 92.15 93.81    253 Q HnHnHnnHHnnnHHnHnnnnnnnHH
  5 11 3.889 4.610  4.955  78.24 69.57 73.50     79 Q nnnHHnHnHnnHHHnHnHHnnHnnn
Solutions limited by voltest

 15 24 3.906 6.034 16.993  82.41 88.47 86.12    396   HHHHHHHHHnHHHHHHHHHHHHHHH

acl/auto [15] auto
selected ACL 15
ACL 15                                          Niggli values
a, b, c :   3.9060   6.0340  16.9930          15.2570    36.4086   288.7615
al,be,ga:   82.406   88.471   86.115          13.5509     1.7707     1.5967
  volume: 396.0141
Nrefls=25 Nfit=24 NNonfit=1

Dirax> lo
   nr      H      K      L  1/err  Netint    dth    dom    dch
H   1:  2.003 -0.002  9.992   911   211.3  0.006  0.044  0.065
H   2:  2.008  1.998  9.012   434   591.9  0.037  0.062  0.094
H   3:  0.994 -1.004 12.988   593   300.5 -0.020  0.033 -0.090
H   4: -0.022  2.001  5.978   176  1015.7 -0.008 -0.178 -0.690
H   5: -0.023  2.997  3.964   164  5119.2 -0.014 -0.181 -0.634
H   6: -0.020  1.002  8.999   189  1258.5  0.005 -0.117 -0.551
H   7:  0.989  1.001  4.985   343  1418.6 -0.045 -0.129 -0.239
H   8:  0.985  0.006  4.994   249  2161.2 -0.059 -0.237 -0.345
H   9:  2.017 -1.996 -2.015   217  4119.0  0.073  0.114  0.241
Nn 10:  1.918 -0.055 -6.374    33   247.9
H  11:  0.989 -1.996  2.005   327  1510.9 -0.044 -0.103 -0.252
H  12: -0.025 -2.005 -5.998   157  1080.8  0.002 -0.048 -0.800
H  13: -0.023 -1.012 -2.990   163 20068.3  0.011 -0.415 -1.480
H  14:  1.008 -1.002 -1.007   477  2789.5  0.039  0.067  0.141
H  15: -0.017 -2.995  5.006   224   727.0 -0.015 -0.131 -0.389
H  16: -0.024 -2.999 -3.995   160  3348.8 -0.014 -0.032 -0.676
H  17:  2.002  0.999 -6.978   692   823.1 -0.009 -0.005  0.114
H  18:  0.993  3.993 -0.975   378  1547.0 -0.040  0.122 -0.085
H  19:  2.007  2.994 -1.971   344  1370.0  0.002  0.067  0.222
H  20:  0.995  4.996  4.062   249   180.5 -0.008  0.259 -0.063
H  21:  0.998  4.006 -4.101   161   705.3  0.072 -0.353 -0.160
H  22:  0.990 -0.001 -7.985   363  1037.6 -0.043  0.015 -0.192
H  23:  0.986  2.004 -5.101   143  1463.7  0.058 -0.284 -0.629
H  24:  0.994  4.011 -6.944   252   608.7 -0.019  0.248 -0.067
H  25: -0.029 -1.008 -6.017   132  4830.3  0.021  0.011 -1.147
1/error for H: from 132 to 911. n: 33.

Note the errors: about 10 times larger than normal

Example 7

Not very accurate data and rather big(?) cell


Dirax> example 7 go
resetting indexfit 2.0
ex07 - Not very accurate data and rather big(?) cell. A run with default
Levelfit 1000 gives a solution with not-fitting reflections which might
be halves.
Raising IndexFit does not help. Try a complete new run with LevelFit 300,
now an all-fitting solution is found. Which solution is to be preferred
crystallographically cannot be decided from this data alone.

  indexfit 4         ! try higher IndexFit
  acl                ! display all solutions
  auto               ! and select 'best' one
  indexfit 2         ! restore default
  levelfit 300
  example 7          ! read data again
  go
  lo                 ! show results

25 reflections from file ../ex07.drx.
2496 triplets
2497 final triplets
2497 triplet vectors
Squishd: 2497 t vectors ==> 687 t vectors
Sorting 687 t vectors...
Reducing 687 t vectors ==> 611 t vectors
Acl nH      a      b      c alpha   beta gamma Volume S Indexstatus
 18 22 20.367  9.589 22.885 90.00 106.34 90.07   4289   HHHHHHHnHHHHHHnHHHHHHHHnH
  9  5  9.588 13.273 22.924 94.36  89.93 91.12   2908   nHnnHnHnnnnnnnnnnnnnnHnnH
  6  3  1.522  1.533  1.834 73.15  81.30 75.57      4 ? nnnHnnnnnnnnnnnnHnnnnnHnn
Solutions limited by voltest

 18 22 20.367  9.589 22.885 90.00 106.34 90.07   4289   HHHHHHHnHHHHHHnHHHHHHHHnH
selected ACL 18

Only 22 fitting reflections. Try to increase indexfit
Dirax> indexfit 4
Dirax> acl
Acl nH      a      b      c alpha   beta gamma Volume S Indexstatus
 18 22 20.367  9.589 22.885 90.00 106.34 90.07   4289   HHHHHHHnHHHHHHnHHHHHHHHnH
  9 10  9.590 13.346 22.895 94.36  89.99 90.92   2921   nHHnHHHnnnnnnnnnnHnnHHHnH
  6  3  1.522  1.533  1.834 73.15  81.30 75.57      4 ? nnnHnnnnnnnnnnnnHnnnnnHnn
Solutions limited by voltest

 18 22 20.367  9.589 22.885 90.00 106.34 90.07   4289   HHHHHHHnHHHHHHnHHHHHHHHnH

acl/auto [18] auto
selected ACL 18
ACL 18                                          Niggli values
a, b, c :  20.3671   9.5887  22.8850         414.8190    91.9437   523.7242
al,be,ga:   90.005  106.339   90.069          -0.0174  -131.1260    -0.2367
  volume: 4288.813
Nrefls=25 Nfit=22 NNonfit=3

Still only 22 fitting reflections.
Reset indexfit to the default value
Dirax> indexfit 2
And lower levelfit
Dirax> levelfit 300
enable all reflections
Dirax> lchh
We could also have used example 7 to reread the reflections, but then levelfit would be also reset to its default value.
Dirax> go
2496 triplets
2497 final triplets
2497 triplet vectors
Squishd: 2497 t vectors ==> 1898 t vectors
Sorting 1898 t vectors...
Reducing 1898 t vectors ==> 1434 t vectors
Acl nH      a     b      c  alpha   beta gamma Volume S Indexstatus
 25 25 22.886 9.589 40.730  89.93 106.31 90.01   8579   HHHHHHHHHHHHHHHHHHHHHHHHH
 22 22 20.367 9.589 22.885  90.00 106.34 89.93   4289   HHHHHHHnHHHHHHnHHHHHHHHnH
 17  7  9.224 9.595 18.348  87.09  76.91 87.14   1578   nnnnnHnHnnnnnHnnHnnnnnHHH
 15  7  7.884 9.592 18.627  89.02  83.00 88.85   1398   HnnnnHnnnnnnnnnnHnnnnHHHH
 13  8  7.979 9.586 18.480  85.25  82.98 84.49   1393   nnnnnnnnnHnHHHnnnHnnnHnHH
 11  3  1.431 2.871  3.247 109.01 101.99 90.10     12 ? nnnnnnnHnnnnnnnnHnnnHnnnn
 10  3  2.436 3.011  5.047  83.65  76.41 66.82     33 ? nnnnnnnnnnnnnnnHnnHnnnnnH
  9  4  1.531 2.906  6.352  86.82  84.46 76.67     27 ? nnHnnnnnnnnHHHnnnnnnnnnnn
Solutions limited by voltest

 25 25 22.886 9.589 40.730  89.93 106.31 90.01   8579   HHHHHHHHHHHHHHHHHHHHHHHHH
selected ACL 25

25 fitting reflections. Which solution is to be preferred crystallographically cannot be decided from this data alone

Example 8

Twinned crystal and ill-distributed data


Dirax> example 8
resetting levelfit 1000
ex08 - Twinned crystal and ill-distributed data. The first default run
gives a cell volume of 933.06. A second run with the 'n' reflections only
gives a volume of 2806.8. Finally, a last run with the reflections that
have become 'n' now gives a volume of 2799.8, so the problem is solved.
This shows that you may have to handle DirAx cunningly.

  go                 ! first run
  lo                 ! show results
  store a            ! save it
  lch invert         ! change n to H
  go                 ! second run
  store b            ! save it
  lch invert         ! change new n to H
  go                 ! third run
  store c            ! save it
  compare b c        ! compare the last two solutions
  .                  ! accept proposed solution

24 reflections from file ../ex08.drx.

Dirax> go
2300 triplets
2300 final triplets
2258 triplet vectors
Squishd: 2258 t vectors ==> 932 t vectors
Sorting 932 t vectors...
Reducing 932 t vectors ==> 694 t vectors
Acl nH     a     b      c  alpha  beta  gamma Volume S Indexstatus
 16  4 7.552 8.510 14.949  90.25 90.14 115.73    865 ? HnnnnnnHnnnHnnnHnnnnnnnn
 15 12 8.932 8.420 12.422  89.98 92.78  90.05    933   HnnnHHnnHnHnHnnHHnHnHHnH
 13  4 2.823 3.625  4.087 115.53 99.46  90.44     37 ? nnnnnnnnnnnnnnHHHnHnnnnn
  7  5 2.286 4.446  7.152  91.10 97.10  93.83     72 ? HnnnnHnnHnnnHnnHnnnnnnnn
Solutions limited by voltest

 15 12 8.932 8.420 12.422  89.98 92.78  90.05    933   HnnnHHnnHnHnHnnHHnHnHHnH
selected ACL 15

Dirax> lo
   nr      H      K      L  1/err Netint    dth    dom    dch
H   1: -1.999  2.001  4.998  4778  984.0 -0.002 -0.021  0.002
Nn  2: -2.099  1.776  5.112    33  833.0
Nn  3: -0.337  3.997  1.334    22 2991.5
Nn  4: -0.554  3.940  1.565    17 2902.5
H   5:  0.997  3.997 -0.998  1864 1290.6 -0.010  0.029 -0.012
H   6: -0.003  4.000  1.001  3382 1580.8  0.001  0.026 -0.023
Nn  7:  1.101  4.085 -1.103    59 1594.7
Nn  8: -0.222  3.963  1.231    33 1473.4
H   9: -1.001  4.001  0.003  3815 2964.1  0.003  0.023  0.011
Nn 10: -1.224  3.940  0.230    32 2866.2
H  11: -0.000  3.996 -1.997  2040 1277.3 -0.010  0.009  0.004
Nn 12: -0.893  3.964 -0.103    67 1411.5
H  13: -2.998  2.001  3.998  3415  791.3 -0.004 -0.024  0.004
Nn 14: -1.332  3.998 -0.664    22 1306.1
Nn 15: -0.894  3.988 -1.100    71  748.6
H  16: -2.996  3.001  1.002  2219 1030.2 -0.003 -0.021  0.045
H  17:  3.002  3.002 -1.004  2061 1065.0  0.008 -0.016 -0.032
Nn 18:  2.824  3.158 -0.827    33  919.6
H  19:  3.001  3.002 -1.007  1608 1045.7  0.008 -0.024 -0.052
Nn 20:  2.824  3.159 -0.828    33  919.2
H  21: -0.001 -1.000  5.999  5151 1035.2 -0.003 -0.006 -0.016
H  22:  0.996 -0.004  5.997  1428 1740.8 -0.008  0.041 -0.052
Nn 23:  1.007 -0.102  5.984    82 1434.0
H  24:  3.005  0.001  4.010   961 3462.8  0.021 -0.026 -0.009
1/error for H: from 961 to 5151. n: from 17 to 82.

Note the large gap in 1/err between fitting and nonfitting reflections.
Save this solution
Dirax> store a
H→N and N→H
Dirax> lch invert
Nfit:12       123456789 123456789 1234
Nonfit:12     nHHHnnHHnHnHnHHnnHnHnnHn

Dirax> go
12 H_reflections selected out of 24
286 triplets
286 final triplets
275 triplet vectors
Squishd: 275 t vectors ==> 95 t vectors
Sorting 95 t vectors...
Reducing 95 t vectors ==> 50 t vectors
Acl nH     a      b      c  alpha  beta gamma Volume S Indexstatus
 10 10 8.428 14.962 22.259  90.03 90.00 90.02   2807   nHnHnnHHnHnHnnHnnHnHnnHn
  7  4 2.055  2.127  4.546  95.99 99.15 91.96     19 ? nnnnnnHnnnnnnnnnnHnHnnHn
  6  5 2.126  4.685  8.221  73.50 88.04 83.33     78 ? nnnnnnHnnnnnnnHnnHnHnnHn
  5  3 2.107  4.474  7.826 105.83 96.19 95.37     70 ? nnnnnnHHnnnHnnnnnnnnnnnn
Solutions limited by voltest

 10 10 8.428 14.962 22.259  90.03 90.00 90.02   2807   nHnHnnHHnHnHnnHnnHnHnnHn
selected ACL 10

and store this one too
Dirax> store b
Now once again H→N and N→H
Dirax> lch invert
Nfit:14       123456789 123456789 1234
Nonfit:10     HnHnHHnnHnHnHHnHHnHnHHnH

Dirax> go
14 H_reflections selected out of 24
390 triplets
391 final triplets
384 triplet vectors
Squishd: 384 t vectors ==> 181 t vectors
Sorting 181 t vectors...
Reducing 181 t vectors ==> 119 t vectors
Acl nH     a      b      c alpha  beta gamma Volume S Indexstatus
 14 14 8.421 14.946 22.246 89.98 89.95 90.01   2800   HnHnHHnnHnHnHHnHHnHnHHnH
  5  5 2.414  2.977  4.199 71.87 85.02 80.95     28 ? nnnnnnnnnnHnHnnnHnHnHnnn
Solutions limited by voltest

 14 14 8.421 14.946 22.246 89.98 89.95 90.01   2800   HnHnHHnnHnHnHHnHHnHnHHnH
selected ACL 14

And store the third solution
Dirax> store c
Now compare the last two
Dirax> compare b c
Correlation=-1.0
            a       b       c      alpha    beta   gamma    volume
Save B :   8.428  14.962  22.259   90.03   90.00   90.02     2806.8
nHnHnnHHnHnHnnHnnHnHnnHn
Save C :   8.421  14.946  22.246   89.98   89.95   90.01     2799.8
HnHnHHnnHnHnHHnHHnHnHHnH
Volume ratio = 1.003 Trying 24 solutions
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.900  0.5644  0.8203  0.0930  12.00  0.01 -1.02 (  0.03)   1.00  0.00 -0.01 (  1.84)   0.220
 2    3.677  0.2650 -0.1067 -0.9583  -0.02  1.00  0.02 (  1.78)  -0.05  1.00  0.01 (  1.79)   0.220
 3  179.943  0.7720 -0.5643  0.2924  -0.01 -0.00 -1.00 (  1.84)  -1.02 -0.02-12.00 (  0.07)   0.240
 4  176.325 -0.2923  0.0932  0.9518   0.00 -1.00  0.00 (  0.07)   0.00 -1.00  0.00 (  0.04)   0.230 U
Selected Solution 2
            a       b       c      alpha    beta   gamma    volume
Save B :   8.428  14.962  22.259   90.03   90.00   90.02     2806.8 <
Save C :   8.421  14.946  22.246   89.98   89.95   90.01     2799.8 <
Save C*:   8.421  14.946  22.246   90.02   89.95   89.99     2799.8 <
        Save C==> Save C*                        Save C*==> Save C
  -1.0000000  -0.0000000   0.0000000       -1.0000000  -0.0000000  -0.0000000
  -0.0000000   1.0000000  -0.0000000       -0.0000000   1.0000000  -0.0000000
  -0.0000000   0.0000000  -1.0000000        0.0000000   0.0000000  -1.0000000
Determinant:   1.000000                                 1.000000
H'= +0.997*H +0.001*K -0.024*L
K'= -0.001*H +0.999*K -0.001*L
L'= +0.170*H +0.003*K +0.997*L
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 2    3.677  0.2650 -0.1067 -0.9583  -0.02  1.00  0.02 (  1.78)  -0.05  1.00  0.01 (  1.79)   0.220  <
bababbaabababbabbababbab
a=10 b=14 0=0 *=0

All reflections are accounted for (see the last line). The relation between the lattices is a rotation of 3.677° around an arbitrary axis: two fragments.
In hindsight, the first solution was a subcell of the definitive solutions. You may want to try compare a b or compare a c

Example 9

Twinned crystal, giving a main lattice and a sub lattice


Dirax> example 9
removing A B C
ex09 - Twinned crystal, giving a main lattice and a sub lattice.
25 reflections from file ../ex09.drx.

Dirax> go
2496 triplets
2497 final triplets
2496 triplet vectors
Squishd: 2496 t vectors ==> 1260 t vectors
Sorting 1260 t vectors...
Reducing 1260 t vectors ==> 1068 t vectors
Acl nH      a      b      c alpha   beta gamma Volume S Indexstatus
 18  7 13.425 14.736 16.370 90.16 113.67 90.07   2966   nHnnnHHnnHnnnHnnnHnnnnnHn
 17 13 13.425 14.799 15.851 89.99 114.61 89.99   2863   HHHnHHHnnnHHnnnnnHnHHnHHn
 15  3  2.422  3.686  7.875 79.59  85.02 77.04     67 ? nnnnnnHnnnnnnnnnnnnnHnnnH
 13  6 14.661 16.165 25.008 78.20  89.48 89.07   5800 ? nnnnnnnnnHnHHHnnnnHnnHnnn
 10 12 15.859 14.804 24.849 90.00 100.81 90.04   5730   nnnHnnnHHHnnHHHHHnHnnHnnH
  8 10 13.426 14.804 15.859 90.04 114.65 89.98   2865   nnnHnnnHnHnnnHHHHnHnnHnnH
Solutions limited by voltest

 17 13 13.425 14.799 15.851 89.99 114.61 89.99   2863   HHHnHHHnnnHHnnnnnHnHHnHHn
selected ACL 17

Dirax> compare 17 8
Correlation=-1.0
            a       b       c      alpha    beta   gamma    volume
ACL 17 :  13.425  14.799  15.851   89.99  114.61   89.99     2863.3
HHHnHHHnnnHHnnnnnHnHHnHHn
ACL 8  :  13.426  14.804  15.859   90.04  114.65   89.98     2865.1
nnnHnnnHnHnnnHHHHnHnnHnnH
Volume ratio = 0.999 Trying 16 solutions
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.953 -0.5701  0.8216  0.0072  -0.00  0.02 -1.00 (  1.00)  -0.99  0.03 -2.00 (  1.03)   1.120
 2  179.956  0.7446  0.5203 -0.4181  -0.00  1.00  0.02 (  1.00)   0.01  1.00  0.02 (  0.98)   0.090
 3  178.024  0.3473  0.2330  0.9084  -2.00 -0.00  0.99 (  0.24)  -1.00 -0.00  0.00 (  0.20)   1.140
 4    1.977 -0.3502 -0.2636 -0.8988   2.00 -0.05 -0.94 (  2.01)   1.00 -0.02  0.02 (  1.69)   0.100 U
Selected Solution 2
            a       b       c      alpha    beta   gamma    volume
ACL 17 :  13.425  14.799  15.851   89.99  114.61   89.99     2863.3 <
ACL 8  :  13.426  14.804  15.859   90.04  114.65   89.98     2865.1 <
ACL 8* :  13.426  14.804  15.859   89.96  114.65   90.02     2865.1 <
         ACL 8==> ACL 8*                          ACL 8*==> ACL 8
  -1.0000000   0.0000000   0.0000000       -1.0000000   0.0000000  -0.0000000
   0.0000000   1.0000000   0.0000000        0.0000000   1.0000000   0.0000000
   0.0000000  -0.0000000  -1.0000000       -0.0000000  -0.0000000  -1.0000000
Determinant:   1.000000                                 1.000000
H'= -1.000*H -0.001*K -0.000*L
K'= +0.017*H +1.000*K +0.035*L
L'= +0.002*H +0.034*K -0.999*L
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 2  179.956  0.7446  0.5203 -0.4181  -0.00  1.00  0.02 (  1.00)   0.01  1.00  0.02 (  0.98)   0.090  <
aaabaaab0baa0bbbbabaabaab
a=13 b=10 0=2 *=0

The correlation (first line) implies a complementary solution. See also the bottom line. Only 2 reflections not accounted for.
Solution 13 is also interesting.
Dirax> compare 13 8
Correlation=-0.33
            a       b       c      alpha    beta   gamma    volume
ACL 13 :  14.661  16.165  25.008   78.20   89.48   89.07     5800.4
nnnnnnnnnHnHHHnnnnHnnHnnn
ACL 8  :  13.426  14.804  15.859   90.04  114.65   89.98     2865.1
nnnHnnnHnHnnnHHHHnHnnHnnH
Volume ratio = 2.025 Trying 32 solutions
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.949 -0.5636  0.8260  0.0029   0.02  1.00  1.00 (  0.99)  -0.00  3.00  0.99 (  0.12)   2.570
 2  179.037  0.3470  0.2334  0.9084  -0.00 -0.99  3.00 (  0.13)   0.00 -1.00  1.00 (  0.13)   2.540
 3    0.966 -0.3074 -0.2688 -0.9128   0.07  1.98 -7.00 (  0.80)   0.02  0.91 -1.00 (  2.92)   2.480
 4  179.988 -0.7496 -0.5130  0.4182  -1.00 -0.00  0.00 (  0.02)  -1.00  0.01  0.00 (  0.99)   2.510
Selected Solution 3
            a       b       c      alpha    beta   gamma    volume
ACL 13 :  14.661  16.165  25.008   78.20   89.48   89.07     5800.4 <
ACL 8  :  13.426  14.804  15.859   90.04  114.65   89.98     2865.1 <
ACL 8* :  14.804  15.859  24.848   79.19   90.00   89.96     5730.1 <
         ACL 8==> ACL 8*                          ACL 8*==> ACL 8
   0.0000000   1.0000000   0.0000000        0.0000000   0.5000000  -0.5000000
   0.0000000  -0.0000000  -1.0000000        1.0000000  -0.0000000   0.0000000
  -2.0000000   0.0000000  -1.0000000       -0.0000000  -1.0000000  -0.0000000
Determinant:   2.000000                                0.5000000
H'= +1.010*H -0.020*K -0.006*L
K'= +0.009*H +0.982*K -0.005*L
L'= +0.008*H -0.016*K +0.996*L
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 3    0.966 -0.3074 -0.2688 -0.9128   0.07  1.98 -7.00 (  0.80)   0.02  0.91 -1.00 (  2.92)   2.480  <
000b000b0*0aa*bbb0*00*00b
a=2 b=6 0=13 *=4

In fact, both solutions are the same. In solution 13, the two previously nonfitting reflections do fit, but the price is the doubling of the volume. A careful examination of other reflections will give the evidence for the correct answer.

Example 10

Area detector data from a protein.


Dirax> example 10
ex10 - Area detector data from a protein.
Set Dmax = 300.
Result: all reflections fit, cell volume 1,561,000 approximately. (Cell
can be transformed to cubic F.)

  dirax example 10
  dmax 300           ! change default
  go

25 reflections from file ../ex10.drx.

Dirax> dmax 300
Dirax> go
2496 triplets
2497 final triplets
2472 triplet vectors
Squishd: 2472 t vectors ==> 2179 t vectors
Sorting 2179 t vectors...
Reducing 2179 t vectors ==> 2105 t vectors
Acl nH       a       b       c  alpha  beta  gamma  Volume S Indexstatus
 25 25 129.763 130.063 130.100  60.09 60.12  89.74 1560925   HHHHHHHHHHHHHHHHHHHHHHHHH
 21  9  48.806  56.450 113.561  83.84 81.49  70.43  290995   nnnnHnHHHnHnnHHnnHnnHnnnn
 20  4  14.076  16.389  46.936  91.04 96.60  90.05   10754 ? nnnnnnnHnnnnnnnnnnnnHnHHn
 19 14  83.817  95.443 113.868 103.92 98.48  93.00  870832 Q nHnnHHHHHnHHnHHnnHnnHnHHn
 18 18  97.818 112.898 124.719  66.03 71.02  75.83 1179983 Q HHHHHHnHHnHHnHHHnnHnHnHHH
 17  8  65.177  95.284 112.916 103.25 90.82 108.32  645138   HnHnnHnnnHnnnHnHHnnHnnnnn
 15 11  59.669 106.050 121.288 109.87 95.61  99.31  702593   HHHnnnnnHnHHnnHHnHnnnnHnH
 14  4   6.423  18.882  38.286  99.11 93.50  92.73    4568 ? nnHnnnnnnnnnnnnHnHnnnnnnH
 13  4  10.909  17.476  25.508  87.08 89.76  73.55    4658 ? nnHnnnnnnnnnnnnHnnnnHnnnH
 12  4  20.534  25.220  52.917  94.35 97.28 112.86   24814 ? HnnHnHnnnnnnnnnnnnnHnnnnn
 11  5  31.503  41.032  48.139  87.68 74.52  87.78   59895 ? nnHnHnnnHnnnnnnHnnHnnnnnn
 10  4   8.816  12.377  12.517  70.51 81.33  74.99    1241 ? HnHnnnnnnnHnnnnHnnnnnnnnn
  9  4   5.915  13.539  16.016 102.33 92.78  99.69    1230 ? nnHnnHnnnnnnnnnHnnHnnnnnn
  5  3   7.883   9.955  20.168  90.24 95.98 110.74    1471 ? nnnnnnnnnnnnnnnnnnHnnHHnn
Solutions limited by voltest

 25 25 129.763 130.063 130.100  60.09 60.12  89.74 1560925   HHHHHHHHHHHHHHHHHHHHHHHHH
selected ACL 25


Example 11

This used to be a really difficult problem for older dirax versions.


Dirax> example 11
resetting dmax 80.0
ex11 - This used to be a really difficult problem for older dirax versions.
Default run. One lattice with 11 fitting reflections, another with 10.
Reflections 3,13,15 and 20 do not fit at all.

  go
  lch invert
  go

25 reflections from file ../ex11.drx.

Dirax> go
2496 triplets
2497 final triplets
2495 triplet vectors
Squishd: 2495 t vectors ==> 1027 t vectors
Sorting 1027 t vectors...
Reducing 1027 t vectors ==> 927 t vectors
Acl nH      a      b      c  alpha  beta gamma Volume S Indexstatus
 16  9 35.152 37.602 40.460 100.22 94.25 94.72  52237 ? nnnHnHnnHnHHnnnHnHHnHnnnn
 14  6  8.368 10.988 30.348  90.35 97.41 89.98   2767 ? nnnHnnHnnnnnnnnnnnHHHnnHn
 13  3  5.473  7.700 29.868  85.61 87.96 83.88   1247 ? nnnnnnHnnnnnnnnnnnnnHnHnn
Solutions limited by voltest

 16  9 35.152 37.602 40.460 100.22 94.25 94.72  52237 ? nnnHnHnnHnHHnnnHnHHnHnnnn
selected ACL 16
WARNING: only one L index is not even. Nr:21

All solutions with a warning. Only 9 'fitting' reflections. Lets try to be more tolerant.
Dirax> indexfit 4
Dirax> acl
Acl nH      a      b      c  alpha  beta gamma Volume S Indexstatus
 16 10 35.161 37.624 40.453 100.22 94.31 94.59  52280   nnnHnHnnHnHHnnnHnHHHHnnnn
 14 13  8.348 11.094 30.331  89.84 82.14 90.02   2783   nnHHHnHnHnHnnnnnHnHHHnHHH
  8  5  7.495  7.793 11.236  70.46 70.64 66.57    552 ? nnnnHnnHnnnnHnnnHnnnnnnnH
Solutions limited by voltest

 14 13  8.348 11.094 30.331  89.84 82.14 90.02   2783   nnHHHnHnHnHnnnnnHnHHHnHHH

Now we have 13 'fitting' reflections. Select the proposed solution.
acl/auto [14] auto
selected ACL 14
ACL 14                                          Niggli values
a, b, c :   8.3482  11.0944  30.3309          69.6929   123.0851   919.9624
al,be,ga:   89.839   82.139   90.024           0.9430    34.6306    -0.0389
  volume: 2782.787
Nrefls=25 Nfit=13 NNonfit=12

Save it, and another run with the 'n' reflections.
Dirax> store a
Dirax> lch invert
Nfit:12       123456789 123456789 12345
Nonfit:13     HHnnnHnHnHnHHHHHnHnnnHnnn

Dirax> go
12 H_reflections selected out of 25
286 triplets
286 final triplets
284 triplet vectors
Squishd: 284 t vectors ==> 104 t vectors
Sorting 104 t vectors...
Reducing 104 t vectors ==> 80 t vectors
Acl nH     a      b      c  alpha   beta gamma Volume S Indexstatus
 10 11 8.341 11.086 30.330  90.02  97.81 90.05   2779 ? HHnnnHnHnHnHnHnHnHnHnHnnn
  9 10 8.340 11.083 16.144 110.06  97.35 89.93   1389   HHnnnHnnnHnHnHnHnHnHnHnnn
  7  6 4.224 11.079  4.794  90.03 107.72 90.07    214 ? nHnnnHnHnnnHnnnHnHnnnnnnn
Solutions limited by voltest

  9 10 8.340 11.083 16.144 110.06  97.35 89.93   1389   HHnnnHnnnHnHnHnHnHnHnHnnn
selected ACL 9

Now manually pick the solution with the same volume as before
Dirax> acl 10
selected ACL 10
ACL 10                                          Niggli values
a, b, c :   8.3409  11.0861  30.3298          69.5710   122.9013   919.8981
al,be,ga:   90.022   97.812   90.049          -0.1301   -34.3841    -0.0783
  volume: 2778.516
Nrefls=25 Nfit=11 NNonfit=14
WARNING: only one K+L is not even. Nr:8

Ignore the warning with so few reflections.
Dirax> store b
Dirax> compare a b
Correlation=-0.91
            a       b       c      alpha    beta   gamma    volume
Save A :   8.348  11.094  30.331   89.84   82.14   90.02     2782.8
nnHHHnHnHnHnnnnnHnHHHnHHH
Save B :   8.341  11.086  30.330   90.02   97.81   90.05     2778.5
HHnnnHnHnHnHnHnHnHnHnHnnn
Volume ratio = 1.002 Trying 16 solutions
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.695 -0.0497 -0.9981  0.0362   0.00  0.01 -1.00 (  2.16)   5.97  1.14-11.00 (  0.28)   0.280
 2  178.605 -0.9988  0.0496 -0.0058  -0.02 10.00  1.03 (  0.18)  -0.01  1.00  0.01 (  2.04)   0.410
 3  175.769 -0.0036  0.0365  0.9993 -11.00 -0.04 -5.97 (  0.15)  -1.00 -0.00 -0.00 (  0.74)   0.380
 4    4.465  0.3190  0.0181 -0.9476  16.00 -7.01 12.10 (  0.10)   4.00 -1.00  0.08 (  3.97)   0.430
Selected Solution 1
            a       b       c      alpha    beta   gamma    volume
Save A :   8.348  11.094  30.331   89.84   82.14   90.02     2782.8 <
Save B :   8.341  11.086  30.330   90.02   97.81   90.05     2778.5 <
Save B*:   8.341  11.086  30.330   89.98   82.19   90.05     2778.5 <
        Save B==> Save B*                        Save B*==> Save B
  -1.0000000  -0.0000000  -0.0000000       -1.0000000   0.0000000  -0.0000000
   0.0000000  -1.0000000   0.0000000       -0.0000000  -1.0000000   0.0000000
  -0.0000000  -0.0000000   1.0000000       -0.0000000  -0.0000000   1.0000000
Determinant:   1.000000                                 1.000000
H'= -0.995*H -0.003*K -0.007*L
K'= +0.022*H -0.996*K -0.027*L
L'= -1.079*H -0.206*K +0.994*L
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.695 -0.0497 -0.9981  0.0362   0.00  0.01 -1.00 (  2.16)   5.97  1.14-11.00 (  0.28)   0.280  <
bbaaabababab0b0baba*abaaa
a=12 b=10 0=2 *=1


Example 12

twin, included because it is so nice


Dirax> example 12 go
resetting indexfit 2.0 removing A B
ex12 - Twin, included because it is so nice. Default run. Two lattices are
found: the most fitting is the 'main' lattice, V=1973.3, 17 fitting
reflections (nr. 3 will fit with IndexFitFactor 3.00), the next best
fitting lattice is the twin sister, V = 1974.12, 7 fitting reflections.
This is an exceptional situation: mostly a run with 'n' reflections is
needed to find the twin lattice, as in ex09. Note that in both lattices h
and k are integer for all reflections.

  lo                   ! show fitting and nonfitting reflections
  compare 18 7         ! compare the two lattices
  .                    ! accept proposed solution

25 reflections from file ../ex12.drx.
2496 triplets
2497 final triplets
2497 triplet vectors
Squishd: 2497 t vectors ==> 1131 t vectors
Sorting 1131 t vectors...
Reducing 1131 t vectors ==> 826 t vectors
Acl nH     a      b      c alpha   beta  gamma Volume S Indexstatus
 18 17 6.869 18.069 16.017 90.02  96.92  89.96   1973   HHnHnHHnHnHnHnHHHHHnHHnHH
  7  7 6.879 18.068 15.998 89.97  96.89  89.99   1974 ? nnnnHnnHnHnHnHnnnnnHnnHnn
  6  3 2.145  2.860  3.027 85.30  85.26  88.87     18 ? nnHnHnnnnnnHnnnnnnnnnnnnn
  5  3 1.732  1.890  3.674 94.31 100.75 100.68     12 ? nnnnnHnHnnnnnnnHnnnnnnnnn
Solutions limited by voltest

 18 17 6.869 18.069 16.017 90.02  96.92  89.96   1973   HHnHnHHnHnHnHnHHHHHnHHnHH
selected ACL 18

Solutions 18 and 7 look similar.
Dirax> compare 18 7
Correlation=-1.0
            a       b       c      alpha    beta   gamma    volume
ACL 18 :   6.869  18.069  16.017   90.02   96.92   89.96     1973.3
HHnHnHHnHnHnHnHHHHHnHHnHH
ACL 7  :   6.879  18.068  15.998   89.97   96.89   89.99     1974.1
nnnnHnnHnHnHnHnnnnnHnnHnn
Volume ratio = 1.0 Trying 32 solutions
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 1  179.989 -0.9955 -0.0918 -0.0251  -0.00  0.00  1.00 (  0.09)   4.99  0.01 18.00 (  0.04)   0.350
 2  179.939  0.0023  0.2410 -0.9705  18.00  0.01 -4.99 (  0.02)   1.00 -0.00  0.00 (  0.09)   0.350 U
Selected Solution 2
            a       b       c      alpha    beta   gamma    volume
ACL 18 :   6.869  18.069  16.017   90.02   96.92   89.96     1973.3 <
ACL 7  :   6.879  18.068  15.998   89.97   96.89   89.99     1974.1 <
H'= +1.002*H -0.000*K +0.001*L
K'= +0.001*H -1.000*K +0.001*L
L'= -0.554*H -0.001*K -0.999*L
Nr Rotangle       Rotvec(xyz)           RotVec(hkl)    ( angle)     RotVec(uvw)    ( angle)     Fom
 2  179.939  0.0023  0.2410 -0.9705  18.00  0.01 -4.99 (  0.02)   1.00 -0.00  0.00 (  0.09)   0.350 U<
aa0abaababababaaaaabaabaa
a=17 b=7 0=1 *=0

Have a detailed look on the reflection indices
Dirax> acl 18
selected ACL 18
ACL 18                                          Niggli values
a, b, c :   6.8686  18.0690  16.0166          47.1770   326.4904   256.5327
al,be,ga:   90.017   96.924   89.956          -0.0869   -13.2617     0.0947
  volume: 1973.300
Nrefls=25 Nfit=17 NNonfit=8

Dirax> lo
   nr      H       K       L  1/err Netint    dth    dom    dch
H   1: -3.998   5.002  -5.991  1503  478.4 -0.011 -0.030  0.003
H   2: -3.000   6.003  -5.997  3821  347.2 -0.001 -0.021 -0.005
Nn  3: -1.994  -4.022  -8.960   333  734.8
H   4: -3.000  -5.015  -7.005  1105  510.7  0.011  0.055 -0.024
Nn  5: -2.975  -0.010 -12.359    45 1097.4
H   6: -2.002   4.002  -6.999  3035  792.3  0.003 -0.018  0.022
H   7: -2.001  -0.994  -7.998  2593  364.2 -0.001 -0.034  0.011
Nn  8: -2.992   5.992  -3.353    45  550.3
H   9: -1.997 -12.988   6.009   998 1708.4 -0.010  0.053 -0.027
Nn 10: -3.005  -5.993   7.676    49  360.3
H  11: -3.002  -5.002   7.998  2993  463.0  0.003 -0.007  0.025
Nn 12: -2.994 -11.010  -5.332    48  430.4
H  13: -3.001 -12.995   6.997  2461  513.1 -0.005  0.000  0.020
Nn 14: -2.004  -6.000   7.124   129  457.9
H  15: -2.002  -9.001   3.999  4078  496.1  0.003 -0.007  0.018
H  16: -2.999  -6.007   5.997  2253 1143.5  0.000 -0.040 -0.004
H  17: -2.998   3.993   9.006  1555  479.9 -0.000 -0.047 -0.022
H  18: -3.000   8.007   1.982   831 1084.9  0.004  0.108 -0.012
H  19: -3.002   4.003   7.001  3001  568.3  0.006  0.016  0.006
Nn 20: -3.004  -1.995   7.673    48  278.4
H  21: -3.999  -2.003  13.993  2180  441.3 -0.008 -0.009  0.011
H  22: -1.002  -2.001   8.006  2121  706.3  0.009  0.006  0.019
Nn 23: -1.006  -1.997   8.570    37  362.3
H  24: -2.000   4.000   7.009  1704 6626.1  0.009 -0.034 -0.019
H  25: -2.000   5.001   6.004  3941 1323.3  0.003 -0.015 -0.016
1/error for H: from 831 to 4078. n: from 37 to 333.

Dirax> acl 7
selected ACL 7
ACL 7                                           Niggli values
a, b, c :   6.8793  18.0679  15.9981          47.3247   326.4497   255.9407
al,be,ga:   89.967   96.890   89.989           0.1681   -13.2034     0.0231
  volume: 1974.121
Nrefls=25 Nfit=7 NNonfit=18
WARNING: only one K index is not even. Nr:12
WARNING: only one K+L is not even. Nr:8

Dirax> lo
   nr      H      K       L  1/err Netint    dth    dom    dch
Nn  1: -4.014 -5.009   8.196    82  478.4
Nn  2: -3.014 -6.010   7.647    44  347.2
Nn  3: -2.008  4.014  10.063   245  734.8
Nn  4: -3.012  5.007   8.668    47  510.7
H   5: -2.995 -0.002  13.998  1409 1097.4 -0.008  0.002 -0.037
Nn  6: -2.015 -4.009   8.098   159  792.3
Nn  7: -2.014  0.986   9.102   153  364.2
H   8: -3.003 -5.997   5.001  1938  550.3  0.005  0.005  0.042
Nn  9: -1.991 12.989  -4.881   129 1708.4
H  10: -3.000  5.996  -5.998  3832  360.3 -0.004  0.013  0.007
Nn 11: -2.997  5.005  -6.323    49  463.0
H  12: -3.003 11.002   7.001  2041  430.4  0.007  0.001  0.024
Nn 13: -2.995 12.996  -5.313    51  513.1
H  14: -1.998  6.003  -6.001  3098  457.9 -0.001 -0.019 -0.024
Nn 15: -1.998  9.002  -2.876   127  496.1
Nn 16: -2.996  6.008  -4.323    49 1143.5
Nn 17: -2.994 -3.989  -7.343    46  479.9
Nn 18: -3.006 -8.008  -0.328    48 1084.9
Nn 19: -3.000 -4.001  -5.337    47  568.3
H  20: -3.000  1.998  -6.000  8662  278.4  0.001  0.010 -0.000
Nn 21: -3.990  2.010 -11.764    66  441.3
Nn 22: -0.994  2.006  -7.443    36  706.3
H  23: -0.998  2.002  -8.003  2668  362.3  0.002 -0.019 -0.033
Nn 24: -1.997 -3.996  -5.901   158 6626.1
Nn 25: -1.998 -4.998  -4.897   153 1323.3
1/error for H: from 1409 to 8662. n: from 36 to 245.
WARNING: only one K index is not even. Nr:12
WARNING: only one K+L is not even. Nr:8

Note: h and k are integer for all reflections in both solutions.
Dirax> exit
dirax ended at 26-Apr-2018 02:40:30 CPU time used 00:00:00


26-Apr-2018 02:40:30