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
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.
- Column 1: H(=fit) or n(=nonfit). There are no n's in this example.
- Column 2: reflection number.
- Columns 3 to 5: reflection indices. The indices are presented as
floating numbers. The values are very close to integers.
- Column 6: 1/err.
There are 2 c-vectors: cobs, the observed c-vector, and ccalc, the
calculated c-vector with all indices rounded to integer. error is
defined as the length of the difference vector between cobs and ccalc.
The reciprocal value of error is given in the table. N.B.: a
reflection is considered to 'fit' if 1/error >
indexfit/levelfit.
The larger the number, the better the correspondance
between observed and calculated c-vector.
- Column 7: reflection intensities.
- Columns 8 to 10: angle differences. These angles are calculated
for the Bisecting geometry.
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.
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.
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.
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
- The first solution has 25 fitting reflections.
- There is a questionmark between Volume and Indexstatus
- Select this solution to see what the questionmark means
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
- alpha and gamma are almost 90°
- Instead of a question mark, we now have a Q. This
indicates a possible qvector.
- Have a look at the nonfitting reflections
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.
- There is something with 0.204 in both H and L
0.204, -0.204 0.408 are multiples of 0.204. What about
0.795. Think 1.0-0.204.
- 0.447 is the fraction part of some K indices. But
we also see 0.553; think 1.0-0.447
- So what about the Q.
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.
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.
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
- Solution 25: all reflections fit but the cell volume is much larger than expected.
- Solution 21: four reflections do not fit. The angles alpha and gamma
are 90°.
- Solution 20: five reflections do not fit. Also monoclinic angles.
Volume much better.
- Solution 18: expected volume. Seven nonfits. The b and c axes are
equal, and so are the angles beta and gamma.
- Solution 7: Not a real solution.
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
- First both saved solutions are presented: cellparameters and indexstatus
- The volume ratio is 1 and the indexstatus correlation is
-0.76. If the
index status of both solutions is equal the correlation will be 1.0.
If the index status of the two solutions is complementary, the
correlation is -1.0. The value here (-0.76) indicates an almost
complete complementary relation.
- There are two possible 180° rotations to map cell a onto cell b.
The interpretation of the rotations axis is:
- Rotvec(xyz). The components of the rotation axis with respect
to the Laboratory system
- Rotvec(hkl). The rotation axis in terms of the reciprocal axes.
- Rotvec(uvw). The rotation axis in terms of the direct axes.
- Solution 1: rotate 180° around uvw= -1 0 0
In this special case (180°) we could also use
uvw= 1 0 0 (the a-axis).
- Solution 2: rotate 180° around hkl= 0 1 1 (the b*+c* diagonal).
- The program selects solution 2 based on the smallest Fom
- The final line shows the indexstatus for the reflections.
- a Reflection fits the first lattice
- b Reflection fits the second lattice
- * Reflection fits both both lattices
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
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
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
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
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.
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
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
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