Fraser Rowan - Assignment VI
Determination of space group and refinement of the unit cell.
Question1
The unit cell for the analyte is monoclinic with lattice parameters a=23.738, b=6.178, c=11.034Å, a=90, b=97.87 g=90° and V=1602.9Å3
The 2q values used to index the diffraction pattern were:-
| 7.50 | 11.77 | 14:82 | 15.05 |
| 16.09 | 16.44 | 16.64 | 16.90 |
| 17.15 | 18.07 | 18.27 | 18.81 |
| 19.36 | 20.63 | 20.84 | 21.64 |
| 22.67 | 23.45 | 24.27 | 24.41 |
In order to use the peaks with the lowest two theta values the most obvious peaks to use would be the first twenty peaks omitting any which were highlighted to have noticeable tails.
The correct unit cell was the first of the most probable solutions, with a figure of merit of 28.6.
Output from Zone Indexing program
The 10 most probable solutions
| N | Q(A) | Q(B) | Q(C) | Q(D) | Q(E) | Q(F) | Indexed | FoM | Lattice |
| 1 | 18.09 | 261.99 | 83.71 | 0.00 | 10.65 | 0.00 | 20 | 28.6 | P |
| 2 | 35.94 | 9.13 | 95.09 | 0.00 | 16.24 | 0.00 | 20 | 3.7 | P |
| 3 | 72.48 | 39.00 | 156.43 | 7.88 | 51.88 | -17.82 | 19 | 8.3 | P |
| 4 | 58.06 | 18.08 | 83.67 | 10.65 | 23.62 | 10.81 | 19 | 6.8 | P |
| 5 | 50.99 | 21.48 | 70.87 | 0.00 | 33.63 | 0.00 | 19 | 6.6 | P |
| 6 | 44.00 | 28.38 | 83.90 | 10.27 | 10.82 | 0.00 | 19 | 5.6 | P |
| 7 | 51.02 | 21.58 | 70.72 | 0.00 | 33.59 | 0.00 | 19 | 4.6 | P |
| 8 | 7.73 | 64.56 | 70.73 | 0.00 | 5.30 | 0.00 | 19 | 4.2 | P |
| 9 | 29.12 | 28.24 | 37.9 | 17.53 | 22.94 | 17.59 | 19 | 3.6 | A |
| 10 | 73.52 | 72.37 | 86.17 | 10.77 | 2.97 | -41.58 | 18 | 12.7 | P |
The Equivalent Real-space Unit Cells
| N | a (Å) | b(Å) | c(Å) | a(°) | b(°) | g(°) | (Å3) |
| 1 | 23.738 | 6.178 | 11.034 | 90.00 | 97.87 | 90.00 | 1603.0 |
| 2 | 16.844 | 33.092 | 10.355 | 90.00 | 97.98 | 90.00 | 5716.0 |
| 3 | 12.325 | 16.317 | 8.282 | 95.48 | 104.83 | 79.30 | 1580.0 |
| 4 | 13.463 | 23.999 | 11.163 | 96.42 | 98.63 | 98.46 | 3493.7 |
| 5 | 14.586 | 21.579 | 12.373 | 90.00 | 106.24 | 90.00 | 3738.9 |
| 6 | 15.137 | 18.876 | 11.022 | 96.06 | 95.14 | 89.46 | 3119.2 |
| 7 | 14.582 | 21.526 | 12.385 | 90.00 | 106.24 | 90.00 | 3732.6 |
| 8 | 36.205 | 12.446 | 11.968 | 90.00 | 96.51 | 90.00 | 5357.9 |
| 9 | 20.325 | 20.103 | 17.600 | 100.45 | 106.68 | 103.70 | 6448.1 |
| 10 | 12.177 | 12.299 | 10.806 | 94.40 | 92.28 | 73.32 | 1545.5 |
Question 2
Indexing scheme for the 39 given peaks
| 2 Theta (obs) | 2 Theta (calc) | Intensity | hkl |
| 7.5 | 7.513 | 67 | 200 |
| 8.07 | 8.082 | 7727 | 001 |
| 10.25 | 10.259 | 3634 | -201 |
| 11.77 | 11.776 | 104 | 201 |
| 14.82 | 14.814 | 1731 | 110 |
| 15.05 | 15.058 | 557 | 400 |
| 16.09 | 16.099 | 199 | -401 |
| 16.44 | 16.468 | 2838 | 011 |
| 16.64 | 16.646 | 108 | -111 |
| 16.9 | 16.914 | 448 | -202 |
| 17.15 | 17.144 | 1861 | 111 |
| 18.07 | 18.071 | 740 | 401 |
| 18.27 | 18.269 | 185 | 310 |
| 18.81 | 18.804 | 2587 | 202 |
| 19.36 | 19.360 | 1031 | -311 |
| 20.36 | 20.631 | 680 | 311 |
| 20.86 | 20.841 | 65 | 410 |
| 21.64 | 21.634 | 685 | -112 |
| 22.67 | 22.670 | 228 | 600 |
| 23.1 | 23.017 | 1897 | -601 |
| 23.45 | 23.444 | 626 | -312 |
| 23.77 | 23.758 | 1524 | 510 |
| 24.27 | 24.266 | 1793 | -511 |
| 24.41 | 24.411 | 135 | 003 |
| 24.54 | 24.549 | 151 | -203 |
| 25.19 | 25.183 | 472 | -412 |
| 25.55 | 25.541 | 182 | 312 |
| 25.98 | 25.973 | 2413 | 511 |
| 26.57 | 26.564 | 5337 | 203 |
| 26.91 | 26.919 | 1425 | 610 |
| 27.37 | 27.356 | 324 | -512 |
| 27.72 | 27.782 | 5418 | 412 |
| 28.27 | 28.217 | 1808 | -113 |
| 29.81 | 29.792 | 1054 | 602 |
| 30.06 | 30.037 | 729 | 021 |
| 30.27 | 30.26 | 1193 | 710 |
| 30.39 | 30.385 | 1246 | 800 |
| 30.74 | 30.723 | 135 | -221 |
| 31.11 | 31.118 | 1207 | -603 |
A monoclinic crystal system can either be primitive (P) or face centred, in only one pair of faces (A, B or C). When a lattice is centred in only one pair of faces the reflection conditions are such that k+l=2n (A), h+l=2n (B) or h+k=2n (C). These criteria are clearly not satisfied for the given set of hkl values. The lattice is, therefore, considered to be primitive.
Question 3 - Reflection conditions.
The reflection conditions present in the above indexing scheme are h0l h=2n and h00 h=2n.
The condition h0l:h=2n indicates that there is a glide plane perpendicular to b, i.e. 201 and 401.
A 21 screw axis appears to exist parallel to the a axis, i.e. 200, 400, 600. However, this is mis-leading as monoclinic cells only have two fold axis parallel to b. The reflection condition for a screw axis parallel to b is 0k0. In the 38 peaks given there were no reflections with the 0k0 indexing. It is therefore, impossible from this data to say whether the 0k0 condition has been violated.
Question 4 - Space group
From the unit cell the structure is monoclinic. There are 13 possible space groups with a monoclinic structure. In Question 2 it was established that the lattice is primitive and not 'pair-face centred'. The table below shows the remaining space groups and settings available for a primitive monoclinic lattice, along with the reflection conditions required.| Space group | Reflection condition | Space group | Reflection condition |
| P2 (#3) | None | P21/c (#14) | h0l:l=2n, 0k0:k=2n |
| Pm (#6) | None | Pa (#7) | h0l:h=2n |
| P2m (#10) | None | P2/a (#13) | h0l:h=2n |
| P21 (#4) | 0k0:k=2n | Pn (#7) | h0l:h+l=2n |
| P21/m (#11) | 0k0:k=2n | P2/n | h0l:h+l=2n |
| Pc (#7) | h0l:l=2n | P21/a | h0l:h=2n, 0k0:k=2n |
| P2/c (#13) | h0l:l=2n | P21/n | h0l:h=2n, 0k0:k=2n |
Through a process of elimination the options can be narrowed down to either non-centrosymmetric Pa (no.7) and centrosymmetric P2/a (no.13). However, as Pa is a non-standard setting the space group in this instance will be assumed to be P2/a (no.13).
Many organic materials derived from natural products such as salts have enantiomorphic space groups which make it impossible to determine the absolute configuration. This is not the case for the analyte given in this work.
Question 5 - Unit cell refinement
The table below fills in the blanks from the assignment questions.
| 2 Theta | h k l | 2 Theta | h k l | 2 Theta | h k l |
| 7.5 | 200 | 14.82 | 110 | 16.90 | -202 |
| 8.07 | 001 | 15.05 | 400 | 17.15 | 17.15 |
| 10.25 | -201 | 16.09 | -401 | 18.07 | 401 |
| 11.77 | 201 | 16.64 | -111 | 18.27 | 310 |
(Note - When running the refinement with the 011 or 311 hkl's they were rejected. I don't quite understand why this is. It would suggest that the indexing scheme is not quite right.)
| a (Å) | b(Å) | c(Å) | a(°) | b(°) | g(°) | |
| Value | 23.72855 | 6.17111 | 11.03219 | 90.0000 | 97.9013 | 90.0000 |
| ESD | 0.00822 | 0.00189 | 0.00453 | 0.0000 | 0.0157 | 0.0000 |
The refined value for the zero offset was -0.0135±0.0047 which is small. This negates the requirement for an internal standard and is indicative of a very well aligned diffractometer.
The unit cell calculated when the zero error is not refined is shown in the table below.
| a (Å) | b(Å) | c(Å) | a(°) | b(°) | g(°) | |
| Value | 23.74671 | 6.17589 | 11.04419 | 90.0000 | 97.8998 | 90.0000 |
| ESD | 0.00404 | 0.00100 | 0.00238 | 0.0000 | 0.0161 | 0.0000 |
Comparison of the lattice parameters obtained when the zero error is refined to those obtained when the zero error is not refined shows minimal variation. This indicates that the zero error is not compensating for any sample displacement. Hence the
Use of reflections from higher angles usually increases the precision of the lattice parameters. This would not be the case in for this crystal lattice as the intensities of the peaks at the higher angles are greatly reduced in comparison to those at low angles. A combination of low intensities and peak broadening due to thermal vibrations and X-ray form factors will lower the precision of the peak position, thus no significant improvement would be observed.