This material belongs to the Monoclinic Crystal System and its unit cell is: a = 23.742, b = 6.181, c = 11.032, a = 90.00°, b = 97.83°, g = 90.00°.
The 2q values of the peaks used in the indexing program are in the following table.
| 2q | I(obs) | 2q | I(obs) | 2q | I(obs) | 2q | I(obs) | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 7.50 | 67 | 16.09 | 199 | 18.07 | 740 | 20.84 | 65 | ||||
| 8.07 | 7727 | 16.44 | 2838 | 18.27 | 185 | 21.64 | 685 | ||||
| 10.25 | 3634 | 16.64 | 108 | 18.81 | 2587 | 22.67 | 228 | ||||
| 14.82 | 1731 | 16.90 | 448 | 19.36 | 1031 | 23.10 | 1897 | ||||
| 15.05 | 557 | 17.15 | 1861 | 20.63 | 680 | 23.45 | 1897 |
Peaks with lowest 2q values are preferable for indexing, even though they provide the least accurate lattice parameters. If hkl triplets are assigned to high-angle data based on poor values of the latice parameters, then the probability of assigning an incorrect hkl value increases rapidly with increasing 2q value.
2 Marks
As a novice at indexing I think I encountered every difficulity possible with this indexing problem. I believe that "Note 2; all the peaks are genuine unless indicated otherwise: etc" let me to include in the initial indexing a weak intensity peak that is apparently from an impurity phase.
Initially the twenty peaks with the lowest 2q values were used for indexing but with this combination of peaks none of the 10 most probable solutions produced valid results. A hint was received to eliminate one of the low intensity peaks from among the 21 peaks of lowest 2q value. I tried the Zone -Indexing Program five times, each time eliminating one of those peaks with the lowest 2q values. When the peak at 11.77 °2q was eliminated the the Zone-Indexing Program produced acceptable results as shown in the tables below.
| N | Q(A) | Q(B) | Q(C) | Q(D) | Q(E) | Q(F) | Lines Indexed |
Figure of Merit |
Lattice Type |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 18.08 | 261.78 | 83.72 | 0.00 | 10.60 | 0.00 | 20 | 17.4 | P |
| 2 | 18.08 | 261.78 | 83.72 | 0.00 | 10.60 | 0.00 | 20 | 17.3 | P |
| 3 | 18.08 | 261.78 | 83.72 | 0.00 | 10.60 | 0.00 | 20 | 17.3 | P |
| 4 | 38.83 | 33.57 | 30.46 | -6.21 | 25.42 | 0.00 | 20 | 3.7 | P |
| 5 | 29.49 | 28.06 | 38.05 | 17.60 | 23.45 | 17.82 | 20 | 3.3 | P |
| 6 | 38.53 | 33.50 | 27.63 | -6.87 | 23.70 | 0.00 | 20 | 2.2 | P |
| 7 | 16.30 | 17.89 | 38.26 | 13.10 | 13.28 | 0.00 | 20 | 2.2 | P |
| 8 | 72.32 | 31.56 | 74.61 | 22.33 | 9.21 | 30.50 | 19 | 8.4 | P |
| 9 | 57.99 | 18.09 | 83.64 | 10.60 | 23.60 | 10.80 | 19 | 5.8 | P |
| 10 | 49.35 | 33.77 | 72.45 | 3.61 | 17.11 | 0.00 | 19 | 4.1 | P |
The Equivalent Real-Space Unit Cells
| N | a (Å) | b (Å) | c (Å) | a (°) | b (°) | g (°) | V (Å3) |
|---|---|---|---|---|---|---|---|
| 1 | 23.742 | 6.181 | 11.032 | 90.00 | 97.83 | 90.00 | 1603.7 |
| 2 | 23.742 | 6.181 | 11.032 | 90.00 | 97.83 | 90.00 | 1603.7 |
| 3 | 23.742 | 6.181 | 11.032 | 90.00 | 97.83 | 90.00 | 1603.7 |
| 4 | 17.284 | 17.355 | 19.608 | 84.00 | 111.80 | 92.22 | 5431.3 |
| 5 | 20.245 | 20.184 | 17.595 | 100.41 | 106.93 | 103.81 | 6432.6 |
| 6 | 17.309 | 17.407 | 20.572 | 83.04 | 111.44 | 92.54 | 5726.6 |
| 7 | 25.759 | 24.484 | 17.367 | 105.06 | 105.94 | 85.91 | 10170.1 |
| 8 | 12.409 | 19.266 | 11.897 | 102.83 | 89.33 | 108.29 | 2627.9 |
| 9 | 13.471 | 23.992 | 11.164 | 96.38 | 98.64 | 98.46 | 3495.6 |
| 10 | 14.383 | 17.220 | 11.879 | 92.12 | 98.23 | 89.70 | 2909.8 |
2 Marks
Comment: Expected difficulties not discussed
This material belongs to the Monoclinic crystal system because a=23.742, b=6.181, c=11.032 and a = 90.00°, b = 97.83°, g = 90.00°, therefore a ¹b¹c and a = b = 90° ¹ g.
Minor comment: You have a typographical error with the Greek characters here
The hkl values in the following table were used to determine that this material has a Primitive lattice centring.
The International Tables for X-Ray Crystallography was used to compare the hkl values of this material to the general conditions limiting possible reflections for all the Monoclinic Space Groups with b as the unique axis. The P2, Pm and P2/m Space Groups are possible because they have no conditions limiting possible reflections. The P21 and P21/m Space Groups could not be eliminated as possibilities despite their reflection condition, 0k0: k=2n, because the reflection, 0k0, was simple not observed in this material.
The remaining Monoclinic Space Groups, C2, Pc, Cm, Cc, C2/m, P2/c, P21/c and C2/c all had at least one of their general conditions for limiting possible reflections violated by an observed hkl reflection.
Comment: You were asked to determine the Bravais lattice only at this point (not space group symmetry)
1 Mark
Table of the reflection indicies, observed peak positions and matching calculated values
| h | k | l | 2qobs (°) | 2qcalc (°) | |
| 2 | 0 | 0 | 7.5000 | 7.511 | |
| 0 | 0 | 1 | 8.0700 | 8.083 | |
| -2 | 0 | 1 | 10.2500 | 10.263 | |
| 2 | 0 | 1 | 11.7700 | 11.771 | |
| 1 | 1 | 0 | 14.8200 | 14.806 | |
| 4 | 0 | 0 | 15.0500 | 15.054 | |
| -4 | 0 | 1 | 16.0900 | 16.101 | |
| 0 | 1 | 1 | 16.4400 | 16.463 | |
| -1 | 1 | 1 | 16.6400 | 16.641 | |
| -2 | 0 | 2 | 16.9000 | 16.920 | |
| 1 | 1 | 1 | 17.1500 | 17.137 | |
| 4 | 0 | 1 | 18.0700 | 18.063 | |
| 3 | 1 | 0 | 18.2700 | 18.262 | |
| 2 | 0 | 2 | 18.8100 | 18.800 | |
| -3 | 1 | 1 | 19.3600 | 19.357 | |
| 3 | 1 | 1 | 20.6300 | 20.622 | |
| 4 | 1 | 0 | 20.8400 | 20.833 | |
| -1 | 1 | 2 | 21.6400 | 21.632 | |
| 6 | 0 | 0 | 22.6700 | 22.664 | |
| 4 | 1 | 1 | 23.1000 | 23.125 | |
| -3 | 1 | 2 | 23.4500 | 23.445 | |
| 5 | 1 | 0 | 23.7700 | 23.750 | |
| -5 | 1 | 1 | 24.2700 | 24.263 | |
| 0 | 0 | 3 | 24.4100 | 24.413 | |
| -2 | 0 | 3 | 24.5400 | 24.556 |
Comment: No mention made of overlapped reflections?
2 Marks
This material has one glide plane, a^y because the reflection condition, h0l: h=2n, is met by many observed peaks (eg 200, 001, -201, 201, etc) and is not negated by any observable reflection.
Excellent
5 Marks
This material has one screw axis parallel to the a axis because the reflection condition, h00: h=2n, is met by several observed peaks (eg 002, 004, 006) and is not negated by any observable reflection.
Comment: Wrong direction chosen
0 Marks
The most likely space group for this material is P21/a.
Comment: Correct choice despite the above error!
2 Marks
Parden my ignorance, but the only thing I find surprising about my answer is that I arrived at it at all and on time.
Comment: Centrosymmetric space groups for natural products are not very common
0 Marks
| 2q | h | k | l | 2q | h | k | l | 2q | h | k | l | ||
| 7.50 | 2 | 0 | 0 | 14.82 | 1 | 1 | 0 | 16.90 | -2 | 0 | 2 | ||
| 8.07 | 0 | 0 | 1 | 15.05 | 4 | 0 | 0 | 17.15 | 1 | 1 | 1 | ||
| 10.25 | -2 | 0 | 1 | 16.09 | -4 | 0 | 1 | 18.07 | 4 | 0 | 1 | ||
| 11.77 | 2 | 0 | 1 | 16.64 | -1 | 1 | 1 | 18.27 | 3 | 1 | 0 |
2 Marks
| a (Å) | b (Å) | c (Å) | a (°) | b (°) | g (°) | |
| Value | 23.72856 | 6.17111 | 11.03219 | 90.0000 | 97.9013 | 90.0000 |
| ESD | 0.00822 | 0.00189 | 0.00453 | 0.0000 | 0.0157 | 0.0000 |
Comment: Should quote less digits, also no decimal places for angles fixed exactly at 90°
2 Marks
Comment: Zero value?
0 Marks
Although lower estimated standard deviations were obtained (I actually tried it) by including higher angle data in the Program to Refine Unit-Cell Parameters, it was not suitable in this case for two reasons:
1. The 16 highest angle peaks (excluding the impurity peak) resulted in five of the peaks being rejected by the Program to Refine Unit-Cell Parameters. Even though the error values were lower, this looked pretty suspect because of the rejected peaks.
2. There is some uncertainity in two of the higher angle peaks due to peak broadening and one higher angle peak has a noticeable tail on the high-angle side.
Comment: See model answer
1 Mark
General comment: well done in places, but lack of understanding in other places.