Lars-Erik Briggner, Assignment 6

1. To determine the unit cell for the given substance the following peaks were used:

values
  1     2     3     4     5     Since the low  angle peaks are more useful for indexing, basically all 20
  6     7     8     9   10     of the lowest were used. The exception was the very weak peak at  20.84
11   12   13   14   15     were the figure of merit improved dramatically when exchanged for a
16   17   18   19   20     stronger peak. There might be more peaks than the one indicated that belong

to some impurity which would make this indexing problem difficult.

The 10 most probable solutions were the following

N Q(A) Q(B) Q(C) Q(D) Q(E) Q(F) Lines
Indexed		 Figure
 of Merit 		 Lattice
Type
1 18.06 261.47 83.65 0.00 10.58 0.00 20 16.1 P
2 18.06 261.47 83.65 0.00 10.58 0.00 20 16.1 P
3 18.06 261.47 83.64 0.00 10.58 0.00 20 16.1 P
4 259.28 20.88 72.23 10.65 11.60 0.00 19 17.1 P
5 259.28 20.88 72.23 10.65 11.62 0.00 19 17.0 P
6 75.02 72.32 83.73 21.47 32.79 42.52 19 12.3 P
7 72.35 41.49 83.51 23.35 21.53 20.38 19 8.1 P
8 13.58 70.04 64.50 0.00 5.93 0.00 18 11.3 P
9 72.23 35.03 83.71 12.80 21.24 21.72 18 9.5 P
10 19.18 64.61 70.07 0.00 17.04 0.00 18 6.5 P

giving the equivalent real-space unit cells

N        a (Å) b (Å) c (Å) a (°) b (°) g (°) V (Å3)  
1 23.754 6.184 11.037 90.00 97.83 90.00 1606.2    
2 23.754 6.184 11.037 90.00 97.83 90.00 1606.2    
3 23.754 6.184 11.037 90.00 97.83 90.00 1606.2    
4 6.216 22.094 11.890 97.89 92.45 89.66 1615.9    
5 6.216 22.094 11.890 97.89 92.46 89.66 1616.0    
6 12.250 12.325 11.209 94.79 100.14 105.57 1589.5    
7 12.033 16.056 11.227 100.22 96.05 99.40 2085.7    
8 27.278 11.948 12.515 90.00 95.75 90.00 4058.4    
9 12.130 17.377 11.080 95.26 96.58 101.71 2255.8    
10 23.473 12.441 12.283 90.00 103.44 90.00 3488.8    

2. The cell parameters indicates that it is most likely a monoclinic system (2 angles equal 90° and 1 angle is larger). There exists reflections that gives and odd number for the sum of 2 indices e g 4,1,1,and -1,1,2 whichs means that no general reflection condition exist and thus it must be lattice centering P. This gives the Bravais lattice mP.

 
h k l J d (Å) 2q (°) 2qob (°)  
2 0 0 2 11.7593 7.522 7.50
0 0 1 2 10.9272 8.095 8.07
-2 0 1 2 8.6110 10.274 10.25
2 0 1 2 7.5107 11.783 11.77
1 1 0 4 5.9771 14.819 14.82
4 0 0 2 5.8797 15.066 15.05
-4 0 1 2 5.4998 16.112 16.09
0 1 1 4 5.3793 16.475 16.44
-1 1 1 4 5.3220 16.654 16.64
-2 0 2 2 5.2349 16.933 16.90
1 1 1 4 5.1691 17.150 17.15
4 0 1 2 4.9063 18.075 18.07
3 1 0 4 4.8533 18.274 18.27
2 0 2 2 4.7155 18.813 18.81
-3 1 1 4 4.5812 19.370 19.36
3 1 1 4 4.3029 20.635 20.63
4 1 0 4 4.2598 20.846 20.84
-1 1 2 4 4.1041 21.646 21.64
6 0 0 2 3.9198 22.676 22.67
4 1 1 4 3.8426 23.138 23.10
-3 1 2 4 3.7907 23.459 23.45
5 1 0 4 3.7429 23.762 23.77
-5 1 1 4 3.6648 24.276 24.27
0 0 3 2 3.6424 24.428 24.41
-2 0 3 2 3.6215 24.571 24.54
-4 1 2 4 3.5327 25.198 25.19
3 1 2 4 3.4854 25.545 25.55
5 1 1 4 3.4288 25.974 25.98
2 0 3 2 3.3526 26.575 26.57
6 1 0 4 3.3101 26.923 26.91
-5 1 2 4 3.2568 27.372 27.37
4 1 2 4 3.2093 27.785 27.72
-1 1 3 4 3.1593 28.233 28.27
2 2 0 4 2.9885 29.882 29.81
0 2 1 4 2.9734 30.038 30.06
7 1 0 4 2.9518 30.263 30.27
8 0 0 2 2.9398 30.389 30.39
-2 2 1 4 2.9084 30.726 30.74

3. Glide plane: there exist reflections like 0,0,1 and 0,1,1 and 0,0,3 which means that there can not exist any plane perependicular to a (k odd, l odd and the sum also odd). There are also reflections like 3,1,0 and 4,1,0 which means that the reflection conditions for a plane perpendicular to C is not fulfilled (h odd, k odd and the sum also odd). On the contrary, the reflelction condition for an a-glide plane perpendicular to b is fulfilled (h=2n). There are no screw axis present (even though it seems to be h=2n, this is only a subset of the glide plane). This then support the thought that this is a monoclinic system.

4.  If it is monoclinic and with the above mentioned glide plane perpendicular to b and a twofold axes parallell to b, it should be space group P2/a. The space group is less common for naturally occuring organic material since they tend to "use" screw axis which facilitates a more efficient packing.

5. The cell refinement program gave the following results which also supports the monoclinic system with a glide plane perpendicular to b. The 2q zero value are within errors the same as the given precision which is reasonable. The value being significantly different from 0 indicates a possible small systematic deviation. The prescence of broad peaks and peaks with tail indicates influence of overlapping peaks or the impurity which makes it difficult to use higher angle data.

Cell parameters
  a (Å)   b (Å)   c (Å)   a (°)   b (°)   g (°)   V (Å3)
Value     23.72856     6.17111     11.03219     90.0000     97.9013     90.0000     1600.125
Error 0.00822 0.00189 0.00453 0.0000 0.0157 0.0000 1.525

Wavelength  l = 1.54056

Zero Error  2qzero = -0.0135 ± 0.0047

Reflections
    h       k       l     2qobs (°)   2qcalc (°) D 2q (°) s (°) D 2q/s    
2   0   0   7.5000 7.5029 -0.0029 0.0100 -0.3    
0   0   1   8.0700 8.0708 -0.0008 0.0100 -0.1    
-2   0   1   10.2500 10.2463 0.0037 0.0100 0.4    
2   0   1   11.7700 11.7692 0.0008 0.0100 0.1    
1   1   0   14.8200 14.8160 0.0040 0.0100 0.4    
4   0   0   15.0500 15.0520 -0.0020 0.0100 -0.2    
-4   0   1   16.0900 16.0878 0.0022 0.0100 0.2    
-1   1   1   16.6400 16.6462 -0.0062 0.0100 -0.6    
-2   0   2   16.9000 16.9015 -0.0015 0.0100 -0.1    
1   1   1   17.1500 17.1466 0.0034 0.0100 0.3    
4   0   1   18.0700 18.0690 0.0010 0.0100 0.1    
3   1   0   18.2700 18.2717 -0.0017 0.0100 -0.2