The modulation patterns

The patterns we see at integerlrepeats itself every six units ofl, as seen at ambient temperatures in Figure 3.16 and even more clearly when the reflections split, as seen in Figure 3.18.

Like the diffraction patterns at integerl, the patterns appearing atl±0.2,l±0.4,l±0.6andl±0.8has a period of six units ofl, but emerge only at the specific temperatures listed in Table 3.11. In all cases, there is no significant change between the temperatures165 Kand155 K. Since the diffractograms show no asymmetry before and after reaching the minimum temperature of90 K, there are effectively just three unique images of each of the six patterns. These are shown in Figure 3.24.

(a) Intermediate reflections at 155 K in the (h, k,3.60)

plane. (b) Intermediate reflections at 155 K in the (h, k,5.60)

plane.

Figure 3.23:Intermediate reflections of the second type at the same temperature, but in two different planes. If we zoom in on the reflections in, we will see that many of them are clusters of two or three spots. In(b)we clearly see that the reflections are arranged in hexagons, and that these follow a hexagonal pattern themselves. The reflections in(a)fit in the middle of the smallest hexagons in(b).

Stian Penev Ramsnes 

Aspects of X-Ray Diffraction UsingMathematica Analysis Thiourea-ferrocene – crystal 1

Stian Penev Ramsnes 

Aspects of X-Ray Diffraction UsingMathematica Analysis Thiourea-ferrocene – crystal 1

Figure 3.24:Reconstructions of reciprocal space for crystal 1 at thel+ 0.2-patterns for the three temperatures where these appear.

Each row corresponds to a certain plane in reciprocal space, while each column a fixed temperature (see bottom corners).

We see the same pattern at each l+ 0.2-plane: As we decrease the temperature from ambient conditions, the intermediate reflections first appear at200 K. They grow in numbers until reaching a maximum at around165 K to155 K, before abruptly disappearing at or before140 K.

Complementary modulation patterns

The relation between the modulation patterns seems to be more complex than theABC ACB pattern for the integerl-planes in ref. Still, the planes come in “pairs” that complement each other in the sense that they do not overlap but belong to the same diffraction pattern. The pair of intermediate patterns atl±0.2are centrosymmetric about that givenl. Some pairs have overlap of reflections; a brief overview is given in Table 3.12.

l₁ l₂ Note on overlapping 0.8 1.2 No overlap

1.8 2.2 No overlap 2.8 3.2 Somewhat overlap 3.8 4.2 No overlap 4.8 5.2 No overlap 5.8 0.2 Somewhat overlap

Table 3.12:Overview for the complementary layers(hkl1)and(hkl2).

The six pairs of the mentioned planes have been combined to produce new images, shown in Figure 3.25. These images have some common features in their patterns, but it is difficult to say anything conclusive. They also seem to bear some resemblance to the planes in Figure 3.18 with split reflections.

Stian Penev Ramsnes 

Aspects of X-Ray Diffraction UsingMathematica Analysis Thiourea-ferrocene – crystal 1

(a)(h, k,0.8)and(h, k,1.2). (b)(h, k,5.8)and(h, k,0.2).

(c)(h, k,1.8)and(h, k,2.2). (d)(h, k,3.8)and(h, k,4.2).

(e)(h, k,2.8)and(h, k,3.2). (f)(h, k,4.8)and(h, k,5.2).

Figure 3.25:Complementaryl±0.2modulations. All reconstructions are from theCrystal_5_(05)_165Kdata subset.

Stian Penev Ramsnes 

Aspects of X-Ray Diffraction UsingMathematica Analysis Crystal 4

3.5 Crystal 4

17 data subsets have been collected also for crystal 4, but they differ from crystal 1 in that we have two data subsets on100 K(one replaces90 K) and one extra «test run» at room temperature. Recall the specific measurement points from Table 3.5. TheCrysAlisprocedure is identical to that of crystal 1. The three mains steps are:

1. Setting the diffractometer instrument parameters to values obtained from room temperature data (Table 3.7).

2. Finding peaks, determining the unit cell, reindexing, removing wrongly indexed peaks and refining the in-strument model parameters.

3. Extracting refined instrument parameters and orientation matrices from log files.

For this crystal, the data was also processed without presetting the refined instrument parameters in order to check the necessity of the refinement procedure. The whole process from peak hunt to right before data reduction is the same.

Like before, once each data subset has been processed and refined they need to be “aligned” by transformation of the orientation matrix, as it affects the orientation of the reconstructions of reciprocal space. We did not experi-ence the same trouble with transformations of the orientation matrix as with crystal 1; the required transformation matrices were obtained using theUBtransformationfunction (as explained on page 47) with Laue class¯3m (orientation¯3m1).

Comments on the analysis without preset instrument parameters

It was discovered at this point that performing the peak hunt using the option «auto analyse unit cell» yielded much better results. Using the «automatic threshold and background detection» method found in Lattice wizard

Peak hunting wizard (see Figure 2.13),CrysAlistends to find a rhombohedral lattice that accounts for about35 % of the found peaks, for the seven first data subsets. When going into the Ewald explorer and checking for twins, the program finds a twin, rotate120°about the original lattice, that indexes about the same amount of peaks. After using the «auto analyse unit cell», however, the amount of matching peaks had risen to about90 %. This method has since been used on all data sets.

The two methods – with and without preset instrument parameters – both had one instance each whereCrysAlis did not succeed in setting a rhombohedral lattice automatically. With preset parameters the case was data subset 09 at100 K, in which the lattice was initially suggested to be2/m,C-centred. The lattice was, rather surprisingly, sat correctly after performing the «auto analyse unit cell» a second time. With no initial instrument settings, we had the same problem with data subset 10 at140 K. In this case the refined parameters were used, giving the rhombohedral lattice after a second peak hunt.

In retroperspective, the desired unit cells could most probably have been obtained with transformation matrices found in chapter 5.1 of theInternational Tables for Crystallography, volume A^[92]†.

†This was accomplished when the same problem arose during a reprocessing of data.

Stian Penev Ramsnes 

Aspects of X-Ray Diffraction UsingMathematica Analysis Crystal 4