4.1 Challenges with CrysAlis
4.2.1 The temperature’s impact on relevant parameters
In our investigation of the crystal structure – via the images of reciprocal space – we use the hexagonal thiourea-lattice as a reference system or a “background” to contrast any temperature related changes we might observe. An underlying assumption is that the thiourea framework is not altered significantly in the cooling process.
The next four pages contain two sets of three plots each; one for the lattice parametersa,candγ, and the another of the three rotations anglesr1,r2andr3. Each page is for a particular crystal, with an additional page for the alternative processing of crystal 4.
Starting with crystal 1, we first notice an abrupt change in the lattice parametersa,candγ as the temperature decreases to140 Kor lower;ais lowered whilecandγ increase. Another feature in the plots is a clear tendency for theaandcparameters to decline with lower temperature, which is also very symmetric about the turning point at 90 K. The same pattern is evident in the rotation angles, too.
Moving on to the first processing of crystal 4 – which followed the same standard procedure as the previous crystal – the same traits observed for crystal 1 also apply fora,candγ. The development of the rotation angles as function of temperature follow a less clear pattern here. All plots, except forγ, in the case where no instrument parameters were preset are very chaotic, even though some resemblance with the previous descriptions can be seen.
The lattice parameteradoes not show the same abruptness as commented for crystal 1.
Finally, in crystal 9 we see the same decline of theaandcparameters with colder temperature, butadoes not follow an obvious pattern around the coldest temperatures.
The uncertainties provided by CrysAlisseem suspiciously small; nonetheless, all data has been subjected to the same calculation procedures by the software.
Stian Penev Ramsnes
Aspects of X-Ray Diffraction UsingMathematica Discussion Thiourea-ferrocene
The temperature’s impact on crystal 1
16.00
Figure 4.3: (a)and(b): Lattice parametersaandcof crystal 1 at various temperatures with ångströms on the vertical axes.(c): The cell parameterγas calculated for an unconstrained cell (in degrees).
-0.95
(a)Rotation angler1.
-9.55
(b)Rotation angler2.
70.7
(c)Rotation angler3.
Figure 4.4:Rotation anglesr1,r2andr3of crystal 1 after transformations. Values on vertical axes are in degrees.
Stian Penev Ramsnes
Aspects of X-Ray Diffraction UsingMathematica Discussion Thiourea-ferrocene
The temperature’s impact on crystal 4(presetting instrument model with refined values)
16.10
Figure 4.5: (a)and(b): Lattice parametersaandcof crystal 4 at various temperatures with ångströms on the vertical axes.(c): The cell parameterγas calculated for an unconstrained cell (in degrees).
-30.0
(a)Rotation angler1.
28.4
(b)Rotation angler2.
-10.0
(c)Rotation angler3.
Figure 4.6:Rotation anglesr1,r2andr3of crystal 4 after transformations. Values on vertical axes are in degrees.
Stian Penev Ramsnes
Aspects of X-Ray Diffraction UsingMathematica Discussion Thiourea-ferrocene
The temperature’s impact on crystal 4(no presetting of the instrument model parameters)
16.0
Figure 4.7: (a)and(b): Lattice parametersaandcof crystal 4 at various temperatures with ångströms on the vertical axes.(c): The cell parameterγas calculated for an unconstrained cell (in degrees).
-15.2
(a)Rotation angler1.
-38.4
(b)Rotation angler2.
96.5
(c)Rotation angler3.
Figure 4.8:Rotation anglesr1,r2andr3of crystal 4 after transformations. Values on vertical axes are in degrees.
Stian Penev Ramsnes
Aspects of X-Ray Diffraction UsingMathematica Discussion Thiourea-ferrocene
The temperature’s impact on crystal 9
16.20
Figure 4.9: (a)and(b): Lattice parametersaandcof crystal 9 at various temperatures with ångströms on the vertical axes.(c): The cell parameterγas calculated for an unconstrained cell (in degrees).
-174.6
(a)Rotation angler1.
22.05
(b)Rotation angler2.
-153.55
(c)Rotation angler3.
Figure 4.10:Rotation anglesr1,r2andr3of crystal 9 after transformations. Values on vertical axes are in degrees.
Stian Penev Ramsnes
Aspects of X-Ray Diffraction UsingMathematica Discussion Thiourea-ferrocene
Mosaicity parameters
The peaks are assumed to follow a Gaussian distribution; the mosaicity is defined as the standard deviation of this curve. Figure 4.11 show plots of mosaicities extracted from data (after data reduction). The degree of mosaicity is given for three different scanning directions.
0.0
Figure 4.11:Mosaicity parameters of crystals 1, 4 and 9. e1ande2are directions in the detector plane, whilee3is in the scanning direction.[47]Note that all vertical axes show the same range;0.0°to2.5°.
It is clear that the colder temperatures affect the mosaicity in thee3direction most.
When looking over the structure solved in Olex2 for the data points in Figure 4.11f and Figure 4.11i with mosaicity over1.0°, we find that they correspond to the cases where the iron atoms had anisotropic displacement parameters visible flattened in the hexagonal plane (normal to the tunnel axis).
Also note that the100 Kdata point with the large mosaicity in Figure 4.11i correspond to when the prominent splitting of reflections occurs, as seen in Figure 3.36d. This provides a link between the three observations: (i) splitting of reflections, (ii) large mosaicity and (iii) the shift of the iron atom’s anisotropic displacement parameters.
Stian Penev Ramsnes
Chapter 5 Conclusion
Structure factors and silicon data
The StructureFactorTable, which is a continuation of Mathematica code written by Thorkildsen and Larsen, has shown to produce values in good agreement with the literature. Structure factors generated with the Mathematicafunction were compared with results from experimental silicon data. We saw a decline in the intensity of the normally strong reflections, which we interpreted as a consequence of dynamical effects.
Room temperature analysis and refinement
An improvement of the instrument model residual factor could be traced back to a thorough inspection of the peak table, while its effect on the analysis and refinement of thiourea-ferrocene data remains inconclusive.
The «auto analyse unit cell» peak hunting method seems to find more peaks than the regular automatic method, and has since its discovery, been the preferred choice.
Temperature-induced phase transitions
Descriptions of the development of reciprocal for the thiourea-ferrocene crystals:
Transition Description 290 Kto240 K (no special remarks) 240 Kto200 K (no special remarks)
200 Kto180 K Emergence of weak satellites and intermediate reflections (crystal 1);
180 Kto165 K Satellites increase in numbers and intensity (crystal 1) 165 Kto155 K (no special remarks)
155 Kto140 K The most significant change – splitting of reflections (crystals 1 and 4);
Disappearance of intermediate reflections (crystal 1)
140 Kto100 K Satellites increase in numbers and intensity (crystal 1); splitting of nodes (crystal 9) 100 Kto90 K (no special remarks)
Table 5.1:Characteristic observations of the reciprocal space at studied temperature transitions.
The observation of splitting of reflections was linked to both a relatively large mosaicity (over1.0°) and a shift of the iron atom’s anisotropic displacement parameters to be most prominent in the plane perpendicular to the tunnel axis.
Twinning
The thiourea-ferrocene sample referred to as «crystal 1» is concluded to be twinned by so-called «reticular merohedry».
Remarkable diffraction patterns emerge in the temperature range from155 Kto200 Kat specific fractions ofl
Stian Penev Ramsnes
Aspects of X-Ray Diffraction UsingMathematica Conclusion Future work