The single-crystal X-ray diffraction pattern from the β-phase of the industrially important Pigment Red 170 (β-P.R.170) consists of a difficult-to-disentangle mixture of Bragg diffraction superimposed by rods of diffuse scattering and satellite peaks. This extremely complicated diffraction pattern illustrates the complexity of real world crystals, whose underlying structure is far from the concept of a crystal being a regular periodic arrangement of unit cells usually presented in introductory crystallography textbooks. Such complex structures still present a big challenge to practitioners of X-ray crystallography.

Understanding of the photochemical properties of this pigment would benefit from knowledge of the specific local arrangement of molecules in the crystal structure, but such information was not available due to the disordered nature of this material. The focus of this thesis was to model the crystal structure of this material by an analysis of the total diffraction pattern.

The disorder in this material manifests itself as rods of strong diffuse scattering in the diffraction pattern. According to the mathematical description presented in the first part of the thesis, the type of disorder present in this material is stacking faults. These faults can occur during the stacking of the two dimensionally ordered molecular layers when the crystal grows. A detailed analysis of the diffraction pattern revealed that the rods of diffuse scattering pass through the Bragg reflections. Furthermore, it showed that a considerable percentage of the Bragg reflections is completely immersed in the strong diffuse streaks. As a result, the unit cell indexation and the accurate Bragg intensity estimation were extremely difficult.

An analysis of only the Bragg reflections resulted in two plausible average structures. Both structures have the same unit cell dimensions, but occur in different space groups, namely B21/g and P21/a. The model developed in B21/g has only one symmetry-independent disordered molecular layer in which there are two symmetry-independent molecules, both of which are disordered over two positions with an occupancy ratio 0.91:0.09 related by the vector [0, -0.158b, 0]. In contrast, the model developed in P21/a has two symmetry independent molecular layers of which only one is disordered. The disordered layer is similar to the unique layer of the other model, but this time the occupancy ratio is 0.65:0.35. In addition, the two models differ in the number of molecules in the asymmetric unit, relative placement of molecular layers in the unit cell and the number of crystallographic and non-crystallographic symmetry elements in the average unit cell. The agreement R-factors calculated from both models implied that the B21/g model is the better description of the average structure.

The basic structural unit in both models is the same. It possesses the layer group symmetry p 1 21/c 1. The geometries of all adjacent layer pairs in both models are equivalent. According to Order-Disorder theory, this implies that the two models belong to the same polytypic family, but they differ in their layer stacking sequences.

The last part of the work presents the initial attempts taken to estimate the layer stacking sequence in the real crystal using model crystals. Two model crystals were constructed in the computer with the aid of a random number generator using the atomic coordinates and site occupancies obtained from the two average structures. The correlations between the interacting layers were introduced and the total interaction energy of each crystal was minimized according to the Monte Carlo (MC) method. The MC minimized crystals were then used to calculate total scattering intensities.

Both disordered model crystals constructed and tested in this work produced broad diffuse scattering features superimposed with some fine structure. So far, the match with the experimental data is poor. It is not yet known whether the observed fine structure in each calculated pattern is due to some underlying periodicity of the molecular layers in the model crystal, or is just a consequence of the statistical noise in the MC simulations. Resolution of this problem will require future additional time-consuming calculations.

Warshamanage, Rangana. *The β-phase of Pigment Red 170: Structure Determination and Disorder Modelling.* 2014, University of Zurich, Faculty of Science.

## Abstract

The single-crystal X-ray diffraction pattern from the β-phase of the industrially important Pigment Red 170 (β-P.R.170) consists of a difficult-to-disentangle mixture of Bragg diffraction superimposed by rods of diffuse scattering and satellite peaks. This extremely complicated diffraction pattern illustrates the complexity of real world crystals, whose underlying structure is far from the concept of a crystal being a regular periodic arrangement of unit cells usually presented in introductory crystallography textbooks. Such complex structures still present a big challenge to practitioners of X-ray crystallography.

Understanding of the photochemical properties of this pigment would benefit from knowledge of the specific local arrangement of molecules in the crystal structure, but such information was not available due to the disordered nature of this material. The focus of this thesis was to model the crystal structure of this material by an analysis of the total diffraction pattern.

The disorder in this material manifests itself as rods of strong diffuse scattering in the diffraction pattern. According to the mathematical description presented in the first part of the thesis, the type of disorder present in this material is stacking faults. These faults can occur during the stacking of the two dimensionally ordered molecular layers when the crystal grows. A detailed analysis of the diffraction pattern revealed that the rods of diffuse scattering pass through the Bragg reflections. Furthermore, it showed that a considerable percentage of the Bragg reflections is completely immersed in the strong diffuse streaks. As a result, the unit cell indexation and the accurate Bragg intensity estimation were extremely difficult.

An analysis of only the Bragg reflections resulted in two plausible average structures. Both structures have the same unit cell dimensions, but occur in different space groups, namely B21/g and P21/a. The model developed in B21/g has only one symmetry-independent disordered molecular layer in which there are two symmetry-independent molecules, both of which are disordered over two positions with an occupancy ratio 0.91:0.09 related by the vector [0, -0.158b, 0]. In contrast, the model developed in P21/a has two symmetry independent molecular layers of which only one is disordered. The disordered layer is similar to the unique layer of the other model, but this time the occupancy ratio is 0.65:0.35. In addition, the two models differ in the number of molecules in the asymmetric unit, relative placement of molecular layers in the unit cell and the number of crystallographic and non-crystallographic symmetry elements in the average unit cell. The agreement R-factors calculated from both models implied that the B21/g model is the better description of the average structure.

The basic structural unit in both models is the same. It possesses the layer group symmetry p 1 21/c 1. The geometries of all adjacent layer pairs in both models are equivalent. According to Order-Disorder theory, this implies that the two models belong to the same polytypic family, but they differ in their layer stacking sequences.

The last part of the work presents the initial attempts taken to estimate the layer stacking sequence in the real crystal using model crystals. Two model crystals were constructed in the computer with the aid of a random number generator using the atomic coordinates and site occupancies obtained from the two average structures. The correlations between the interacting layers were introduced and the total interaction energy of each crystal was minimized according to the Monte Carlo (MC) method. The MC minimized crystals were then used to calculate total scattering intensities.

Both disordered model crystals constructed and tested in this work produced broad diffuse scattering features superimposed with some fine structure. So far, the match with the experimental data is poor. It is not yet known whether the observed fine structure in each calculated pattern is due to some underlying periodicity of the molecular layers in the model crystal, or is just a consequence of the statistical noise in the MC simulations. Resolution of this problem will require future additional time-consuming calculations.

## Downloads

## Additional indexing

Item Type: | Dissertation |
---|---|

Referees: | Bernstein Joel, Linden Anthony, Ernst K-H, Bürgi Hans-Beat |

Communities & Collections: | 07 Faculty of Science > Department of Chemistry |

Dewey Decimal Classification: | 540 Chemistry |

Uncontrolled Keywords: | diffuse scattering, disorder, pigment red 170, crystal structure |

Language: | English |

Date: | November 2014 |

Deposited On: | 20 Jan 2015 14:50 |

Last Modified: | 05 Apr 2016 18:53 |

Number of Pages: | 123 |

Funders: | SNF project 200021_137866, UZH |

## Download

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.