Modulation of incommensurately modulated structures studied by the maximum entropy method [Elektronische Ressource] / von Li Liang

Modulation of IncommensuratelyModulated Structures Studied bythe Maximum Entropy MethodVon der Universit¨at Bayreuthzur Erlangung der Grades einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigte AbhandlungvonLi Liangaus Jinan, China1. Gutachter: Prof. dr. Sander van Smaalen2. Gutachter: PD. Dr. Natalia DubrovinskaiaTag der Einreichung: 26. 10. 2010Tag der Kolloquiums: 17. 01. 20112，34Contents1 Introduction 12 Aperiodic crystallography and superspace 32.1Aperiodiccrystallography........................ 32.1.1 Incommensuratemodulatedstructures.. 42.1.2 Incommensuratecompositestructures... 62.1.3 Quasicrystals........................... 72.2Superspace........... 72.2.1 Reciprocalanddirectsuperspace..... 72.2.2 Symmetryinsuperspace.....................102.3Modulationfunctions................122.3.1 Differenttypesofmodulationfunctions..132.3.2 Modulationfunctionsusedinthepresentthesis........143 The Maximum Entropy Method 173.1ApplicationsoftheMEM ........................173.2PrincipleoftheMEM-BayMEM.........184 Integration of aperiodic crystals diffraction data 234.1 The EVAL15method...........................234.2Integratingofdiffractiondataofaperiodiccrystals...........234.3 Case study: data integration of Rb ZnCl by EVAL15.........252 44.3.1 Indexingofreflections......................294.3.2 Refinement.................30iii CONTENTS4.3.3 Finding the q-vector.......................354.3.4 Integration ........384.3.