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7. Woche Quasikristalle W. Steurer

Anorganische Kristallchemie. Zeitplan. 1.-4. Woche Ionenkristalle Perowskit kovalente anorganische Verbindungen Zeolithe DLS (Geometrie optimierung) intermetallische Verbindungen 5.-6. Woche Pulverdiffraktometrie. 7. Woche Quasikristalle W. Steurer.

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7. Woche Quasikristalle W. Steurer

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  1. Anorganische Kristallchemie Zeitplan 1.-4. Woche Ionenkristalle Perowskit kovalente anorganische Verbindungen Zeolithe DLS (Geometrie optimierung) intermetallische Verbindungen 5.-6. Woche Pulverdiffraktometrie 7. Woche Quasikristalle W. Steurer 7.-15. Woche organische Kristallchemie und B. Schweizer Strukturdatenbanken

  2. Kristallchemie und Kristallstrukturdatenbanken Pulverdiffraktometrie • Einkristall Strukturanalyse • Strukturanalyse mittels Pulverdaten • Kristallchemie in der Strukturanalyse • Modellbau • Simulated annealing • Evolutionäre Algorithmen • FOCUS • Charge flipping

  3. Zeolithe FOCUS • 3-dimensionale, 4-fach verknüpfte Gerüststruktur

  4. Zeolithe • 3-dimensionale, 4-fach verknüpfte Gerüststruktur FOCUS • Eckenverknüpfte TO4 Tetraeder

  5. O-Si-O 109.5˚ Si-O-Si 145˚ Si-O 1.61 Å • Zeolithe • 3-dimensionale, 4-fach verknüpfte Gerüststruktur • Eckenverknüpfte TO4 Tetraeder FOCUS • bekannte T-O Bindungslängen, O-T-O und T-O-T Winkel

  6. startingphases electron density map • assignment of atoms by • peak height • minimum distances framework search peak search assignment of atoms to largest fragment framework classification histogram convergence? approximate unit cell contents individual minimum distances selected reflection intensities FOCUS new phase set no yes

  7. 1.4 Å 2.6 Å approximate unit cell contents individual minimum distances selected reflection intensities FOCUS • AlPO-ZON • a14.548 Å • b15.301 Å • c16.629 Å • RaumgruppePbca • Chemische Zusammensetzung |(RF)x|[Al32P32O128] V = 3956 Å3 16 T-Atome pro 1000 Å3 3.1 Å • Al - Al • Al - P • P - P • Al - O • P - O 1.6 Å O - O 2.3 Å 2.7 Å

  8. 10 15 20 25 30 35 40 45 AlPO-ZON • a = 14.548 Å, b = 15.301 Å, c = 16.629 Å • Pbca

  9. startingphases electron density map • assignment of atoms by • peak height • minimum distances framework search peak search assignment of atoms to largest fragment framework classification histogram convergence? approximate unit cell contents individual minimum distances selected reflection intensities FOCUS new phase set no yes

  10. Peak-Positionen und -Höhen

  11. startingphases electron density map • assignment of atoms by • peak height • minimum distances framework search peak search assignment of atoms to largest fragment framework classification histogram convergence? approximate unit cell contents individual minimum distances selected reflection intensities FOCUS new phase set no yes

  12. Atome durch Peakhöhe und miminale Abstände zugeordnet

  13. startingphases electron density map • assignment of atoms by • peak height • minimum distances framework search peak search assignment of atoms to largest fragment framework classification histogram convergence? approximate unit cell contents individual minimum distances selected reflection intensities FOCUS new phase set no yes

  14. Atome durch grösstes Fragment zugeordnet

  15. Atome durch grösstes Fragment zugeordnet

  16. Strukturfaktor Streufaktor new phase set • assignment of atoms by • peak height • minimum distances assignment of atoms to largest fragment Elektronendichte berechnete Phasen gemessene Amplituden

  17. startingphases electron density map • assignment of atoms by • peak height • minimum distances framework search peak search assignment of atoms to largest fragment framework classification histogram convergence? approximate unit cell contents individual minimum distances selected reflection intensities FOCUS new phase set no yes

  18. Gerüst-Klassifikation • Wie kann man ein Gerüst eindeutig erkennen? Coordination sequence 4 9 16 25 37 53 73 96 120 145 Loop configuration Vertex symbol 4 · 4 · 4 · 6 · 6 · 12

  19. VPI-9 • Chemische Zusammensetzung • Original K4Rb20[Si48Zn12O120]·64H2O • NH4-ausgetauscht (NH4)24[Si48Zn12O120]·64H2O • Daten Original NH4-ausgetauscht • Synchrotron SNBL an ESRF SNBL an ESRF • Wellenlänge 0.99995 Å 0.94734 Å • Elementarzelle • RaumgruppeP41212 P42/ncm • a 9.8837 Å 9.8946 Å • c 73.6505 Å 36.8715 Å P41212 73.6505 Å

  20. VPI-9 - FOCUS Input Raumgruppe P42/ncm Elementarzelle a 9.8946 Å b 36.8715 Å Atome / EZ Zn (4-fach verknüpft) 12 12 Si (4-fach verknüpft) 44 48 O (brückend) 112 120 minimale Abstände Zn - O 1.7 Å Zn - Si 2.9 Å Si - O 1.5 Å Zn - Zn 4.0 Å O - O 2.3 Å Si - Si 2.9 Å Reflexe 258 Gerüst-Typen gefunden (übernacht) 1356 (ein Typ 102 Mal gefunden)

  21. wahrscheinlichster Gerüst-Typ Histogramm der Gerüst-Typen Gerüst-Typen

  22. VPI-9 Gerüststruktur mit 7 (Si,Zn) pro asymmetrische Einheit

  23. VPI-9 Rubidium Zinkosilikat VPI-9 12 Si, 3 Zn, 30 O, 9 Rb, 2 K und 3 H2O pro asymmetrische Einheit

  24. Kristallchemie und Kristallstrukturdatenbanken Pulverdiffraktometrie • Einkristall Strukturanalyse • Strukturanalyse mittels Pulverdaten • Kristallchemie in der Strukturanalyse • Modellbau • Simulated annealing • Evolutionäre Algorithmen • FOCUS • Charge flipping

  25. assign random phases flip sign of ed < δ Fourier transform Charge Flipping |Fhkl(obs)| δ (ed threshold for flipping) phase shifts for weak reflections? electron density map combine |Fhkl(obs)| with φhkl(calc) perturbed electron density map |Fhkl(calc)| φhkl(calc) R-value (|Fhkl(calc)| vs |Fhkl(obs)| Oszlányi, G. and Sütõ, A. (2004). Acta Cryst. A60, 134-141 Oszlányi, G. and Sütõ, A. (2005). Acta Cryst. A61, 1347-1352

  26. assign random phases flip sign of ed < δ Fourier transform Charge Flipping (powder) |Fhkl(obs)| with overlap groups δ (ed threshold for flipping) phase shifts for weak reflections? repartitioning after n cycles electron density histogram |Fhkl(obs)| δ (ed threshold for flipping) phase shifts for weak reflections? new|Fhkl(obs)| electron density map repartition overlapping reflections combine |Fhkl(obs)| with φhkl(calc) perturbed electron density map |Fhkl(calc)| φhkl(calc) |Fhkl(calc)| φhkl(calc) R-value Fourier transform modified electron density map yes n cycles? no histogram matching

  27. Histogram matching 12 Å Electronendichte alle ¼ Å 48 x 32 x 20 = 30720 points 8 Å 5 Å

  28. typischer Zeolith Karte nach ein paar Zyklen Charge Flipping Histogram matching Elektronendichte Werte nach Intensität ordnen Liste in 50 Bereiche aufteilen Durchschnittsdichte pro Bereich rechnen

  29. Powder Charge Flipping [Zr12P16O60(OH)4F8]

  30. Powder Charge Flipping [Zr12P16O60(OH)4F8]

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