7. Woche Quasikristalle W. Steurer

Zeitplan

1.-4. Woche IonenkristallePerowskit

kovalente anorganische VerbindungenZeolitheDLS (Geometrie optimierung)

intermetallische Verbindungen

5.-6. Woche Pulverdiffraktometrie

7.-15. Woche organische Kristallchemie und B. SchweizerStrukturdatenbanken

Anorganische Kristallchemie

Kristallchemie und Kristallstrukturdatenbanken

Pulverdiffraktometrie

Einkristall Strukturanalyse

Strukturanalyse mittels Pulverdaten

Kristallchemie in der StrukturanalyseModellbauSimulated annealingEvolutionäre AlgorithmenFOCUSCharge flipping

3-dimensionale, 4-fach verknüpfte Gerüststruktur

FOCUS

Zeolithe

Zeolithe3-dimensionale, 4-fach verknüpfte Gerüststruktur

Eckenverknüpfte TO4 Tetraeder

FOCUS

O-Si-O 109.5˚

Si-O-Si 145˚

bekannte T-O Bindungslängen, O-T-O und T-O-T Winkel

Si-O 1.61 Å

FOCUS

Zeolithe3-dimensionale, 4-fach verknüpfte GerüststrukturEckenverknüpfte TO4 Tetraeder

convergence?

framework search

yesno

FOCUS approximate unit cell contentsindividual minimum distancesselected reflection intensities

electron density map

peak searchassignment of atoms by

peak heightminimum distances

assignment of atoms to largest

fragment

new phase set

starting phases

framework classification

histogram

FOCUS approximate unit cell contentsindividual minimum distancesselected reflection intensities

AlPO-ZON

a 14.548 Åb 15.301 Åc 16.629 Å

Raumgruppe Pbca

Chemische Zusammensetzung |(RF)x|[Al32P32O128]

Al - AlAl - PP - P

V = 3956 Å3

16 T-Atomepro 1000 Å3

Al - OP - O

3.1 Å

2.7 Å2.6 Å

1.4 Å

2.3 Å

1.6 Å

O - O

10 15 20 25 30 35 40 45

AlPO-ZONa = 14.548 Å, b = 15.301 Å, c = 16.629 ÅPbca

convergence?

framework search

yesno

FOCUS approximate unit cell contentsindividual minimum distancesselected reflection intensities

electron density map

peak searchassignment of atoms by

peak heightminimum distances

assignment of atoms to largest

fragment

new phase set

starting phases

framework classification

histogram

Peak-Positionen und -Höhen

convergence?

framework search

yesno

FOCUS approximate unit cell contentsindividual minimum distancesselected reflection intensities

electron density map

peak searchassignment of atoms by

peak heightminimum distances

assignment of atoms to largest

fragment

new phase set

starting phases

framework classification

histogram

Atome durch Peakhöhe undmiminale Abstände zugeordnet

convergence?

framework search

yesno

FOCUS approximate unit cell contentsindividual minimum distancesselected reflection intensities

electron density map

peak searchassignment of atoms by

peak heightminimum distances

assignment of atoms to largest

fragment

new phase set

starting phases

framework classification

histogram

Atome durch grösstes Fragment zugeordnet

Atome durch grösstes Fragment zugeordnet

new phase set

assignment of atoms by

peak heightminimum distances

assignment of atoms to largest

fragment

Elektronendichte

Strukturfaktor

Streufaktor

berechnete Phasen

gemessene Amplituden

convergence?

framework search

yesno

FOCUS approximate unit cell contentsindividual minimum distancesselected reflection intensities

electron density map

peak searchassignment of atoms by

peak heightminimum distances

assignment of atoms to largest

fragment

new phase set

starting phases

framework classification

histogram

Gerüst-Klassifikation

Wie kann man ein Gerüst eindeutig erkennen?

4 9 16 25

Coordination sequence

Loop configuration

Vertex symbol

37 53 73 96 120 145

4 · 4 · 4 · 6 · 6 · 12

ElementarzelleRaumgruppe P41212 P42/ncma 9.8837 Å 9.8946 Åc 73.6505 Å 36.8715 Å

P4121

2

VPI-9

Chemische ZusammensetzungOriginal

K4Rb20[Si48Zn12O120]·64H2ONH4-ausgetauscht

(NH4)24[Si48Zn12O120]·64H2O

Daten Original NH4-ausgetauscht

Synchrotron SNBL an ESRF SNBL an ESRFWellenlänge 0.99995 Å 0.94734 Å

73.6505 Å

VPI-9 - FOCUS Input

Raumgruppe P42/ncm

Elementarzelle a 9.8946 Åb 36.8715 Å

Atome / EZ Zn (4-fach verknüpft) 12 12Si (4-fach verknüpft) 44 48O (brückend) 112 120

minimale Abstände Zn - O 1.7 Å Zn - Si2.9 Å

Si - O 1.5 Å Zn - Zn 4.0 ÅO - O 2.3 Å Si - Si 2.9 Å

Reflexe 258Gerüst-Typen gefunden (übernacht) 1356

(ein Typ 102 Mal gefunden)

Histogramm der Gerüst-Typen

Gerüst-Typen

wahrscheinlichster Gerüst-Typ

VPI-9

Gerüststruktur mit 7 (Si,Zn) pro asymmetrische Einheit

Rubidium Zinkosilikat VPI-912 Si, 3 Zn, 30 O, 9 Rb, 2 K und 3 H2O pro asymmetrische Einheit

VPI-9

Kristallchemie und Kristallstrukturdatenbanken

Pulverdiffraktometrie

Einkristall Strukturanalyse

Strukturanalyse mittels Pulverdaten

Kristallchemie in der StrukturanalyseModellbauSimulated annealingEvolutionäre AlgorithmenFOCUSCharge flipping

assign random phases

flip sign of ed < δ

Fourier transform

R-value(|Fhkl(calc)| vs |Fhkl(obs)|

combine

|Fhkl(obs)|

with

φhkl(calc)

Charge Flipping

|Fhkl(obs)|

δ (ed threshold for flipping)phase shifts for weak reflections?

electron density map

perturbed electron density map

|Fhkl(calc)|φhkl(calc)

Oszlányi, G. and Sütõ, A. (2004). Acta Cryst. A60, 134-141Oszlányi, G. and Sütõ, A. (2005). Acta Cryst. A61, 1347-1352

|Fhkl(obs)|

δ (ed threshold for flipping)phase shifts for weak reflections?

|Fhkl(obs)| with overlap groups

δ (ed threshold for flipping)phase shifts for weak reflections?

repartitioning after n cycleselectron density histogram

assign random phases

flip sign of ed < δ

Fourier transform

R-value

combine

|Fhkl(obs)|

with

φhkl(calc)

electron density map

perturbed electron density map

|Fhkl(calc)|φhkl(calc)

yes no

histogram matching

modified electron density map

Fourier transform

|Fhkl(calc)|φhkl(calc)

repartitionoverlappingreflections

new|Fhkl(obs)|

n cycles?

Charge Flipping(powder)

12 Å

8 Å

5 Å

Electronendichte alle ¼ Å

48 x 32 x 20 = 30720 points

Histogram matching

Histogram matching

Elektronendichte Werte nach Intensität ordnenListe in 50 Bereiche aufteilenDurchschnittsdichte pro Bereich rechnen

typischer Zeolith

Karte nach ein paar Zyklen Charge Flipping

Powder Charge Flipping[Zr12P16O60(OH)4F8]

Powder Charge Flipping[Zr12P16O60(OH)4F8]