Introduction to Volume H of International Tables for Crystallography

Powder Diffraction

James A. Kaduk Poly Crystallography Inc.

Naperville IL 60540 kaduk@polycrystallography.com

Part A: Instrumentation and Methods

1. Overview and principles of powder diffraction

Robert Dinnebier and Simon Billinge

6

2. Instrumentation – Laboratory X-rays

Arnt Kern

3. Synchrotron radiation and powder diffraction

Andy Fitch

Synchrotron Radiation

• Production of synchrotron radiation – Bending magnets, insertion devices

• Optics – Monochromators, mirrors, compound refractive lenses

• Diffractometers • Experimental factors

– Polarization, radiation damage, beam heating, choice of wavelength, angular and spatial and time resolution

4. Instrumentation - Neutrons

Juan Rodriguez-Carvajal

5. Instrumentation - Electrons

J. M. Zuo, J. L. Labar, J. Zhang, T. E. Gorelik, and U. Kolb

6. Sample Preparation

Pam Whitfield and Ashfia Huq

Sample (Specimen) Preparation

• Particle statistics • Preferred orientation • Absorption (surface roughness),

microabsorption, and extinction • Specimen holders – reflection, transmission,

zero background, capillaries • Neutron powder diffraction

7. Sample Environment – Temperature

C. Reiss

8. Sample Environment – High Pressure

A. Katrusiak

9. Sample Environment – Magnetic and Electric Fields in

Powder Diffraction H. Ehrenberg and H. Fuess

10. Sample Environment – Reaction Cells

P. Pattison and W. van Beck

11. Data Processing – Diffraction from Powders

Peter Stephens

12. Data Processing – Powder Diffraction and Peak Profiles

Bob Von Dreele

13. Data Processing - Indexing

Angela Altomare, C. Cuocci, A. Moltineri, and Rosanna Rizzi

Indexing

• Traditional and non-traditional algorithms • Programs • Examples

14. Data Processing – Data Reduction to |Fhkl|

Armel Le Bail

16. Qualitative Analysis – Whole Powder Pattern Modeling:

Microstructure Determination from Powder Diffraction Data

Matteo Leoni

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40 TEM WPPM

fre

quen

cy

grain diameter D (nm)

Size Distribution in Ceria Powder

Size Distribution of Cuprite

0 2 4 6 8 10 12 14 16 18 20 22 240.00

0.05

0.10

0.15

0.20

0.25

g(D)

(ar

b. u

nits

)

D (nm)0 2 4 6 8 10 12 14 16 18 20 22 24

0

10

20

30

40

50

60

70

g(D)

D3 (ar

b. u

nits

)D (nm)

17. Qualitative Analysis – Total Scattering Analysis

Thomas Proffen and Simon Billinge

18. Qualitative Analysis – Crystallographic Databases and

Powder Diffraction Jim Kaduk

Powder Diffraction File

• History • Search/match algorithms • Quality marks • Features • Boolean logic – trace analysis

Structural Databases

• Cambridge Structural Database – Mercury • Inorganic Crystal Structure Database

– ANX, reduced cell, distance searches • Pearson’s Crystal Data • Metals Data File • Protein Data Bank – calculation of protein patterns • Crystallography Open Database • Other internet resources

19. Qualitative Analysis – The Clustering and Visualization of

Powder Diffraction Data Chris Gilmore

Aspirin data into which 5 amorphous samples have been incorporated. (a) The resulting dendrogram with the amorphous samples isolated at the right side of the dendrogram. (b) The corresponding MMDS plot, with the amorphous samples isolated.

20. Standards and instrument Performance – The Optics,

Alignment, and Calibration of the Bragg-Brentano Laboratory X-ray

Diffractometer Jim Cline, David Black, Donald

Windover, and Albert Henins

21. Two-Dimensional Powder Diffraction

Bob He

22. Quantitative Phase Analysis

Ian Madsen, Nikki Scarlett, Reinhard Kleeberg, and Karsten Knorr

44

Quantitative Phase Analysis

• Classical and Rietveld • Alternative methods

– Phase and instrument constants • PONKCS • Quantification of amorphous material • QPA from energy-dispersive data • Increasing accuracy

23. Solving Crystal Structures – An Overview of Currently Used

Structure Determination Methods for Powder Diffraction Data

Kenneth Shankland

Structure Solution • Conventional and modified direct methods • Patterson function • Resonant scattering • Isomorphous replacement • Maximum entropy methods • Charge flipping • Molecular envelopes • Model building • Molecular replacement • Global optimization

24. Solving Crystal Structures – Reciprocal Space Methods

Angela Altomare, C. Cuocci, A. Moltineri, and R. Rizzi

Reciprocal Space Methods

• Patterson, maximum entropy, direct methods, charge flipping

• Direct methods • Structure model optimization

• Fourier recycling, weighted least squares, resolution bias modification

• EXPO

25. Solving Crystal Structures – Real Space Methods for Structure Solution from Powder Diffraction

Data: Application to Molecular Structures

Bill David

26. Solving Crystal Structures – The Use of Supplementary Information

to Solve Crystal Structures Alistair Florence

Supplementary Information

• Molecular volume • Bond lengths and angles • Flexible ring conformations • Torsion angle constraints • Solid state NMR information • Intermolecular distance constraints • Hydrogen atoms • Crystal structure prediction

43. Solving Crystal Structures – Solving and Refining Inorganic

Structures Radovan Cerny

41. Solving Crystal Structures – Solving and Refining Zeolite

Structures Lynne McCusker and Christian Baerlocher

27. Rietveld Refinement

Brian Toby

Rietveld Refinement

• History • Rietveld vs. single crystal refinements • Multiphase and multi-dataset fitting • Mechanism of Rietveld fitting • Agreement factors • Restraints and constraints • The order to introduce parameters in a fit

28. Maximum Entropy Methods Applied to Powder Diffraction Data

Robert Dinnebier

29. Structure Validation

Jim Kaduk

Structure Validation

• Statistical measures (with Brian Toby) • Graphical measures (with Brian Toby and Judy Stalick)

• Chemical reasonableness – Organic and inorganic

• checkCIF/PLATON

XRD and DFT

Cations Reference Experiment RMS Δ, Å

H3 CITRAC10 Single crystal 0.030a

H3(H2O)1 CITARC Single crystal 0.036a

Li1H2 LIHCIT Single crystal 0.418a

Li1(H2O)1 PIGPUQ Single crystal 0.082c

Li3(H2O)4 FUQFUS Single crystal 0.091c

Li3(H2O)5 CADJIA Single crystal 0.101c

Na1H2 New powder Powder 0.261a

Na1H2 NAHCIT Single crystal 0.040a

Na2H1(H2O)1.5 New single crystal Single crystal 0.048b

Na3 New powder Powder 0.080a

Na3(H2O)2 UMOGAE Single crystal 0.068c

RMS differences (Å) between the non-hydrogen atoms in experimental and DFT optimized crystal structures of Group 1 citrate salts, C6H5O7

3-

30. Powder CIF

Brian Toby

Part B: Defects, Texture, Microstructure, and Fibres

31. Disordered Heterogeneous Materials

Andrew Allen

Obtainable information SAXS SANS WAXS and WANS (powder

diffraction)

Total scattering

lattice spacings, crystal phases X

mean precipitate or pore

diameter, shape

X X

size distribution X X

pore or particle volume fraction X X

pore or particle surface area X X

composition, density of solid

phases

X X X

interparticle interactions X X

particle or pore pair

distribution function

X X

local structure X X

atomic pair distribution

function

X X

Quantitative Information Available

Small-Angle Scattering

• (U)SAXS tools and optics • Data reduction and calibration • Reflectivity and grazing incidence • Quantitative interpretation • Anomalous and contrast variation SAXS • SAS effects in WAS

34. Stress and Strain

Nicolae Popa

Stress and Strain This chapter is a review of the basic concepts, models, methods and approaches in the investigation by diffraction of the stress and strain in polycrystalline materials. The chapter contains eight sections that can be grouped in three parts. In the first part the specific quantities in single crystals and polycrystals are defined Together with the mathematical background. The state of art in the field and the classical models allowing determining the macro strain and stress in the most of samples are described in the second part. The third part is dedicated to the modern analysis by generalized spherical harmonics of the diffraction lines shift and breadth caused by strain in textured polycrystalline sample.

35. Multigrain Crystallography and Three-Dimensional Grain Mapping

H. F. Poulsen and Gavin Vaughan

Rendition of the 3D grain structure in a cylindrical beta-Ti specimen containing 1008 Grains, as obtained by the DCT algorithm. From Ludwig et al., 2008.

36. Quantitative Texture Analysis and Combined Analysis

Daniel Chateigner, Luca Lutterotti, and Magali Morales

38. Thin Films and Multilayers

Mario Birkholz

Thin Films and Multilayers

• Effects of absorption • Grazing incidence configurations • Textures and depth dependence • Stress and strain analysis • X-ray reflectivity • Grazing incidence X-ray scattering

39. Fibres

Paul Langan

xx. Wide-Angle Scattering by Noncrystalline Materials

Simon Bates

Figure 1. Calculated Debye diffraction response for a single mannitol molecule displayed with the Coherent and incoherent diffraction responses. The Y axis is in electron units.

Figure 8: measured Bragg-Brentano data form Si SRM 640d displayed with the calculated full background response including the instrumental contribution, Brehmstrallung, thermal diffuse scattering and Compton scattering. The Derived instrumental response is shown in red.

Figure 10: Normalized analytical data for dry and partially dry sucrose lyophilizates. Each analytical data set has the same integrated intensity and matching asymptotic behavior towards 70 degrees 2Theta. An additional constraint of matching low angle analytical signal was also imposed during the normalization.

Part C: Applications

40. Macromolecular Powder Diffraction

Irene Margiolaki

42. Mining and Mineral Processing

Nikki Scarlett and Dave Bish

44. Applications in Glass Ceramics

Scott Misture

45. Ceramic Materials and Powder Diffraction

Winnie Wong-Ng

XRPD of Ceramics

• Qualitative and quantitative analysis • Phase equilibria • Phase evolution and transformation • Structure and microstructure

– Size, strain, imperfections, texture, roughness • Processing and performance

– Sintering, kinetics, toughening, …

47. Powder Diffraction Characterization of Cements

Miguel Aranda, A. De La Torre, and L. Leon-Reina

110

Concentration Errors in Synthetic Portland Cements

Weight Concentration, %10

Con

cent

ratio

n Er

ror,

wt%

abs

olut

e

-3

-2

-1

0

1

2

3

49. Powder Diffraction and Pharmaceuticals

Joel Bernstein, S. M. Reutzel-Edens, and J.-O. Henck

Powder Diffraction and Pharmaceuticals

• Identification and characterization • Indexing • Quantification (crystalline and amorphous) • QC and regulatory issues • Creating and protecting intellectual property • Counterfeit medicines

50. Forensic Applications of X-ray Powder Diffraction

David Rendle

Forensic XRD • Drugs and toxicology • Paint and pigments • Pathology • Metals and alloys • Soils and minerals • Gunshot residues and explosives • Paper • Polymers • Experimental and procedural issues

51. Materials for Energy Storage and Conversion

Mark Rodriguez

XRD for Energy Materials

• Fossil fuels and processing • Wind • Solar • Battery

54. X-ray Diffraction in the Petroleum Industry

Bob Morton and Dave Simon (+ Jim Kaduk?)

55. Superconductivity

Qing Huang

57. Organic Pigments

Martin Schmidt

58. Application of Powder Diffraction to the Study of Phase

Stabilities in Piezoelectric Ceramics Dhananjai Pandey

Phase Diagram of PZT

59. Selected Applications of Rietveld XRD Analysis in the

Aluminum Industry Frank Feret

MATERIAL NO OF PHASES SAMPLE TYPE

SUCCESS RATE

Bauxite 14 - 24 cavity slide limited

Red Mud 30 - 60 cavity slide limited

Alumina 8 cavity slide limited - high

Electrolytic Bath 9 - 16 briquette, cavity high

Spent Potlining 30 - 60 cavity slide limited - high

Dross 10 - 20 cavity slide high

Intermetallics > 20 cavity slide high

Typical Rietveld Applications in the Aluminum Industry

Rietveld Analysis of BXT-12

60. Powder Diffraction in Art and Archaeology

Gilberto Artioli

62. Minerals

G. Cruciani

61. Software

Chris Gilmore, Jim Kaduk, and Henk Schenk