1. Presentation Outline ANAELU: 2-D XRD texture analysis Experimental 2D XRD patterns Representation of structure Simulation of single-crystal XRD Polycrystal XRD: IPF, PF and Debye rings Practical examples ESMERALDA: Laue data analysis (under development) Image Visualizations Algorithms for finding peaks Tools for orienting Intensity integration By: Luis Fuentes-Montero (Luiso)

2. A typical grazing incidence diffaction/scattering experiment 2-D position sensitive detector, BL11-3 SSRL L. Fuentes: “Synchrotron Radiation Diffraction and Scattering in Ferroelectrics”. Ch. 6, Handbook “Multifunctional polycrystalline ferroelectric materials”. Eds: L. Pardo, J. Ricote, Springer-Verlag (2011)

3. Starting an ANAELU run. Experimental parameters: Radiation wave- length, sample-detector distance, detector resolution, data format

4. Determination of direct beam position. Several options

5. Reading the scattering angle, inter-planar distance and intensity associated to a measurement point

6. Ploteo de cortes radial y azimutal. Exploring the 2D XRD pattern: Radial and azimuthal cuts

7. Azimutal integration and conventional 1D diffraction pattern I = I (2  ).

8. Zo o o o o o o om

9. Intensity scales (linear, sqrt, 4th_root and log) and color conventions.

10. Virtual Laue experiment, as generated by Anaelu. The “Cell” window shows the crystal system and the atoms of a Pt unit cell. The “Reciprocal Lattice” window represents the stereographic projection (blue points) and the Laue spots (red).

11. Observed and calculated “randomized” 1D XRD patterns

12. Calculation of textured polycrystal pattern as sum of different single-crystal patterns. MODELING AND COMPARISON WITH EXPERIMENT Single-crystal programmed rotations

13. Fuentes: Textures and Microstructures 10, 347-360 (1989) Fibre textures – one minute of theory Complete statistical description of “fibre textures” is given by the symmetry axis inverse pole figure R(h). (Direct) Pole figures are calculated by means of the Fundamental Equation for Fibre Textures: –Texture statistical descriptors (1)

14. Determination of the P 111 (  ) direct pole figure, calculated by applying equation (1) to a hypothetical inverse pole figure. The model IPF is formed by Gaussian components at (1, 1, 1) and at orientations generated by (Laue) crystal cubic symmetry. Pole figure calculation in ANAELU

15. Relation among Bragg angle θ, polar angle  and azimuth . Pole figures determine the intensities’ distributions along the Debye rings

16. Application example 1: Randomly oriented powder of Ni 0.25 Zn 0.75 Fe 2 O 4 (Elizalde et al, 2007) Elizalde et al - observedANAELU - calculations

17. Observed and calculated 2D-XRD patterns for a Pt textured sample. Rotating crystal (sharp texture) model. Application example 2a

18. Application example 2b: Pt textured sample. Inverse pole figure treatment Fuentes-Montero et al (2008)

19. http://blogs.cimav.edu.mx/luis.fuen tes/archivos Application example 3: Experimental and simulated 2D XRD of textured sepiolite Si 12 O 30 Mg 8 (OH) 4 (OH 2 )4·8H 2 O. Inverse pole figure approach. Sanchez del Río et al. American Mineralogist (2011) For details about program ANAELU, please read: Fuentes et al: J. Appl. Cryst. 44, 241-246 (2011)

20. Comparison of programs Similarities: Same approach in the design of the GUI. Very similar convention for visualizations and geometry. Differences: Different purposes Different programming languages. Didactic vs practical.

21. ESMERALDA: Laue data analysis (under development) Image Visualizations Algorithms for finding peaks Tools for crystal orientation Intensity integration

22. Image Handling Different colour Palettes

23. Image Handling Adjustable contrast

24. Image Handling 3D view

25. Image Handling Peak finding Tool

26. Image Handling Peak finding Tool

27. Image Handling Peak finding Tool

28. Image Handling Peak finding Tool

29. Two algorithms for orienting the crystal automatically Angular comparison Faster Almost completely automatic No need of starting point Increasing resolution scanning Slower Completely automatic If there is a starting point becomes not so slow

30. orienting the crystal

32. Peak integration Background subtraction

33. Peak integration Background Treatment I1

34. Peak integration Background subtraction

35. Peak integration Pixel treatment

36. Peak integration Pixel treatment

37. Peak integration Pixel treatment

38. Peak integration d1 d2 Pixel treatment P I1 I2I2 (-312.6782, -50.82541 ) I= 373636.9 (-307.6769, -49.22461 ) I= 145032.8

39. Integration along a curve

40. Summarizing: Anaelu: Good for texture analysis with monochromatic XRD. Finished project, ready to download from the ESRF web page. Esmeralda: Good for orienting the crystal and extracting information directly from image. Now under active development, next step is to work with structure factor and the intensities.