1. Selected examples: advantages/inconveniency of Powder/Single crystal data A.Daoud-aladine, (ISIS-RAL)

2. Nuclear Phase: Scattering vector Structure Factor/ Intensity Magnetic Phase: h=H Atomic positions Structural model Arrangement of the moments For non-polarised neutrons Recall: structure factors formulas

3. Difficulties of single crystal studies Constant Wavelength (4-circle) TOF-Laue Powder diffraction and pitfalls of Rietveld refinements

4. x1 y1 a* 4-circle angles   Sample Reciprocal lattice cell and UB matrix Q=H x0 y0   kf ki 1/ b* Punctual or Small area detector D10  min  max  min  max D9 Single crystal diffraction: 4-circles Q=4 .sin  / hmi kf ki

5. x1 y1 a* Sample Reciprocal lattice cell and UB matrix Q=H x0 y0   kf ki 1/ b* 1/ min 1/ max Goniometer angles  Only on SXD SXD  Q=4 .sin  / Single crystal diffraction: 4-circles

6. x1 y1 a* Sample Reciprocal lattice cell and UB matrix Q x0 y0 kf max kf min  kf ki 1/ 90° detector b* Goniometer angles  Only on SXD   1/ min 1/ max 37° detector SXD  Single crystal diffraction: 4-circles

7. In a single crystal job, we only need to minimize the difference between the observed and the calculated integrated intensities (G 2 ) or structure factors (F) against the parameter vector  I corresponding to magnetic structure parameters only Observed intensities are corrected for absorption, extinction before the magnetic structure determination : is the variance of the "observation" Optimization of extracted integrated intensities Single crystal diffraction: data treatment

8. Ex: CaV 2 O 4 (Coll. O.Pieper, B.Lake, HMI) Extraction of integrated intensities G obs can de difficult Motivation: CaV 2 O 4 is a Quasi one dimensional magnet V 3+ S=1 => weakly coupled frustrated Haladane chains T N =75K J2J2 J1J1 J2J2 J1J1 Otho-monoclinic k=( 0 ½ ½ ) Magnetism Structure J4J4 J3J3

9. Single crystal diffraction: data treatment Extraction of integrated intensities G obs can de difficult

10. Single crystal diffraction: data treatment k=( 0 ½ ½ ) (a*,b*) plane (b*,c*) plane Ex: CaV 2 O 4 (Coll. O.Pieper, B.Lake, HMI) T=15K Extraction of integrated intensities G obs can de difficult 1 st problem: Crystal quality check on SXD

11. (-4 -2 2), det=11 SXD19323.raw (-9 -8 2), det=10 d=1.35 d=1.22 d=0.71 Orthorhombic Pnam (a=9.20,b=10.77,c=3.01) => Monoclinic (  ~89.6) below T~190K T=15K

12. Cryst1 (a*,b*) plane T=15K (a*,b*) plane T=RT Cryst2

13. Single crystal diffraction: data treatment k=( 0 ½ ½ ) (b*,c*) plane Ex: CaV 2 O 4 (Coll. O.Pieper, B.Lake, HMI) T=15K Extraction of integrated intensities G obs can de difficult 2 nd problem: Monoclinic splitting-Crystal Twinning (a*,b*) plane (-2 k l) plane T=15K Cryst1 Cryst2

14. Constant Wavelenght Diffraction : E4-two-axis, (b*,c* plane survey at LT) 12 12

15. Constant Wavelenght Diffraction : E5-4-circle (b*,c*) Data containing Split peaks Merged peaks Observations compared to the sum S 1.F 2 (hkl) 1 + S 2.F 2 (hkl) 2 12 S 1.F 2 (hkl) 1 separated from S 2.F 2 (hkl) 2

16. Magnetic structure solution from E5 4-circle (HMI) Old powder results:

17. AFF F F F 2 1 2 1 2 1 2 1 AF- k=( 0 ½ ½ ) Rf=17%Rf=14%

18. Canting, but what type? Rf=14%

19. Magnetic structure solution 4 4 /2=128 constrained models generated with controlled Canting (2 params each)… Unconstrained models 3x4=12 params

20. Rf=6% Rf=14%

21. Rf=6%

22. Difficulties of single crystal studies Constant Wavelength (4-circle) TOF-Laue Powder diffraction and pitfalls of Rietveld refinements

23. Sample: Crystal Reciprocal lattice Powder averaged Q kf max kf min kf ki 1/ 1/ min 1/ max Powder diffraction CW-scan ( fixed)  TOF-scan (  fixed) S D kf ki Ex: DMC-SINQ

24. Powder diffraction: beneficiate from the power of the rieteveld technique, d s 22 22 Int d=Detector opening 90° T=2  Int 22 Powder diffraction

25. at the position “i”: T i Bragg position T h y i -y ci The “MODEL” Intensity y i (obs) The Rietveld model

26. List of refinable parameters  I h refinable = profile matching mode Or I h modeled by a “structural model” (atom positions, magnetic moments) to calculate the structure factor F 2 Contains the profile, combining instr. resolution, and the additional broadening coming from defects, crystallite size,... Background: noise, diffuse scattering,... The “MODEL” The Rietveld model

27. Least square refinement of the RM model for powder data The RM allows refinement of the parameters, by minimising the weighted squared difference between the observed and the calculated pattern against the “parameter vector”:  = (  I,  P,  B ) : is the variance of the "observation" y i The Rietveld method

28. meaning of the result R-pattern R-weighted pattern Expected R-weighted pattern Profile R-factors Bragg R-factor Crystallographic R F -factor. Crystallographic like R-factors Chi-square The Rietveld method

29. Powder diffraction: problem of accidental overlap… Nuclear Reciprocal space AF order on a centred lattice b1b1 b2b2 (110) (-110) Int a1a1 a2a2 a1a1 a2a2 b1b1 b2b2 (110) (-100) (-110) (010) (-100) (010) (-100) (b) (a) (b) Nuclear Magnetic Magnetic Absent Powder diffraction vs. single crystal: main limitations of NPD

30. Structure solution methods: simulated annealing (Fullprof) Extract (Profile matching) Minimize with an algorythm (ex: simulated annealing in Fullprof) Constraint the obtained models Refine them back the with the Rietveld method Beyond the Rietveld method

31. T. Arima, et al. Phys. Rev. B 66, 140408 (2002) AF? Mn 3+ + + - - c mag YBaMn 2 O 6 DMC(PSI) T=1.5K 8 Mn atoms per cell = 24 spin components No symmetry analysis possible Powder diffraction : example of quasi-model degeneracy

32. T. Arima, et al. Phys. Rev. B 66, 140408 (2002) New model ?? Powder diffraction : example of quasi-model degeneracy

33. AF? Mn 3+ + + - - c mag DMC(PSI) T=1.5K Powder diffraction : example of quasi-model degeneracy

34. Structure determination methods Except for simple cases, the Rietveld “refinement” can only be a final stage of a magnetic structure determination Before using it, a maximum number of constraints on the magnetic model are desirable (ex: symmetry analysis), or starting models can be obtained using structure solution approaches Single crystal data are always better, but can be tricky! For advanced topics: see the Fullprof Suite documentation and tutorials at: http://www.ill.fr/dif/Soft/fp/php/tutorials.html