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Selected examples: advantages/inconveniency of Powder/Single crystal data

Selected examples: advantages/inconveniency of Powder/Single crystal data. A.Daoud-aladine, (ISIS-RAL). Recall: structure factors formulas. For non-polarised neutrons. Nuclear Phase:. Magnetic Phase:. Scattering vector. h=H. Arrangement of the moments. Atomic positions. Structural

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Selected examples: advantages/inconveniency of Powder/Single crystal data

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

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

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

  4. Gmax wmin Gmin y0 x0 D10 D9 wmax Single crystal diffraction: 4-circles Q=4p.sinq/l Punctual or Small area detector 4-circle angles w, c,j Q=H 1/l y1 kf b* 2q a* ki w x1 Sample Reciprocal lattice cell and UB matrix ki kf hmi

  5. y0 x0 SXD w Single crystal diffraction: 4-circles Q=4p.sinq/l Goniometer angles w Only on SXD Q=H 1/l 1/lmin y1 kf b* 2q a* ki w x1 1/lmax Sample Reciprocal lattice cell and UB matrix

  6. y0 x0 Single crystal diffraction: 4-circles 90° detector Goniometer angles w Only on SXD 37° detector Q kfmax c 1/l 1/lmin y1 kf b* G kfmin a* ki SXD w x1 w 1/lmax Sample Reciprocal lattice cell and UB matrix

  7. : is the variance of the "observation" Single crystal diffraction: data treatment In asingle crystal job, we only need to minimize the difference between the observed and the calculated integrated intensities (G2) 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 Optimization of extracted integrated intensities

  8. Single crystal diffraction: data treatment Extraction of integrated intensities Gobs can de difficult Ex: CaV2O4 (Coll. O.Pieper, B.Lake, HMI) Motivation: CaV2O4 is a Quasi one dimensional magnet V3+ S=1 => weakly coupled frustrated Haladane chains Structure J3 Magnetism J4 J1 J2 J2 Otho-monoclinic J1 k=( 0 ½ ½ ) TN=75K

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

  10. Single crystal diffraction: data treatment Extraction of integrated intensities Gobs can de difficult Ex: CaV2O4 (Coll. O.Pieper, B.Lake, HMI) 1st problem: Crystal quality check on SXD (a*,b*) plane (b*,c*) plane T=15K T=15K k=( 0 ½ ½ )

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

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

  13. Single crystal diffraction: data treatment Extraction of integrated intensities Gobs can de difficult Ex: CaV2O4 (Coll. O.Pieper, B.Lake, HMI) 2nd problem: Monoclinic splitting-Crystal Twinning Cryst1 (b*,c*) plane (-2 k l) plane (a*,b*) plane T=15K T=15K Cryst2 k=( 0 ½ ½ )

  14. Constant Wavelenght Diffraction : E4-two-axis, (b*,c* plane survey at LT) 2 1 2 1

  15. Constant Wavelenght Diffraction : E5-4-circle (b*,c*) Data containing Split peaks Merged peaks S1.F2(hkl)1 separated from S2.F2(hkl)2 Observations compared to the sum S1.F2(hkl)1 + S2.F2(hkl)2 2 1

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

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

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

  19. Magnetic structure solution Unconstrained models 3x4=12 params 44/2=128 constrained models generated with controlled Canting (2 params each)…

  20. Rf=6% Rf=14%

  21. Rf=6% Rf=6%

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

  23. D S Powder diffraction TOF-scan (q fixed) CW-scan (l fixed) Q kfmax 1/l 1/lmin kf 2q kfmin ki 1/lmax Sample: Crystal Reciprocal lattice Powder averaged kf ki Ex: DMC-SINQ

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

  25. The “MODEL” The Rietveld model Intensity yi (obs) Bragg position Th yi-yci at the position “i”: Ti

  26. The “MODEL” The Rietveld model List of refinable parameters b • Ih refinable = profile matching mode • Or Ih modeled by a “structural model” • (atom positions, magnetic moments) • to calculate the structure factor F2 • Contains the profile, combining instr. • resolution, and the additional broadening • coming from defects, crystallite size, ... • Background: noise, diffuse scattering, ...

  27. : is the variance of the "observation"yi The Rietveld method 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)

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

  29. Powder diffraction vs. single crystal: main limitations of NPD Powder diffraction: problem of accidental overlap… AF order on a centred lattice Reciprocal space (a) (010) (110) (b) (-110) a2 (a) a2 b2 Nuclear a1 a1 b1 (-100) Magnetic Absent Magnetic (b) (110) (010) (-110) b2 Nuclear Int b1 (-100) (010) (-100) Magnetic Absent

  30. Beyond the Rietveld method • 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

  31. Mn3+ - - + cmag + AF? YBaMn2O6 Powder diffraction : example of quasi-model degeneracy • 8 Mn atoms per cell = 24 spin components • No symmetry analysis possible DMC(PSI) T=1.5K T. Arima, et al. Phys. Rev. B 66, 140408 (2002)

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

  33. Mn3+ - - + cmag + AF? Powder diffraction : example of quasi-model degeneracy DMC(PSI) T=1.5K

  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

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