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Juan Rodríguez-Carvajal Laboratoire L é on Brillouin (CEA-CNRS), Saclay, France

Neutron Powder Diffraction: a powerful technique for studying structural and magnetic phase transitions A-site ordered perovskite YBaMn 2 O 6 : atomic versus larger scales charge ordering. Juan Rodríguez-Carvajal Laboratoire L é on Brillouin (CEA-CNRS), Saclay, France.

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Juan Rodríguez-Carvajal Laboratoire L é on Brillouin (CEA-CNRS), Saclay, France

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  1. Neutron Powder Diffraction: a powerful technique for studying structural and magnetic phase transitionsA-site ordered perovskite YBaMn2O6: atomic versus larger scales charge ordering Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France

  2. Generalities about the properties and use of neutrons for condensed matter research Neutron powder diffraction. Data treatment. Introduction to the programs of the FullProf Suite Study of the phase transitions in YBaMn2O6. Charge/orbital/spin ordering. Content of the talk

  3. Neutrons as constituents of matter Chadwick 1932

  4. Properties of neutrons

  5. Neutron production: nuclearreactors • The reactor geometry is optimized to produce the maximum number of neutrons. • The fission of a 235U nucleus produce in average 2.5 neutrons. 1.5 are used to keep the chain reaction, only 1 is used for making neutron beams. • Main research reactors in Europe: • France, • ILL (57 MW) in Grenoble • Orpheé (14 MW) in Saclay • Germany • FRJ-2 (23 MW) in Julich (closed) • BER-2 (10 MW) in Berlin • FRM-II (24 MW) in Munich (new)

  6. Neutron production: spallation sources • H+ accelerated to 1 GeV • Targetsof W, Pb, Hg, U • 20 to 25 neutrons by H+ • Pulses of 50 Hz • Fluxof 3.7 1016 ns-1 (ISIS) • Pulse length of µs • Relatively small average flux • Switzerland, SINQ quasi-continuous ( 10 MW) • United Kingdom, ISIS (1.5 MW) • SNS, Oak Ridge (USA) – in construction

  7. Neutron reactors: ILL

  8. Neutron reactors: ILL

  9. Particle-wave properties kinetic energy (E) velocity (v) temperature (T). E= mnv2/2= kB T = p2/2mn=(ħk)2/2mn=(h/l)2/2mn p= mnv = ħ k momentum (p) wavelength (l) ħ=h/2p k= 2p/l = mnv/ħ wavevector (k)

  10. Particle-wave properties (moderators) E = mn v 2 /2 = kB T = (ħk)2/2mn ; k = 2p/l = mnv/ħ • Neutrons moderated by heavy water at 300K (Thermal neutrons) • Also cold moderating source, liquid deuterium at 25K (Cold neutrons) • And hot moderating source, graphite at ~2000K

  11. Particle-wave properties (Energy-Temperature-Wavelength) COLD THERMAL HOT Cold Sources E = mnv2/2 = kB T = (ħk)2/2mn ; k = 2p/l = mnv/ħ Energy (meV)Temp (K)Wavelength (Å) Cold 0.1 – 10 1 – 120 4 – 30 Thermal5 – 10060 – 1000 1 – 4 Hot100 – 5001000 – 6000 0.4 – 1

  12. Interaction neutron-nucleus k’ Direction q, f dS r f k q z dW Target = number of incident neutrons /cm2 / second q = total number of neutrons scattered/second/ Fermi’s golden rulegives the neutron-scattering Cross-section  number of neutrons of a given energy scattered per second in a given solid angle (the effective area presented by a nucleus to an incident neutron)

  13. Interaction neutron-nucleus Plane wave e ik’·r Detector k’ r k’ Q 2q k k Sample V(r) Spherical wave (b/r)e ik·r Plane wave e ik·x Weak interaction with matter aids interpretation of scattering data The range of nuclear force (~ 1fm) is much less than neutron wavelength so that scattering is“point-like” • Fermi Pseudo potential of a nucleus in rj Potential with only one parameter

  14. Neutron scattering lengths

  15. X-rays and neutron scattering lengths X-Rays H D N Mn Fe Neutrons H Mn Fe D N negative negative Neutron scattering is a nuclear interaction

  16. Elastic Scattering: Diffraction For elastic scattering: Where v0 is the unit cell volume and t a reciprocal lattice vector The coherent elastic scattering takes place only for Bragg Law

  17. Form Factor

  18. Magnetic Scattering kI=2/uI kF=2/uF Q= kF - kI Dipolar interaction (n , m): vector scattering amplitude

  19. Magnetic Scattering - Magnetic interactions are long range and non-central – Nuclear and magnetic scattering have similar magnitudes – Magnetic scattering involves a form factor: Fourier Transform of unpaired electron spatial distribution – Magnetic scattering depends only on the component of m perpendicular to Q Q=Q e Only the perpendicular component of m to Q contributes to scattering m m

  20. Generalities about the properties and use of neutrons for condensed matter research Neutron powder diffraction. Data treatment. Introduction to the programs of the FullProf Suite Study of the phase transitions in YBaMn2O6. Charge/orbital/spin ordering. Content of the talk

  21. Diffractometers: Powder high flux D1B(ILL)or G41(LLB)

  22. Experimental powder pattern A powder diffraction pattern can be recorded in numerical form for a discrete set of scattering angles, times of flight or energies. We will refer to this scattering variable as : T. The experimental powder diffraction pattern is usually given as three arrays : The profile can be modelled using the calculated counts: yciat the ith step by summing the contribution from neighbouring Bragg reflections plus the background.

  23. Powder diffraction profile: scattering variable T: 2, TOF, Energy Bragg position Th yi zero yi-yci Position “i”: Ti

  24. The calculated profile of powder diffraction patterns Contains structural information: atom positions, magnetic moments, etc Contains micro-structural information: instr. resolution, defects, crystallite size… Background: noise, incoherent scattering diffuse scattering, ...

  25. The calculated profile of powder diffraction patterns The symbol {h} means that the sum is extended only to those reflections contributing to the channel “i” . This should be taken into account (resolution function of the diffractometer and sample broadening) before doing the actual calculation of the profile intensity. This is the reason why some Rietveld programs are run in two steps

  26. Several phases ( = 1,n) contributing to the diffraction pattern Several phases ( = 1,n) contributing to several (p=1,np) diffraction patterns

  27. Integrated intensities are proportional to the square of the structure factor F. The factors are: Scale Factor (S), Lorentz-polarization (Lp), preferred orientation (O), absorption (A), other “corrections” (C) ...

  28. The Structure Factor contains the structural parameters(isotropic case)

  29. Structural Parameters(simplest case) Atom positions (up to 3n parameters) Occupation factors (up to n-1 parameters) Isotropic displacement (temperature) factors (up to n parameters)

  30. Structural Parameters(complex cases) • As in the simplest case plus additional (or alternative) parameters: • Anisotropic temperature (displacement) factors • Anharmonic temperature factors • Special form-factors (Symmetry adapted spherical harmonics ), TLS for rigid molecules, etc. • Magnetic moments, coefficients of Fourier components of magnetic moments , basis functions, etc.

  31. The Structure Factor in complex cases Complex form factor of object j Anisotropic DPs Anharmonic DPs

  32. The approximation of the peak shape profile function and microstructural effects Precise refinements can be done with confidence only if the intrinsic and instrumental peak shapes are properly approximated. At present  The approximation of the intrinsic profile is mostly based in the Voigt (or pseudo-Voigt) function  The approximation of the instrumental profile is also based in the Voigt function for constant wavelength instruments  For TOF the instrumental+intrinsic profile is approximated by the convolution of a Voigt function with back-to-back exponentials or with the Ikeda-Carpenter function.

  33. The peak shape function of powder diffraction patterns contains the Profile Parameters In most cases the observed peak shape is approximated by a linear combination of Voigt (or pseudo-Voigt) functions

  34. The Voigt function The pseudo-Voigt function

  35. The Rietveld Method : is the variance of the "observation"yi The Rietveld Method consist of refining a crystal (and/or magnetic) structure by minimising the weighted squared difference between the observed and the calculated pattern against the parameter vector:

  36. Minimum necessary condition: A Taylor expansion of around allows the application of an iterative process. The shifts to be applied to the parameters at each cycle for improving c2 are obtained by solving a linear system of equations (normal equations) Least squares: Gauss-Newton (1)

  37. Least squares: Gauss-Newton (2) The shifts of the parameters obtained by solving the normal equations are added to the starting parameters giving rise to a new set The new parameters are considered as the starting ones in the next cycle and the process is repeated until a convergence criterion is satisfied. The variances of the adjusted parameters are calculated by the expression:

  38. Neutron and synchrotron powder diffraction Neutrons Synchrotron X-rays • Constant scattering length. Contrast. • Low absorption: easy sample environment • Magnetic structures • High precision in structure refinement • Moderate resolution • Extremely high resolution • Subtle distortions • Indexing and Structure determination • Anomalous scattering • Texture effects

  39. Directory structure of the FullProf Suite

  40. WinPLOTR: program to access the whole FullProf Suite

  41. Configuration of WinPLOTR File: winplotr.set

  42. Indexing demo with WinPLOTR New facility: DICVOL04 Two other indexing programs: TREOR, ITO

  43. Other features of WinPLOTR Two other indexing programs: TREOR, ITO Access to other programs: EdPCR, Fp_Studio, DICVOL04, BasIreps

  44. A program for : Simulation of powder diffraction patterns Pattern decomposition integrated intensities Structure refinement Powder and single crystal data Crystal and magnetic structures Multiple data sets: simultaneous treatment of several powder diffraction patterns (CW X-rays & neutrons, Energy dispersive X-rays, TOF neutron diffraction) Combined treatment of single crystal and powder data Crystal and magnetic Structure determination capabilities: simulated annealing on integrated intensity data A program for analysis of diffraction patterns: FullProf

  45. How works FullProf Minimal input: Input control file (extension ‘ .pcr ’): PCR-file Model, crystallographic/magnetic information PCR file Output files, Plot diffr. patterns DAT file(s) Eventually, experimental data FullProf

  46. The PCR file: steep learning curve PCR file DAT file(s) Format depending on the instrument, usually simple Many variables and options  Complex to handle Hint: copy an existing (working) PCR-file and modify it for the user case,or...  USE the new GUI: EdPCR

  47. A new GUI for FullProf: EdPCR GUI using Winteracter: http://www.winteracter.com

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