陈小龙 中国科学院物理研究所  2006.10 杭州 Phase transition of BaTiO3 from tetragonal to cubic at about 132?C YBa3B3O9: Phase transition and structure determination LiAlB2O5:   Search for new SHG materials Structure vs Temperature:KCaCO3F What is a Rietveld Refinement?   -a standard treatment of powder diffraction data to make the final structural model achieve the accepted criterion;    -a best known method that fully  makes use of the step-mode scanned data to dig out  a lot of structural and other information;    - a  procedure for structural solution in nature.    What can  we get to perform a Rietveld refinement?  Lattice Parameters           Quantitative phase Analysis Atomic Positions             Grain size Atomic Occupancy          Incommensurate Structure Debye Temperatures       Structure factors Crystallinity                     Phase transitions Magnetic structures                                   …… History  Review Rietveld originally introduced the Profile Refinement method (Using step-scanned data rather than integrated Powder peak intensity) (1966,1967) Rietveld developed first computer Program for the analysis of neutron data for Fixed-wavelength diffractometers (1969) Malmos & Thomas first applied the Rietveld refinement method (RR) for analysis of x-ray powder data collected on a Ginier Hagg focusing Camera (1977) Khattack & Cox first applied the RR to x-ray powder data collected on a diffractometer (1977) Conference on Diffraction Profile Anlysis Sponsored by IUCr in Poland, suggested the term “Rietveld Method”(1978) Wiles and Yang developed a general computer program (max.book118.com) for both x-ray & neutron diffraction data (fixed wavelength)(1981) Von Dreele, Jorgensen and Windsor extended to the program to the neutron diffraction data (1982) Fitch et al, 193 refined parameters,UO2 DAs.4D2O (1982) Aminoff Prize, Stockholm,1995 How RM works? Given a solution ?=?opt(?1, ?2… ?p) that approximately satisfy the above equation. To find a better solution, we begin an iterative process by expanding           into a Taylor series. A??1=b S? is the scale factor of the phase ?Lh contains the Lorentz, polarisation and multiplicity factors.Fh is the structure factorAh is the absorption correctionPh is the preferred orientation functionΩ is the reflection profile function that models both        instrumental and sample effects where, fi  atomic scattering factor for ith atom  xi, yi and zi the fractional coordinates for ith atom      What we need to perform a RR?     A  set of step-mode scanned data,    usually 2?=10-120? or more,  step ? 2?=0.02?    collecting time is instrument dependent from 1-20s    for laboratory diffractometer;   An initial structural model having roughly accurate lattice  constants, correct space group and approximate atomic positions  How we obtain an initial structural model?  -   solid solutions usually adopt same structure types of their parent compounds;        NaSr4-xBaxB3O9 (0≤x≤4)  Compounds with same chemical formula      YBa2Cu3O7 and NdBa2Cu3O7       but always alert that except
Rietveld原理.ppt