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Procedure for structure analysis Overview of strategy. What is needed lattice parameters space group equipoint occupation positional parameters. reflection positions. reflection intensities. Procedure for structure analysis Overview of strategy. What is needed lattice parameters
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Procedure for structure analysis Overview of strategy What is needed lattice parameters space group equipoint occupation positional parameters reflection positions reflection intensities
Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously reflection positions
Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired reflection positions
Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired small no. reflections needed for crystal system and approx. LPs reflection positions
Procedure for structure analysis Overview of strategy What is needed lattice parameters space group done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired small no. reflections needed for crystal system and approx. LPs large no. for precise LPs reflection positions
Examples for LP detn Get a-value for each reflection Which one is correct? or best?
Examples for LP detn Depends upon Consider effect of expt'l error on a-values at different s Braggs' law says error in d depends on error in sin
Examples for LP detn Braggs' law says error in d depends on error in sin d eqn says error in a (cubic) depends on error in d d2 = a2/(h2 + k2 + l2) Thus, error in a depends on error in sin
Precise LPs Best a-value at = 90° extrapolate a-values vs. cos2
Precise LPs Best a-value at = 90° extrapolate a-values vs. cos2
Precise LPs Best a-value at = 90° extrapolate a-values vs. cos2
Precise LPs Another common extrapolation fcn - Nelson-Riley fcn
Procedure for structure analysis Overview of strategy LPs & SG done simultaneously need crystal system for size & shape of UC some info on symmetry also acquired systematic extinctions ––> Bravais lattice glide planes, screw axes space group - almost ex: Imma (centric) ––– Im21a (non-centric) get correct SG in final structure detn
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume)
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) Ex: Al9Co3Ce do search on LPs
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) Ex: Al9Co3Ce do search on LPs
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) Ex: Al9Co3Ce do search on LPs Ga9Co3Nd (structure known) only need to "refine" Al9Co3Ce structure
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) • Measure intensities of as many reflections as possible - correct for LP, absorption
Techniques for structure detn • Gather supplemental info chemical structure density = (# formula units/UC x form. wt.)/(No x UC volume) atom sizes properties (centric?) isostructural materials (use databases) • Measure intensities of as many reflections as possible - correct for LP, absorption 3. Determine atom positions a.Patterson techniques b. heavy atom method
Techniques for structure detn 3. Determine atom positions a.Patterson techniques b. heavy atom method
Techniques for structure detn 3. Determine atom positions a.Patterson techniques b. heavy atom method c. isomorphous replacement, anomalous scattering
Techniques for structure detn 3. Determine atom positions a.Patterson techniques b. heavy atom method c. isomorphous replacement, anomalous scattering d. direct methods Unitary structure factors
Techniques for structure detn 3. Determine atom positions d. direct methods Unitary structure factors Example: center of symmetry Additional symmetry elements give other relationships
Techniques for structure detn • Refine structure adjust positional parameters to get best agreement betwn Fobs & Fcalc use least squares technique FOM – the R factor
Techniques for structure detn • Refine structure adjust positional parameters to get best agreement betwn Fobs & Fcalc use least squares technique FOM – the R factor • Include thermal parameters for each atom
Techniques for structure detn • Refine structure • Include thermal parameters for each atom • or
Techniques for structure detn • Refine structure • Include thermal parameters for each atom • or • For anisotropic vibration, thermal ellipsoid for • each atom
Techniques for structure detn Rietveld refinement • For powder diffraction data • Not a structure determination procedure • Whole pattern used • Need to model peak shapes
Techniques for structure detn Rietveld refinement • For powder diffraction data • Not a structure determination procedure • Whole pattern used • Need to model peak shapes • Many data, many parameters: • lattice params, backgrd curve coeffs, • positional params,temp factors, peak • shape params, texture factor, etc.
Techniques for structure detn Rietveld refinement