Procedure for structure analysis Overview of strategy

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Presentation transcript:

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