Brief tutorial on X ray powder diffraction data analysis Some bibliography Some bibliography X-ray powder diffraction (XRPD): brief summary X-ray powder diffraction (XRPD): brief summary Qualitative Analysis: evaluate your pattern and look for possible phase(s) Qualitative Analysis: evaluate your pattern and look for possible phase(s) Quantitative Analysis: Rietveld refinementQuantitative Analysis: Rietveld refinement Dr Carlo Meneghini Dip. Di Fisica, Università di Roma Tre II African School on X-ray in materials Jan XRPD_tutorial.exe

Pwder diffraction: technique and data analysis B.E. Warren, X-Ray Diffraction (Addison-Wesley, 1990). H.P. Klug and L.E. Alexander, X-Ray Diffraction Procedures (Wiley Interscience, 1974). B.D. Cullity, Elements of X-Ray Diffraction (Wiley, 1978). Modern Powder Diffraction Reviews in Mineralogy, Volume 20 D.L. Bish and J.E. Post, Editors Mineralogical Society of America, Fundamentals of Crystallography IUCr Texts on Crystallography -2 C. Giacovazzo, Editor Oxford Science Publication, The Rietveld Method IUCr Monographs on Crystallography - 5 R.A. Young, Editor Oxford Science Publication, X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials H.P Klug and L.E. Alexander Wiley-Interscience, 1974, 2nd edition. Defects and Microstructure Analysis by Diffraction R.L. Snyder, J. Fiala and H.J. Bunge, IUCr Monographs on Crystallography, Vol 10, Oxford Science Publications, Bibliography On line resources International centre for diffraction data The collaborative computational projects A resource page for XRD

Atomic distribution in the unit cell Peak relative intensities Unit cell Symmetry and size Peak positions a c b Peak shapes Particle size and defects Background Diffuse scattering, sample holder, matrix, amorphous phases, etc... X-ray Powder Diffraction

NOTE Ab initio recognition and refinement of the crystallogrphic structure of unknown phase(s) (direct methods) is a very hard, complex and delicate task.** It is easier, and it is more often the case, to refine the crystallographic structure and phase composition of a sample starting from models, hypothesis, database structures, exploiting some a-priori sample knowledge ** Ab initio structure determination from Powder diffraction data Harris, K.D.M., M. Tremayne, and M. Kariuki. Contemporary Advances in the Use of Powder X-Ray Diffraction for Structure Determination, Angew. Chem. Int. Ed. 40 (2001) Giacovazzo, C. Direct Methods and Powder Data: State of the Art and Perspectives, Acta Crystallogr. A52 (1996) Scardi, P., et al. International Union of Crystallography Commission for Powder Diffraction.

Programs gp400win32.exePCW23.exeGSAS Data Analysis Y2O3_PCW Y2O3_GSAS CMPR Au_GSAS Download and install: XRD_tutorial.exe XRD_tutorial folder expand gnuplot wgnuplot.exe bin XRPD_tutorial.exe

XRPD experiment done!

gnuplot> pl [:][:] 'y2o3.dat' u 1:2 w l x-range y-range file using x:y columns with lines plot Firstly: get a look to the data!.../data plo_y2O3.plt More information on Gnuplot at:

Is the statistics good enough also for weaker peaks? Can you distinguish different peaks? Are the resolution, the angular step, etc... appropriate? Main peaks: are symmetric? Are there saturation effects?

If the patterns are good......go ahead If not consider to recollect the XRPD patterns

SECOND: compare your data with models based on your a priori knowledge about the sample Find the structure of know compounds on (public) database! Compare your diffractograms with patterns expected for compounds of similar composition

y2o3.dat

ICSD public version

y2o3.dat database Our data Literature Data go ahead! They reasonably match!

save file: icsd_86815.cel save file: icsd_86815.cif Go deeper into the data

icsd_86815.cel icsd_86815.cif

pcw23.exe Programs Gnuplot PCW GSAS Data Analysis Y2O3_PCW Y2O3_GSAS CMPR Au_GSAS icsd_86815.cel y2o3.x_y Install pcw.exe XRD_tutorial folder PowderCell is a simple to handle program allowing: -structural visualization, -theoretical XRPD pattern calculation -Rietveld refinement - etc... PCW

Load structure file (.cel) Modify/Create the unit cell look at the whole cell Play with the structure generate the pattern pattern refinement

Load structure file icsd_86815.cel

diffracted beam incoming beam   Give the experimental information, mainly: Wavelength experimental geometry

y2o3.x_y SNLS – XRPD tutorial/dati Data and model patterns are closely similar, our model/hypothesis seems correct, now we must derive quantitative crystallographic information from the XRPD patterns!

Rietveld method I calc = I bck + S  hkl  C hkl  F 2 hkl  P hkl  background Scale factor Corrections Miller Structure factor Profile function Structure Symmetry Experimental Geometry set-up Atomic positions, site occupancy & thermal factors particle size, stress-strain, texture + Experimental resolution

Sample diffracted beam incoming beam 22 displacement zeroshift

I calc = I bck + S  hkl  C hkl  F 2 hkl  P hkl 

Refinement of y2o3.x_y 12/10/ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ R-values Rp=18.08 Rwp=24.85 Rexp= iterations of 6 parameter old new icsd_86815 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ scaling : lattice a : profile U : PsVoigt2 V : W : overall B : global parameters ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ zero shift : displacement : backgr. polynom : coeff. a0 : a1 : a2 : a3 : a4 : a5 : a6 : -6.29E E-7 a7 : 3.161E E-8 a8 : E E-12 a9 : E E-12 a10 : 2.97E E-1 a11 : 1.251E E-1 a12 : E E-1 a13 : 8.173E E-2

CMPR XRPD tutorial Programs GnuplotPCWGSAS Data Analysis CMPR Install CMPR program on the PC (defaults options) Getting some other information from our data

Windows installation CMPR can be integrated with PDF2 (commercial) database for search match procedures. (use LOGIC options)

read several data file formats

export ASCII files

select the diffractogram you are working on

Combine different data sets to simulate multiphase systems

(multi-) peak fitting routines 1

To Select diffraction peaks 1) position the mouse at the peak maximum and 2) pres the p key

Check box to refine or fix the parameters

(XP)gsas+expgui.exe GSAS XRPD tutorial Programs GnuplotPCWGSAS Data Analysis Y2O3_PCW Y2O3_GSAS UTIL Au_GSAS Obtaining GSAS y2o3.gs, inst_xry.prm Make a new directory in the path: C:\gsas\MyWork Copy into the new folder

Move to your new directory Choose a file name for your experiment

Use the icsd_86815.cel file

I calc = I bck + S  hkl  C hkl  F 2 hkl  P hkl 

peak breadth Gaussian: peak breadth Gaussian:  2 = GU tan 2  + GV tan  + GW tan 2 q + GP/cos 2  sample shift:shft sample shift: s = -  R shft / 3600 sample absorption: sample absorption:  eff = / (  R Asym) peak breadth Lorentzian :LXptecLYstec peak breadth Lorentzian :  = (LX - ptec cos  )/cos  (LY - stec cos  ) tan  Gaussian Sherrer broadening Lorentzian Sherrer broadening (particle size) Anisotropy Lorentzian strain broadening Anisotropy (stacking faults)

Gaussian Breadth: Gaussian Breadth:  2 = GU tan 2  + GV tan  + GW tan 2 q + GP/cos 2  Lorentzian Breadth:LXptecLYstec Lorentzian Breadth:  = (LX - ptec cos  )/cos  (LY - stec cos  ) tan  Strain: S =  d/d Gaussian contrib. S = sqrt[8 ln 2 (GU- U i )] (  /18000) · 100% Instrumental contribution Lorentzian contrib. S =  LY –Y i ) (  /18000) · 100% Instrumental contribution Particle size: P P = (18000/  ) K / LX Scherrer constant

1 23 Mp =  w (I exp -I calc ) 2 Rp =  (I exp -I calc ) /  I exp wRp = sqrt[ Mp /  I 2 exp ]  2 = Mp / (N obs - N var ) 4

(XP)gsas+expgui.exe GSAS SNLS – XRPD tutorial Programmi GnuplotPCWGSAS Dati Analisi Y2O3_PCW Y2O3_GSAS UTIL Au_GSAS c:\gsas\mywork

GOLD S F m3m = Au= a = Ps ~ 50 Å Au nanosized particles supported on wax wide broad peaks on intense structured background! Too structured background may partially masks true peaks and introduce artifacts and errors in your structural parameters

Now... you can (must) try! For comments, suggestions, support request etc... contacts: Dr Carlo Meneghini skype: carlo_meneghini address: Dip. di Fisica, Univ. RomaTre via della vasca navale 84, I Roma, Italia