Brief X ray powder diffraction analysis tutorial
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1 Brief X ray powder diffraction analysis tutorial Bibliografia essenziale X-ray powder diffraction (XRPD): un breve richiamo Analisi qualitativa Analisi quantitativa (metodo Rietveld) Dr Carlo Meneghini Dip. Di Fisica, Università di Roma Tre meneghini@fis.uniroma3.it OGG-INFM GILDA c/o ESRF Grenoble, France
2 Bibliografia essenziale 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, On line resources
3 X-ray Powder Diffraction Particle size and defects Peak shapes Peak positions Background θ Peak relative intensities Atomic distribution in the unit cell c b a Unit cell Symmetry and size Diffuse scattering, sample holder, matrix, amorphous phases, etc...
4 NOTA Determinare una struttura cristallografica ab-initio (metodi diretti) da misure XRPD è cosa molto difficile, complessa e delicata**. Piú normale è "raffinare" le informazioni strutturali a partire da modelli, ipotesi e conoscenze a-priori sul campione. ** 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.
5 Powder diffraction patterns k = k q=sin(θ) 4πλ 1 (exchanged momentum vector) q k Bragg law 1 2d hkl sin(2θ) = nλ Unit cell Symmetry and size k d hkl Peak intensity I hkl ~ F hkl 2 2a F hkl = structure factor F hkl = Σ f n e ik.r n Atomic distribution in the unit cell 2b Structural Disorder: f n = f no e -q2 u 2 e -q2 u 2 = Debye Waller factor u = mean square displacement u=<r n -r o >
6 Line shape breath anisotropy Crystallite defects Crystallite size Sherrer Law β τ =D-d
7 analisi dati SNLS XRPD tutorial Programmi Dati Analisi Gnuplot PCW GSAS UTIL gp400win32.zip Y2O3_PCW Y2O3_GSAS Au_GSAS
8 'y2o3.dat' u 1: SNLS/dati plo_y2o3.plt gnuplot> pl [:][:] 'y2o3.dat' u 1:2 w l plot x-range xrd-file using y-range x:y columns with line
![plt 5000 0 0 20 40 60 80 100 120 gnuplot> pl [:][:]](/docs-images/41/2975494/images/page_8.jpg "'y2o3.")
9 Possibili candidati
10 25000 'y2o3.dat' u 1: y2o3.dat database
11 'y2o3.dat' u 1:2 y2o3.dat
12 save file: icsd_86815.cel
13 SNLS XRPD tutorial Programmi Dati Analisi Gnuplot PCW GSAS UTIL pcw23.exe Y2O3_PCW icsd_86815.cel y2o3.x_y Y2O3_GSAS Au_GSAS
14 Load structure file icsd_86815.cel
15 incoming beam θ diffracted beam θ
16 SNLS XRPD tutorial/dati y2o3.x_y
17 Rietveld method I calc = I bck + S Σ hkl C hkl (θ) F 2 hkl (θ) P hkl (θ) background Scale factor Miller Corrections Structure factor Profile function Structure Symmetry Experimental Geometry set-up Atomic positions, site occupancy & thermal factors particle size, stress-strain, strain, texture + Experimental resolution
18 incoming beam diffracted beam 2θ displacement Sample zeroshift
19 I calc = I bck + S Σ hkl C hkl (θ) F 2 hkl (θ) P hkl (θ)
20
21 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
22 Obtaining GSAS GSAS SNLS XRPD tutorial Programmi Dati Analisi Gnuplot PCW GSAS UTIL (XP)gsas+expgui.exe c:\gsas\mywork Y2O3_PCW Y2O3_GSAS Au_GSAS y2o3.gs gs, y2o3.exp exp, inst_xry xry.prm
23
24 I calc = I bck + S Σ hkl C hkl (θ) F 2 hkl (θ) P hkl (θ)
25 peak variance: sample shift: sample absorption: Lorentzian : σ 2 = GU tan 2 θ + GV tan θ + GW tan 2 q + GP/cos 2 θ s= -π R shft / 3600 µ eff = / (π R Asym) Gaussian Sherrer broadening γ = (LX - ptec cos φ)/cos θ + (LY - stec cos φ) tan θ Lorentzian Sherrer broadening (particle size) Anisotropy Lorentzian strain broadening Anisotropy (stacking faults)
26 peak variance: Lorentzian : σ 2 = GU tan 2 θ + GV tan θ + GW tan 2 q + GP/cos 2 θ γ = (LX - ptec cos φ)/cos θ + (LY - stec cos φ) tan θ Strain: S = d/d Gaussian contrib. S = sqrt[8 ln 2 (GU- U i )] (π/18000) 100% Instrumental contribution Lorentzian contrib. S = (LY Y i ) (π/18000) 100% Instrumental contribution Particle size: P P = (18000/ π) K λ / LX Scherrer constant
27 2 1 3 Mp = Σ w (I exp -I calc ) 2 Rp = Σ (I exp -I calc ) / Σ I exp wrp = sqrt[ Mp / Σ I 2 exp ] χ 2 = Mp / (N obs -N var )
28 GSAS SNLS XRPD tutorial Programmi Dati Analisi Gnuplot PCW GSAS UTIL (XP)gsas+expgui.exe c:\gsas\mywork Y2O3_PCW Y2O3_GSAS Au_GSAS
29 GOLDSF m3m λ= Au= a = Ps ~ 50 Å
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