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Brief X ray powder diffraction analysis tutorial
•• Bibliografia essenziale Bibliografia essenziale •• XX--ray powder diffraction (XRPD): un ray powder diffraction (XRPD): un breve breve
richiamorichiamo•• Analisi qualitativaAnalisi qualitativa•• AnalisiAnalisi quantitativaquantitativa ((metodometodo Rietveld)Rietveld)
Dr Carlo Dr Carlo MeneghiniMeneghiniDip. Di Fisica, Università di Roma Tre
[email protected] GILDA c/o ESRF Grenoble, France
Bibliografia essenzialePwder 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, 1989. • Fundamentals of Crystallography IUCr Texts on Crystallography -2 C. Giacovazzo, Editor Oxford Science
Publication, 1992. • The Rietveld Method IUCr Monographs on Crystallography - 5 R.A. Young, Editor Oxford Science Publication,
1993. • 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, 1999.
On line resources
http://epswww.unm.edu/xrd/resources.htm
http://www.ccp14.ac.uk/
http://www.icdd.com/
10 20 30 402θ
Atomic distribution in
the unit cell
Peak relative intensities
Unit cell Symmetry and size
Peak positions
ab
Peak shapes
Particle size and defects
Background
Diffuse scattering, sample holder,
matrix, amorphous phases, etc...
X-ray Powder Diffraction
c
NOTADeterminare 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) 1626-1651.
•Giacovazzo, C. Direct Methods and Powder Data: State of the Art and Perspectives, Acta Crystallogr. A52 (1996) 331-339.
•Scardi, P., et al. International Union of Crystallography Commission for Powder Diffraction. http://www.iucr.org/iucr-top/comm/cpd/
Powder diffraction patterns
2dhklsin(2θ) = nλBragg law Unit cell
Symmetry and size
1
k
k’q
dhkl
|k|=|k’|q=sin(θ) 4πλ−1
(exchanged momentum vector)
Peak intensity Ihkl ~ |Fhkl|2
e-q2u2= Debye Waller factor
u = mean square displacement u=<rn-ro>
Structural Disorder: fn= fno e-q2u2
2bFhkl = structure factorFhkl = Σ fneik.rn
Atomic distribution in the unit cell 2a
www.fis.uniroma3.it/~meneghini
analisi dati
SNLS – XRPD tutorial
Programmi
Gnuplot PCW GSAS
gp400win32.zip
Analisi Dati
Y2O3_PCW Y2O3_GSAS
UTIL
Au_GSAS
www.gnuplot.info
0
5000
10000
15000
20000
25000
0 20 40 60 80 100 120
'y2o3.dat' u 1:2
SNLS/dati
plo_y2O3.plt
gnuplot> pl [:][:] 'y2o3.dat' u 1:2 w lx-range xrd-file using
x:y columns
with line plot y-range
http://database.iem.ac.ru/mincryst/
0
5000
10000
15000
20000
25000
10 20 30 40 50 60
'y2o3.dat' u 1:2
y2o3.dat
SNLS – XRPD tutorial
http://users.omskreg.ru/~kolosov/bam/a_v/v_1/powder/details/pcwindex.htm
pcw23.exe
Programmi
Gnuplot PCW GSAS
Analisi Dati
Y2O3_PCW Y2O3_GSAS
UTIL
Au_GSAS
icsd_86815.cely2o3.x_y
Rietveld method
Icalc = Ibck + S Σhkl Chkl (θ) F2hkl (θ) Phkl(θ)
backgroundScale factor Corrections
Miller
Structure factor
Profile function
Structure Structure SymmetrySymmetry
Experimental Experimental Geometry Geometry
setset--upup
Atomic positions, Atomic positions, site occupancy site occupancy
& thermal & thermal factorsfactors
particle size, particle size, stressstress--strain, strain,
texturetexture++
Experimental Experimental resolutionresolution
Refinement of y2o3.x_y 12/10/2005 12.58.11¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
R-values Rp=18.08 Rwp=24.85 Rexp=2.012 iterations of 6
parameter old new
icsd_86815¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯scaling : 1.2000 1.2000lattice a : 10.5968 10.6090
profile U : -0.1870 -0.4973PsVoigt2 V : 0.0020 0.7986
W : 0.1050 -0.2679
overall B : 0.0000 -
global parameters¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯zero shift : -0.1475 -0.1997
displacement : 0.0000 -
backgr. polynom : 13 13
coeff. a0 : 4515.8630 6590.1070a1 : -841.4 -1060a2 : 68.74 75.86a3 : -2.669 -2.745a4 : 0.05247 0.0522a5 : -0.0004457 -0.0004386a6 : -6.29E-7 -5.966E-7a7 : 3.161E-8 3.121E-8a8 : -3.797E-12 -8.06E-12a9 : -1.953E-12 -1.947E-12a10 : 2.97E-16 6.361E-1a11 : 1.251E-16 1.261E-1a12 : -6.315E-19 -6.571E-1a13 : 8.173E-22 8.861E-2
GSASGSASSNLS – XRPD tutorial
(XP)gsas+expgui.exe
Programmi
Gnuplot PCW GSAS
Analisi Dati
Y2O3_PCW Y2O3_GSAS
UTIL
c:\gsas\mywork Au_GSAS
y2o3.y2o3.gsgs, , y2o3.y2o3.expexp, , instinst__xryxry..prmprm
http://www.ccp14.ac.uk/solution/gsas/gsas_with_expgui_install.htmlObtaining GSASObtaining GSAS
peak variance: peak variance: σ2 = GU tan2θ + GV tan θ + GW tan2 q + GP/cos2 θ
sample shift:sample shift: s = - π R shftshft / 3600
sample absorption:sample absorption: µeff = - 9000 / (π R Asym)
Gaussian Sherrer
broadening
LorentzianLorentzian :: γ = (LXLX - ptecptec cos φ)/cos θ + (LYLY - stecstec cos φ) tan θ
Anisotropy Lorentzian strain
broadening
Anisotropy(stacking faults)
Lorentzian Sherrer
broadening(particle size)
peak variance: peak variance: σ2 = GU tan2θ + GV tan θ + GW tan2 q + GP/cos2 θ
LorentzianLorentzian :: γ = (LXLX - ptecptec cos φ)/cos θ + (LYLY - stecstec cos φ) tan θ
Strain: S = ∆d/d
Gaussian contrib. S = sqrt[8 ln 2 (GU- Ui)] (π/18000) · 100% Instrumental contribution
Lorentzian contrib. S = (LY –Yi ) (π/18000) · 100% Instrumental contribution
Particle size: P
P = (18000/ π) K λ / LXScherrer constant
12 3
Mp = Σ w (Iexp-Icalc)2
Rp = Σ (Iexp-Icalc) / Σ Iexp
wRp = sqrt[ Mp / Σ I2exp ]
χ2 = Mp / (Nobs - Nvar )
GSASGSASSNLS – XRPD tutorial
(XP)gsas+expgui.exe
Programmi
Gnuplot PCW GSAS
Analisi Dati
Y2O3_PCW Y2O3_GSAS
UTIL
Au_GSASc:\gsas\mywork