brief XRD tutorial - Dipartimento di Matematica e...

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Brief X ray powder diffraction analysis tutorial Bibliografia essenziale Bibliografia essenziale X X - - ray powder diffraction (XRPD): un ray powder diffraction (XRPD): un breve breve richiamo richiamo Analisi qualitativa Analisi qualitativa Analisi Analisi quantitativa quantitativa ( ( metodo metodo Rietveld) Rietveld) Dr Carlo Dr Carlo Meneghini Meneghini Dip. Di Fisica, Università di Roma Tre [email protected] OGG-INFM GILDA c/o ESRF Grenoble, France

Transcript of brief XRD tutorial - Dipartimento di Matematica e...

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

Line shape anisotropyCrystallite defects

βτ=D-d

Crystallite size

Sherrer Law

breath

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

Possibili candidatihttp://barns.ill.fr

0

5000

10000

15000

20000

25000

10 20 30 40 50 60

'y2o3.dat' u 1:2

y2o3.dat

database

http://database.iem.ac.ru/mincryst/

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5000

10000

15000

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25000

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'y2o3.dat' u 1:2

y2o3.dat

save file: icsd_86815.cel

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

Load structure file icsd_86815.cel

diffracted beamincoming

beam θθ

y2o3.x_yy2o3.x_ySNLS – XRPD tutorial/dati

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

Sample

diffracted beamincoming

beam 2θ

displacement

zeroshift

Icalc = Ibck + S Σhkl Chkl (θ) F2hkl (θ) Phkl(θ)

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

Icalc = Ibck + S Σhkl Chkl (θ) F2hkl (θ) Phkl(θ)

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

GOLDSF m3m λ=0.688011Au= 0. 0. 0. a = 4.0782

Ps ~ 50 Å