Brief X ray powder diffraction analysis tutorial

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Brief X ray powder

diffraction analysis tutorial

•

• Bibliografia essenziale

Bibliografia essenziale

•

• X

X

-

ray powder diffraction (XRPD): un

breve

richiamo

•

• Analisi qualitativa

Analisi qualitativa

•

• Analisi

Analisi

quantitativa

(

metodo

Rietveld)

Dr Carlo

Meneghini

Dip. Di Fisica, Università di Roma Tre

[email protected]

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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, 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/

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10

20

30

40 2θ

Atomic

distribution in

the unit cell

Peak relative

intensities

Unit cell

Symmetry

and size

Peak

positions

a

b

Peak shapes

Particle size

and defects

Background

Diffuse scattering,

sample holder,

matrix, amorphous

phases, etc...

X-ray Powder Diffraction

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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) 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/

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Powder diffraction patterns

2d

_hkl

sin(2θ) = nλ

Bragg law

Unit cell

Symmetry

and size

1 k

k’

q

d

_hkl

|k|=|k’|

q=sin(θ) 4πλ

−1 (exchanged momentum vector)

Peak intensity

I

_hkl

~ |F

_hkl

|

2 e

-q

2

u

2

₌

_{Debye Waller factor}

u = mean square displacement u=<r

_n

-r

_o

>

Structural Disorder:

f

_n

= f

_no

e

-q

2

u

2

2b

F

_hkl

= structure factor

F

_hkl

= Σ f

_n

e

ik.r

_n

Atomic distribution

in the unit cell

2a

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Line shape

_anisotropy

Crystallite defects

β

_τ

=D-d

Crystallite size

Sherrer Law

breath

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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

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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 l

x-range

xrd-file

_u

_sing

x:y

columns

w

ith

l

ine

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Possibili candidati

http://barns.ill.fr

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0 5000 10000 15000 20000 25000 10 20 30 40 50 60 'y2o3.dat' u 1:2

y2o3.dat

database

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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

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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.cel

y2o3.x_y

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diffracted

beam

incoming

beam

_θ

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y2o3.x_y

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Rietveld method

I

_calc

= I

_bck

+ S

Σ

_hkl

C

_hkl

(θ)

_F

2 hkl

(θ)

P

hkl

(θ)

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

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Sample

diffracted

beam

incoming

beam

_2θ

displacement zeroshift

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I

_calc

= I

_bck

+ S

Σ

_hkl

C

_hkl

(θ)

_F

2

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Refinement of y2o3.x_y 12/10/2005 12.58.11

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

R-values Rp=18.08 Rwp=24.85 Rexp=2.01 2 iterations of 6

parameter old new icsd_86815 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ scaling : 1.2000 1.2000 lattice a : 10.5968 10.6090 profile U : -0.1870 -0.4973 PsVoigt2 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 6590.1070 a1 : -841.4 -1060 a2 : 68.74 75.86 a3 : -2.669 -2.745 a4 : 0.05247 0.0522 a5 : -0.0004457 -0.0004386 a6 : -6.29E-7 -5.966E-7 a7 : 3.161E-8 3.121E-8 a8 : -3.797E-12 -8.06E-12 a9 : -1.953E-12 -1.947E-12 a10 : 2.97E-16 6.361E-1 a11 : 1.251E-16 1.261E-1 a12 : -6.315E-19 -6.571E-1 a13 : 8.173E-22 8.861E-2

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GSAS

SNLS – XRPD tutorial

(XP)gsas+expgui.exe

Programmi

Gnuplot

PCW

GSAS

Analisi

Dati

Y2O3_PCW

Y2O3_GSAS

UTIL

c:\gsas\mywork

Au_GSAS

y2o3.

gs

,

y2o3.

exp

,

inst

_

xry

.

prm

http://www.ccp14.ac.uk/solution/gsas/gsas_with_expgui_install.html

Obtaining GSAS

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I

_calc

= I

_bck

+ S

Σ

_hkl

C

_hkl

(θ)

_F

2

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peak variance:

σ

2

₌

_GU

_tan

2

_θ

₊

_GV

_{tan θ +}

_GW

_tan

2

_{q +}

_GP

_/cos

2

_θ

sample shift:

s = - π R

shft

/ 3600

sample absorption:

µ

_eff

= - 9000 / (π R

Asym

)

Gaussian Sherrer broadening

Lorentzian

:

γ

= (

LX

-

ptec

cos φ)/cos θ + (

LY

-

stec

cos φ) tan θ

Anisotropy _Lorentzian strain broadening Anisotropy (stacking faults) Lorentzian Sherrer broadening (particle size)