Rietveld_applications_tr.pdf

7/27/2019 Rietveld_applications_tr.pdf

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Applications ofApplications of thethe RietveldRietveldmethodmethod

Thierry Roisnel

Laboratoire de Chimie du Solide et Inorganique Molculaire

UMR6511 CNRS Universit de Rennes 1 (France)


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Crystal structuresMagnetic structures (neutron data)

1.1 Isomorphic or partially known structure

structure refinement + difference Fourier maps examination

1.2 Unknown structure

1.1. Unit cell determination

1.2 Space group determination1.3 Crystal structure determination:1.4 Structure refinement (Rietveld method)

1. Structure refinement


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1.1 Unit cell determination

indexation of diffraction pattern:. Determination of cell parameters. Crystal symmetry. (hkl) Miller indices for every Bragg line

*2 2 *2 2 *2 2 *2 * * * * * *

2 . 2 . 2 .= = + + + + +hkl hklQ d h a k b l c klb c lhc a hka b

Simple problem:

Needs only a list of angular positions of Bragg lines:

. Accuracy and precision of Bragg positions !

!! . Single phase ?. Diffractometer zero-shift ?


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1.2 Space group determination

. Whole profile refinement of the diffraction pattern (FullProf):. No structural model. Cell parameters previously determined (1.1). Space group: Lau group

. Detailed examination of systematic absences:. Extinctions due to Bravais lattice. Extinctions to symmetry elements


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1.3 Crystal structure determination

. Extraction of integrated intensities + Use of traditionnalmethods used in single crystal crystallography:

. Direct methods (EXPO, SHELXS )

. Patterson map

. Direct space methods:. Genetic algorithm, Monte Carlo, Simulating annealing


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. X-rays (conventionnal):

. Instrumental resolution" weak cell distortions

. Laboratory device

. Form factor:. decrease with sin/:

" Low diffracted intensity at high angles

. Increase with Z" diffracted intensities dominated by heavy atoms

1.4 Crystal structure refinement: X-rays versusneutron data


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. Neutrons : interaction neutron with atom nuclei

. Scattering power is independent of atomic number:

" localization of light atoms (H/D, Li):" important contrast: cationic distribution (ex: Fe/Mn)

. Low absorption:" experiments versus external parameter (temperature,

pressure)

. Scattering powder is independent of sin/:" accurate thermal displacement parameters

. Gaussian profile function


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. Neutron diffraction

. Instrumental resolution

. Need a particular installation (nuclear reactor, spallation source)

. Large volume of powdered sample (2-3 cm3)


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FullProf exercices

(http://www-llb.cea.fr/fullweb/fp2k/fp2k_exercices.htm)

Exercice #1: Analysis of the spinel MgAl2O4

(ref. V. Montouillot, PhD Thesis, Univ. Orlans 1998)

Spinel structure : cubic unit cell (space group: F d 3 m)

AB2X4: A2+ (Mg, Ca, FeII, Zn) tetrahedral (Td) &B3+ (Al, FeIII, MnIII, ) octaedral (Oh) sitesX: O2-


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AB2X4 spinel structrure

Different ways to fill the Td (nTd=8) and Oh sites (nOh=4):

( ) ( )Td Oh

2 3 2 31 x x x 2 x 4A B A B O+ + + +

x=0

x=1

( ) ( )Td Oh2 3

1 2 4A B O+ +

( ) )Td Oh

3 2 31 1 1 4B A B O+ + +

" direct spinel

" inverse spinel


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Space Group: F d -3 m

Setting 1:Tetrahedral A-positions (Mg,Al) 8a (1/4,1/4,1/4)

Octahedral B-positions (Mg,Al) 16d (5/8,5/8,5/8)Oxygen positions (O) 32e (x,x,x) x=0.386

Setting 2:Tetrahedral A-positions (Mg,Al) 8a (1/8,1/8,1/8)Octahedral B-positions (Mg,Al) 16d (1/2,1/2,1/2)

Oxygen positions (O) 32e (x,x,x) x=0.261


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Two neutron powder diffraction data files:

MgAl2O4s.dat -> Sample obtained by conventional hightemperature solid state reaction

neutron powder diffractometer: 3T2 (LLB, Saclay)

. = 1.227

. Resolution parameters: U = 0.276, V=0.340, W=0.147


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MgAl2O4 exercice

Refine the structure allowing the distribution of Mn and

Al between the two available cationic sites. Calculate the value of the spinel structure:

3

3B in Td siteB total

+

+ =

Winplotr (mgal2o4s)

Introduction of a structural model: Rietveld refinement


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JBT=0 cristal. Structure factor

IRF=0 automatic generation of reflections from the space group symbol!Phase 1: MgAl2O4-sharp

!Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More

5 0 0 0.0 0.0 1.0 0 0 0 0 0 0.00 0 7 0

F d 3 m


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!Phase 1: MgAl2O4-sharp

!Nat Dis Ang Pr1 Pr2 Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More

5 0 0 0.0 0.0 1.0 0 0 0 0 0 0.00 0 7 0F d 3 m


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Micro-structural features:

* apparent size of coherent domains in the direction perpendicularto the diffraction planes

* apparent strains in the direction perpendicular to the diffractionplanes:

Origin of micro-strains: . Defaults: dislocations, vacancies

. local fluctuations of composition (solid solutions )

2.Micro-structure refinement

( ) ( ) ( )x f x g x =

Observed profile Intrinsic profileInstrumental profile

h l d


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Diffracted intensity for a phase is proportional to the quantity of irradiatedmatter (absorption effects are not taken into account).

3.Quantitative phase analysis and

Rietveld method

For a multiple phase pattern:

1

( )=

= +

h, h,

hci i i

N

b I T T S

With:

SScale factor for phase


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3.Quantitative phase analysis

. .

mS

Z V

. . .m S M Z V

with m

ZV

Mass of the phase in the sample

Molecular weight

Number of molecules per unit cell

Volume of the unit cell


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3.Quantitative phase analysis

1 1

( )

.( )= =

= = N N

i i i

i i

m S ZMV

Wm S ZMV

determination of weight fraction w of every phase present in the sample


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3.Quantitative phase analysis in FullProf

Take care of:

. Sample preparation: homogeneity, number of particleswith random orientation (beware of preferential orientation)

. Correct calculation of structure factors for every phase

3 Q tit ti h l i i F llP f


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2

2

1 1

( ) . .

.( ) . .= =

= =

i

N N

i i i

i

ii i

i

t AS ZMV f V S

S

TZ

t

W

S ZMV f V ATZ

with

Scale factor in FullProf (refinable variable)FullProf parameter

Brindley factor (particle absorption contrastfactor).t is tabulated as a function of (i-).RFullProf parameter

S2= i ii iiZ MATZ f t

it

3 Q tit ti h l i i F llP f


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Used to transform the site multiplicities in PCR FullProf input file, totheir real values. For a stoichimetric phase, f= 1 if thesemultiplicities are calculated by dividing the Wyckoff multiplicity mof the site by the general multiplicity Mof the space group.Otherwise, f=occ.M/m, where occ. is the occupation number in thePCR file

if

In order to GET PROPER VALUES OF WEIGHT FRACTIONS LETTHE PROGRAM RE-CALCULATE ATZ by putting them to ZERO.The correct ATZ value to be rewritten in the PCR input file.

(First atom in the PCR file has to be fully occupied)

3 Quantitative phase analysis in FullProf


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1. Crystal structure has to be refined:

JBT=0 (IRF=0)

refine the structural parameters as usually

2. Crystal structure is well known:

2.1 create hkl file containing hkl list with corresponding F2(JLKH=5)

2.2 refine the pattern without entering atomic positionsJBT=-3, IRF=2 (Profile Matching mode with constantrelative intensities for the current phase, butrefinable scale factor)

Winplotr (Si3N4)

3 Rietveld Q P A


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3.Rietveld Q.P.A.

easy to operate (automatic analysis in FullProf) no internal standard

non destructive method

up to 16 phases in FullProf

polymorphism

neutron case: large amounts of powder analysis (real samples) industrial applications (cements, clays )

structure model dependent: {Fhkl} have to be known

beware of preferential orientation

3.Quantitative phase analysis:


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.Q p ydetermination of an amorphous phase

content ?

If an amorphous phase is present in the sample:S Cm m m=

Sample weight

Amorphous phase weight Crystalline partweight

Amorphous phase weight fraction:

1CA

S S

mm

m m=



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Q p ydetermination of an amorphous phase

content ?

. . . .m k S M Z V =

1 1

. . . .N N

C i i i i i

i i

m m k S M Z V = =

= =

For each crystalline phase:

For N crystalline phase sample:

Introduction of an internal standard in the powder:(mst

is known)

. . . .st st st st stm k S M Z V =

. . .

st

st st st st

mk

S M Z V =



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Q p ydetermination of an amorphous phase

content ?

Remarks:

same strategy can be applied for unknownstructure phase

difficult to manage for bulk sample

if the structure of the amorphous phase is known,a QPA can be realized through broadening linetreatment for the amorphous phase (small coherentdiffraction domains)

3 Rietveld Q P A : -Si N4 and Si N4 mixture


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3.Rietveld Q.P.A.: -Si3N4 and _Si3N4 mixture

Neutron data: Si3N4: 93% wgtSi3N4: 7% wgt

3 Rietveld Q P A : -Si3N4 and Si3N4 mixture


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3.Rietveld Q.P.A.: Si3N4 and _Si3N4 mixture

X-rays data: Si3N4: 91.6% wgtSi3N4: 8.4% wgt

Some references on Q P A by Rietveld method


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Some references on Q.P.A.by Rietveld method

R.J. Hill & C.J. Howard, J. Appl. Cryst. 20, 467-476 (1987)Quantitative phase analysis from neutron powder diffraction data using the

Rietveld method

G.W. Brindley, Phil. Mag. 36, 347-369 (1945)The effect of grain or particle size on X-ray reflections from mixedpowders and alloys considered in relation to the quantitative determination ofcrystalline substances by X-ray methods

D.L. Bish & S.A. Howard, J. Appl. Cryst. 21, 86-91 (1988)Quantitative phase analysis using the Rietveld method

J.C. Taylor, Powder Diffraction 6, 2-9 (1991)Computer programs for standardless quantitative analysis of minerals

using the full powder diffraction profile

R.J. Hill, Powder Diffraction 6, 74-77 (1991)

Expanded use of Rietveld method in studies of phase abundance inmultiphase mixtures

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Rietveld_applications_tr.pdf