Combined Texture-Structure- Microstructure analysis using - - PowerPoint PPT Presentation

Combined Texture-Structure- Microstructure analysis using diffraction

• Elaboration de matériaux de complexité croissante, applications

de + en + spécifiques

• Désir d'optimisation et de compréhension des anisotropies

physico-chimiques de matériaux

matériaux cristallins ou micro-cristallisés à propriétés anisotropes

Métallurgie et Géophysique QTA Propriétés anisotropes

• mécaniques
• ferro/piezo-électriques
• supraconductrices
• conductrices anioniques
• aimantation

Méthodes d’analyses

• diffraction
• spectroscopiques

(EXAFS, ESR) Modes de croissance (épitaxie) Optimisation d’élaboration Biologie (mollusques)

Summary

• Usual up-to-date approaches for polycrystals

– Texture – Structure-Microstructure – Problems on ultrastructures

• Combined approach

– Experimental needs – Methodology-Algorithm – Ultrastructure implementation – Case studies

• Future trends

Texture Analysis

X=010 Y=100 Z=001

c α β

X Y

φ χ χ χφ π χφ d d n si ) P( 4 1 = V ) dV(

{hkl} pole figure measurement + corrections:

dg (g) f 8 1 = V dV(g)

2

π

We want f(g) (ODF): with g = (α,β,γ)

X=010 Y=100 Z=001

c a b α β γ

X Y

S-space G-space Y-space

∫

> <

ϕ π

y // hkl hkl

~ d f(g) 2 1 = ) y ( P

!

!

We have to invert (Fundamental equation of Texture Analysis):

( ) ⎥

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ =

∏

+ hkl I 1 n hkl n 1 n

) y ( P ) g ( f ) g ( f N ) g ( f !

WIMV refinement method: Williams-Imhof-Matthies-Vinel

• {001} pole figure

for a cubic crystal system γ−sections {hkl} pole figure path path

Recalculation of pole figures or inverse pole figures from the ODF

) g ( T C ) g ( f

n , m n , m n m ! ! !

∑ ∑ ∑

=

Bunge - Esling Ruer - Baro (vector method)

) y ( P f(g)

h

!

!

σ =

Helming (Components)

∑ ∑

=

phases i i

) FWHM , s , g ( S ) g ( f

Pawlik (ADC)

ODF Completion

• Several {hkl} pole figures needed to calculate f(g)
• Each f(g) cell (98000 at total) needs 3 paths from experiments
• More than 3 is better !
• Spectrometer space is complicated (5 angles, 2 shaded area)

Needs for a tool for an automatic search

• f the best experimental conditions:

2θmin

τ

ω 2θ χ ϕ

XS ZS YS n,ZA nGR

C0

• defocusing (high χ)
• blind area (low χ)
• increase at low ω, where high

intensity peaks are (LP factor)

BETA > 0| 1| 2| 3| 4| 5|

BETA >0

• 3| *

4| 5| 6| 7| 8| 9| 10| 11| 12|

Quartz sample Path number

BETA >0

• 15| *

16| * 17| * 18| * 19| * 20| * 21|

τ = 0°; ω = 7° τ = 0°; ω = 17° τ = 40°; ω = 37°

Fortran code to estimate the orientation space completion: τ, ω, χ, φ and CPS ranges, 2θ hkl’s, cradle shades (in BEARTEX)

Usual Structure-Microstructure Analysis

) bkg(2 ) 2 ( S ) 2 ( I = ) I(2

phases hkl, phases hkl, phases hkl,

θ + θ θ θ

∑

(Full pattern fitting, Rietveld Analysis)

Si3N4 matrix with SiC whiskers: Random powder:

hkl 2 c P hkl 2 hkl hkl

P V L m F S ) 2 ( I = θ

S: scale factor (phase abundance) Fhkl: structure factor (includes Debye-Waller term) Vc: unit-cell volume Fhkl: texture parameter (March-Dollase …)

) 2 ( S * ) 2 ( S ) 2 ( S

S hkl I hkl hkl

θ θ = θ

SI: instrumental broadening SS: Sample aberrations crystallite sizes (iso. or anisotropic) rms microstrains ε

Problems on ultrastructures

Ferroelectric film (PTC) Electrode (Pt) Antidiffusion barrier (TiO2) Oxide (native, thermally grown) SC Substrate (Si)

• Strong intra- and inter-phase
• verlaps
• Mixture of very strong and

lower textures

• texture

effect not fully removable: structure

• structure unknown: texture

001/100 PTC 111 PTC + 111 Pt 011/110 PTC + Si (λ/2)

Sum diagram

Direct Integration of Peaks up to recently: best existing technique for texture Integration + corrections + ODF refinement Limited nb of PFs (polyphase) Only access to PTC, badly ! No control of ultrastructure parameters

Combined approach

Experimental needs

ω = 20° ω = 40°

Mapping Spectrometer space for correction of:

• instrumental resolution
• instrumental misalignments

χ 60° 0° χ 60° 0°

Methodology-Algorithm Rietveld Structure, Microstructure WIMV Texture Rietveld and WIMV algorithm are alternatively used to correct for each others contributions: Marquardt non- linear least squares fit is used for the Rietveld. Pole figure extraction (Le Bail method): Phkl(χ,ϕ) Correction of intensities for texture: Ihkl(2θ,χ,ϕ) = Ihkl(2θ) Phkl(χ,ϕ)

Polyphase texture analysis: Direct Integration vs Combined Dolomite/Calcite mixture: well separated peaks

a)

Direct Combined Dolomite Calcite Textures show 0.2 mrd difference at max. only texture reliability factors lowered by 3 % + microstructural parameters

Phase analyses: Structures are found the ones in litterature refined cell parameters: dolomite a=4.8063(4)Å c=16.0098(4)Å calcite a=4.9755(4)Å c=16.998(3)Å Phase quantity: Combined approach: dolomite 93.7 % calcite 6.3 % Optically/Chemically:dolomite 90 % calcite 10 % + dolomite mean crystallite size: 2000(80) Å

Quantitative phase and texture-analysis ceramic-matrix composites Si3N4 matrix with SiC whiskers

Goodness of fit: 1.806665 Rwp (%): 17.10033 Rb (%): 12.54065 Rexp (%): 9.465139

Si3N4 SiC

• Vol. fraction (%): 75.8 24.2
• Part. Size (Å): 3800 2200

rms micro-strains (%): 4.2 10-4 2.8 10-4

Ultrastructure implementation Corrections are needed for volumic/absorption changes when the samples are rotated. With a CPS detector, these correction factors are:

( ) ( ) ( ) ( )

χ ω µ − − χ µ − − =

χ

cos sin / T 2 exp 1 / cos / Tg exp 1 g C

2 1 film top

( ) ( ) ( ) ( )

χ ω µ − χ µ − =

∑ ∑

χ χ

cos sin / T 2 exp / cos / T g exp C C

' i ' i ' i ' i 2 film top layer cov.

Gives access to individual Thicknesses in the refinement

PTC Pt a = 3.945(1) Å c = 4.080(1) Å T = 4080(10) Å tiso = 390(7) Å ε = 0.0067(1) a = 3.955(1) Å T' = 462(4) Å t'iso = 458(3) Å ε' = 0.0032(1) PTC/Pt/TiO2/SiO2/Si-(100)

WIMV vs Entropy modified WIMV approach WIMV E-WIMV Better refinement with E- WIMV:

• lower

reliability factors (structure and texture)

• better high density level

reproduction

Texture Pt Texture Index (m.r.d.2) PTC Texture Index (m.r.d.2) Pt RP0 (%) PTC RP0 (%) Rw (%) RBragg (%) WIMV 48.1 1.3 18.4 11.4 12.4 7.7 EWIMV 40.8 2 13.7 11.2 7 4.7

Polarised-EXAFS and QTA correlations: textured self-supporting films of clays

Main Collaborators:

• A. Manceau, B. Lanson: LGIT, Grenoble, France

Film surface

Z X Y

hν ε

Rij α φ θij Ω α absorbing atom backscattering atom ρ

atom isolated = − = µ µ µ µ χ

Amplitude of EXAFS spectra (then RSF): Stern & Heald, 1983

plane-wave approx., single-scattering processes

∑

=

j j iso j ij

k k ) ( cos 3 ) , (

2

! ! χ θ θ χ

j iso

χ

j: nb of neighbouring atomic shell Nj: nb of backscatterers in the jth shell taken at magic angle (α=35.3°) for fibre textures

∑∑

=

=

j j iso ij N i

k

j

) ( cos 3

2 1

! χ θ

➯ P-EXAFS: provides directional structural information

Isotropic powder:

∑

= =

j j iso ij

k k k ) ( ) , ( ) ( ! ! ! χ θ χ χ For fibre texture (around Z): signal averaged on Ω 2 sin cos sin cos cos 2 1 cos

2 2 2 2 2 2 2

φ α α φ θ π θ

π

+ = Ω =

∫

d

ij ij

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = 2 sin cos sin cos 3

2 2 2 2

φ α α φ

real

• bs

N N which allows to calculate the real number of jth atoms:

0.20 0.20 0.40 0.40 0.60 0.60 0.80 0.80 1.2 1.2 1.4 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 20 40 60 80 20 40 60 80

1 1

α° φ°

Nobs / 3 Nreal correction factor

2 magic angles: α = 35.3° φ = 54.7°

P-EXAFS of clays

Beam direction ε ε α = 0° α = 90° c* βtet

Absorber Mg, Al, Fe Si, Al

βtet

Oct-Tet: min Oct-Oct: max Oct-Tet: max Oct-Oct: 0

P-EXAFS oscillations of Garfield nontronite

k3χ k (Å-1) Fe K-edge Powder spectra Strong α dependence = strong texture High quality range up to 14-15Å-1

Texture experiments

5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 35 70

200 130 020 110 004 11+/-3 001

PVO

θ ° ρ°

Intensity (a.u.)

Garfield

OD-WIMV refinement

RP0 = 16.9% RP1 = 10.1% Rw0 = 6.8% Rw1 = 5.6% Crystal system: a=5.279Å, b=9.14Å, c=12.563Å, β=99.25°,

004/113/11-3 = 0.85/0.1/0.05 020/110 = 0.7/0.3 200/130 = 0.4/0.6

<001>* fibre, fibre axis ⊥ film plane

Octahedra flattening angle ψ (Edge-sharing octahedral structures) ψ

54.4°

c* a

( )( ) ( )

1 cos 3 2 1 1 1 cos 3 1 sin 3 2 1 1

2 2 2

− − − − + = ψ ψ α

α

I I

Fe O For ideally textured films:

(Stöhr, NEXAFS spect., 1992)

Flattened Regular

• The use of textured self-supporting films allow an

extension of the k exploitable range of EXAFS spectra, when polarised radiation is used, and their quality

• Texture-corrected spectra permits the determination of

the real number of neighbours

• The angular variation of the P-EXAFS spectra can

provide the determination of structural distorsions

Some conclusions

QTA and anisotropic magnetisation curves

Main Collaborator:

• M. Morales: Lab. Cristallographie, Grenoble, France

j i j j j j j j j j j j j i i i i i i i i i i i 2a 2a 2a 2a 2a z=0 z=1/2 z=1/4 et 3/4 a b f f f f

ErMn4Fe8C Structural determination:

• M. Morales et al.: J. Magn.

And Magn. Mat. 196 (1999) 703

Easy-plane tetragonal phase magnetic moments in the (a,b) planes

N S

Htext

θ θ

S(Q)

Htext radial Sample B N S z

Htext

θ θ

S(Q)

Htext axial Sample A

Hmeas // z ⊥ (a,b) // (a,b)

Same demagnetising factor

28 29 30 31 32 33 34 35 36 37 38 20 40 60 80 100 120 140 160

002 301 220 + 211

Intensity (a.u.) 2 θ (°) A B

max {001}: 3.9 mrd min: 0.5 mrd Quantitative Texture Analysis

• --- // (a,b)
• --- ⊥

“ RP0 = 1.2 % F2 = 1.3 mrd2 S = -0.13 {001} radial distribution: ρ0 (0.5 mrd) + PV (HWHM = 12°)

1 2 3 4 5 6 7 8 2 4 6 8 10

aimantation ( µ

B / fu )

H (T) ErMn

4Fe 8C

T= 300K

Μ

/ / /

Μ

⊥

M

random

Anisotropic magnetisation curves HA

M(Hmeas) = MS cos(θg - θ) E(Hmeas) = K1 sin2θ −Η MS cos(θg - θ) d dE = θ

θ) (θ sin M θ cos θ sin K 2 H

g S 1 meas

− =

HA = 2K1/MS

) θ

• θ

( sin θ cos θ sin H H

g A meas =

Model for M⊥:

c

!

M

!

x

O ⊥ (a,b)

H meas

θg θ φ

anisotropy energy Zeeman energy

MS = 5.24 µB/fu

1 dφ dθ sinθ ) φ , F(θ

g g 2 π 2 g

g

=

∫ ∫

= θ π = ϕ

Normalised Probability function F, to find c-axes in dy: Fibre texture:

1 dθ sinθ ) G(θ 2

g g 2 π g

g

= π ∫

= θ

( )

random 2 π g g g g S

M θ d ) θ θ cos( θ sin ) θ PV( 1 2 M M ρ + − ρ − π =

∫

⊥

Finally:

( )

) ( PV 1 ) ( G

g g

θ ρ − = θ

0.0 0.5 1.0 1.5 2.0 0.6 0.8 1.0 1.2

M / MS H / HA

calcul expérimental

Some conclusions

• This model strongly deviates from reality at fields

higher than 1.5 T

• But it takes account of the real (exp. measured)
• rientation distribution of crystallites, rather than

trying to fit it

• Its

merit is to separate purely magnetic and crystallographic effects

SiO2 (150 Å)/Si

Reflectivity and Electron Density Profile

EDP SIMS SiOxNy / Si-(100)

2 z iq

• z

dz e dz d 1 ) R(q

z

∫

∞ ∞ − ∞

ρ ρ =

Future trends

• Combining with reflectivity measurements: independently

measured and refined thicknesses, electron densities and roughnesses

• Adding residual stress determinations
• Multiple Analysis Using Diffraction, a web-based tutorial for

the combined approach: search MAUD (Luca Lutterotti)

• Quantitative

Texture Analysis Internet Course: http://lpec.univ-lemans.fr/qta(Daniel Chateigner)

Quantitative Texture Analysis Internet Course http://lpec.univ-lemans.fr/qta