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

Combined Texture-Structure- Microstructure analysis using diffraction matériaux cristallins ou micro-cristallisés à propriétés anisotropes ● Elaboration de matériaux de complexité croissante, applications de + en + spécifiques ● Désir d' optimisation et de compréhension des anisotropies physico-chimiques de matériaux

Métallurgie et Géophysique Méthodes d’analyses Propriétés anisotropes - diffraction - mécaniques - spectroscopiques - ferro/piezo-électriques (EXAFS, ESR) QTA - supraconductrices - conductrices anioniques - aimantation Modes de croissance (épitaxie) Biologie (mollusques) Optimisation d’élaboration

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 {hkl} pole figure measurement + corrections: dV( ) 1 c χφ β = P( ) si n d d α χφ χ χ φ V 4 π Z=001 X Y=100 S-space Y-space X=010 Y We want f(g) (ODF): with g = ( α , β , γ ) a c dV(g) 1 β α = f (g) dg Z=001 2 V 8 X Y=100 π γ b G-space

We have to invert (Fundamental equation of Texture Analysis): ! 1 ~ P ( y ) = f(g) d ∫ ϕ hkl 2 π ! hkl // y < > ⎡ ⎤ ⎢ ⎥ n 0 f ( g ) f ( g ) WIMV refinement method: n 1 f ( g ) N + ⎢ ⎥ = Williams-Imhof-Matthies-Vinel ! 1 ⎢ ⎥ ( ) ⎥ n P ( y ) ∏ I ⎢ hkl ⎣ ⎦ hkl

Recalculation of pole figures or Bunge - Esling inverse pole figures from the m , n m , n f ( g ) C T ( g ) ODF ∑ ∑ ∑ = ! ! ! m n path Ruer - Baro (vector method) ! f(g) P ( y ) = σ ! path h Helming (Components) γ− sections f ( g ) S ( g , s , FWHM ) ∑ ∑ = i phases i ● ● Pawlik (ADC) ● ● {hkl} pole figure {001} pole figure for a cubic crystal system

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) - defocusing (high χ ) - blind area (low χ ) - increase at low ω , where high n,Z A intensity peaks are (LP factor) ϕ 2 θ C 0 τ Y S ω 2 θ min χ n GR Needs for a tool for an automatic search X S Z S of the best experimental conditions:

Fortran code to estimate the orientation space completion: τ , ω , χ , φ and CPS ranges, 2 θ hkl’s, cradle shades (in BEARTEX) Quartz sample BETA > 0| 1| τ = 0°; ω = 7° 2| 3| 4| 5| BETA >0 --- Path number 3| * 4| 5| 6| τ = 0°; ω = 17° 7| 8| 9| 10| 11| 12| BETA >0 -- 15| * 16| * τ = 40°; ω = 37° 17| * 18| * 19| * 20| * 21|

Usual Structure-Microstructure Analysis (Full pattern fitting, Rietveld Analysis) Si 3 N 4 matrix with SiC whiskers: I(2 ) = I ( 2 ) S ( 2 ) bkg(2 ) Random powder: ∑ θ θ θ + θ hkl, phases hkl, phases hkl, phases

L 2 I ( 2 ) S F m P P θ = hkl hkl hkl hkl 2 V c S: scale factor (phase abundance) F hkl : structure factor (includes Debye-Waller term) V c : unit-cell volume F hkl : texture parameter (March-Dollase …) I S S ( 2 ) S ( 2 ) * S ( 2 ) θ = θ θ hkl hkl hkl S I : instrumental broadening S S : Sample aberrations crystallite sizes (iso. or anisotropic) rms microstrains ε

Problems on ultrastructures Ferroelectric film (PTC) Sum diagram Electrode (Pt) Antidiffusion barrier (TiO 2 ) Oxide (native, thermally grown) SC Substrate (Si) - Strong intra- and inter-phase overlaps 001/100 PTC 011/110 PTC + Si ( λ /2) 111 PTC + 111 Pt - Mixture of very strong and lower textures - texture effect not fully removable: structure - structure unknown: texture

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 Mapping Spectrometer space for correction of: - instrumental resolution - instrumental misalignments ω = 20° ω = 40° 60 ° 60 ° χ χ 0° 0°

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

Polyphase texture analysis: Direct Integration vs Combined Dolomite/Calcite mixture: well separated peaks Dolomite a) Calcite Direct Combined 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 Goodness of fit: 1.806665 Rwp (%): 17.10033 Si 3 N 4 matrix with SiC whiskers Rb (%): 12.54065 Rexp (%): 9.465139

Si 3 N 4 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: top film ( ( ) ) ( ( ) ) C g 1 exp Tg / cos / 1 exp 2 T / sin cos = − − µ χ − − µ ω χ 1 2 χ ( ( ) ) ( ( ) ) cov. layer top film ' ' ' ' C C exp g T / cos / exp 2 T / sin cos ∑ ∑ = − µ χ − µ ω χ 2 i i i i χ χ Gives access to individual Thicknesses in the refinement

PTC/Pt/TiO 2 /SiO 2 /Si-(100) PTC a = 3.945(1) Å c = 4.080(1) Å T = 4080(10) Å a = 3.955(1) Å t iso = 390(7) Å T' = 462(4) Å Pt ε = 0.0067(1) t' iso = 458(3) Å ε ' = 0.0032(1)

WIMV vs Entropy modified WIMV approach Better refinement with E- WIMV: WIMV - lower reliability factors (structure and texture) - better high density level reproduction E-WIMV Texture Pt PTC Pt PTC Texture Texture RP 0 RP 0 Rw R Bragg Index Index (m.r.d. 2 ) (m.r.d. 2 ) (%) (%) (%) (%) 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

µ − µ 0 χ = µ Z 0 isolated atom ε µ = 0 ρ α h ν α θ ij φ R ij Y Ω Film surface absorbing atom X backscattering atom

Amplitude of EXAFS spectra (then RSF): Stern & Heald, 1983 plane-wave approx., single-scattering processes ! ! 2 j ( k , ) 3 cos ( k ) ∑ χ θ = θ χ ij j iso j ! N j 2 j 3 cos ( k ) ∑∑ = θ χ ij iso j i 1 = j: nb of neighbouring atomic shell N j : nb of backscatterers in the j th shell j χ taken at magic angle ( α =35.3°) for fibre textures iso ➯ P-EXAFS: provides directional structural information

! ! ! j ( k ) ( k , ) ( k ) Isotropic powder: ∑ χ = χ θ = χ ij iso j For fibre texture (around Z): signal averaged on Ω 2 2 2 π 1 cos sin α φ 2 2 2 2 cos cos d cos sin θ = ∫ θ Ω = φ α + ij ij 2 2 π 0 which allows to calculate the real number of j th atoms: 2 2 cos sin ⎡ ⎤ α φ 2 2 N 3 N cos sin = φ α + ⎢ ⎥ obs real 2 ⎣ ⎦

N obs / 3 N real correction factor 2.8 1.6 80 0.20 2.0 2.4 2.6 2.2 0.40 1.2 2 magic angles: 0.80 60 0.60 1.4 α = 35.3° 1.8 α ° 1 φ = 54.7° 40 1 0.80 1.2 20 0.60 0.40 0.20 1.4 0 0 20 40 60 80 φ °

P-EXAFS of clays Beam direction α = 0° α = 90° β tet Absorber β tet ε Mg, Al, Fe c* Si, Al Oct-Tet: max Oct-Tet: min Oct-Oct: 0 Oct-Oct: max ε

P-EXAFS oscillations of Garfield nontronite Fe K-edge High quality range up to 14-15Å -1 k 3 χ Powder spectra Strong α dependence = strong texture k (Å -1 )

Texture experiments Garfield 1.8 001 PVO 1.6 1.4 Intensity (a.u.) 1.2 1.0 004 0.8 11+/-3 0.6 0.4 0.2 0.0 200 020 35 ρ ° 130 110 70 5 10 15 20 θ °

OD-WIMV refinement Crystal system : a=5.279Å, b=9.14Å, c=12.563Å, β =99.25°, RP0 = 16.9% RP1 = 10.1% Rw0 = 6.8% Rw1 = 5.6% 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 c* For ideally textured films: 54.4° (Stöhr, NEXAFS spect., 1992) O 1 ( )( ) 2 2 1 3 sin 1 3 cos 1 + α − ψ − I 2 α = Fe 1 a I ( ) 2 1 3 cos 1 0 − ψ − 2 Flattened Regular