Mapping Texture in Thin Films D. Chateigner CRISMAT-ISMRA, Caen, - PowerPoint PPT Presentation

Mapping Texture in Thin Films D. Chateigner CRISMAT-ISMRA, Caen, France ISMRA

Summary • Introduction – Texture with regular scans – Pole figures – Typical pole figures • Different approaches – Experimental needs – Choice of the detector – Choice of a reference frame

• Methodology – Pole Figure Corrections (defocusing, volumic/ absorption, location, fluorescence) – ODF calculation – Estimators of refinement quality – Estimators of Texture strength – Measurements / Orientation space coverage • Simple objects to deal with – Recalculated low-indices pole figures – Inverse pole figures (fibre textures) – Volumic ratios (single-crystal like and epitaxy) – Deal with components in the ODF space

• Why Texture Analysis – Anisotropic Physical Properties • Elastic properties • Seismic wave velocities • Magnetic ferro or antiferro compounds • Anionic conductivity • Superconducting currents and Levitation forces – Anisotropic measurements • Polarised EXAFS • ESR, Raman • Diffraction !!!! • Conclusions

Estimators of Refinement Quality RP Factors: Individual pf: J ~ ~ o c P (y ) - P (y ) ∑ h j h j ~ i i ( ) j= 1 o RP (h ) = x, P (y ) θ x i h j J ~ i o P (y ) ∑ h j 1 for t > x ⎧ i j= 1 ( x , t ) θ = ⎨ 0 for t x ≤ Averaged: ⎩ x , 1, 10 ... = ε 1 I RP = RP (h ) ∑ x x i I i = 1

Bragg R-Factors: J ~ ~ [ ] 2 o c P (y ) - P (y ) ∑ h j h j ~ i i ( ) j= 1 o RB (h ) = x, P (y ) θ x i h j J ~ i 2 o P (y ) ∑ h j i j= 1 Weighted Rw-Factors: J [ ] 2 o o c c 1 w I (y ) - w I (y ) ∑ ij h j ij h j w ~ = i i ( ) j= 1 ij o Rw (h ) = x, P (y ) θ o I (y ) x i h j J i h j 2 o z i w I (y ) ∑ ij h j i j= 1

RPs vary much with texture strength than Rws gRw0 150 RP 140 gRw1 RP1 120 125 100 100 80 75 60 50 40 25 20 0 0 0 100 200 300 400 500 600 700 800 0 200 400 600 800 F 2 F 2

Estimators of Texture Strength Texture Index: 1 2 F f ( g ) g ∑ = Δ i i 2 8 π i Entropy: - 1 S f ( g ) ln[ f ( g )] g ∑ = Δ i i i 2 8 π i

Measurements / Orientation Space Coverage Say 20 measured (5° x 5°) complete pole figures: = 20 x 1398 = 27960 experimental points ODF (5° x 5° x 5°, triclinic): 98496 points to refine strongly underdetermined system !

Evaluation of the OD coverage Cubic Crystal Structure: 2 {100} pole figure, measured up to c = 45°: 0 5 {100} + {110}, measured up to c = 45°: 3 6 {100} + {110} + {111}, up to c = 45°: 3

Deal with components in the ODF space α γ β ODF γ -sections Pole figures Component: (Hexagonal system) g = {85,80,35}