SLIDE 1
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
Mapping Texture in Thin Films D. Chateigner CRISMAT-ISMRA, Caen, - - PowerPoint PPT Presentation
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
SLIDE 2
SLIDE 3
- 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
SLIDE 4
- 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
SLIDE 5
Estimators of Refinement Quality
RP Factors:
( )
) (y P ~ x, ) (y P ~ ) (y P ~
- )
(y P ~ = ) (h RP
j
- h
J 1 j= j
- h
J 1 j= j c h j
- h
i x
i i i i
θ
∑ ∑
∑
I 1 = i i x x
) (h RP I 1 = RP
Individual pf:
... 10 1, , x x for t x > for t 1 ) t , x ( ε = ⎩ ⎨ ⎧ ≤ = θ
Averaged:
SLIDE 6
[ ] ( )
) (y P ~ x, ) (y P ~ ) (y P ~
- )
(y P ~ = ) (h RB
j
- h
J 1 j= j 2
- h
J 1 j= 2 j c h j
- h
i x
i i i i
θ
∑ ∑ Bragg R-Factors: Weighted Rw-Factors:
[ ] ( )
) (y P ~ x, ) (y I w ) (y I w
- )
(y I w = ) (h Rw
j
- h
J 1 j= j 2 z h
- ij
J 1 j= 2 j c h c ij j
- h
- ij
i x
i i i i
θ
∑ ∑
) (y I 1 w
j
- h
ij
i
=
SLIDE 7
RPs vary much with texture strength than Rws
100 200 300 400 500 600 700 800 25 50 75 100 125 150
RP RP1 F2
200 400 600 800 20 40 60 80 100 120 140
gRw0 gRw1 F2
SLIDE 8
Estimators of Texture Strength
Texture Index:
i i i 2 2
g ) g ( f 8 1 F Δ π =
∑
Entropy:
i i i i 2
g )] g ( f ln[ ) g ( f 8 1
- S
Δ π =
∑
SLIDE 9
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 !
SLIDE 10
Evaluation of the OD coverage
Cubic Crystal Structure: {100} pole figure, measured up to c = 45°:
2
{100} + {110}, measured up to c = 45°:
5 3 6 3
{100} + {110} + {111}, up to c = 45°:
SLIDE 11
Deal with components in the ODF space
α β γ Pole figures ODF γ-sections Component: (Hexagonal system) g = {85,80,35}