RECENT DEVELOPMENTS IN THE ANAELU-MPOD SOFTWARE SYSTEM FOR - PowerPoint PPT Presentation

RECENT DEVELOPMENTS IN THE ANAELU-MPOD SOFTWARE SYSTEM FOR POLYCRYSTAL CHARACTERIZATION L. E. Fuentes-Cobas 1 , E. E. Villalobos-Portillo 1 , D. C. Burciaga-Valencia 1 , L. Fuentes-Montero 2 , M. E. Montero-Cabrera 1 , D. Chateigner 3 1 Centro de Investigación en Materiales Avanzados (CIMAV), Chihuahua, Mexico 2 Diamond Light Source, Didcot, UK. 3 Université de Caen Normandie, Caen, France http://cimav.edu.mx/investigacion/software/ http://mpod.cimav.edu.mx

Outline 1) Recap on Texture Analysis. The program ANAELU (Analytical Emulator Laue Utility) 2) Structure-Properties: MPOD (Material Properties Open Database) a) Single Crystals. b) Textured Polycrystals ANAELU

Crystallographic Texture: Preferred Orientation a b a) Random distribution of orientations b) Texture AURIVILLIUS POLYCRYSTALS Rolling Texture (COURTESY J. A. EIRAS, UFSC, BRASIL)

The “classical” description of textures: (Direct) Pole Figures https://www.researchgate.net/figure/Figure-Initial-pole-figures-for-single-crystal-FCC-cube- texture-simulations_fig6_319446954

Direct pole figures follow the sample symmetry Pole figures in axial symmetry (fiber) textures D. Chateigner, J. Ricote. Ch 8 of Handbook “Multifunctional polycrystalline ferroelectric materials”. Eds: L. Pardo y J. Ricote, Springer-Verlag (2011)

Inverse Pole Figure (IPF) 001

Inverse pole figures follow the crystal symmetry Hexagonal Cúbico Trigonal Tetragonal

Model IPFs for poled BaTiO 3 0,0,1 1,1,1 SAMZ-Poly program “Structural” IPF 4mm point group Diffraction (Laue) IPF 4/m 2/m 2/m

Euler space http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=100&pageid=1039432491

The Orientation Distribution Function (ODF) dV/V = f(g) dg f ( g ) = f ( G s •g •G c ) Frequent ODFs in cubic phases Bunge (1982) Texture Analysis in Materials Science: Mathematical Methods

Texture Measurement DRX - Bragg-Brentano I = [ I 0 K |F| 2 p (LP) A T / v 2 ] ⋅ R( φ , β ) 3 / 2 − 1 ⎛ ⎞ ⎛ ⎞ 2 2 2 R G cos sin ⎜ ⎟ ⎜ ⎟ = φ + φ ⎜ ⎟ h 1 h h ⎜ ⎟ G ⎝ ⎠ ⎝ ⎠ 1 0,0,1 2 R G ( 1 G ) exp ( G ) = + − φ h 2 2 1 h 1,0,0 0,0,1 1,0,0 1,0,0 0,0,1 Textured BaTiO 3 ceramic

Texture Measurement Texture goniometer (ideally with neutrons) M. Betzl, L. Fuentes, J. Tobisch: "Texture study of rolling conditions for zinc ‑ based alloys". JINR comm. E14 ‑ 85 ‑ 473, Dubna 1985.

Polycrystal aggregate function g = [ ϕ 1 , Φ , ϕ 2 ] = g ( r ) Focus on “stereography”

Texture Measurement g ( r ) investigated by means of Kikuchi lines at the SEM (BSED, OIM)

Texture Measurement Nano-systems texture analysis by 2D - XRD 2-D position sensitive detector, BL11-3 SSRL

“Fibre textures” (axial symmetry): A frequent case in nano-structured functional materials If a sample shows fibr ibre text xtur ure , then the inverse pole figure (IPF) of the symmetry axis plays Nano-islands ↑ the ODF role. Nano-rods ↑ Nano-plates à ß Direct Pole Figure

ANA LYTICAL E MULATOR L AUE U TILITY J. Appl. Cryst . Vol. 44, pp. 241-246 (2011) http://cimav.edu.mx/investigacion/software/ http://www.esrf.eu/computing/scientific/ANAELU/Anelu_Page.htm https://www.iucr.org/resources/other-directories/software/anaelu

Combined 2D grazing incidence XRD + Electron microscopy texture analysis of ZnO thin layers Observed Calculated Preferred growth direction: [001] Distribution width Ω = (20 ± 2)° A. Sáenz-Trevizo, M. Miki-Yoshida et al Materials Characterization 98 (2014) 215–221

- Friendly GUI - Background modeling - Quantitative semi- automatic refinement of parameters

Physical properties: Y = K · X “Principal” and “Coupling” Interactions. Some effects and their constitutive equations: Paraelectricity: P = ε 0 χ P · E Paramagnetism: µ 0 M = µ 0 χ M · H Elasticity: S = s · T Thermal expansion S = η ·Δ θ Piezoelectricity: P = d · T S = d · E Magnetoelectricity: P = α · H µ 0 M = α · E L. Fuentes: Magnetic Coupling Properties in Polycrystals Textures and Microstructures 30 : 167-189 (1998).

THERMO-ELASTO-ELECTRO-MAGNETIC EQUILIBRIUM PROPERTIES Property Related magnitudes Tensor Heat capacity C Entropy (P0) / Temperature (P0) P0 Elasticity s Strain (P2) / Stress (P2) P4 Electr. susceptibility χ P Polarization (P1) / Elec. Intensity (P1) P2 Magn. susceptibility χ M Magnetization (A1) / Magn. Intensity (A1) P2 Strain (P2) / Temperature (P0) P2 Thermal expansion η Pyroelectricity p Polarization (P1) / Temperature (P0) P1 Pyromagnetism i Magnetization (A1) / Temperature (P0) A1 Piezoelectricity d Polarization (P1) / Stress (P2) P3 Piezomagnetism b Magnetization (A1) / Stress (P2) A3 Magnetization (A1) / Elec. Intensity (P1) A2 Magnetoelectricity α P à POLAR; A à AXIAL; r = Tensor rank Tensor ranks: m, n, m+n

MATRIX NOTATION A ij (for example): strain or sress tensor MATRIZ 3X3 HIPERVECTOR PIEZOELECTRICITY T ⎡ ⎤ 1 ⎢ ⎥ T d d d d d d ⎡ ⎤ 2 ⎢ ⎥ P 11 12 13 14 15 16 ⎡ ⎤ 1 T ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 3 ó P d d d d d d • = ⎢ ⎥ ⎢ ⎥ 21 22 23 24 25 26 2 ⎢ ⎥ T ⎢ ⎥ ⎢ ⎥ 4 P ⎢ ⎥ ⎣ ⎦ d d d d d d 3 ⎢ ⎥ T ⎢ ⎥ ⎣ ⎦ 31 32 33 34 35 36 5 d · T = P ⎢ ⎥ T ⎢ ⎥ ⎣ ⎦ 6

ELASTO-PIEZO-DIELECTRIC MATRIX S = s ⋅ T + d ⋅ E D ( ≈ P) = d ⋅ T + ε⋅ E S s s s s s s d d d T ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 1 11 12 13 14 15 16 11 12 13 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S s s s s s s d d d T ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2 21 22 23 24 25 26 21 22 23 2 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S s s s s s s d d d T 31 32 33 34 35 36 31 32 33 3 ⎢ ⎥ 3 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S s s s s s s d d d T 41 42 43 44 45 46 41 42 43 4 4 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ s s s s s s d d d S = T 51 62 53 54 55 56 51 52 53 5 5 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ s s s s s s d d d ⎢ ⎥ S T 6 61 62 63 64 65 66 61 62 63 6 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ d d d d d d D E ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ε ε ε 1 11 12 13 14 15 16 11 12 13 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ D d d d d d d E ε ε ε ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2 21 22 23 24 25 26 21 22 23 2 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ D d d d d d d E ε ε ε ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 3 31 32 33 34 35 36 31 32 33 3

CRYSTALLOGRAPHIC ELASTO-PIEZO- DIELECTRIC MATRICES, IEEE

CRYSTALLOGRAPHIC ELASTO-PIEZO- DIELECTRIC MATRICES, IEEE

MAGNETOELECTRIC MATRICES

THE NEUMANN PRINCIPLE Ø Effect’s symmetry is always -at least- equal to cause’s symmetry Cause Effect Electromagnetism Charges E and B fields and currents Crystal Physics Structure Properties

Scalars, polar and axial vectors Scalars (Q) are invariant under symmetry operations E E r dq ˆ Q d E = p 2 4 r m πε m* 0 Polar vectors ( E) transform as position vectors Axial (or “pseudo-”) vectors ( B ) B µ transform almost like polar x • vectors. Except … they ignore m the inversion transformation i d l r ˆ µ × 0 d B = 2 4 r π L.Fuentes, R. Font (1993) Rev. Esp. Fís. 7 (2), 49

The irreps approach: Piezoelectricity in C 2v T ⎡ ⎤ 1 ⎢ ⎥ T d d d d d d ⎡ ⎤ 2 ⎢ ⎥ P 11 12 13 14 15 16 ⎡ ⎤ 1 T ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 3 P d d d d d d = • ⎢ ⎥ ⎢ ⎥ 21 22 23 24 25 26 2 ⎢ ⎥ T ⎢ ⎥ ⎢ ⎥ 4 P ⎢ ⎥ ⎣ ⎦ d d d d d d 3 ⎢ ⎥ ⎢ T ⎥ ⎣ ⎦ 31 32 33 34 35 36 5 ⎢ ⎥ T ⎢ ⎥ ⎣ ⎦ 6 L. Fuentes, Ma. E. Fuentes: “La Relación Estructura-Simetría-Propiedades en Cristales y Policristales”. Reverté, México D.F. (2008)

A selection of material properties databases and representation tools: - The classical: Landolt-Börnstein (http://materials.springer.com/) - The materials project. UC Berkeley (https://www.materialsproject.org/) - WinTensor. Univ. Washington ( http://cad4.cpac.washington.edu/ wintensorhome/wintensor.htm) - MPOD. UniCaen, CIMAV et al ( http://mpod.cimav.edu.mx)

THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD) http://mpod.cimav.edu.mx

BaTiO 3 4mm Piezoelectric constant d Dielectric constant Elastic compliance s Young modulus

BaTiO 3 4mm Piezoelectric charge Dielectric constant constant d à ∞ mm ∞ ⁄ mmm Elastic compliance s Young modulus 4 ⁄ mmm 4 ⁄ mmm

Magnetoelectricity in LiCoPO 4 . Olivine structure, magnetic space group: Pnma’ Magnetic point group: mmm’= D 2h :C 2v Single-crystal ME tensor (T = 10 K) ∝= [█ 0 & 15 & 0 @ 30 & 0 & 0 @ 0 & 0 & 0 ] y x Data from Vaknin et al. (2002). x = 0 and y = 0 à symmetry planes; z = 0 à anti-symmetry plane