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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD) http://mpod.cimav.edu.mx OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

Daniel Saulius Giancarlo

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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/wi ntensorhome/wintensor.htm)

  • MPOD. UniCaen, CIMAV et al

(http://mpod.cimav.edu.mx)

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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Tensor nature of physical properties

(an example) P, E P, E

P = εo χP· E χP is a 2nd rank tensor.

Properties are associated with constitutive equations:

Y = K · X (K = Y / X)

Tensor ranks:

m, n, m+n

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THERMO-ELASTO-ELECTRO-MAGNETIC EQUILIBRIUM PROPERTIES

Pà POLAR; Aà AXIAL; r = Tensor rank

Property Related magnitudes Tensor Heat capacity C Entropy (P0) / Temperature (P0) P0 Elasticity s Strain (P2) / Stress (P2) P4

  • Electr. susceptibility χP

Polarization (P1) / Elec. Intensity (P1) P2

  • Magn. susceptibility χM

Magnetization (A1) / Magn. Intensity (A1) P2 Thermal expansion η Strain (P2) / Temperature (P0) P2 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 Magnetoelectricity α Magnetization (A1) / Elec. Intensity (P1) A2

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Paraelectricity:

P = ε0χP·E

Paramagnetism: µ0M = µ0χM·H Elasticity:

S = s · T

Thermal expansion S = η·Δθ Piezoelectricity:

P = d · T S = d · E

Magnetoelectricity: P = α · H

µ0M = α · E

Physical properties: “Principal” and “Coupling” Interactions.

Some effects and their constitutive equations:

Textures and Microstructures 30: 167-189 (1998).

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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CIF format

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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Dielectric constant Piezoelectric constant d Elastic compliance s

BaTiO3 4mm

Young modulus

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THE NEUMANN PRINCIPLE Ø Effect’s symmetry is always -at least- equal to cause’s symmetry

Cause Effect Electromagnetic theory Charges and currents E and B fields Crystal Physics Structure Properties

Structure-properties relationships: The role of Symmetry

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Dielectric constant

∞⁄mmm

Piezoelectric charge constant d à ∞mm Elastic compliance s

4⁄mmm

BaTiO3 4mm

Young modulus

4⁄mmm

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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HYPERVECTOR

MATRIX NOTATION

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡

  • ⎥

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡

3 2 1 6 5 4 3 2 1

P P P T T T T T T d d d d d d d d d d d d d d d d d d

36 35 34 33 32 31 26 25 24 23 22 21 16 15 14 13 12 11

Aij (for example): strain or sress tensor

3X3 MATRIX

  • r

d · T = P

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ELASTO-PIEZO-DIELECTRIC MATRIX

S = s⋅T + d⋅E D (≈ P) = d⋅T + ε⋅E

S S S S S S D D D = s s s s s s d d d s s s s s s d d d s s s s s s d d d s s s s s s d d d s s s s s s d d d s s

1 2 3 4 5 6 1 2 3 11 12 13 14 15 16 11 12 13 21 22 23 24 25 26 21 22 23 31 32 33 34 35 36 31 32 33 41 42 43 44 45 46 41 42 43 51 62 53 54 55 56 51 52 53 61 62 63

⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ s s s s d d d d d d d d d d d d d d d d d d d d d T T T T T T E E E

64 65 66 61 62 63 11 12 13 14 15 16 11 12 13 21 22 23 24 25 26 21 22 23 31 32 33 34 35 36 31 32 33 1 2 3 4 5 6 1 2 3

ε ε ε ε ε ε ε ε ε ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

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CRYSTALLOGRAPHIC ELASTO-PIEZO- DIELECTRIC MATRICES, IEEE

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CRYSTALLOGRAPHIC ELASTO-PIEZO- DIELECTRIC MATRICES, IEEE

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⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⋅ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡

3 2 1 33 32 31 23 22 21 13 12 11 3 2 1

H H H P P P α α α α α α α α α

Magnetic coupling: Magnetoelectricity

LiCoPO4

Rivera, Ferroelectrics 161, 147 (1994)

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K1 = -6.0; K2 = -34 λ100 = 90.0; λ111 = 1640.0

Terfenol-D

Magnetocrystalline anisotropy Magnetostriction

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THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL PROPERTIES OPEN DATABASE (MPOD)

http://mpod.cimav.edu.mx

OUTLINE Contents of MPOD. Data files. Coupling properties. Piezoelectricity in MPOD. Implications of crystal symmetry (matrices’ elements and longitudinal moduli surfaces are checked for consistency with the Neumann Principle). Magnetic coupling. MPOD and polycrystals’ properties.

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Inverse pole figure: PbBi4Ti4O15 . Single crystal dielectric constant: ε11 = ε22 = 18300; ε33 = 426

The effect of texture on the physical properties of polycrystals (work in progress)

2

) (

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Ω −

=

φ

e R h R

Single crystal Polycrystal Ω = 30° Polycrystal Ω = 60° Random polycrystal

DIELECTRIC CONSTANT. TEXTURED AURIVILLIUS CERAMICS

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SLIDE 34

Longitudinal piezoelectric module. Quartz polycrystals

e f = f(g)

) / (

  • j

j 2

Ω Ω

∑

1]

  • +

) + ( ) + [(1 2 1 =

1

φ ϕ ϕ φ cos cos cos cos

2 1

Ω Ω(°) 10 à 30 à Tridimensional texture. ODF: Euler space

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THANKS FOR YOUR ATTENTION! luis.fuentes@cimav.edu.mx CONCLUSIONS

Ø MPOD (http://mpod.cimav.edu.mx ) is an open database that delivers measured materials properties in matrix, surface and 3D printing descriptions. Ø Crystal thermo - electro – magneto – elastic couplings exhibit a wide spectrum of anisotropic responses, linked with structural and magnetic symmetry, polar and axial nature of magnitudes and tensor ranks. Ø Polycrystals’ properties are derived from single-crystal ones, with texture as a modulating agent.

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  • G. Pepponi, S. Grazulis, D. Chateigner: MPOD: A Material Property

Open Database linked to structural information. Nuclear Instruments and Methods in Physics Research (2012), B284, 10–14.

  • L. Fuentes-Cobas, D. Chateigner, G. Pepponi et al: Implementing

graphic outputs for the Material Properties Open Database (MPOD). Acta Cryst. (2014), A70, C1039.

  • P. Moeck, W. Kaminsky, L. Fuentes-Cobas, J. C. Baloche, D.

Chateigner: 3D printed models of materials tensor representations and the crystal morphology of alpha quartz. Symmetry, Culture and Science (2016), 27, 319-330.

  • L. Fuentes-Cobas, A. Muñoz-Romero, M. E. Montero-Cabrera, L.

Fuentes-Montero, M. E. Fuentes-Montero: Predicting the Coupling Properties of Axially-Textured Materials. Materials 6 (11), 4967- 4984 (2013).

  • L. Fuentes, J. Matutes, Ma. E. Fuentes: Magnetoelectricity. Ch. 3,
  • Vol. 19 (2011) & Ch.3 Vol. 24 (2015), “Handbook of Magnetic

Materials”. Ed: K.H.J. Buschow. Elsevier.

References: