THE REPRESENTATION OF COUPLING INTERACTIONS IN THE MATERIAL - PowerPoint PPT Presentation

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 .

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

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)

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 .

Tensor nature of physical properties (an example) P = ε o χ P · E χ P is a 2nd rank tensor. P, E Properties are associated with constitutive equations: Y = K · X (K = Y / X) Tensor ranks: P, E m, n, m+n

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

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

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 .

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 .

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

Structure-properties relationships: The role of Symmetry THE NEUMANN PRINCIPLE Ø Effect’s symmetry is always -at least- equal to cause’s symmetry Cause Effect Electromagnetic Charges and E and B fields theory currents Crystal Physics Structure Properties

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

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 .

MATRIX NOTATION A ij (for example): strain or sress tensor 3X3 MATRIX HYPERVECTOR T ⎡ ⎤ 1 ⎢ ⎥ T d d d d d d ⎡ ⎤ 2 ⎢ ⎥ P 11 12 13 14 15 16 ⎡ ⎤ 1 T ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 3 or 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 d d d S 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 3 31 32 33 34 35 36 31 32 33 3 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S s s s s s s d d d T 4 41 42 43 44 45 46 41 42 43 4 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S = s s s s s s d d d T 5 51 62 53 54 55 56 51 52 53 5 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ S s s s s s s d d d T 61 62 63 64 65 66 61 62 63 6 6 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ D d d d d d d E ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ε ε ε 11 12 13 14 15 16 1 11 12 13 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ D d d d d d d E ε ε ε ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 21 22 23 24 25 26 2 21 22 23 2 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ D d d d d d d E ε ε ε ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 3 31 32 33 34 35 36 3 31 32 33

CRYSTALLOGRAPHIC ELASTO-PIEZO- DIELECTRIC MATRICES, IEEE

CRYSTALLOGRAPHIC ELASTO-PIEZO- DIELECTRIC MATRICES, IEEE

Magnetic coupling: Magnetoelectricity P H α α α ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 1 11 12 13 1 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ P H = α α α ⋅ 2 21 22 23 2 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ P H ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ α α α ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ 3 31 32 33 3 LiCoPO 4 Rivera, Ferroelectrics 161 , 147 (1994)

Terfenol-D Magnetocrystalline anisotropy Magnetostriction K 1 = -6.0; K 2 = -34 λ 100 = 90.0; λ 111 = 1640.0

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 .

The effect of texture on the physical properties of polycrystals (work in progress) DIELECTRIC CONSTANT. TEXTURED AURIVILLIUS CERAMICS Inverse pole figure: 2 φ ⎛ ⎞ − ⎜ ⎟ R ( h ) R e Ω ⎝ ⎠ = 0 Polycrystal Ω = 30° Single crystal Polycrystal Ω = 60° Random polycrystal PbBi 4 Ti 4 O 15 . Single crystal dielectric constant: ε 11 = ε 22 = 18300; ε 33 = 426

Longitudinal piezoelectric module. Quartz polycrystals Ω (°) Tridimensional texture. ODF: 2 ( / ) f(g) = f - ∑ e Ω Ω j 0 0 10 j 1 à cos = [(1 + cos ) cos ( + ) + cos - 1] φ ϕ ϕ φ Ω 1 1 2 2 Euler space 30 à

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