Analyse locale de l'essai de force bloquée - MINES...

Laurent DANIEL

GeePs, UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Univ. Paris-Saclay,Sorbonne Univ. and UPMC Univ.,11 rue Joliot-Curie - 91192 Gif sur Yvette Cedex - France

[email protected]

Analyse locale de l'essai de force bloquée sur les céramiques piézoélectriques

• Electro-mechanical conversion

– Direct piezoelectric effect : mechanical -> electric

– Inverse piezoelectric effect : electric -> mechanical

Piezoelectricity

L. Daniel Rencontres Franciliennes de Mécanique 2016 2

F

+

–F+

–

+

–+

–

Applications of piezoelectricity


Equations of piezoelectricity• Coupled – linear – constitutive equations

• Voigt notation

• Longitudinal mode with axial stress


P

Outline

• Blocking force experiment• Ferroelectric behaviour• Synchrotron diffraction on piezoelectric ceramics• In situ blocking force experiment• A piezoelectric test ?• Conclusion

L. Daniel 5Rencontres Franciliennes de Mécanique 2016

Outline



Blocking force experiment


• A standard test for piezoelectric actuators» Performed on a poled piezoelectric ceramic

• A standard test for piezoelectric actuators» Piezoelectric strain generated by an applied electric field



* Stress free strain (d33 E)

• A standard test for piezoelectric actuators» Suppression of the piezoelectric strain

by application of a compressive stress



* Stress free strain (d33 E)

* Blocking stress (d33 E Y)

Determination of d33 and Y

Blocking force experiment• Definition of actuators operating configurations

L. Daniel 10

[Webber et al., J. Phys. D: Appl. Phys., 2010]

Rencontres Franciliennes de Mécanique 2016

Outline



Ferroelectric behaviour• Origins of ferroelectric behaviour

L. Daniel 12

T > Tc

T < Tc

[Ferroelectric domains in tetragonal PZT, courtesy of D.A. Hall]


Ferroelectric behaviour

L. Daniel 13

,E

• Piezoelectric effect(« intrinsic »)

• Domain switching(« extrinsic »)

E

+ role of internal stresses


Outline



Synchrotron x-ray diffraction


• In situ analysis using high energy x-ray diffraction• PZT 51-49 (tetragonal), λ = 0.1515 Å

[ESRF, ID11-MA1727, 2013]


L. Daniel 16

2 dhkl sin θhkl = nλ

[Svitlyk et al., J. Phys.: Condens. Matter, 2013]

[Diamond, I15-EE8699, 2013]Rencontres Franciliennes de Mécanique 2016

Synchrotron x-ray diffraction• Polycrystals

– Different crystallographic orientations• Diffraction rings

– Radius : particular plane {hkl}– Angular position :

particular crystallographic orientation


2 dhkl sin θhkl = nλ

E

Diffraction profiles• Typical diffraction profiles


• Analysis of single (111) and double peaks (200,110)

Diffraction profiles


Spontaneous polarisation strain : o = 2(c-a)/(c+2a) ≈ 1.6%

Outline



In situ BF experiment• External loading sequence

– (re-)poling (electric field)– application of a static electric field– application of a progressive uniaxial compression


[PZT51-49,ESRF, ID11-MA1727, 2013]

In situ BF experiment• Evolution of {111} lattice spacing

(piezoelectricity + internal stresses)


[PZT51-49,ESRF, ID11-MA1727, 2013]

• Evolution of domain orientations (002): • Multiple of random distribution (mrd)

In situ BF experiment


[Jones et al., J. Appl. Phys., 2005]

[PZT51-49,ESRF, ID11-MA1727, 2013]

• Evolution of domain orientations (101): • Multiple of random distribution (mrd)



[Jones et al., J. Appl. Phys., 2005]

[PZT51-49,ESRF, ID11-MA1727, 2013]

• In situ blocking stress curves (ψ=0, different E levels)


L. Daniel 25

Approximately parallel lines (fixed ψ) Slope depends on crystalline orientation Non-uniform blocking stress (orientation dependent), up to 20% var. (fixed E)

[PZT51-49,ESRF, ID11-MA1727, 2013]


P

• In situ blocking stress curves (E=2.5 kV/mm, different ψ)



ψ-dependent (contraction for ψ=0, expansion for ψ=90o) Stress does not “cancel” the effect of electric field

[PZT51-49,ESRF, ID11-MA1727, 2013]

In situ BF experiment• Identification of local coefficients


Very high level of crystalline anisotropy[PZT51-49,ESRF, ID11-MA1727, 2013]

Apparent Young modulusApparent longitudinal

piezoelectric coefficient

Outline



A piezoelectric test ?• Non linearities


Linear fitting not fully satisfactory (200)[PZT51-49,ESRF, ID11-MA1727, 2013]

Blocking force Blocking force slope

A piezoelectric test ?• Domain switching during blocking force test (non 180o, ψ=0)


Moderate amount of domain switching (5%vol. for ψ=0, 2.5 kV/mm) Enough to generate significant strain (o = 1.6%)

[PZT51-49,ESRF, ID11-MA1727, 2013]

[PZT51-49,ESRF, ID11-MA1727, 2013]

A piezoelectric test ?• Correlation between strain and mrd (vol. fraction of domains)


[PZT51-49,ESRF, ID11-MA1727, 2013]

First poling (all ψ)



[PZT51-49,ESRF, ID11-MA1727, 2013]

All measurements (all ψ)



{200} = 4 10-4

{110} = 8 10-4

{110} = 8 10-4

[PZT51-49,ESRF, ID11-MA1727, 2013]

Domain switching isthe dominant factor

Intrinsic Piezoelectricity isalmost negligible

A piezoelectric test ?• Irreversibility of the experiment


[PZT51-49,ESRF, ID11-MA1727, 2013]

A piezoelectric test ?

• Phase transformation


P

The application of stress can induce phase transformation Appearance of a rhombohedral phase

Conclusion• The blocking force test is a complex experiment

No “cancellation” of the effect of electric field by stress Heterogeneous state from the beginning (residual stresses) Non-purely piezoelectric and nonlinear elastic test (domain switching)

• No local information can be extracted from the macroscopic piezoelectric interpretation

• In-situ synchrotron experiment can provide local information Local piezoelectric coefficients, local elastic properties Domain switching process Level of internal stresses

Need for advanced micro-mechanical analysis tools Highly material dependent


L. Daniel1,2, D.A. Hall1, J. Koruza3, K.G. Webber3, A. King4,5, P.J. Withers1, J. Appl. Phys., 117, 174104 (2015)

1 School of Materials, University of Manchester, Manchester, M13 9PL, UK2 GeePs (UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Univ. Paris-Saclay, UPMC, France3 Institute of Materials Science, Technische Universität Darmstadt, 64287 Darmstadt, Germany4 European Synchrotron Radiation Facility (ESRF), 38043 Grenoble, France5 Synchrotron SOLEIL, BP 48, 91192 Gif sur Yvette cedex, France

[email protected]

Acknowledgement

In situ BF experiment• Definition of local strain (R refers to the reference state Ri just after repoling)

• {111} = (d111-dR111) / dR

111

• {200} = (d200-dR200) / dR

200 with d200 = (mrd{002} d002 + (3-mrd{002})d200)/3

• {110} = (d110-dR110) / dR

110 with d110 = (mrd{101} d101 + (3-mrd{101})d110)/3


• A uniaxial experiment ?



• A uniaxial experiment ?



Blocking force experiment• A uniaxial experiment ?


Uniaxial stress does not “cancel” the effect of electric field Polycrystalline materials: what happens at a local scale ?

Diffraction profiles• Characterisation in the unpoled state






Unpoled state

d110(ψ) = 2.7491 ± 0.0003 Åd101(ψ) = 2.7176 ± 0.0003 Å

d111(ψ) = 2.2361 ± 0.0004 Å

d002(ψ) = 1.9686 ± 0.0003 Åd200(ψ) = 1.9218 ± 0.0003 Å

• Diffraction profiles under electric field (first poling)


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E = 0 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 46

E = 1 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 47

E = 2 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 48

[PZT51-49,ESRF, ID11-MA1727, 2013]

E = 3 kV/mm




L. Daniel 49

E = 4 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 50

E = 0 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 51

E = 1 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 52

E = 2 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 53

E = 3 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]




L. Daniel 54

E = 4 kV/mm

[PZT51-49,ESRF, ID11-MA1727, 2013]


• Poled state– Heterogeneous strain– E = 0, = 0



• Electric field– E = 2.5 kV/mm, = 0



• Compressive stress– E = 2.5 kV/mm– = -30 MPa



Conclusion• Contribution of synchrotron diffraction in materials science

(smart materials, surface vs bulk)• A tool for the validation of micro-mechanical tools• Prediction of the impact on lifetime performance, fatigue, …• Applicability to ferroics in general (domain microstructures)

L. Daniel 58

E



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Analyse locale de l'essai de force bloquée - MINES...

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