Tieqi Liu

Ferroelectric properties of [110], [001] and [111] poled relaxor single crystals: measurements and modeling

Abstract A combination of modeling and experimental work has led to the identification of a crystal cut of PZN-4.5%PT with enhanced piezoelectric coefficients for bending mode applications d 31 =690 pC/N, d 32 =−1670 pC/N and direct evidence of a rhombohedral-orthorhombic phase transformation under [110] electric field loading. A crystal variant model enables the calculation of the physical properties of the single crystals with an engineered domain state (the piezoelectric, elastic, and dielectric coefficients) from the properties of the single domain [111] poled rhombohedral phase. This work focuses on the piezoelectric coefficients. Not all of the [111] piezoelectric coefficients have been measured. The modeling approach is used to compute the missing coefficients, d 15 and d 16 of the [111] poled crystal from the [001] and [110] properties. Criteria for variant and phase evolution in the model reproduce the observed hysteresis loops, remanent strain and remanent polarization.

Orientation Dependence of Nonlinearity and Hysteresis in PZN-4.5%PT Single Crystals II: Bipolar Electromechanical Response

Relaxor ferroelectric single crystals exhibit orientation dependent hysteresis. In this study, combined bipolar electric field and compressive stress are applied to relaxor single crystals of [Pb(Zn1/3Nb2/3)O3]0.955-[PbTiO3]0.045 (PZN-4.5%PT) in a series of crystal orientations between h001i and h111i. The resulting bipolar electromechanical response is presented. The observed hysteresis and nonlinear phenomena related to polarization reorientation and phase transitions are discussed.

Thermodynamics of Stress and Electric Field Induced Phase Transition in Relaxor Ferroelectric Crystals

A thermodynamics based analysis of measured material behavior in (110) orientated (PMN-32%PT) and (PZN-4.5%PT) crystals under combined stress, electric field and temperature loading leads to a determination of the relative energy levels of phases. The approach is to perform path integrals to determine external work done by electrical and mechanical loads at constant temperature and to remove the effect of heat generated by irreversible strain and electric displacement increments. This yields relative internal energy density levels of phases. It also yields Gibbs energy density, a measure of the driving force for the phase transformation. The approach is used to analyze two types of phase transition, a jump type transition from rhombohedral to orthorhombic with associated hysteresis in (011) loaded PZN-4.5%PT, and a continuous transition from rhombohedral to orthorhombic with rotation through an intermediate monoclinic phase in (001)loaded PMN-32%PT.

Orientation Dependence of Nonlinearity and Hysteresis in PZN-4.5%PT Single Crystals I: Unipolar Response

Relaxor ferroelectric crystals exhibit excellent electromechanical properties as well as strong anisotropy. In this study, compressive stress and electric field are applied to relaxor single crystals [Pb(Zn1/3Nb2/3)O3]0.955–[PbTiO3]0.045 (PZN-4.5%PT) in a series of crystal orientations between h001i and h111i, and the corresponding strain and electric displacement are measured. It is found that as the angle of the orientation cut is rotated from h001i to h111i, the piezoelectric coefficient d33 drops and hysteresis loss increases dramatically. The piezoelectric coefficients, remnant strain, and remnant electric displacement are modeled using a volume averaging of crystal variant volume fractions.

Effect of field driven phase transformations on the loss tangent of relaxor ferroelectric single crystals

The effect of a bias stress induced phase transformation on the large field dielectric loss in [001] cut and poled single crystal stack actuators of (1 − x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT, x = 32) was experimentally characterized. Dielectric loss was observed to increase with compressive preload and electric field amplitude. The dielectric loss was determined by measuring the area within electric displacement vs. electric field hysteresis loops and the measured area was expressed in terms of an effective loss tangent. This approach matches the measured area within the hysteresis loop to an equivalent area ellipse in which the electric displacement lags the electric field by an amount, delta, under sinusoidal loading. The results collapse the measured loss as a function of bias stress and electric field amplitude reasonably close to a single curve. The measured dielectric loss behavior was attributed to the compressive stress preload driving a partial phase transformation from rhombohedral to orthorhombi...

CHARACTERIZATION AND MODELING OF RELAXOR SINGLE CRYSTALS

ABSTRACT The engineered multi-domain features and phase transition behavior of ⟨110⟩ and ⟨001⟩ oriented relaxor PZN-4.5%PT and PMN-32%PT single crystals have been characterized and modeled. A crystal variant approach to modeling the electromechanical properties has led to the identification of engineered domain states with properties optimized for specific applications, including the large transverse piezoelectric coefficients of the ⟨110⟩ orientation and large 33-mode piezoelectric coefficients of the ⟨001⟩ orientation. Polarization switching and phase transitions under combinations of stress, electric field, and temperature loading are reported. Features of field induced phase transitions in these crystals are discussed.

Crystal-variant-based modeling of relaxor single crystals

Rhombohedral relaxor single crystals are a class of materials that includes PZN-xPT and PMN-xPT in a certain range of compositions. This work presents an approach to predicting the physical properties of engineered domain state crystals. A model based on the properties of the crystal variants and volume averaging provides a method for determining a full set of the piezoelectric coefficients for the rhombohedral <111> single domain. The model suggests there is a large d15 and the existence of d16 for the <111> orientation cuts of PZN-PT and PMN-PT crystals. The approach has led to the identification of engineered domain states with properties optimized for specific applications such as the large transverse piezoelectric coefficients of the <110> orientation. This cut has optimal properties for actuator and sensor applications that utilize the transverse mode piezoelectric coupling coefficients (d31 and d32).

FINITE ELEMENT ANALYSIS WITH A FERROELECTRIC AND FERROELASTIC MATERIAL MODEL

ABSTRACT Domain wall motion and phase transformations are driven by stress and electric field, are rate and temperature dependent, and can occur at relatively low stress and electric field levels due to field concentrators such as pores and electrode edges. Analysis of this behavior requires multiaxial material models with hysteresis in a finite element code. This work describes the current state of research in the area of constitutive modeling and finite element analysis of ferroelectric materials. It begins with a description of the large field experimental characterization of ferroelectric behavior including observed effects of field induced phase transformations. Constitutive modeling using a phenomenological approach (macroscale) is discussed followed by the micromechanical approach (microscale). These constitutive models connect the variables of stress, strain, electric field, electric displacement, temperature, and entropy. In addition to these relations, mechanics problems require satisfying electro-mechanical equilibrium and compatibility conditions. The final section presents results of finite element analysis using a ferroelectric material model.

Behavior of relaxor single crystals

The constitutive behavior of relaxor rhombohedral single crystal is discussed in terms of the constitutive behavior of crystal variants. The domain engineered cut gives rise to a stable domain state. Resulting crystal behavior is described. The cut and poled single crystal should display the volume average behavior of single domain crystal variants, but comparison of a crystal variant model with measured properties leads to the identification of inconsistencies. Several possible reasons for these inconsistencies are discussed.