Elizabeth A. McLaughlin

Mechanical and thermal transitions in morphotropic PZN-PT and PMN-PT single crystals and their implication for sound projectors

Isothermal compression experiments on multidomain [001] oriented and poled ferroelectric rhombohedral PZN-0.07PT and PMN-0.30PT single crystals revealed elastic instabilities corresponding to zero field ferroelectric-ferroelectric phase transition under mechanical compression. The application of an appropriate dc bias field doubled the stability range of the ferroelectric rhombohedral state under uniaxial compression for both crystals and maintained a linear elastic response. Youngs modulus as derived from the quasistatic, zero field stress-strain linear response agreed well with that derived from small signal resonance for the ferroelectric rhombohedral FR state of both PZN-PT and PMN-PT. Elastic compliances S33 E as determined from high temperature resonance revealed a monotonically decreasing Youngs modulus as a function of temperature in the ferroelectric rhombohedral state with a sudden stiffening near the ferroelectric rhombohedral (FR)-ferroelectric tetragonal (FT) transition. The reversible ferroelectric-ferroelectric transition of morphotropic PZN-PT and PMN-PT single crystals as accessed by mechanical compression is discussed in terms of strain calculations from Devonshires theory, domain unfolding, and morphotropic phase boundary shift with mechanical stress. The mechanically-induced and thermally-induced ferroelectric-ferroelectric transition trajectories are discussed in terms of the Devonshire theory. Implications of these observations for sound projectors are discussed. A single crystal tonpilz projector fabricated into a 16-element array and a segmented cylinder transducer demonstrated the outstanding capabilities of single crystals to achieve compact, broadband, and high-source level projectors when compared to conventional lead zirconate-titanate PZT8 projectors.

Transitions in Morphotropic PMN-PT Single Crystals

Single crystals in the relaxor-ferroelectric lead magnesium niobate (PMN)-lead titanate (PT) and lead zinc niobate (PZN)-lead titanate (PT) systems provide a significant advantage for detecting and classifying objects in littoral waters. Their extremely large electromechanical coupling factor (k 33 > 0.90) and piezoelectric coefficient (d 33 > 1000 pC/N) offer both broadband and high acoustic source level capabilities. Two different transition pathways can be accessed in a morphotropic PMN-0.30PT composition. Resonance experiments on a length extensional bar fabricated from a multi-domain, [001] oriented and poled PMN- 0.30PT crystal revealed a monotonically decreasing Youngs modulus as a function of temperature with a sudden stiffening near 85°C corresponding to a ferroelectric rhombohedral (F R )-ferroelectric tetragonal (F T ) transition. Quasi-static, zero field stress-strain response revealed an elastic instability of the F R near 30 MPa compression. This instability is attributed to a ferroelectric rhombohedral (F R )–ferroelectric orthorhombic (F O ) transition. A dc bias field of 0.59 MV/m stabilized the F R state up to 40 MPa compressive stresses. The implications of these results on sonar projector design and performance will be 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.

Mechanical and Electromechanical Properties of PMN-PT Single Crystals for Naval Sonar Transducers

Single crystals in the relaxor-ferroelectric lead magnesium niobate (PMN)-lead titanate (PT) system provide significant advantage for underwater sonar transducers. Compared to lead zirconate titanate ceramics, the large electromechanical coupling factor provides significant increases in transducer bandwidth. The superior strain energy density generates higher source level across the band, and the lower Youngs modulus allows considerably smaller transducers. These payoffs occur even when PMN-PT crystals are subject to navy relevant conditions such as uniaxial mechanical compressive stresses up to 42 MPa, electric fields up to 1.2 MV/m, and a range of temperatures from 5 to 50degC. This research will provide insight into the impact of navy relevant electric fields and mechanical stress conditions on the cracking and failure of the piezocrystals. The compressive, flexural, and tensile strength of PMN-PT crystal will be reported and discussed with respect to mechanical stress conditions in a typical naval transducer. The dielectric constant, piezoelectric coefficient, Youngs modulus, electromechanical coupling factor and energy density under large signal quasi-static conditions will be discussed from the perspective of the implications for sonar projector design and performance.

Errata for "Full solution, for crystal class 3m, of the Holland-EerNisse complex material-constant theory of lossy piezoelectrics for harmonic time dependence" [Jun 2007, 1250]

A complex material-constant theory of lossy piezoelectrics is fully solved for crystal class 3 m for harmonic time dependence of the fields and stresses. A new demonstration that the theorys eigen coupling factor equation applies to the lossy alternating current (AC) case also is given. The solution presented for crystal class 3 m provides a complete orthonormal set of eigenvectors and eigenvalues for the eigen coupling factor problem, and it also provides a complete orthonormal set of eigenvectors and eigenvalues for the eigen loss tangent problem, for this crystal class. It is shown that two positive coupling factors are sufficient to express an arbitrary 3 m crystal state. Despite the complex nature of the material constants, the Holland-EerNisse theory produces fully real expressions for the coupling factors. The loss tangent eigenvalues also are fully real and positive. The loss eigenstates are important because driving a crystal in a loss eigenstate tends to minimize the impact of material losses. Given also is a set of loss inequalities for crystal class 3 m. The loss inequalities of crystal class 6 mm are recovered from these when d22 and sE 4 both vanish.

The use of real or complex coupling coefficients for lossy piezoelectric materials

Two competing approaches for calculating coupling coefficients for lossy piezoelectric materials, one producing a real result and the other a complex result, are compared and analyzed. It is found that the complex coupling coefficient suffers from mathematical difficulties, which the real coupling coefficient does not exhibit. Moreover, it is pointed out that a prediction made by the complex coupling coefficient theory conflicts with experiment while the corresponding real coupling coefficient theory prediction does not. When a coupling coefficient of interest has been computed from the real coupling coefficient theory using piezoelectric equations having intensive independent variables, the resulting expression has the same algebraic form as the corresponding static coupling coefficient formula. Moreover, only the real parts of the piezoelectric, elastic, and dielectric material properties appear.

Model of the polarization response of single-crystal lead magnesium niobate-lead titanate for transducer applications

A theoretical model is developed and applied to experimentally measured polarization acquired from lead magnesium niobate lead titanite (PMN–PT) single crystals. The model is shown to describe well the polarization behavior with respect to changes in temperature and applied electric field at a variety of levels of applied prestress. Including the effects of prestress is important if the model is to be used in transducer design and output control. Large prestresses are applied to the active materials used in transducers in order to prevent the driver from extending. (Damage to the driver is much more likely should it go into extension during operation, and large applied prestress reduces this possibility.) Physically, the model accounts for both rotation and stretching of elementary dipoles, and realistic values for the elementary dipole moment and dipole concentration are deduced from the measurements using the model. Reasonable dipole behavior with respect to changes in temperature, stress, and electric ...

Generalized Weiss molecular-field basis for a phenomenological polarization model of lead magnesium niobate

A simple physical picture, useful for extended applications of a well-demonstrated phenomenological polarization model [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 101, 289 (1997)] is presented. The Weiss model of interacting dipoles (orginally suggested by Weiss for magnetic dipoles but applied here to electric dipoles) is generalized for high field levels. The generalization permits the model to describe the polarization measurements well, across a significant temperature range extending well below Tmax, for applied electric field levels as high as 1.35 MV/m. The measurements reported here were acquired from various polycrystalline samples of lead magnesium niobate (PMN) in a solid solution with lead titanate (PT) doped with lanthanum (La), having Tmax values ranging from −11 to +41 °C. Agreement between theory and data is good. (The overall rms error of fit is less than 0.5% in all cases considered.) The new model, when combined with a suitable model of hysteresis, is useful for describing a...