Lead-free piezoelectric materials and ultrasonic transducers for medical imaging

Piezoelectric materials have been vastly used in ultrasonic transducers for medical imaging.In this paper,firstly,the most promising lead-free compositions with perovskite structure for medical imaging applications have been reviewed.The electromechanical properties of various lead-free ceramics,composites,and single crystals based on barium titanate,bismuth sodium titanate,potassium sodium niobate,and lithium niobate are presented.Then,fundamental principles and design considerations of ultrasonic transducers are briefly described.Finally,recent developments in lead-free ultrasonic probes are discussed and their acoustic performance is compared to lead-based transducers.Focused transducers with different beam focusing methods such as lens focusing and mechanical shaping are explained.Additionally,acoustic characteristics of lead-free probes including the pulse-echo results as well as their imaging capabilities for various applications such as phantom imaging,in vitro intravascular ultrasound imaging of swine aorta,and in vivo or ex vivo imaging of human eyes and skin are reviewed.

AN INTERFACE INCLUSION BETWEEN TWO DISSIMILAR PIEZOELECTRIC MATERIALS

The generalized two_dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh theory. The problem was reduced to a Hilbert problem, and then closed_form expressions were obtained, respectively, for the complex potentials in piezoelectric media, the electric field inside the inclusion and the tip fields near the inclusion. It is shown that in the media, all field variables near the inclusion_tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity. In addition, it is found that the electric field inside the inclusion is singular and oscillatory too, when approaching the inclusion_tips from inside the inclusion.

ANALYTICAL SOLUTIONS FOR A MODE Ⅲ CRACK IN PIEZOELECTRIC MATERIALS

A mode Ⅲ crack problem in a transversely isotropic piezoelectric material subjected to uniform loads at infinity is studied based on exact boundary conditions. The complex potential approach is used to reduce the problem to Hilbert problem. As a result, closed form field solutions in the piezoelectric material and inside the crack are presented. It is shown that the stresses and electric displacement have square root singularities at the crack tips, but the electric field is uniform everywhere in the material and equal to the remote applied one. It is also found that the electric displacement intensity factor depends on both material properties and the mechanical loads, but not the electric loads. Hence it may be concluded that the electric loads have no influence on the field singularities.

Exact Solutions for Piezoelectric Materials with an Elliptic Hole or a Crack under Uniform Internal Pressure

The existing investigations on piezoelectric materials containing an elliptic hole or a crack mainly focus on remote uniform tensile loads.In order to have a better understanding for the fracture behavior of piezoelectric materials under different loading conditions,theoretical and numerical solutions are presented for an elliptic hole or a crack in transversely isotropic piezoelectric materials subjected to uniform internal pressure and remote electro-mechanical loads.On the basis of the complex variable approach,analytical solutions of the elastic and electric fields inside and outside the defect are derived by satisfying permeable electric boundary condition at the surface of the elliptical hole.As an example of PZT-4 ceramics,numerical results of electro-elastic fields inside and outside the crack under various electric boundary conditions and electro-mechanical loads are given,and graphs of the electro-elastic fields in the vicinity of the crack tip are presented.The non-singular term is compared to the asymptotic one in the figures.It is shown that the dielectric constant of the air in the crack has no effect on the electric displacement component perpendicular to the crack,and the stresses in the piezoelectric material depend on the material properties and the mechanical loads on the crack surface and at infinity,but not on the electric loads at infinity.The figures obtained are strikingly similar to the available results.Unlike the existing work,the existence of electric fields inside an elliptic hole or a crack is considered,and the piezoelectric solid is subjected to complicated electro-mechanical loads.

Influence of Sb_2O_3 doping on the properties of KBT-NBT-BT lead-free piezoelectric ceramics

0.144（K0.5Bi0.5）TiO3-0.85（Na0.5Bi0.5）TiO3-0.006BaTiO3（KBT-NBT-BT） lead-free piezoelectric ceramics were prepared using a conventional solid state method.The influence of Sb2O3 doping on the crystal phase,surface microstructure and properties of the KBT-NBT-BT lead-free piezoelectric ceramics were investigated using X-ray diffraction（XRD）,scanning electron microscope（SEM） and other analytical methods.The results show that all compositions are of pure perovskite structure solid states.Sb2O3 doping does not influence the microstructure of KBT-NBT-BT lead-free piezoelectric ceramics obviously in the Sb2O3 doping range of 0.1-0.5 wt.%.Sb2O3 functions as a donor when doped small amount,while functions as a acceptor when doped large amount.The piezoelectric strain constant（d33） increases first and then decreases;the dielectric constant（ε33^T/ε0） and the dielectric loss（tanδ） decrease continuously when the amount of Sb2O3 dopant increases.When the doping amount of Sb2O3 is 0.1 wt.%,the KBT-NBT-BT piezoelectric ceramics with good comprehensive properties are obtained,whose d33,ε33^T/ε0 and tanδ are 147 pC/N,1510 and 4.2%,respectively.

Electro-elastic Fields of Piezoelectric Materials with An Elliptic Hole under Uniform Internal Shearing Forces

The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields inside and outside the elliptic hole are considered.

SCATTERING OF HARMONIC ANTI-PLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS

In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

Research progress in lead-less or lead-free three-dimensional perovskite absorber materials for solar cells

The trend toward lead-free or lead-less perovskite solar cells(PSCs) has attracted increasing attention over the past few years because the toxicity of lead(Pb) is one of the substantial restrictions for large-scale applications. Researchers have investigated the viability of substituting Pb with other elements(group 14 elements, group 2 elements, transition-metal elements, and group 13 and 15 elements) in the three-dimensional(3 D) perovskites by theoretical calculations and experimental explorations. In this paper, recent research progress in Pb-less and Pb-free PSCs on the perovskite compositions, deposition methods, and device structures are summarized and the main problems that hinder the enhancement of device efficiency and stability are discussed in detail. To date, the fully Sn-based PSCs have shown a power conversion efficiency(PCE) of 8.12% and poor device stability. However, lead-less PSCs have shown higher PCE and a better stability. In addition, the introduction of double-perovskite materials also draws researchers' attention. We believe that the engineering of elemental composition, perovskite deposition methods, and interfacial modification are critical for the future development of Pb-less and Pb-free PSCs.

ANALYSIS OF THE DYNAMIC BEHAVIOR OF A GRIFFITH PERMEABLE CRACK IN PIEZOELECTRIC MATERIALS WITH THE NON-LOCAL THEORY

The dynamic behavior of a Griffith permeable crack under harmonic anti-plane shear waves in the piezoelectric materials is investigated by use of the non-local theory. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By means of Fourier transform, the problem can be solved with a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved with the Schmidt method and numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularities are present at the crack tip. The finite hoop stress and the electric displacement depend on the crack length, the lattice parameter of the materials and the circle frequency of the incident waves. This enables us to employ the maximum stress hypothesis to deal with fracture problems in a natural way.

THE BEHAVIOR OF TWO PARALLEL SYMMETRIC PERMEABLE CRACKS IN PIEZOELECTRIC MATERIALS

The behavior of two parallel symmetric cracks in piezoelectric materials under anti-plane shear loading was studied by the Schmidt method for the permeable crack face conditions. By using the Fourier transform, the problem can be solved with two pairs of dual integral equations in which the unknown variable is the jump of the diplacement across the crack surfaces. These equations were solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on the geometry of the crack. Contrary to the impermeable crack surface condition solution, it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions.

Piezoelectric Materials for Controlling Electro-Chemical Processes

Piezoelectric materials have been analyzed for over 100 years,due to their ability to convert mechanical vibrations into electric charge or electric fields into a mechanical strain for sensor,energy harvesting,and actuator applications.A more recent development is the coupling of piezoelectricity and electro-chemistry,termed piezo-electro-chemistry,whereby the piezoelectrically induced electric charge or voltage under a mechanical stress can influence electro-chemical reactions.There is growing interest in such coupled systems,with a corresponding growth in the number of associated publications and patents.This review focuses on recent development of the piezo-electro-chemical coupling multiple systems based on various piezoelectric materials.It provides an overview of the basic characteristics of piezoelectric materials and comparison of operating conditions and their overall electro-chemical performance.The reported piezo-electro-chemical mechanisms are examined in detail.Comparisons are made between the ranges of material morphologies employed,and typical operating conditions are discussed.In addition,potential future directions and applications for the development of piezo-electro-chemical hybrid systems are described.This review provides a comprehensive overview of recent studies on how piezoelectric materials and devices have been applied to control electro-chemical processes,with an aim to inspire and direct future efforts in this emerging research field.

THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS

The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum. It is assumed that the material inhomogeneity is represented as the spatial variation of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform, and the singular integral equation is solved numerically by using the Gauss-Chebyshev integration technique. Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity.

PENNY-SHAPED CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the dis- placement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordi- nate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r^(-1/2)) singularity.

Manufacture and Cytotoxicity of a Lead-free Piezoelectric Ceramic as a Bone Substitute—Consolidation of Porous Lithium Sodium Potassium Niobate by Cold Isostatic Pressing

Aim The piezoelectric properties and cytotoxicity of a porous lead-free piezoelectric ceramic for use as a direct bone substitute were investigated. Methodology Cold isostatic pressing （CIP） was applied to fabricate porous lithium sodium potassium niobate （Li0.06Na0.5K0.44） NbO3 specimens using a pore-forming method. The morphologies of the CIP-processed specimens were characterized and compared to those of specimens made by from conventional pressing procedures. The effects of the ceramic on the attachment and proliferation of osteoblasts isolated from the cranium of 1-day-old Sprague- Dawley rats were examined by a scanning electron microscopy （SEM） and metbylthiazol tetrazolium （MTT） assay. Results The results showed that CIP enhanced piezoelectricity and biological performance of the niobate specimen, and also promoted an extracellular matrix-like topography of it. In vitro studies showed that the CIP-enhanced material had positive effects on the attachment and proliferation of osteoblasts. Conclusion Niobate ceramic generated by CIP shows a promise for being a piezoelectric composite bone substitute.

Effect of Li content on the microstructure and properties of lead-free piezoelectric(K_(0.5)Na_(0.5))_(1-x)Li_xNbO_3 ceramics prepared by SPS

Lead-free piezoelectric （K0.5sNa0.5）1-xLixNbO3 （x = 0at%-20at%） ceramics were synthesized by spark plasma sintering （SPS） at low temperature and the effects of LiNbO3 addition on its crystal structure and properties were also studied. When the Li content was less than 6at%, a single proveskite phase with the similar structure of （K0.5Na0.5）NbO3 was formed; and a secondary phase with K3Li2Nb5O15 structure was observed in the 6at% 〈 x 〈 20at% compositional range. Furthermore, LiNbO3 existed as the third phase when the Li content was higher than 8at%. The grain sizes increased from 200-500 nm to 5-8 μm when the K3Li2Nb5O15 and LiNbO3 like phases were formed. With increasing Li content, the relative density of the ceramics first decreased from 97% to 93% and then kept constant. The piezoelectric coefficient d33, dielectric constant, and planner electromechanical coupling factor exhibited a decreasing tendency with increasing Li content because of the decrease in density and the formation of the secondary phase such as K3Li2Nb5O15 and LiNbO3. The formation of dense microstructure with a single phase is necessary in improving the properties of the （K0.5Na0.5）1-xLixNbO3 ceramics.

SCATTERING OF THE HARMONIC STRESS WAVE BY CRACKS IN FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS

The present paper considers the scattering of the time harmonic stress wave by a single crack and two collinear cracks in functionally graded piezoelectric material （FGPM）. It is assumed that the properties of the FGPM vary continuously as an exponential function. By using the Fourier transform and defining the jumps of displacements and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the influences of material properties on the dynamic stress and the electric displacement intensity factors.

Preparation and Piezoelectric Properties of CuO-added(Ag_(0.75)Li_(0.1)Na_(0.1)K_(0.05_)NbO_3 Lead-free Ceramics

CuO-doped（Ag0.75Li0.1Na0.1K0.05）NbO3（ALNKN-xCuO, x = 0.2mol%） lead-free piezoelectric ceramics were prepared by the solid-state reaction method in air atmosphere. The effects of CuO addition on the phase structure, microstructure, and piezoelectric properties of the ceramics were investigated. The experimental results show that the ALNKN ceramics without doping CuO possess rhombohedral phase along with K2NbrO16- type phase and metallic silver phase. For all of the CuO-doped ALNKN ceramics, a pure perovskite structure with the orthorhombic phase was obtained by enclosing the samples in a corundum tube. A homogeneous microstructure with＇the grain size of about 1 ~tm was formed for the ceramics with 0.5mo1% CuO. The grain size increases with increasing amount of CuO. The temperature dependence of dielectric properties indicates that the ferroelectric phase of the ALNKN-xCuO ceramics becomes less stable with the addition of CuO. The ceramics with x = lm01% exhibit relatively good electrical properties along with a high Curie temperature. These results will provide a helpful guidance to preparing other AN-based ceramics by solid-state reaction method in air atmosphere.

AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS

An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.

Modified phase transition and electrical properties of [Li_(0.05)(Na_(0.535)K_(0.48))_(0.95)]- (Nb_(0.94)Sb_(0.06))O_3 lead-free piezoelectric ceramic by sintering temperature

Li/Sb-doped (Na,K)NbO3 with a nominal composition of [Li0.05(Na0.535K0.48)0.95](Nb0.94Sb0.06)O3 ceramic was synthesized by normal sintering. The phase structure, microstructure, and electrical properties were investigated with a special emphasis on the influence of the sintering temperature. A polymorphic phase transition (PPT) from orthorhombic to tetragonal symmetry was observed when the sintering temperature was raised from 1040 to 1050 ℃, whereby the piezoelectric coefficient d33 and the electromechanical coupling coefficient kp reached the peak values of 245 pC·N-1 and 41.2%, respectively. The PPT induced by varying the sintering temperature is due to the different volatilization extents of alkali metals and appears to a lower sintering temperature with increasing Li content. The trace modifying of alkali metal content is more effective than doping B site element to enhance the d33 value.

DYNAMIC BEHAVIOR OF TWO UNEQUAL PARALLEL PERMEABLE INTERFACE CRACKS IN A PIEZOELECTRIC LAYER BONDED TO TWO HALF PIEZOELECTRIC MATERIALS PLANES

The dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half-piezoelectric material planes subjected to harmonic anti-plane shear waves is investigated. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables were the jumps of the displacements across the crack surfaces. Numerical results are presented graphically to show the effects of the geometric parameters, the frequency of the incident wave on the dynamic stress intensity factors and the electric displacement intensity factors. Especially, the present problem can be returned to static problem of two parallel permeable interface cracks. Compared with the solutions of impermeable crack surface condition, it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller.