Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Electromechanical influence of crack velocity at bifurcation for poled ferroelectric materials

The piezoelastodynamic field equations are solved to determine the crack velocity at bifurcation for poled ferroelectric materials where the applied electrical field and mechanical stress can be varied. The underlying physical mechanism, however, may not correspond to that assumed in the analytical model. Bifurcation has been related to the occurrence of a pair of maximum circumferential stress oriented symmetrically about the moving crack path. The velocity at which this behavior prevails has been referred to as the limiting crack speed. Unlike the classical approach, bifurcation will be identified with finite distances ahead of a moving crack. Nucleation of microcracks can thus be modelled in a single formulation. This can be accomplished by using the energy density function where fracture initiation is identified with dominance of dilatation in relation to distortion. Poled ferroelectric materials are selected for this study because the microstructure effects for this class of materials can be readily reflected by the elastic, piezoelectic and dielectric permittivity constants at the macroscopic scale. Existing test data could also shed light on the trend of the analytical predictions. Numerical results are thus computed for PZT-4 and compared with those for PZT-6B in an effort to show whether the branching behavior would be affected by the difference in the material microstructures. A range of crack bifurcation speed upsilon(b) is found for different r/a and E/sigma ratios. Here, r and a stand for the radial distance and half crack length, respectively, while E and a for the electric field and mechanical stress. For PZT-6B with upsilon(b) in the range 100-1700 m/s, the bifurcation angles varied from +/-6degrees to +/-39degrees. This corresponds to E/sigma of -0.072 to 0.024 V m/N. At the same distance r/a = 0.1, PZT-4 gives upsilon(b) values of 1100-2100 m/s; bifurcation angles of +/-15degrees to +/-49degrees; and E/sigma of -0.056 to 0.059 V m/N. In general, the bifurcation angles +/-theta(0) are found to decrease with decreasing crack velocity as the distance r/a is increased. Relatively speaking, the speed upsilon(b) and angles +/-theta(0) for PZT-4 are much greater than those for PZT-6B. This may be attributed to the high electromechanical coupling effect of PZT-4. Using upsilon(b)(0) as a base reference, an equality relation upsilon(b)(-) < upsilon(b)(0) < upsilon(b)(+) can be established. The superscripts -, 0 and + refer, respectively, to negative, zero and positive electric field. This is reminiscent of the enhancement and retardation of crack growth behavior due to change in poling direction. Bifurcation characteristics are found to be somewhat erratic when r/a approaches the range 10(-2)-10(-1) where the kinetic energy densities would fluctuate and then rise as the distance from the moving crack is increased. This is an artifact introduced by the far away condition of non-vanishing particle velocity. A finite kinetic energy density prevails at infinity unless it is made to vanish in the boundary value problem. Future works are recommended to further clarify the physical mechanism(s) associated with bifurcation by means of analysis and experiment. Damage at the microscopic level needs to be addressed since it has been known to affect the macrocrack speeds and bifurcation characteristics. (C) 2002 Published by Elsevier Science Ltd.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

Electrochromism accompanying ferroelectric domain inversion in congruent RuO2 : LiNbO3 crystal

Electrochromic phenomena accompanying the ferroelectric domain inversion in congruent RuO2-doped z-cut LiNbO3 crystals at room temperature are observed in experiments. During the electric poling process, the electrochromism accompanies the ferroelectric domain inversion simultaneously in the same poled area. The electrochromism is completely reversible when the domain is inverted from the reverse direction. The influences of electric field and annealing conditions on domain inversion and electrochromism are also discussed. We propose the reasonable assumption that charge redistribution within the crystal structure caused by domain inversion is the source for electrochemically oxidation and reduction of Ru ion to produce the electrochromic effect. (c) 2005 Optical Society of America.

Digital holographic interferometry and the angular spectrum method applied to measuring the domain inversion in ferroelectric crystal

The application of digital holographic interferometry on the quantitative measurement of the domain inversion in a RuO2: LiNbO3 crystal wafer is presented. The recorded holograms are reconstructed by the angular spectrum method. From the reconstructed phase distribution we can clearly observe the boundary between the inverted and un-inverted domain regions. Comparisons with the results reconstructed by use of the Fresnel transform method are given. Factors that influence the measurement include the spectrum filter size and the spectrum movement are discussed. The spectrum filter size has an effect on the measurement of the details. Although the spectrum movement affects every single reconstructed image, it has no influence on the final measurement.

Abnormal ferroelectric response and enhancement of piezoelectricity of PbTiO3 under uniaxial compression

The ferroelectricity of rhombohedral PbTiO3 under uniaxial compression is investigated from first-principles study. Upon compression, the ferroelectricity decreases until a critical stress of -29 GPa and then increases with a further increase of the magnitude of the uniaxial compressive stress. We also find that uniaxial compression could enhance piezoelectricity and that the maximum piezoelectric coefficient d(33) occurs at sigma(33)=-49 GPa, which supports the experimentally observed piezoelectric behavior in rhombohedral Pb(Mg1/3Nb2/3O3)-0.32PbTiO(3) [Q. Wan, C. Chen, and Y. P. Shen, J. Appl. Phys. 98, 024103 (2005)]. Our calculated results show that the Pb, Ti, and O atoms have different contributions to the total polarization with increasing the magnitude of uniaxial compressive stress, and that when -sigma(33)>55 GPa, the Ti atoms no longer have contributions to the polarization, which leads to the changes of ferroelectricity and piezoelectricity. (C) 2008 American Institute of Physics.

Effect of incorporating nonlanthanoidal indium on optical properties of ferroelectric Bi4Ti3O12 thin films

Bi4Ti3O12 (BTO) and Bi3.25In0.75Ti3O12 (BTO:In) thin films were prepared on fused quartz and LaNiO3/Si (LNO) substrates by chemical solution deposition (CSD). Their microstructures, ferroelectric and optical properties were investigated by X-ray diffraction, scanning electron microscope, ferroelectric tester and UV-visible-NIR spectrophotometer, respectively. The optical band-gaps of the films were found to be 3.64 and 3.45 eV for the BTO and BTO:In films, respectively. Optical constants (refractive indexes and extinction coefficients) were determined from the optical transmittance spectra using the envelope method. Following the single electronic oscillator model, the single oscillator energy E-0, the dispersion energy E-d, the average interband oscillator wavelength lambda(0), the average oscillator strength S-0, the refractive index dispersion parameter (E-0/S-0), the chemical bonding quantity beta, and the long wavelength refractive index n(infinity) were obtained and analyzed. Both the refractive index and extinction coefficient of the BTO:In films are smaller than those of the BTO films. Furthermore, the refractive index dispersion parameter (E-0/S-0) increases and the chemical bonding quantity beta decreases in the BTO and BTO:In films compared with those of bulk. (C) 2007 Published by Elsevier B.V.

Domains in ferroelectric nanodots

Almost free-standing single crystal mesoscale and nanoscale dots of ferroelectric BaTiO(3) have been made by direct focused ion beam patterning of bulk single crystal material. The domain structures which appear in these single crystal dots, after cooling through the Curie temperature, were observed to form into quadrants, with each quadrant consisting of fine 90 degrees stripe domains. The reason that these rather complex domain configurations form is uncertain, but we consider and discuss three possibilities for their genesis: first, that the quadrant features initially form to facilitate field-closure, but then develop 90 degrees shape compensating stripe domains in order to accommodate disclination stresses; second, that they are the result of the impingement of domain packets which nucleate at the sidewalls of the dots forming "Forsbergh" patterns (essentially the result of phase transition kinetics); and third, that 90 degrees domains form to conserve the shape of the nanodot as it is cooled through the Curie temperature but arrange into quadrant packets in order to minimize the energy associated with uncompensated surface charges (thus representing an equilibrium state). While the third model is the preferred one, we note that the second and third models are not mutually exclusive.

V5+-doped Bi3.4Yb0.6Ti3O12 fatigue resistant ferroelectric thin films

In this paper, a serial of Bi3.4Yb0.6Ti3-xVxO12 (BYTV) thin film with different V5+ contents were deposited on Pt/Ti/SiO2/Si substrates by chemical solution deposition (CSD). The crystallized phase and electrical properties of the films were investigated using X-ray diffraction, polarization hysteresis loops, leakage current-voltage, and fatigue test. From our experimental results, it can be found that the ferroelectric properties can be improved greatly using V5+-doped in Bi3.4Yb0.6Ti3O12 (BYT) thin film, compared with the reported BYT thin film. The remanent polarization was enhanced and excellent leakage current characteristic with 10(-11)A at the bias voltage of 4V, which is much lower than the BYT thin film or some reported bismuth layer-structure ferroelectric films. Fatigue test shows that the fabricated films have good anti-fatigue characteristic after 10(10) switching cycles. (c) 2008 Published by Elsevier B.V.

Bilayer formation of two chiral ferroelectric liquid crystal molecules at the air-water interface

The bilayer formation behavior of two chiral ferroelectric liquid crystal molecules at the air-water interface was studied.

A pseudo-spin model for the wall of cytoskeletal microtubule

A pseudo-spin model is intended to describe the physical dynamics of unbound electrons in the wall of cytoskeletal microtubule (MT). Due to the inherent symmetry of the structure and the electric properties in the MT, one may treat it as a one-dimensional ferroelectric system, and describe the nonlinear dynamics of dimer electric dipoles in one protofilament of the MT by virtue of the double-well potential. Consequently, the physical problem has been mapped onto the pseudo-spin system, and the mean-field approximation has been taken to get some physical results.

紫外激光诱导近化学计量比钽酸锂晶体铁电畴反转

对紫外激光诱导近化学计量比钽酸锂晶体铁电畴反转进行了实验研究。波长为351 nm的连续紫外激光被聚焦在近化学计量比钽酸锂晶体的-z表面,同时沿与晶体自发极化相反的方向施加均匀外电场。实验证实紫外激光辐照可以有效地降低晶体畴反转所需的矫顽电场,采用数字全息干涉测量技术检测证实在激光辐照区域实现局域畴反转。研究表明采用紫外激光诱导可以实现对近化学计量比钽酸锂晶体铁电畴反转的局域控制。提出了物理机理的理论分析,认为外电场和激光辐照场的共同作用在晶体内部产生高浓度、大尺寸的缺陷结构,缺陷一定程度上降低畴体成核和畴