Ferroelectrics elastic properties

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

Ferroelectrics and piezoceramics Ferroelectricity, sometimes combines with elastic properties Sensors, actuators (AT), ML-AT, membranes, resonators, inkjet printer heads... 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Pozhidayev, E.P., Blinov, L.M., Beresnev, L.A., Belyayev, V.V. The dielectric anomaly near the transition from the smectic A to smectic C phase and visco-elastic properties of ferroelectric liquid crystals. Mol. Cryst. Liq. Cryst. 124, 359-377 (1985)... 

Jona F, Shirane G (1993) Ferroelectric crystals. Dover Publications, New York, NY Jung HR, Jin BM, Cha JW, Kim JN (1997) Piezoelectric and elastic properties of Li2B407 single crystal. Mater Lett 30 41 5... 

Wada S, Park SE, Cross LE, Shrout TR (1999) Engineered domain configuration in rhombohedral PZN-PT single crystals and their ferroelectric related properties. Eerroelectrics 221 147-155 Wallnofer W, Stadler J, Krempl P (1993) Temperature dependence of elastic constants of GaP04 and its influence on BAW and SAW devices. Proceedings of 7th European frequency and time forum, pp 653-657... 

Book content is otganized in seven chapters and one Appendix. Chapter 1 is devoted to the fnndamental principles of piezoelectricity and its application including related histoiy of phenomenon discoveiy. A brief description of crystallography and tensor analysis needed for the piezoelectricity forms the content of Chap. 2. Covariant and contravariant formulation of tensor analysis is omitted in the new edition with respect to the old one. Chapter 3 is focused on the definition and basic properties of linear elastic properties of solids. Necessary thermodynamic description of piezoelectricity, definition of coupled field material coefficients and linear constitutive equations are discussed in Chap. 4. Piezoelectricity and its properties, tensor coefficients and their difierent possibilities, ferroelectricity, ferroics and physical models of it are given in Chap. 5. Chapter 6. is substantially enlarged in this new edition and it is focused especially on non-linear phenomena in electroelasticity. Chapter 7. has been also enlarged due to mary new materials and their properties which appeared since the last book edition in 1980. This chapter includes lot of helpful tables with the material data for the most today s applied materials. Finally, Appendix contains material tensor tables for the electromechanical coefficients listed in matrix form for reader s easy use and convenience. 

In this chapter piezoelectric crystals and polymers ferroelectric and ferromagnetic solids resistance of metals shock-induced electrical polarization electrochemistry elastic-plastic physical properties. 

In this book those ferroelectric solids that respond to shock compression in a purely piezoelectric mode such as lithium niobate and PVDF are considered piezoelectrics. As was the case for piezoelectrics, the pioneering work in this area was carried out by Neilson [57A01]. Unlike piezoelectrics, our knowledge of the response of ferroelectric solids to shock compression is in sharp contrast to that of piezoelectric solids. The electrical properties of several piezoelectric crystals are known in quantitative detail within the elastic range and semiquantitatively in the high stress range. The electrical responses of ferroelectrics are poorly characterized under shock compression and it is difficult to determine properties as such. It is not certain that the relative contributions of dominant physical phenomena have been correctly identified, and detailed, quantitative materials descriptions are not available. 

The contrast in knowledge is a result of the degree of complexity of materials properties elastic piezoelectric solids have perhaps the least complex behaviors, whereas ferroelectric solids have perhaps the most complex mechanical and electrical behaviors of any solid under shock compression. This complexity is further compounded by the strong coupling between electrical and mechanical states. Unfortunately, much of the work studying ferroelectrics appears to have underestimated the difficulty, and it has not been possible to carry out careful, long range, systematic efforts required to develop an improved picture. 

Joern Petersson, Julio Gonzalo, and Jinzo Kobayashi, Dielectric, Elastic and Thermal Properties, Computer Simulations and NMR of Ferroelectrics and Related Materials, Gordon 8c Breach, Amsterdam, The Netherlands, 1998. 

The ferroelectric materials show a switchable macroscopic electric polarization which effectively couples external electric fields with the elastic and structural properties of these compounds. These properties have been used in many technological applications, like actuators and transducers which transform electrical signals into mechanical work [72], or non-volatile random access memories [73]. From a more fundamental point of view, the study of the phase transitions and symmetry breakings in these materials are also very interesting, and their properties are extremely sensitive to changes in temperature, strain, composition, and defects concentration [74]. 

Baranov, A.I. Anisimova, V.N. Khripunov, A.K Baklagina Y.G. (2003). Dielectric Properties and Dipole Glass Transition in Cellulose Acetobacter Xylinium Ferroelectrics, Vol.286, No.l, (n. d. 2003), pp. 141-151, ISSN 0015-0193 Biot, M. A. (1955). Theory of Elasticity and Consolidation for a Porous Anisotropic Solid. 

Bogs, M., Beige, H., Pitzius, R, Schmitt, H. Linear and nonlinear dielectric, elastic and electromechanical properties of Pb(Sci/2Tai/2)03 ceramics. Ferroelectrics 126,197-202 (1992)... 

New multiferroic on the base of quantum paraelectric EuTiOs thin films has been discussed briefly previously in the Sect. 4.2.2. While the idea [10] to induce new multiferroic properties by elastic strain seems to be very attractive, its realization could meet some difficulties in epitaxial films, since relatively high misfit strains ( l-3 %) between the film and substrate relaxes due to e.g. the appearance of misfit dislocations. It is extremely difficult to synthesize a strongly strained epitaxial film without rather special, complex and thus high cost deposition processes. It has been demonstrated [10] that strain relaxation to the values lower than 1 % eliminates ferroelectric ferromagnetic (FE + FM) phase appearance in EuTiOs thin film. 

An understanding of hardening-softening properties can be achieved through the analysis of the domain wall contribution to the polarization response of ferroelectrics. It should be noted here that this is not the only contribution to the polarization response rather, the intrinsic polarization response as well as surface, boundary, and interface effects may also contribute significantly to the total polarization of a ferroelectric material, especially in thin films. However, the dominant contribution to the dielectric, elastic, and piezoelectric properties in ferroelectric materials is extrinsic, and typically originates from displacement of the domain walls [59]. 

Recently, semirigid-rod diacrylate compounds were investigated by Hikmet et al. in order to obtain densely crosslinked LC network materials [57] as well as loosely crosslinked anisotropic gel [58-60]. Copolymerization of an LC monoacrylate having a chiral group and LC diacrylate led to a ferroelectric LC network. In a series of papers by Broer et al. [48,49,61,62], highly crosslinked LC networks were prepared by the photopolymerization of diacrylate LC monomers. Photo-polymerization allowed control of the initiation of polymerization and, therefore, the temperature of polymerization. Orientation was induced using surface treatment technique as applied in liquid crystal display, such as a rubbed polyimide film. The resulting ordered networks showed anisotropic behavior in a number of physical properties, such as coefficient of thermal expansion, modulus of elasticity, and refractive index. 

Here, the first term describes the nematic-like elastic energy in raie crmstant approximation (K in 9). This term allows a discussion of distortions below the AF-F threshold (a kind of the Frederiks transition as in nematics in a sample of a finite size). In fact, the most important specific properties of the antiferroelectric are taken into account by the interaction potential W between molecules in neighbour layers the second term in the equation corresponds to interaction of only the nearest layers (/) and (/ + 1). Let count layers from the top of our sketch (a) then for odd layers i, i + 2, etc. the director azimuth is 0, and for even layers / + 1, / + 3, etc. the director azimuth is n. The third term describes interactimi of the external field with the layer polarization Pq of the layer / as in the case of ferroelectric cells. Although for substances with high Pq the dielectric anisotropy can be neglected, the quadratic-in-field effects are implicitly accounted for by the highest order terms proportiOTial to P. ... 

Li Z, Grimsditch M, Xu X, Chan SK (1993) The elastic, piezoelectric and dielectric constants of tetragonal PbTiOs single crystals. Ferroelectrics 141 313-325 MarraSP, Ramesh KT, Douglas AS (1999) The Mechanical properties of lead-titanate/polymer 0-3 composites. Compos Sci Technol 59 2163-2173 Materials Data Sheets of APC International, Tokin, Ferroperm, Morgan Matroc, Siemens Mattiat OE (1971) Ultrasonic transducer materials. Plenum Press, Tokyo McLachlan DS, Blaszkiewicz M, Newnham RE (1990) Electrical resistivity of composites. J Am Ceram Soc 73 2187-2203... 

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