Elastic ferroelectrics

Parameters of the three-dimensional structures function as operators between the properties of elements on the one hand, e.g., electronic structure, electronegativity, atomic radii, and properties of the compounds on the other hand, e.g., chemical reactivity, hardness, elasticity, ferroelectricity, electrical conductivity, optical rotatory power, refraction. Mathematical procedures lead from the elements to the structures and from the structures to the properties. If these are formulated as computer programs, they need data given in databases. If databases are used in this way, existing theories cannot only be demonstrated for individual examples but also verified as generally true. 

Lithium niobate is strongly ferroelectric, yet the material behavior under elastic shock loading is apparently fully described by nonlinear piezoelec-... 

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. 

In this chapter studies of physical effects within the elastic deformation range were extended into stress regions where there are substantial contributions to physical processes from both elastic and inelastic deformation. Those studies include the piezoelectric responses of the piezoelectric crystals, quartz and lithium niobate, similar work on the piezoelectric polymer PVDF, ferroelectric solids, and ferromagnetic alloys which exhibit second- and first-order phase transformations. The resistance of metals has been investigated along with the distinctive shock phenomenon, shock-induced polarization. 

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.)... 

L. Sandrin, M. Tanter, J. L. Gennisson, S. Catheline and M. Fink, Shear elasticity probe for soft tissues with 1-D transient elastography, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2002, 49, 436-446. 

FERROELECTRIC EFFECT. The phenomenon whereby certain crystals may exhibit a spontaneous dipole moment twhich is called ferroelectric by analogy with ferromagnetic—exhibiting a permanent magnetic moment). The effect in the most typical case, barium manate. seems to he due to a polarization catastrophe, in which the local electric fields due lo the polarizuiion itself increase faster than die elastic restoring forces on the ions in Ihe crystal, thereby leading to an asymmetrical shift in ionic positions, and hence lo a permanent dipole moment. Ferroelectric crystals... 

Crosslinked LC elastomers (Figure 19d) are very promising for piezoelectric and ferroelectric applications, and also as non-linear optic materials. The first synthetic step to such materials is the preparation of usual side chain or combined LC copolymers doped with a small part of side chains containing a polymerizable >C=C< double bond at the end (Figure 23 shows a particular example of a crosslinkable LC polymer64). The copolymer can be further photocrosslinked, giving an elastic polymer film which reveals... 

When a ferroelectric single crystal is cooled below the phase transition temperature the electrical stray field energy caused by the non-compensated polarization charges is reduced by the formation of ferroelectric domains, see Figure 1.19. The configuration of the domains follows a head-to-tail condition in order to avoid discontinuities in the polarization at the domain boundary, VP = a. The built-up of domain walls, elastical stress fields as well as free charge carriers counteract the process of domain formation. In addition, an influence of vacancies, dislocations and dopants exists. 

In such a measurement, the sample is clamped as lightly as possible, and the displacement of the surface in monitored. The amount of sample clamping is important, because the mechanical constraints can impact the ferroelastic response of the sample. That is, in samples where the mechanical coercive stress is low, it is possible to change the domain state of the material by improperly clamping it in the sample fixture. This is especially important in elastically soft piezoelectrics, such as many of the relaxor ferroelectric PbTiC>3 single crystals. 

As a ferroelectric perovskite in ceramic form cools through its Curie point it contracts isotropically since the orientations of its component crystals are random. However, the individual crystals will have a tendency to assume the anisotropic shapes required by the orientation of their crystal axes. This tendency will be counteracted by the isotropic contraction of the cavities they occupy. As a consequence a complex system of differently oriented domains that minimizes the elastic strain energy within the crystals will become established. 

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]. 

In most papers referenced above, the standard molecular formulation of the B3LYP functional has been employed, and its results graded against a set of other Hamiltonians available in CRYSTAL. These usually include at least HP, LDA and one GGA functional (PW or PBE), and thus enable a critical appraisal of the B3LYP performance compared to other well established Hamiltonians in solid-state chemistry. Several observables have been examined, such as the equilibrium structure, elastic constants and bulk moduli, thermochemical data, electric field gradients, phonon spectra and vibrational frequencies, polarisation of the ferroelectric phases, magnetic coupling in open-shell transition metal oxides. We shall comment on each observable separately. 

A more complete description of smectic A needs to take into account the compressibility of the layers, though, of course, the elastic constant for compression may be expected to be quite large. The basic ideas of this model were put forward by de Gennes. > We consider an idealized structure which has negligible positional correlation within each smectic layer and which is optically uniaxial and non-ferroelectric. For small displacements u of the layers normal to their planes, the free energy density in the presence of a magnetic field along z, the layer normal, takes the form... 

Here a = a (T—T ), being the transition temperature for the corresponding racemate, b>0 and is temperature independent, k the elastic constant, e the high temperature dielectric constant (i.e., in the absence of ferroelectricity), // and C are the constants describing respectively the... 

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

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