Ferroelastic effect

An externally applied stress will affect the internal strain and the domain structures will respond this process is termed the ferroelastic effect. Compression will favour polar orientations perpendicular to the stress while tension will favour a parallel orientation. Thus the polarity conferred by a field through 90° domain changes can be reversed by a compressive stress in the field direction. Stress will not affect 180° domains except in so far as their behaviour may be coupled with other domain changes. 

Since the polar axes in barium titanate and PZT (see Fig. 2.40(b) and Fig. 2.44) are longer than the perpendicular axes, ceramics expand in the polar direction during poling. The application of a high compressive stress in the polar direction to a poled ceramic causes depoling since the 90° domains switch direction as a result of the ferroelastic effect and the polar directions of the crystallites become randomized. 

Another special case of pyroelectricity is ferrodastidty. In these materials, the direction of the spontaneous polarization can be changed by applying a mechanical stress. In some crystals such as gadolinium molybdate [Gd2(Mo04)3 GMO] the ferroelastic effect is coupled with a ferroelectric effect (Bohm and Kiirten, 1973). 

External stress, locally applied, can have nonlocal static effects in ferroelastics (see Fig. 4 of Ref. [7]). Dynamical evolution of strains under local external stress can show striking time-dependent patterns such as elastic photocopying of the applied deformations, in an expanding texture (see Fig.5 of Ref. [8]). Since charges and spins can couple linearly to strain, they are like internal (unit-cell) local stresses, and one might expect extended strain response in all (compatibility-linked) strain-tensor components. Quadratic coupling is like a local transition temperature. The model we consider is a (scalar) free energy density term... 

Because structural phase transitions are often ferroelastic or coelastic in character it is essential to have a well-defined stress applied to the crystal at high pressures. In effect, this means that a hydrostatic pressure medium must be used to enclose the crystal. A 4 1 mixture by volume of methanol ethanol remains hydrostatic to just over 10 GPa (Eggert et al. 1992) and is convenient and suitable for many studies. If the sample dissolves in alcohols, then a mixture of pentane and iso-pentane which remains hydrostatic to 6 GPa (Nomura et al. 1982), or a solidified gas such as N2, He, or Ar can be employed. Water appears to remain hydrostatic to about 2.5 GPa at room temperature, just above the phase transition from ice-VI to ice-VII (Angel, unpublished data). The solid pressure media such as NaCl or KCl favoured by spectroscopists are very non-hydrostatic even at pressures below 1 GPa and have been shown to displace phase transitions by at least several kbar (e g. Sowerby and Ross 1996). Similarly, the fluorinert material used in many neutron diffraction experiments because of its low neutron scattering power becomes significantly non-hydrostatic at -1.3 GPa. Decker et al. (1979) showed that the ferroelastic phase transition that occurs at 1.8 GPa in lead phosphate under hydrostatic conditions is not observed up to 3.6 GPa when fluorinert was used as the pressure medium. At pressures in excess of the hydrostatic limit of the solidified gas and fluid... 

Bismayer U, Hensler J, Salje E, Giittier B (1994) Renormalization phenomena in Ba-diluted ferroelastic lead phosphate, (Pbi j,Baj,)3(P04)2. Phase Trans 48 149-168 Bismayer U, Rower RW, Wruck B (1995) Ferroelastic phase transition and renormalization effect in diluted lead phosphate, (Pbi j,Srj,)3(P04)2 and (Pbi xBax)3(P04)2. Phase Trans 55 169-179 Bismayer U, Salje E (1981) Ferroelastic phases in Pb3(P04)2-Pb3(As04)2 x-ray and optical experiments. Acta CrystallogrA37 145-153... 

Salje EKH (1995) Chemical mixing and stmctural phase transitions The plateau effect and oscillatoiy zoning near surfaces and interfaces. Eur J Mineral 7 791-806 Salje EKH (1999) Ferroelastic phase transitions and mesoscopic stractures. Ferroelectrics 221 1-7 Salje E, Bismayer U, Wrack B, Hensler J (1991) Influence of lattice imperfections on the transition temperatures of structural phase transitions The plateau effect. Phase Trans 35 61-74 Salje E, Devarajan V (1981) Potts model and phase transition in lead phosphate Pb3(P04)2. J Phys C 14 L1029-L1035... 

In this work we focus on the short range order in ferroelastic lead phosphate, Pb3(P04)2, in Sr-doped lead phosphate crystals, in antiferroelectric titanite, CaTiSiOs, and isosymmetric effects in malayaite, CaSnSiOs. 

Although the properties of ferroelectric superlattices can be governed by domain structure, no systematic study of this effect has been performed. In other words, the physics of the domain structure formation at the FE phase transition temperature T=Tc in the FE multilayers remains poorly understood. Here we address the question of a phase transition temperature in a periodic superlattice structure consisting of alternate ferroelectric (FE) and paraelectric (PE) layers of nanometric thickness. To get rid of the effect of 90° ferroelastic domains we assume that FE layers have either natural or strain-induced c-oriented uniaxial symmetry. 

The main results of experimental studies of size effects in nanoferroics are presented in second chapter. In particular, we collect the extensive experimental data about size effects in nanoparticles and thin films of ferroelectrics, ferroelastics and magnetically ordered ferroics. The data have been collected for different nanoparticles geometries like spherical and cylindrical as well as for nanowires, nanotubes and nanopills. As for nanosizes the local properties play a decisive role, we pay attention to the results of electron spin resonant measurements, which are sensitive to the local properties. To obtain the reliable information about the physical properties of the entire nanostructure, the above local methods should be augmented by other experimental techniques like dielectric, magnetic and optical methods. We hope that our collection of available experimental data will give the idea about both local and average static and dynamic properties of nanostructures. 

Other transformations, such as ferroelastic transformation and twin formation in a system may also induce toughening effects. The former discussion on stress-induced transformation was Martensitic, involving both dilation and shear components of the transformation strain. Twin transformation typically only has a... 

Padro et al. reported QI and CS parameters for BaTi03 in 2002 that were different from the majority of values in the literature, which the authors attributed to local ferroelastic strain in the individual crystallites and their preparation [49]. The authors also studied the effects of an A-site substitution on the Ti atoms in ATiOs compounds by examining the compound Nao.sBio.sTiOs. It was observed that the resulting distribution in Ti environments caused a smearing out of the SSNMR lineshape singu-... 

The purpose of the nonlinear constitutive law is to provide the evolution of the remanent strain history given the stress or total strain history. Consistent with the facts that domain switching gives rise to deviatoric strains and ferroelastic ceramics exhibit kinematic hardening effects, it is assumed that the material responds elastic-ally within a switching (yield) surface described by... 

Due to this strain saturation effect, the stresses near the crack tip in the ferroelastic material increase severely. In fact, the numerical results suggest that very close to the crack tip the stresses have a 1 / /r radial dependence. Hence the crack tip stress intensity factor Kiup can be defined such that on the plane ahead of the crack tip... 

Figure 3. The distribution of effective remanent strain near a growing crack in a ferroelastic material. The active switching zone, elastically unloaded wake, and unloaded elastic sector behind the crack tip are each denoted on the illustration. The material law is given in Section 2, and the material parameters for this computation are s if/cro 5, ffo oq, m 0.01 and v 0.25.

Fenoelectric materials are pyroelectric materials whose polarization can be reoriented by applying an electric field. On acconnt of their significance, a specific section is dedicated to them. If reorientation takes place under the effect of stress, we speak of ferroelasticity. 

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