Ferroelastics

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

Tetragonal 2inconia is a stmctural ceramic that exhibits ferroelasticity and the toughness enhancement has been estimated to be as high as 5. An example of a partial hysteresis loop for this material is shown in Figure 4 (35). Domains do not have to be present prior to the stress... 

In particular cases, oxyfluoride compounds with island-type crystal structures, such as K3NbOF6, K3TaOF6, K3Nb02F4 and K3Ta02F4, display ferroelectric-ferroelastic properties, with Curie temperatures of 283, 310, 420, 465°K, respectively [150, 191]. 

Tantalum and niobium fluoride compounds that crystallize in coordination-type structures also seem to be perspective candidates for the investigation of ferroelectric properties. Ravez and Mogus-Milancovic [404] showed that some fluoride and oxyfluoride compounds with crystal structures similar to the Re03 type exhibit ferroelastic properties. For instance, ferroelastic properties were found in some solid solutions based on Nb02F and Ta02F [405,406]. 

Ferroelasticity is the mechanical analogon to ferroelectricity. A crystal is ferroelastic if it exhibits two (or more) differently oriented states in the absence of mechanical strain, and if one of these states can be shifted to the other one by mechanical strain. CaCl2 offers an example (Fig. 4.1, p. 33). During the phase transition from the rutile type to the CaCl2 type, the octahedra can be rotated in one or the other direction. If either rotation takes place in different regions of the crystal, the crystal will consist of domains having the one or the other orientation. By exerting pressure all domains can be forced to adopt only one orientation. 

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

E. K. H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals. Cambridge Cambridge University Press, 1990. 

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

Figure 4.21 Portion of the (010) plane in the reciprocal lattice of K2Se04. On the left is the lattice for the high-temperature phase and on the right that for the ferroelastic phase. In the high-temperature phase, a softening occurs at a point displaced by 5 from q = (j, 0, 0), shown by a cross. In the incommensurate phase a satellite reflection develops at X.

Ferroelastic Spontaneous strain Mechanical stress CaAljSijOg... 

At high temperatures, ferroelectric materials transform to the paraelectric state (where dipoles are randomly oriented), ferromagnetic materials to the paramagnetic state, and ferroelastic materials to the twin-free normal state. The transitions are characterized through order parameters (Rao Rao, 1978). These order parameters are characteristic properties parametrized in such a way that the resulting quantity is unity for the ferroic state at a temperature sufficiently below the transition temperature, and is zero in the nonferroic phase beyond the transition temperature. Polarization, magnetization and strain are the proper order parameters for the ferroelectric. 

Ferroelectric-ferroelastic, Gd2(M 004)3, KNb03, Ferroelectric-antiferromagnetic, YMn03, HoMn03,... 

Salje, E. (1990) Phase Transitions in Ferroelastic and Coelastic Crystals, Cambridge University Press, Cambridge... 

Each ferroelastic transition has its own characteristic compatibility kernel, that can be evaluated in 2D [7,8,12,16] and 3D [9]. The sign variation with direction of U(r-r ) implies local strain has ferro/antiferro (elastic) frustration, that tends to favour spatial strain texturing, or patterns of domain walls. Since Y fcomPat >0 from its origin in... 

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... 

Clathrates are useful for the control of the stereo- and regiospecificity of intra-cavity chemical reactions and can be used to engineer materials properties such as a polarity leading to non-linear optical materials, and ferroelastic or ferroelectric behaviour. 

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