Ferroelastic ordering

In case of the ferroelastic ordering in the crystal (for example, for a ground doublet state of the JT center)... 

Renormalization phenomena are induced in lead phosphate by fields conjugate to the ferroelastic order paramter. The energy contributions of impurities can generally be described by field terms//d (Levanyuk et al. 1979 Salje 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. 

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. 

Both the order parameter and the spontaneous strain for a phase transition have symmetry properties. The relationship between them is therefore also constrained by symmetry. Only in the case of proper ferroelastic transitions is the symmetry-breaking strain itself the order parameter. For most transitions, the order parameter relates to some... 

Hemley RJ, Shu J, Carpenter MA, Hu J, Mao H-K, Kingma KJ (2000) Strain-order parameter coupling in the pressure-induced ferroelastic transition in dense Si02. Phys Rev Lett (accepted)... 

The change in the sign of the order parameter at the surface has been observed (for ferroelectricty) by using a model of imaging developed for the detection of static surface charge (Saurenbach and Terris 1990). For ferroelastics, this corresponds to the profile of the lateral reactive force. The SFM non-contract dynamic mode images (Lithi et al 1993) would correspond to the distribution of the normal reactive force. The divergence of the lateral force distribution away from the centre of the wall can be attributed to the simulated infinite extension of the lattice. In the simulated array, the lateral component of the force reached a finite value between two adjacent domain walls. 

Ferroelasticity and order/disorder in leucite-related frameworks... 

Redfern, S.A.T., Dove, M.T., Wood, D.R.R. (1997b) Static lattice simulation of feldspar solid solutions ferroelastic instabilities and order/disorder. Phase Trans 61 173-194 Redfern, S.A.T., Knight, K.S., Henderson, C.M.B., Wood, B.J. (1998) Fe-Mn cation ordering in fayalite-tephroite (FexMni U2Si04 olivines a neutron diffraction study. Mineral Mag 62 607-615 Redfern, S.A.T., Harrison, R.J., O Neill, H.St.C., Wood, D.R.R. (1999) Thermodynamics and kinetics of cation ordering in MgAl204 spinel up to 1600°C from in situ neutron diffraction. Am Mineral 84 299-310... 

PhuB trankions At high temperatures, the space groi for the so-called a polymorph is R im, and on cooling this phase transforms to the monoclinic b phase with space group C2/c. The ferroelastic transition temperature decreases with increasing solute concentration from either endmember, such that the minimum Tc in Pb3(Pi cAS c04)2 occurs close to = 0.5 (Fig. 19). Likewise, the order of the transition decreases with increasing solute concentration. The critical e onent in... 

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. 

Figure 2. Temperature-evolution of the intensity of the Ag phonon at 80cm relative to the Eg-phonon at T Tc (top) and morphic optical birefringence A bc along (100) in Pb3(Po4)2. The ferroelastic phase transition is weakly first order and appears as a step in A bc at 45 IK. No such step occurs for the phonon intensity indicating short range order decreasing gradually with increasing temperature.

Computer simulation of the tweed microstructure induced during a ferroelastic phase transition. Green indicates ares of the crystal in which the order parameter is positive, and red indicates areas in which it is negative. Yellow areas are domain boundaries in which the order parameter is close to zero. 

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