| Summary: | <p>General symmetry arguments show that an elastic constant should vanish when a crystal undergoes a second order structural phase transition. A detailed theory of the elastic anomaly is developed for DyVO<sub>4</sub>, TbVO<sub>4</sub>, and TmVO<sub>4</sub>, which have crystallographic phase changes caused by the Jahn-Teller effect at 14, 34 and 2.1°K respectively. The theory predicts that the elastic constant &half;(c<sub>11</sub>-c<sub>12</sub>) should fall to zero at the transition temperature T<sub>D</sub> for DyVO<sub>4</sub>, and that c<sub>66</sub> should vanish for TbVO<sub>4</sub>, and TmVO<sub>4</sub>. These conclusions have been verified experimentally. For DyVO<sub>4</sub> the electron lattice interaction is predominantly of short range and a cluster theory has been used to interpret the results. For the other crystals a molecular field theory has been used to calculate the elastic constants under different thermodynamic regimes and the random phase approximation has been used in a treatment of the elementary excitations. In TbVO<sub>4</sub> and TmVO<sub>4</sub>, the theory predicts that the elastic constant only falls to zero at T<sub>D</sub> when measured at a sufficiently low frequency. This frequency dependence has been observed in TbVO<sub>4</sub>, and is satisfactorily described by the theory.</p> <p>At the first order 9-5°K phase change in DySb the elastic constant &half;(c<sub>11</sub>-c<sub>12</sub>) is observed to soften but not to vanish, consistent with general symmetry arguments. A theory of this anomaly has been developed within the molecular field approximation. Satisfactory agreement with experiment is obtained for T>T<sub>D</sub> but there are large unresolved discrepancies in the low temperature phase.</p> <p>A theory for the elastic constant and spontaneous polarization of the ferroelectric KH<sub>2</sub>PO<sub>4</sub> has been developed. One of the lattice vibrational modes is written in a pseudc-spin formalism and four spin interactions have been included in the model. Although the theory gives a reasonable account of the data some discrepancies still remain.</p> <p>Coupling between pairs of phonons and the soft mode in hydrogen bonded ferroelectrics has been investigated in the pseudospin model. An anomalous dielectric response is predicted similar to earlier work on the anharmonic phonon theory [71]. A frequency dependence of the elastic constants is expected but this has not yet been observed. An analysis of Raman scattering data shows that the low frequency anomaly is a small effect in KDP, KDA and CsDA contrary to an earlier analysis of the data [70].</p> <p>When a magnetic field is applied in the hard direction of an anisotropic ferromagnet qualitative arguments show that an elastic constant should vanish when the moments line up parallel to the hard axis. These conclusions have been verified for a particular model of the ferromagnetic phase of Dy and Tb metal.</p>
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