Elastic anomalies

Equations of the form of Equation (4) form the basis of the analysis of strain and elasticity reviewed in this chapter. The issues to be addressed are (a) the geometry of strain, leading to standard equations for strain components in terms of lattice parameters, (b) the relationship between strain and the driving order parameter, and (c) the elastic anomalies which can be predicted on the basis of the resulting free energy functions. The overall approach is presented as a series of examples. For more details of Landau theory and an introduction to the wider literature, readers are referred to reviews by Bruce and Cowley (1981), Wadhawan (1982), Toledano et al. (1983), Bulou et al. (1992), Salje (1992a,b 1993), Redfern (1995), Carpenter et al. (1998a), Carpenter and Salje (1998). 

Each of these three examples of elastic anomalies associated with a phase transition is for a pure phase as a function of pressure or temperature. As seen for the CaTiOs-SrTiOs system (Fig. 13), however, changes in bulk composition across a solid solution also give rise to phase transitions. For these, the elastic anomalies accompanying changes... 

Carpenter MA, Salje EKH (1998) Elastic anomalies in minerals due to structural phase transitions. Eur J Mineral 10 693-812... 

Lcolivet. C. Mierzejewski, A. Brillouin scattering study of the elastic anomalies at the structural phase transition in anthracene-tetracyanobenzene. Phys. Rev. B 1990.42 (13). 8471. 

Fig. 14. Longitudinal modulus and magnetic susceptibilty of Fe-18Cr-3Ni-13Mn. Elastic anomalies in these alloys are due clearly to a paramagnetic-antiferromagnetic (Neel) transition.

Perhaps a sensible procedure is to consider an approach which incorporates both interatomic potentials (classical forces) and fully quantum mechanical methods. One can compute the properties of smaller systems with quantum mechanical approaches and establish the accuracy, or inaccuracy, of interatomic potentials. For example, some elastic anomalies have been reported for a-cristobalite. These elastic anomalies indicated the presence of a negative Poisson ratio in this crystalline form of silica. With the use of interatomic potentials, it is a trivial matter to compute these properties. If the anomalies are confirmed via such calculations, it is likely that the experimental measurements are accurate, and more computationally intense calculations with quantum forces are merited. Another useful role of interatomic potentials is to perform molecular dynamics simulations, e.g., to examine the amorphization of quartz under pressure. One can easily compute the free energy of large systems as a function of both temperature and pressure via interatomic potentials. Sueh calculations can be useful as guides if interpreted in a judicious fashion. 

Elastic Anomalies and the Structural Stability of Crystalline Silica... 

In the spirit of a unified picture for IV and heavy-fermion phenomena, which has been promoted above, we ascribe elastic anomalies in these systems to a dependence of basic electronic parameters, like the position of f-levels and their hybridization strength with band states, upon the location of neighbouring atoms in the crystal. An expansion of the form (Grewe et al. 1980)... 

Elastic anomalies in actinide-based heavy-fermion systems are most pronounced for UPt3. The temperature dependences of two representative elastic modes are shown in flg. 36 (Yoshizawa et al. 1985). Unlike the case of UPdj, CF effects as a possible source do not seem very likely. The phonon dispersions of UBOjj, as measured by neutron scattering (Robinson et al. 1986), do not show strong anomalies. The elastic constant Cj2, however, is negative at low temperatures, similar to some IV compounds. Remarkably, UBejj possesses a low Debye... 

The sublattice contains 48 molecules of [DEME][Bp4]. If we assume that one water molecule exists in two sets of sublattices, the elastic anomaly is explained by a water network over the... 

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