Quartz soft mode

The fact that the order parameter vanishes above does not mean that Nature does not have an inkling of things to come well below (or above) T. Such indicators are indeed found in many instances in terms of the behaviour of certain vibrational modes. As early as 1940, Raman and Nedungadi discovered that the a-) transition of quartz was accompanied by a decrease in the frequency of a totally symmetric optic mode as the temperature approached the phase transition temperature from below. Historically, this is the first observation of a soft mode. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In Fig. 4.4, we show the temperature dependence of the soft-mode frequency. While in a second-order transition the soft-mode frequency goes to zero at T, in a first-order transition the change of phase occurs before the mode frequency is able to go to zero. 

One of the most striking features of the scattered spectrum for either neutrons or light in the vicinity of a phase transition is the appearance of a divergent elastic or quasielastic peak centred near zero frequency shift that lies entirely outside the quasiharmonic soft-mode description of the dynamics (Fleury Lyons, 1983). The first observation of a divergence in scattered intensity is due to Yakovlev et ai, (1956), who observed the phenomenon in the a-fi transition of quartz. The scattered intensity increases dramatically, sometimes by a factor of 10000 near and the maximum value of line width of the diverging feature is itself rather small ( 1 cm ). In Fig. 4.7, typical central peaks are shown for the purpose of illustration. 

Ito and Suetaka (78, 173) obtained a spectrum from ethene adsorbed at room temperature on a Pt film evaporated on a quartz plate. They assigned absorptions at 3300 and 3200 cm"1 to adsorbed ethyne (acetylene) obtained by dissociative adsorption, and broad bands at ca. 2900 and 2725 cm "1 to saturated adsorbed species. The 2900-cm-1 band could be from di-cr or ethylidyne. The low wavenumber of 2725 cm 1 (a soft mode) probably implies an end-on interaction of CH bonds with surface metal atoms. 

The typical and much discussed effect of phase transitions is a so-called soft mode, A soft mode is a vibration, the frequency of which nears zero as the physical parameter (mostly the temperature but sometimes also the pressure or the external electric field) approaches its critical point. One of the fir.st soft modes was observed by Raman et al. in the a / quartz transition (Raman and Nedungadi, 1940). The theory of these modes was proposed by Cochran (Cochran, 1960, 1961). It turns out that the soft mode is simply the vibration that, due to its form, allows the transformation from one phase to the other. At the transition point, the restoring forces disappear and the frequency approaches zero. Extensive reviews of the application of spectroscopy in connection with the investigation of phase transitions have been provided by Rao and Iqbal (Rao and Rao, 1978 Iqbal, 1986). 

There have been several measurements of the lattice dynamics of quartz by inelastic neutron scattering. Early results showed that the soft mode in the high-temperature phase is overdamped (Axe 1971). Other work on RUMs at wave vectors not directly associated with the phase transition showed that on cooling through the phase transition the RUMs rapidly increase in frequency since they are no longer RUMs in the low-temperature phase (Boysen et al. 1980). The most definitive study of the RUMs associated with the phase transition was that of Dolino et al. (1992). 

We argue that in quartz, the phase transition arises as a result of a classical soft-mode instability (Dolino et al 1992, Tezuka et al. 1991), but unlike in the classical soft-mode model the phase transition into the high-temperature phase also allows the... 

Because RUMs are low-energy deformations of a framework structure, they are natural candidates for soft modes associated with displacive phase transitions (Dove 1997a,b, Dove et al. 1992, 1993, 1995, Hammonds et al. 1996). Indeed, we started by noting that the soft mode that gives the displacive a-P phase transition in quartz is a RUM, and we summarised the model by which the existence of a line of RUMs gives rise to the intermediate incommensurate phase transition. We have used the RUM analysis to explain the displacive phase transitions in a number of silicates (Dove et al. 1995, Hammonds et al. 1996). 

Schmahl WW, Swainson IP, Dove MT, Graeme-Barber A (1992) Landau free energy and order parameter behavior of the a-p phase transition in ciistobalite. Z Kristallogr 201 125-145 Sollich P, Heine V, Dove MT (1994) The Ginzburg interval in soft mode phase transitions Consequences of the Rigid Unit Mode picture. JPhys Condensed Matter6 3171-3196 Strauch D, Domer B (1993) Lattice dynamics of a-quartz. 1. Experiment. J Phys Condensed Matter 5 6149-6154... 

Data of Tezuka et al. (1991) for the soft mode in 3-quartz extrapolate as first order transition (with d = 0)... 

Figure 10. Phonon dispersion curves for the T-K direction in a-quartz. A soft mode appears along this direction under pressure.

Swainson IP, Dove MT (1995b) On the thermal expansion of p-cristobalite. Phys Chem Minerals 22 61-65 Tantz FS, Heine V, Dove MT, Chen X (1991) Rigid unit modes in the molecular dynamics simulation of qnartz and the incommensurate phase transition. Phys Chem Minerals 18 326-336 Teznka Y, Shin S, Ishigame M (1991) Observation of the silent soft phonon in p-quartz by means of hyper-raman scattering. Phys Rev Lett 66 2356-2359... 

A soft zone-edge mode is expected to induce a crystalline-to-crystalline transition. Such a transition has been reported recently from a detailed x-rays diffraction study of quartz, just below the amorphization pressure[45, 46], The transformed material appears to involve a microstructure, and the amorphous phase seems to nucleate and grow as the sample is pressur-ized[45]. In view of the small width for the whole acoustic branch at such pressure, these results are not too surprising. 

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