Phase transition displacive

Displacive phase transitions Atoms experience small shifts if at all, only intermolec-ular bonds (e.g. hydrogen bonds) are broken and rejoined, but no primary chemical bonds. The transition may be but need not be a second-order transition. 

An enormous number of phase transitions are known to occur in common solid compounds. For example, silver nitrate undergoes a displacive phase transition from an orthorhombic form to a hexagonal form at a temperature of approximately 162°C that has a enthalpy of 1.85 kj/mol. In many cases, the nature of these transitions are known, but in other cases there is some uncertainty. Moreover, there is frequently disagreement among the values reported for the transition temperatures and enthalpies. Even fewer phase transitions have been studied from the standpoint of kinetics, although it is known that a large number of these transformations follow an Avrami rate law. There is another complicating feature of phase transitions that we will now consider. 

The behavior of a-quartz PON under pressure has been studied, in particular the pressure dependence of the cell parameters (200, 202). A displacive phase transition to an a-quartz II structure occurs at close to 20 GPa. Progressive and irreversible amorphization is observed above 30 GPa and, above 42 GPa, the product becomes com-... 

Keywords Anharmonic effects Displacive phase transition Isotope effects KDP-type ferroelectrics Order-disorder phase transition... 

FarrugiaLJ, Macchi P, Sironi A (2003) Reversible displacive phase transition in P fi(en)3] (N03 )2 a potential temperature calibrant for area-detector diffractometers. J Appl Crystallogr 36 141-145... 

Thus we might expect that symmetry could reduce the number of independent constraints in a framework silicate, allowing the total number of degrees of freedom to exceed the number of independent constraints, so that the structure will have some internal degrees of flexibility. We might also expect that as symmetry is lowered, perhaps as a result of a displacive phase transition, the number of independent constraints will be increased and the flexibility of the structure will be reduced. We will see that this is found in practice (Hammonds et al. 1996). 

APPLICATIONS OF THE RIGID UNIT MODE (RUM) MODEL Displacive phase transitions... 

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). 

Figure 19. Rotations of octahedra associated with the RUMs and the displacive phase transition in the perovskite structure.

Cristobalite undergoes a first-order displacive phase transition at around 500 K at ambient pressure (Schmahl et al. 1992, Swainson and Dove 1993, 1995a). The distortion of the structure can be associated with a RUM with wave vector (1,0,0), which is at the corner of the Brillouin zone (Dove et al. 1993, Swainson and Dove 1993, 1995a Hammonds et al. 1996). At ambient temperature there is another first-order displacive phase transition to a monoclinic phase on increasing pressure (Palmer and Finger 1994). A recent solution of the crystal structure of the monoclinic phase (Dove et al. 2000c) has... 

A lot of theoretical work on displacive phase transitions has focussed on a simple model in which atoms are connected by harmonic forces to their nearest neighbors, and each neighbor also sees the effect of the rest of the crystal by vibrating independently in a local potential energy well (Bruce and Cowley 1980). For a phase transition to occur, this double well must have two minima, and can be described by the following function ... 

Dolino G (1990) The a-inc-p transitions of qrrartz A centrrry of research on displacive phase transitions. Phase Trans 21 59-72... 

Dove MT (1993) Introdnction to lattice dynamics. Cambridge University Press, Cambridge Dove MT, Giddy AP, Heine V (1993) Rigid unit mode model of displacive phase transitions in framework silicates. Trans Am Crystallogr Assoc 27 65-74... 

Giddy AP, Dove MT, Pawley GS, Heine V (1993) The determination of rigid rmit modes as potential soft modes for displacive phase transitions in framework crystal structures. Acta Crystallogr A49 697-703 Grimm H, Domer B (1975) On the mechanism of the a-p phase transformation of qrrartz. Phys Chem Solids 36 407-413... 

Tucker MG, Dove MT, Keen DA (2000) Direct measurement of the thermal expansion of the Si-O bond by neutron total scattering. J Phys Condensed Matter 12 L425-L430 Tucker MG, Dove MT, Keen DA (2000) Simultaneous measurements of changes in long-range and short-range structural order at the displacive phase transition in quartz. Phys Rev Letters (submitted)... 

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