Order-disorder/displacive phase transition

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

The distinctions between these two pure types may also be viewed from entropic considerations and the nature of the driving mode. The entropic change in an order-disorder phase transition is mainly configurational, and the driving mode is of diffusive (nonpropagating) nature. On the contrary, for a displacive phase transition, the entropy change is mainly vibrational, with an associated underdamped soft phonon. 

Order-disorder component in displacive phase transition perovskites... 

Here the statistical assembly is distributed through W complexions with equal fractions in each. Such a phase transition is an order-disorder or X transition. As a consequence of such a change the single-well potential of an ordered crystal changes to a multiple-well potential of the disordered system. If the transition is approached from the lower temperature side, a small displacement of the ionic sites may also occur, giving rise to a unit cell of higher symmetry. 

Martensitic transformations in alloys are essentially order-disorder displacive transitions that take place very rapidly, because atomic diffusion does not occur. The discussion of the formation of martensite in the Fe-C system, in Section 8.2.5, is an example. This transition is the transformation of a cubic phase containing excess carbon in interstitial sites into a tetragonal phase. As any one of three cubic axes can be elongated, three orientations of the martensite c axis can occur. This is a general feature of martensitic transformations and the different orientations that can arise are called variants or domains of the martensitic phase. These variants are simply twins (see Section 3.4.10). 

In a displacive phase transition, the positions of atoms are ordered in both phases, but the position changes from a less symmetric site to a more symmetric one as the crystal undergoes the phase transition. Order-disorder transitions are distinguished from displacive transitions by, among other properties, a large entropy of phase transition, dielectric dispersion at low frequencies, and directly, by crystal structure revealing two or more sites fractionally occupied by the same atom. 

The crystal structures of this composition belong to three basically different structural families with a total of six well characterized structural types a) defect scheelite structures which can be disordered (1), or ordered of La2(Mo04)3 type (2) or Eu2(W04)3 type (3) b) /3-Gd2(Mo04)3 above (4) and below (5) its displacive phase transition and c) the- Sc2(W04)3 type (6) structure. For y-Dy2(Mo04)3 a seventh structure was tentatively identified by Brixner (1973) as... 

Salje (1985) interpreted overlapping (displacive plus Al-Si substitutional) phase transitions in albite in the light of Landau theory (see section 2.8.1), assigning two distinct order parameters Q n and to displacive and substitutional disorder and expanding the excess Gibbs free energy of transition in the appropriate Landau form ... 

Fig. 8 Temperature dependence of the four NMR peaks of squaric acid [20]. Note how the four peaks coalesce to one above the phase transition, but that the average of the peak positions does not stay constant, as required for a pure order/disorder transition. It increases around the transition temperature, emphasizing an additional displacive component, coexisting with the order/disorder one...

Fig. 9 Temperature dependence of 5iso for the NMR peaks in squaric acid in the close vicinity of the phase transition temperature left panel). Note that the change starts as a smooth curve, followed by a jump caused by the first-order character of the phase transition. This is considered evidence for the coexistence of an order/disorder and displacive character in the phase transition mechanism [20]. The right panel gives a comparison between theoretical and experimental data. For details, see text...

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

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