Continuous and Discontinuous Transformations

This leads to the general classification of continuous and discontinuous transformations. 

The thermodynamics of phase equilibria is reviewed in Chapter 17 and the fundamental thermodynamic differences between conserved and nonconserved order parameters are reinforced with a geometrical construction. These order parameters are used in the kinetic analyses of continuous and discontinuous phase transformations. 

The z-scores are then transformed into scores between 0 and 1 by calculating the cumulative probability distribution for each score under the assumption of a normal distribution, which yields the final continuity and discontinuity scores ... 

Our focus in this text will be on diffusional transformations. Diffusional transformations can be further subdivided into two main types continuous and discontinuous. Gibbs (of the Gibbs phase rule and the Gibbs free energy) articulated the difference between continuous and discontinuous phase transformations as follows ... 

Diffusional transformations require the net transport/rearrangement of atoms. Diffusional can be further subdivided into two main types continuous and discontinuous. 

Medronho B, Shafaei S, Szopko R, Miguel MG, Olsson U, Schmidt C (2008) Shear-induced transitions between a planar lamellar phase and multilamellar vesicles continuous versus discontinuous transformation. Langmuir 24 6480-6486... 

The structures and phase transformations observed in steels have been dealt with in some detail not only because of the great practical importance of steels, but also because reactions similar to those occurring in steels are also observed in many other alloy systems. In particular, diifusionless transformations (austenite -> martensite), continuous precipitation (austenite -> pearlite) and discontinuous precipitation (austenite -> bainite and tempering of martensite) are fairly common in other alloy systems. 

The Fourier transform of an object, a distribution of scattering points like those in Figures 5.2 and 5.3, whether it be continuous or discontinuous, is its diffraction pattern. 

Simulations of octahedral molecular clusters at constant temperature show two kinds of structural phase changes, a high-temperature discontinuous transformation analogous to a first-order bulk phase transition, and a lower-temperature continuous transformation, analogous to a second-order bulk phase transition. The former shows a band of temperatures within which the two phases coexist and hysteresis is likely to appear in cooling and heating cycles Fig. 10 the latter shows no evidence of coexistence of two phases. The width of the coexistence band depends on cluster size an empirical relation for that dependence has been inferred from the simulations. 

Figure 4.35 illustrates the different temperature—time zones of age-hardening of the Pb—0.11 wt% Ca—0.57 wt% Sn alloy. Zone A covers the discontinuous transformations zone B is the zone of continuous precipitation of (Pbi xSnx)3Ca and zone C is the zone of discontinuous precipitation of lamellar (Pbi xSnx)3Ca phase [75]. 

Figure 6.2 schematically illustrates the differences between a continuous spinodal phase transformation and a discontinuous nucleation and growth transformation. 

In the McMillan model, the smectic A-nematic transition can be continuous or discontinuous. If a is less than 0.7, then o decreases to zero continuously and S is continuous at the smectic A- nematic transition. If a is between 0.7 and 0.98, then a jumps to zero discontinuously and S has a small discontinuity at the smectic A-nematic transition. When a is greater than 0.98, the smectic phase transforms directly into the isotropic phase with discontinuities in both order parameters. So just as in the extended Landau-de Geimes theory for the smectic A phase, a tricritical point is predicted at a=0.7, which corresponds to a ratio in the smectic A—nematic transition temperature to the nematic-isotropic transition temperature of 0.87. A great deal of experimental work has been done on the smectic A-nematic transition, and the results seem to indicate that the tricritical point occurs when the ratio of the two transition temperatures is significantly larger than 0.87. 

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