Spinodal and Order-Disorder Transformations

Spinodal decomposition and certain order-disorder transformations are the two categories of continuous phase transformations. Both arise from an order parameter instability in the case of spinodal decomposition, it is a conserved order parameter for continuous ordering, it is a nonconserved order parameter. 

Fine-scale, spatially periodic microstructures are characteristic of spinodal decomposition. In elastically anisotropic crystalline solutions, spinodal microstructures are aligned along elastically soft directions to minimize elastic energy. Microstructures resulting from continuous ordering contain interfaces called antiphase boundaries which coarsen slowly in comparison to the rate of the ordering transformation. 

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In the examples given below, the physical effects are described of an order-disorder transformation which does not change the overall composition, the separation of an inter-metallic compound from a solid solution the range of which decreases as the temperature decreases, and die separation of an alloy into two phases by spinodal decomposition. 

Continuous transformations are treated in detail in Chapter 18. Spinodal decomposition and certain types of order-disorder transformations follow from similar principles but differ only in the kinetics of conserved and nonconserved variables. 

As an example, consider the study by Banerjee et al. (1984) on the effect of electron irradiation on the order-disorder transformation in (DIJ Ni4Mo. Electron micrographs and diffraction patterns were obtained during in situ electron irradiations at 50-1050 K in a HVEM. At temperatures below 200 K, the alloy completely disorders. At 200-450 K, only SRO was observed, and the transition between LRO and SRO, which occurs via the completely disordered state, is consistent with the concentration-wave description of the SRO structure and supports the concept of spinodal ordering. It is believed that an interstitial mechanism is responsible for maintaining the SRO. Above 450 K, LRO persisted for samples initially in this state and SRO was only preserved up to 550 K for samples initially in that state. Between 550 and 720 K, a mixed SRO-LRO state occurred, and at temperatures above 720 K a complete transition to SRO was obtained. It is believed that maintenance of LRO requires a vacancy mechanism. At temperatures below 800 K the SRO-LRO transition occurred in a continuous fashion, while above 800 K a nucleation and growth mechanism was operative. This behavior is characteristic of an ordering transition of the first kind below and above the coherent instability temperature. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

The addition of water to solutions of PBT dissolved in a strong acid (MSA) causes phase separation in qualitative accord with that predicted by the lattice model of Flory (17). In particular, with the addition of a sufficient amount of water the phase separation produces a state that appears to be a mixture of a concentrated ordered phase and a dilute disordered phase. If the amount of water has not led to deprotonation (marked by a color change) then the birefringent ordered phase may be reversibly transformed to an isotropic disordered phase by increased temperature. This behavior is in accord with phase separation in the wide biphasic gap predicted theoretically (e.g., see Figure 8). The phase separation appears to occur spinodally, with the formation of an ordered, concentrated phase that would exist with a fibrillar morphology. This tendency may be related to the appearance of fibrillar morphology in fibers and films of such polymers prepared by solution processing. 

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