Phase transformations spinodal decomposition

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. 

The kinetics of spinodal decomposition is complicated by the fact that the new phases which are formed must have different molar volumes from one another, and so tire interfacial energy plays a role in the rate of decomposition. Anotlrer important consideration is that the transformation must involve the appearance of concenuation gradients in the alloy, and drerefore the analysis above is incorrect if it is assumed that phase separation occurs to yield equilibrium phases of constant composition. An example of a binary alloy which shows this feature is the gold-nickel system, which begins to decompose below 810°C. 

Lipson (1943, 1944), who had examined a copper-nickeMron ternary alloy. A few years ago, on an occasion in honour of Mats Hillert, Cahn (1991) mapped out in masterly fashion the history of the spinodal concept and its establishment as a widespread alternative mechanism to classical nucleation in phase transformations, specially of the solid-solid variety. An excellent, up-to-date account of the present status of the theory of spinodal decomposition and its relation to experiment and to other branches of physics is by Binder (1991). The Hillert/Cahn/Hilliard theory has also proved particularly useful to modern polymer physicists concerned with structure control in polymer blends, since that theory was first applied to these materials in 1979 (see outline by Kyu 1993). 

The third and the most common type is complex phase transformations, including the following (i) some components in a phase combine to form a new phase (e.g., H2O exsolution from a magma to drive a volcanic eruption the precipitation of calcite from an aqueous solution, Ca + + COf calcite the condensation of corundum from solar nebular gas and the crystallization of olivine from a basaltic magma), (ii) one phase decomposes into several phases (e.g., spinodal decomposition, or albite jadeite + quartz), (iii) several phases combine into one phase (e.g., melting at the eutectic point, or jadeite +... 

Spinodal decompositions, often observed in binary solid solutions of metals and in glasses, on the other hand, arise from thermodynamic instabilities caused by composition (Cahn, 1968). A special feature of this type of solid state transformation is the absence of any nucleation barrier. There is a class of transformation called eutectoid decomposition in which a single phase decomposes into two coupled phases of different compositions, the morphology generally consisting of parallel lamellae or of rods of one phase in the matrix of the other. 

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. 

Figure 18.7 Interfaces resulting from two types of continuous transformation, (a) Initial structure consisting of randomly mixed alloy, (b) After spinodal decomposition. Regions of B-rich and B-lean phases separated by diffuse interfaces formed as a result of long-range diffusion, (c) After an ordering transformation. Equivalent ordering variants (domains) separated by two antiphase boundaries (APBs). The APBs result from A and B atomic rearrangement onto different sublattices in each domain.

In crystalline solids, only coherent spinodal decomposition is observed. The process of forming incoherent interfaces involves the generation of anticoherency dislocation structures and is incompatible with the continuous evolution of the phase-separated microstructure characteristic of spinodal decomposition. Systems with elastic misfit may first transform by coherent spinodal decomposition and then, during the later stages of the process, lose coherency through the nucleation and capture of anticoherency interfacial dislocations [18]. 

A more sophisticated DIA was proposed for the studies of sphemlite formation and phase separation in polymer blends [Tanaka, 1986 Tanaka and Nishi, 1987]. With a different computer vision, shape features of phase-separated structure was obtained [Gur et al., 1989]. The digitalization gives the possibility of two-dimensional Fourier transformation. A power spectrum of the two-dimensional Fourier transformation was given for the structure developed by spinodal decomposition [Tanaka et al., 1986]. In the real space, one cannot see the order in the image clearly, whereas the characteristic wavelength and the distribution can be seen in the reciprocal space representation. 

The Alnico microstructures are prepared by a process which involves spinodal decomposition. In this phase transformation, the high-temperature phase decomposes into two phases, usually known as and a2. Fig. 6.25. A spinodal curve inside the solvus curve separates the regions where either spinodal decomposition (compositions and temperatures inside the spnodal curve) or normal, nucleation and growth transformation (between solvus and spinodal) occur. Spinodal decomposition occurs by periodic composition fluctuations (Burke, 1965) as transformation proceeds, composition fluctuations increase ( i becomes richer in A and 2 in B, for instance), but the spatial periodicity is conserved. 

Binder, K. (1991). Spinodal decomposition. Phase Transformations in Materials. 

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