Spinode, binary

Figure A3.3.2 A schematic phase diagram for a typical binary mixture showmg stable, unstable and metastable regions according to a van der Waals mean field description. The coexistence curve (outer curve) and the spinodal curve (iimer curve) meet at the (upper) critical pomt. A critical quench corresponds to a sudden decrease in temperature along a constant order parameter (concentration) path passing through the critical point. Other constant order parameter paths ending within tire coexistence curve are called off-critical quenches.

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

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. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

The T-p plot shown in Figure 5.11 (b) resembles the T-x plot of a binary solution. The equilibrium between the two phases is, as we have seen above, given by a similar set of equilibrium conditions in both cases. Within the spinodal regions of the... 

For analytical comprehension of the kinetics of spinodal decomposition processes, we must be able to evaluate the Gibbs free energy of a binary mixture of nonuniform composition. According to Cahn and Hilliard (1958), this energy can be expressed by the linear approximation... 

Figure 3.14 Stability relations in a binary mixture (A,B)N as a function of temperature. Heavy, solid line activity trend for component (B)N in the case of binodal decomposition. Dashed line activity trend in the case of spinodal decomposition.

In pyroxenes, exsolutive processes proceed either by nucleation and growth or by spinodal decomposition (see sections 3.11, 3.12, and 3.13). Figure 5.30B shows the spinodal field calculated by Saxena (1983) for Cag sMgo sSiOj (diop-side) and MgSi03 (chnoenstatite) in a binary mixture, by application of the subregular Margules model of Lindsley et al. (1981) ... 

Non-Random Systems. As pointed out by Cahn and Hilliard(10,11), phase separation in the thermodynamically unstable region may lead to a non-random morphology via spinodal decomposition. This model is especially convenient for discussing the development of phase separating systems. In the linearized Cahn-Hilliard approach, the free energy of an inhomogeneous binary mixture is taken as ... 

Curve defining the region of composition and temperature for a binary mixture across which a transition occurs from conditions where single-phase mixtures are metastable to conditions where single-phase mixtures are unstable and undergo phase separation by spinodal decomposition. 

Note 1 The spinodal curve for a binary mixture is defined as the geometrical locus of all states with... 

Uphill diffusion in binary systems and spinodal decomposition... 

From the above analysis, it can be seen that D in Pick s first law J = -DVC (Equation 3-6) may be either positive or negative (accounting for uphill diffusion), and it can vary from positive to negative along a spinodal decomposition diffusion profile. If, on the other hand. Pick s law is modified as J = -(T>/y)Va (Equation 3-61), then V is always positive in a binary system. 

Uphill diffusion in a binary system is rare and occurs only when the phase undergoes spinodal decomposition. In multicomponent systems, uphill diffusion occurs often, even when the phase is stable. The cause for uphill diffusion in multicomponent systems is different from that in binary systems and will be discussed later. 

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. 

Let us examine the critical dynamics near the bulk spinodal point in isotropic gels, where K + in = A(T — Ts) is very small, Ts being the so-called spinodal temperature [4,51,83-85]. Here, the linear theory indicates that the conventional diffusion constant D = (K + / )/ is proportional to T — Ts. Tanaka proposed that the density fluctuations should be collectively convected by the fluid velocity field as in near-critical binary mixtures and are governed by the renormalized diffusion constant (Kawasaki s formula) [84],... 

T. Miyazaki, S. Takagishi, H. Mori, and T. Kozakai. The phase decomposition of iron-molybdenum binary alloys by spinodal mechanism. Acta Metall.. 28(8) 1143-1153, 1980. 

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