investigate how these optimized microstructures evolve under irradiation. It is anticipated that, under appropriate conditions, ballistic mixing can lead to the dissolution of precipitates, and to the disordering of chemically ordered phases.129 Matsumura et at}30 used a 1D PF approach on a model binary alloy system to specifically investigate what evolution irra­diation may produce. In that model, the composition field is represented by the globally conserved order parameter X(r), while the degree of order is repre­sented by the nonconserved order parameter S(r). X is chosen to vary from — 1 to +1 for pure A and pure B composition, respectively, and S takes a value ranging from 0 to 1 for fully disordered and fully ordered phases, respectively. The free energy func­tional of the system is written as

f (X, S, T)

(X — Xm)2 — b(T ){X0(T )2 — X2}S2 + b(T )2 X1(T )2S4

[29;

where f0 is the mean field free energy of the disor­dered phase with composition xm, and a, b, xj2 are positive constants depending on temperature. The equilibrium phase diagram for this model system is given in Figure 10. Notice, in particular, that at low temperature and for compositions sufficiently far from the equiatomic composition, an ordered phase coexists with a disordered phase.

The kinetic evolution of these two fields is gov­erned by

dr

[30]

[28]

and

where f(X, S, T) is the mean field free energy of a homogeneous alloy, and H and K are positive constants of the interfacial energy coefficients in the presence of varying field X and S, respectively. The homogeneous free-energy density is given by a Landau expansion

@S, 8F({X, S, T})

— =-£fS — M(T, f) ({8’s’ })

[31]

where f is the atomic displacement rate, m is the chemical potential, Dmix and e are positive coefficients characterizing the efficiency of mixing and disordering

Figure 10 Equilibrium phase diagram for model alloy system given by eqns [28] and [29]. The dotted lines correspond to the metastable extrapolation of the order-disorder transition into the miscibility gap. Reprinted with permission from Matsumura, S.; Muller, S.; Abromeit, C. Phys. Rev. B 1996, 54(9), 6184-6193. Copyright by the American Physical Society.