The coarsening of particles dispersed in a solution was found by Ostwald in 1900. Then, the following cubic law between mean radius (r) and annealing time (t) was established by Lifshitz-Slyozov and Wagner in 1961.-r3--r3/0=[8σVCW/9RT]XαB·t It should be noted, however, that the above equation is valid in the coarsening of B particles in A-B solution. Therefore, some modification is necessary in the case of multi-component materials. For instance, the coarsening of (Fe,Cr)aCb in γFe-M-C matrix is described as follows[1,2] ;-r3--r3/0=[8σVCW/9RT][a+b/a]urM/(uoM-urM)2·t According to Eq. (2), the coarsening rate of M23C6 in heat-resistant steel (9%Cr-1%W-0.1%C) depends on the diffusion rate of Cr, because uαCr/(uθCr- uαCr)2＜＜uαw/(uθw- uaw)2. However, experimental data inform us that the rate-determining element is not Cr but W as shown in Fig. 1[3].Fig.1 Effect of W on coarsening of heat-resistant steel Fig.2Equilibrium between M23C6 in this case The problem is solved by modifying the formula of M23C6 from (Fe, Cr, W)23C6 to Fe4 (Cr, W)19C6 in this case(Fig. 2). Consequently, the coarsening equation is expressed as follows.-r3--r3/0=[8σVCW/9RT][29/23][uaW/uow-uaW][1-uaCr-uaW/(19/23)-uaCr-uaW]·t
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