Algorithm and Results for the Model System

2) For each point of the path, the dependence of AG(V) (advantage in Gibbs potential at formation of the new phase nucleus) on its volume was built. Thus, the possibility of formation of the intermediate phase nucleus was analyzed at the given point. In order to do this, the shape optimization for each of the nucleus volumes in AG(V) was carried out So, a ratio of Ri/Ri for the given volume V was chosen, such that for it AG was minimal (37, 38]. After this, for each V the value of AG was calculated from Equation 9.60. 

3) The maximum AG (AGmax) of the obtained dependence AG(V) was found. This maximum is the nucleation barrier for the intermediate phase in the given point of the diffusion path (the point for which the function AG( V) was built in step (2) of this algorithm). If the function AG(V) constantly increases, or its maximum AG ax exceeds the critical nucleation barrier (taken as 60kT [43]), the nucleation of the intermediate phase in this point of diffusion path should be considered impossible. 

4) Similarly, for all points, the whole diffusion path was examined. It was considered that formation of the intermediate phase nucleus will most probably occur in the region of the diffusion zone where the concentration composition corresponds to the point with minimal nucleation barrier. If there are no points with possible nucleation on the difiusion path, then the intermediate phase is not supposed to form during the armeahng of the diflfusion couple with the set initial composition (which the studied diffusion path corresponds to). 

Similar to the case of a binary system, the theory for finding the incubation time of the intermediate phase formation was proposed for ternary systems. This time strongly depends not only on diffusion parameters of the system (diffusivities), but also on the initial composition of the samples which undergo isothermal diffusion. Unlike the binary system, the ternary initial composition influences not only the incubation time, but the result of the whole diffusion process. 

Number of points Annealing time Concentration composition 

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