Because of these difficulties, simulations of diffusive phase transformation kinetics are commonly based on various broken-bond models, in the framework of rigid lattice approximations.5,76 The total energy of the system is considered to be a sum of constant pair interaction energies, for example, e^B between A and

B atoms located on nth nn sites. Interactions between atoms and point defects can also be used to provide a better description of their formation energies and interactions with solute atoms, and other defects.

Various approximations are used to compute the migration barriers: a common one77 is writing the saddle-point energy of the system as the mean energy between the initial energy E and final energy Ef, plus a constant contribution Q(which can depend on the jumping atom, A or B). The migration barrier for an A-V exchange is then:

DEAVg = El——El + Qa [22]

where Ef — E corresponds to the balance of bonds destroyed and created during the exchange.

Another solution is to explicitly consider the interaction energy eAV of the jumping atom A with the system, when it is at the saddle point:

ifA7 = eAV — E *A? — E eVj [23]

i, n j, n

eAV itself can be written as a sum of interactions between A and the neighbors of the saddle point.12,78,79

Both approximations are easily extended to inter­stitial diffusion mechanisms, and their parameters can be fitted to experimental data and/or ab initio calculations. The first one has the drawback of imposing a linear dependence between the barrier and the difference between the initial and final ener­gies, which is not justified and has been found to be unfulfilled in the very few cases where it has been checked72 (with empirical potentials). The second one should better take into account the effect of the local configuration and, according to the theory of activated processes, does not impose a dependence of the barrier on the final state. However, a model of pair interactions on a rigid lattice does not give a very precise description of the energetic landscape in a metallic solid solution, so, the choice of approxima­tions [22] or [23] may not be crucial. Taking into account many-body interactions (fitted to ab initio calculations, using cluster expansion methods) could improve the description of migration barriers, but would significantly increase the simulation time.80,81