Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum energy paths on the energy surface emerging from the atomic interactions in the system. The challenge is to find which intermediate states to include and to construct a path going through these intermediates in such a way that the overall activation energy for the transition is minimal. In the numerical approach presented here, intermediate minima are constructed by heredity transformations of known minimum energy structures and by identifying local minima in minimum energy paths calculated using a modified version of the nudged elastic band method. Several mechanisms for the formation of a 90• misfit dislocation at the Ge-Si interface are identified when this method is used to construct transition paths connecting a homogeneously strained Ge film and a film containing a misfit dislocation. One of these mechanisms which has not been reported in the literature is detailed. The activation energy for this path is calculated to be 26% smaller than the activation energy for half loop formation of a full, isolated 60• dislocation. An extension of the common neighbor analysis method involving characterization of the geometrical arrangement of second nearest neighbors is used to identify and visualize the dislocations and stacking

The calculation of minimum energy paths for transitions such as atomic and/or spin rearrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio or electron density functional calculations are used to evaluate the energy since they can require large computational effort. Gaussian process regression is used here to reduce significantly the number of energy evaluations needed to find minimum energy paths of atomic rearrangements. By using results of previous calculations to construct an approximate energy surface and then converge to the minimum energy path on that surface in each Gaussian process iteration, the number of energy evaluations is reduced significantly as compared with regular nudged elastic band calculations. For a test problem involving rearrangements of a heptamer island on a crystal surface, the number of energy evaluations is reduced to less than a fifth. The scaling of the computational effort with the number of degrees of freedom as well as various possible further improvements to this approach are discussed.

The size dependence of the phase diagram of nanoalloys with a tendency to phase separate is investigated. As the critical temperature may depend on both the size and the morphology of the nanoparticles, we consider nanowires with different cross-sections and also nanotubes with different circumferences. The variation of the critical temperature with the length of all these nanoparticles is systematically studied using Monte Carlo simulations based on an Ising model. A non-monotonic variation of the critical temperature is observed as a function of the length. The maximal value of the critical temperature is reached when the length and the circumference of the nanoparticles are similar. The phase diagrams obtained within two thermodynamic ensembles (the canonical ensemble and the pseudo grand canonical ensemble) are compared and discussed in terms of the behaviour of a single particle or an assembly of nanoparticles in mutual equilibrium with each other.

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