Transition Path Sampling Studies of Solid-Solid Transformations in Nanocrystals under Pressure

In the past few decades, molecular dynamics simulation has grown into a very pow-erful tool that today is used routinely to study the dynamics of condensed matter systems consisting of up to a few million particles with atomistic resolution. Many processes occurring in nature and technology such as the folding of a protein or the transport of a dopant through a semiconductor, however, are still beyond the reach of this methodology due to widely disparate time scales that are present in the prob-lem. Consider, for instance, the nucleation of a crystal from the undercooled liquid. For moderate undercooling, this process typically proceeds through the formation of a critical nucleus that then grows, eventually transforming the whole sample into the crystalline state. Since this process involves the creation of an interface between the crystallite and the metastable liquid, which is associated with a free energetic barrier, the formation of the critical nucleus is rare on the time scale of basic molec-ular motions. Indeed, it has been known for a long time that water, carefully cooled below the freezing point, can remain in this supercooled state for hours or even days. Thus, the time scale for nucleation exceeds the picosecond time scale for the formation and cleavage of hydrogen bonds by many orders of magnitude. Similar rare but important events, related to high energy barriers or entropic bottlenecks in phase space, can also dominate the dynamics of folding proteins, chemical reactions or transport on surfaces. Naturally, such a wide separation of time scales is a problem for molecular dy-namics simulation. In this method, the equations of motion of the system are solve