Computer simulations of heterogeneous crystallization

This project will study the formation and transformation of crystalline structures in the course of crystallization transition in undercooled fluids, respectively, martensitic phase transformation between crystalline structures. We will apply advanced computer simulation methods to obtain detailed knowledge about the mechanisms of the transitions, which is essential to the production, the manipulation and the design of crystalline materials. Particularly, we will pay attention to the details of the heterogeneous transitions induced by the presence of pre- structured seeds. Seeded crystallization is a well-established technique for the production of crystals. However, the size of the seed crystals is usually large enough to induce the growth of a crystal, thereby omitting its nucleation. Hence, not much is known about the exact effects the presence of the impurities has on the crystal nucleation process. Thus, we propose an in-depth study of these effects, such that we can offer a technique to influence the crystallization process already at the nucleation stage in contrast to the current technologies, which manipulate the process of crystalline growth. In addition, we will assess the possibility to study the structural transformations in atomic solids using the example of colloidal crystals, which are more convenient to handle in experiments. This similarity is proven for the crystallization transition, but not for a solid-solid transformation. The detailed knowledge about the solid-solid transformation will also allow us to get insight into the process of the crystallization transition, which includes, among others, the structural relaxation.

Heterogeneous crystallization is often used in the production of solid substances, where the addition of seeds induces crystallization of an undercooled or oversaturated solution. The formation of a crystal in such solutions is a first-order phase transition, in which thermodynamic fluctuations generate a nucleus of the new phase. On the initial stages of the transition, when the nucleus is still relatively small, the probability that it will dissolve again is comparatively large. If, however, the size of the nucleus becomes larger than a certain (critical) size, the probability of the nucleus to grow to macroscopic dimensions increases. In general, it is assumed that the process is well described with classical nucleation theory. The results of this project indicate, however, that this is not always the case. In particular, when the seeds are small enough to affect the process of crystal nucleation (and not only the crystal growth), the structure of the seeds plays an important role in the process of crystallization. We made this observation already in previous studies and showed in this project that the distance between the seeds also affects the value of the crystal nucleation rate. Classical nucleation theory states that the addition of multiple seeds simply increases the number of nucleation sites and hence the nucleation rate, which is linearly dependent on this number, will increase accordingly. Our simulations showed, however, that this prediction is valid only if the seeds, which are able to induce heterogeneous crystal nucleation, are far away from each other. When the distance between these seeds decreases, the crystal nucleation rate increases in a way that cannot be explained with classical nucleation theory. Furthermore, if, in contrast, the structure of the seeds is incommensurate with the bulk crystalline structure and hence they do not induce heterogeneous crystallization in the classical sense, the value of the crystal nucleation rate still depends on the distance between the seeds. In this case, however, a decrease of distance between the seeds is associated with a decrease in the crystal nucleation rate. The length scales, at which the effects appear, are comparable with the dimensions of the critical crystalline clusters and depend on the structure of the seeds. Furthermore, we have shown that an established method for computations of nucleation rates, the mean first-passage time technique, has to be applied with care when used to determine crystal nucleation rates. The reason for that lies in the definition of the reaction coordinate, which describes the progress of a reaction. Classical nucleation theory, for instance, uses the size of the droplet of the forming phase as a reaction coordinate. Similarly, in the most investigations of crystal nucleation, one considers the number of particles in the largest crystalline cluster as a reaction coordinate, although it is generally adreed that it is not the optimal choice. The theories from which the mean first-passage time method is derived assume, for the sake of convenience, that it is possible to find a one-dimensional coordinate which completely describes the progress of a reaction. Considering successive passage times, we could, however, find indications that the widely used one-dimensional definition is not sufficient for the description of the process. In principle, the shortcomings of the currently used definition of a reaction coordinate for crystal nucleation are widely known but we could link this fact to the effects on the mean first-passage time method used for the computation of the crystal nucleation rates. The observation is quite general and should apply to any case of a first-order phase transition, where the definition of a good reaction coordinate is elusive. At the same time, we proposed an analysis of the successive recurrence times that provides a necessary even if not sufficient criterion for the identification of a good reaction coordinate.