Competitive Nucleation in Nanoclusters
Date
2015-07-23
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Degree Level
Doctoral
Abstract
Nucleation is the primary mechanism by which systems change phase and it plays a major role in the formation of new materials in nature and industrially. In particular, experiments and molecular dynamic simulations have shown that nanoclusters, at the same initial conditions, freeze to different structures through a competitive process. Understanding the mechanism of nucleation requires the knowledge of the reaction coordinate, which consists of a set of variables that accurately describe the formation of the critical nucleus. In classical nucleation theory (CNT), the embryo size is solely used as the reaction coordinate, but this does not capture the formation of different structures in a competitive nucleation event.
Competitive nucleation is modeled using a two dimensional Potts model undergoing heterogeneous nucleation on to a nanoscale impurity. The rates of formation of the different stable phases are calculated using transition state theory and compared with the rates obtained from the mean first passage time and survival probability methods. Transition state theory is shown to predict the rates to the different structures under various conditions when the nucleation barrier is correctly normalized relative to the metastable state. A multiple path maximum likelihood analysis, (MPMLA), is developed to extract accurate reaction coordinates to the different phases. The results show that the linear combination of size and surface area of a given component is the accurate variable that describes the transition to the phase.
Molecular dynamics simulations are used to study the competitive freezing of gold nanoclusters for a range of cluster sizes and temperatures. Measuring the probability of observing each cluster type in an ensemble of freezing events, along with the overall rate at which liquid drops freeze to any structure, allows the rate of formation for each structure to be calculated. The rate of formation of icosahedral structures is about an order of magnitude higher than the rates for other structures. Also, as the size of the cluster increased, the rate of formation of icosahedral structure decreased while that of decahedral and FCC structures increases. The MPMLA is applied to the transition path ensembles to obtain the best reaction coordinate for the different transitions. Order parameters such as size, the Steinhardt bond orientational parameters, local order parameters such as Qe, ratio of local atom type in the largest embryo, and structural order parameters are tested as reaction coordinates. A linear combination of size, the fcc-fcc correlation parameter, and the Qe provided the maximum estimate for the liquid-icosahedral transition, making it the best reaction coordinate. The critical embryo for this transition consists of bulk fcc-type atoms arranged in a small group, and capped by surface 111 atoms to form a tetrahedron. There is at least one 5-fold symmetric cap for this critical embryo. For the liquid-decahedral transition, the linear combination of size, Qe and the Ihedge-<111> correlation parameter is the best reaction coordinate. Analysis of the critical embryo shows the formation of blocks of bulk fcc atoms. The number of fcc-type atoms in these blocks is greater than those observed in the case of the icosahedral transition, hence, the Qe parameter has a stronger effect. There is also the presence of <111> and the Ihedge atoms positioned to form the 5-fold cap. The formation of the FCC structures follows the growth of the bulk fcc atoms with a corresponding elimination of the 5-fold facets. Hence, the linear combination of Qe, the Ihbulk-Hcpbulk and the Ihedge-<111> correlation parameters, is the best reaction coordinate that describes the formation of FCC clusters.
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Keywords
Competitive Nucleation, Reaction Coordinates, Rates, Aimless Shooting, Transition Path Sampling, Multiple Path Maximum Likelihood Analysis, Correlation Parameter, Free Energy Surface
Citation
Degree
Doctor of Philosophy (Ph.D.)
Department
Chemistry
Program
Chemistry