Mean First Passage Time Analysis Research Articles

Cavity nucleation in single-component homogeneous amorphous solids under negative pressure

Understanding the cavity formation and cavity growth mechanisms in solids has fundamental and applied importance for the correct determination of their exploitation capabilities and mechanical characteristics. In this work, we present the molecular dynamics simulation results for the process of homogeneous formation of nanosized cavities in a single-component amorphous metallic alloy. To identify cavities of various shapes and sizes, an original method has been developed, which is based on filling cavities by virtual particles (balls) of the same diameter. By means of the mean first-passage time analysis, it was shown that the cavity formation in an amorphous metallic melt is the activation-type process. This process can be described in terms of the classical nucleation theory, which is usually applied to the case of first order phase transitions. Activation energy, critical size and nucleation rate of cavities are calculated, the values of which are comparable with those for the case of crystal nucleation in amorphous systems.

Molecular Dynamics Simulation of Homogeneous Crystal Nucleation in Polyethylene

Using a realistic united-atom force field, molecular dynamics simulations were performed to study homogeneous nucleation of the crystal phase at about 30% supercooling from the melts of n-pentacontahectane (C150) and a linear polyethylene (C1000), both of which are long enough to exhibit the chain folding that is characteristic of polymer crystallization. The nucleation rate was calculated and the critical nuclei were identified using a mean first-passage time analysis. The nucleation rate was found to be insensitive to the chain length in this range of molecular weight. The critical nucleus contains about 150 carbons on average and is significantly smaller than the radius of gyration of the chains, at this supercooling. A cylinder model was used to characterize the shape of the crystal nuclei and to calculate the interfacial free energies. A chain segment analysis was performed to characterize the topology of the crystal surface in terms of loops (including folds) and tails. The length distribution of loops is broad, supporting the “switchboard model” for the early stage crystals formed at deep supercooling. Using the survival probability method, the critical nucleus size was determined as a function of temperature. The interfacial free energies were found to be temperature-dependent. The free energy barrier and nucleation rate as functions of temperature were also calculated and compare favorably with experiments.

Crystal nucleation and cluster-growth kinetics in a model glass under shear

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster-growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster-growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency.