Related Experiment Video
Updated: Jul 19, 2026

Optimization of Crystal Growth for Neutron Macromolecular Crystallography
Published on: March 13, 2021
Upper critical dimension for irreversible cluster nucleation and growth in the point-island regime
Feng Shi1, Yunsic Shim, Jacques G Amar
1Department of Physics & Astronomy, University of Toledo, Toledo, Ohio 43606, USA. fengshi@physics.utoledo.edu
Abstract:
We compare the results of kinetic Monte Carlo (KMC) simulations of a point-island model of irreversible nucleation and growth in four dimensions (4D) with the corresponding mean-field (MF) rate-equation predictions for the monomer density, island density, island-size distribution (ISD), capture-number distribution (CND), and capture-zone distribution (CZD), in order to determine the critical dimension d(c) for mean-field behavior. The asymptotic behavior is studied as a function of the fraction of occupied sites (coverage) and the ratio DF of the monomer hopping rate D to the (per site) monomer creation rate F. Excellent agreement is found between our KMC simulation results and the MF rate equation results for the average island and monomer densities. For large D/F, the scaled CND and CZD do not depend on island size, in good agreement with the MF prediction, while the scaled ISD also agrees well with the MF prediction except for a slight difference at the peak values. Coupled with previous results obtained in d = 3 , these results indicate that for growth in the point-island regime, the upper critical dimension for irreversible cluster nucleation and growth is equal to 4.
Related Concept Videos
Crystal Growth: Principles of Crystallization
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
Precipitate Formation and Particle Size Control
The obtained precipitate should be either a pure substance of known composition or easily converted to one by a simple process, such as ignition or drying. In addition, the precipitate should be insoluble and easily filterable. In general, filterability...
Phase Diagrams of Ternary Systems
Phase Transitions: Vaporization and Condensation
pV-Diagrams
Recrystallization: Solid–Solution Equilibria

