Related Experiment Video
Updated: Jul 7, 2026
11:51
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Capture-zone scaling in island nucleation: universal fluctuation behavior
Alberto Pimpinelli1, T L Einstein
1LASMEA, UMR 6602 CNRS/Université Blaise Pascal-Clermont 2, F-63177 Aubière Cedex, France. alpimpin@univ-bpclermont.fr
Physical Review Letters
|February 1, 2008
Summary
Island nucleation and growth capture zone distributions are described by a generalized Wigner surmise. This model relates the power-law exponent to critical nuclei and substrate dimensionality, matching simulation and experimental data.
Area of Science:
- Surface science
- Statistical physics
- Materials science
Background:
- Island nucleation and growth is a fundamental process in thin film formation.
- Understanding capture zone distributions is key to controlling film morphology.
- Existing models often lack a unified description for various fluctuation phenomena.
Purpose of the Study:
- To present a generalized Wigner surmise for island nucleation and growth.
- To establish a relationship between the model's parameter and physical properties like critical nucleus size and substrate dimensionality.
- To validate the model against simulation and experimental data.
Main Methods:
- Theoretical modeling using a generalized Wigner surmise.
- Analysis of capture zone distributions.
- Comparison with extensive published kinetic Monte Carlo simulation data.
- Comparison with limited experimental data.
Main Results:
- A simple expression generalizing the Wigner surmise accurately describes capture zone distributions.
- The power-law exponent in the distribution is linked to critical nucleus size and substrate dimensionality.
- The model shows good agreement with both simulation and experimental results.
Conclusions:
- The generalized Wigner surmise provides a powerful tool for understanding island nucleation and growth.
- The model offers insights into the relationship between microscopic growth parameters and macroscopic distributions.
- This work unifies the description of spacing distributions across different fluctuation phenomena.
Related Concept Videos
02:39Phase Transitions: Vaporization and Condensation
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
01:16Precipitate Formation and Particle Size Control
In precipitation gravimetry, the precipitating agent should react specifically or selectively with the analyte. While a specific reagent reacts with the analyte alone, a selective reagent can react with a limited number of chemical species.
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...
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...
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...
01:18Uniform Depth Channel Flow: Problem Solving
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
01:27Uniform Depth Channel Flow
Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
02:39Phase Transitions: Melting and Freezing
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...