Atomic size effects in continuum modeling

Area of Science:

• Physics
• Materials Science
• Computational Modeling

Background:

• Continuum modeling simplifies physical systems by treating atoms as point-like.
• This assumption is often valid for large-scale phenomena but may fail in specific applications.
• The spatial extent of atoms can influence nanoscale processes.

Purpose of the Study:

• To investigate the validity of neglecting atomic spatial extent in continuum modeling.
• To develop an improved model for epitaxial growth that accounts for atomic dimensions.
• To accurately predict key quantities in epitaxial growth, such as island densities.

Main Methods:

• Developed a novel continuum model for epitaxial growth.
• Utilized the level-set method for modeling.
• Implemented boundary conditions within a region of atomic width.

Main Results:

• Demonstrated that neglecting atomic spatial extent is only asymptotically valid.
• Showed that accounting for atomic width is essential for accurate predictions in practical scenarios.
• Successfully predicted island densities by incorporating atomic-scale boundary conditions.

Conclusions:

• The spatial extent of discrete atoms cannot be neglected in many practical continuum modeling applications.
• Accurate modeling of epitaxial growth requires boundary conditions with atomic width.
• The developed model provides a more accurate approach for understanding nanoscale material formation.