A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements.

Area of Science:

• Materials Science
• Crystallography
• Nanotechnology

Background:

• Discrete atomistic modeling is limited to small nanoparticles (< 15 nm).
• Small-box modeling for larger nanoparticles often ignores or inaccurately models nanoparticle shape.
• Accurate shape description is crucial for reliable nanoparticle structural refinement.

Purpose of the Study:

• To develop a methodology for deriving numerical approximations of nanoparticle shape functions.
• To enable accurate structural refinement of larger nanoparticles by accounting for their specific shapes.
• To provide a computationally feasible approach for incorporating shape effects in nanoparticle size refinement.

Main Methods:

• Deriving numerical approximations of nanoparticle shape functions by fitting to a training set of known shape functions.
• Employing these numerical approximations on larger nanoparticle sizes.
• Demonstrating the method on simulated and real data sets.

Main Results:

• A methodology for numerical approximation of nanoparticle shape functions is presented.
• The approach allows for more accurate and physically meaningful refined nanoparticle sizes, even for larger particles.
• Pre-calculated shape function expressions for common nanoparticle shapes are provided.

Conclusions:

• The developed methodology effectively addresses the limitations of current nanoparticle structural refinement techniques.
• This approach enhances the accuracy and applicability of small-box modeling by incorporating realistic shape effects.
• The findings facilitate more precise characterization of nanoparticle size and structure across various applications.