Beyond Magic Numbers: Atomic Scale Equilibrium Nanoparticle Shapes for Any Size.

Area of Science:

• Computational materials science
• Nanoparticle synthesis and characterization
• Thermodynamics and statistical mechanics

Background:

• Controlling nanoparticle morphology is crucial for applications.
• Existing methods for predicting equilibrium shapes are limited to very small (<2 nm) or large (>10-20 nm) particles.
• The intermediate size regime (1-7 nm) remains largely unexplored.

Purpose of the Study:

• To develop an efficient algorithm for predicting thermodynamic equilibrium shapes of nanoparticles across a wide size range.
• To investigate the energy landscape and shape transitions in intermediate-sized metal nanoparticles.
• To provide a tool for interpreting experimental data in nanoparticle synthesis.

Main Methods:

• Atomistic simulations within a constrained thermodynamic ensemble.
• Development of a novel algorithm for shape prediction.
• Application to copper (Cu), silver (Ag), gold (Au), and palladium (Pd) nanoparticles (1-7 nm).

Main Results:

• The algorithm efficiently predicts equilibrium shapes for nanoparticles from tens to thousands of atoms.
• Revealed a more intricate energy landscape than previously assumed.
• Demonstrated gradual transitions between icosahedral, decahedral, and truncated octahedral shapes.
• Obtained particle type distributions for Cu, Ag, Au, and Pd nanoparticles.

Conclusions:

• The new algorithm accurately predicts nanoparticle equilibrium shapes in the experimentally relevant intermediate size regime.
• The energy landscape is complex, with gradual shape transitions impacting experimental data interpretation.
• The method is extensible to alloy nanoparticles and adaptable to different chemical environments.