# Impact of Interaction Range and Curvature on Crystal Growth of Particles Confined to Spherical Surfaces

## TL;DR

This study uses computer simulations to explore how interaction range and curvature influence crystal growth on spherical surfaces, revealing conditions for ribbon formation and defect incorporation.

## Contribution

It demonstrates the formation of ribbons at short interaction ranges and defect-packed structures at longer ranges, highlighting a two-step nucleation process.

## Key findings

- Ribbons form above a critical crystal size.
- Short-range interactions favor ribbon growth.
- Longer-range interactions promote defect incorporation.

## Abstract

When colloidal particles form a crystal phase on a spherical template, their packing is governed by the effective interaction between them and the elastic strain of bending the growing crystal. For example, if growth commences under appropriate conditions, and the circular crystal that forms reaches a critical size, growth continues by incorporation of defects to alleviate elastic strain. Recently it was found experimentally that, if defect formation is somehow not possible, the crystal instead continues growing in ribbons that protrude from the original crystal. Here we report on computer simulations in which we observe both the formation of ribbons at short interaction ranges and packings that incorporate defects if the interaction is longer-ranged. The ribbons only form above some critical crystal size, below which the nucleus is roughly spherically shaped. We find that the scaling of the critical crystal size differs slightly from the one proposed by the Manoharan group, and reason this is because the actual process is a two-step heterogeneous nucleation of ribbons on top of roughly circular crystals.