Size-Dependent Growth Rates Amplify Infinitesimal Asymmetry in Nanocrystals
Abstract
The kinetic Wulff construction predicts symmetric nonequilibrium shapes when crystallographically equivalent facets share a fixed growth rate. However, nanocrystals grow through finite facets whose nucleation barriers and ligand coverages depend on facet size. Here we develop a size-dependent kinetic construction and show that as a consequence infinitesimal seed asymmetries can be amplified into strongly asymmetric nanocrystal morphologies even when all symmetry-related facets obey the same microscopic growth law. Spatially heterogeneous nucleation rates and boundary limited growth generate facet growth velocities that depend on size, and deterministic shape evolution translates these local rates into global shape symmetry breaking. We illustrate the mechanism of persistent anisotropic growth on square and triangular lattices in two dimensions and on FCC seeds in three dimensions, where cuboctahedra can evolve toward rods or tetrahedra depending on which facet-area perturbations are amplified.
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BibTeX
@misc{oaksleaf2026sizedependent,
title = {{Size-Dependent Growth Rates Amplify Infinitesimal Asymmetry in Nanocrystals}},
author = {Sam Oaks-Leaf and David T. Limmer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00145},
eprint = {2609.00145},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00145},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Size-Dependent Growth Rates Amplify Infinitesimal Asymmetry in Nanocrystals
AU - Sam Oaks-Leaf
AU - David T. Limmer
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00145
UR - https://arxiv.org/abs/2609.00145
AB - The kinetic Wulff construction predicts symmetric nonequilibrium shapes when crystallographically equivalent facets share a fixed growth rate. However, nanocrystals grow through finite facets whose nucleation barriers and ligand coverages depend on facet size. Here we develop a size-dependent kinetic construction and show that as a consequence infinitesimal seed asymmetries can be amplified into strongly asymmetric nanocrystal morphologies even when all symmetry-related facets obey the same microscopic growth law. Spatially heterogeneous nucleation rates and boundary limited growth generate facet growth velocities that depend on size, and deterministic shape evolution translates these local rates into global shape symmetry breaking. We illustrate the mechanism of persistent anisotropic growth on square and triangular lattices in two dimensions and on FCC seeds in three dimensions, where cuboctahedra can evolve toward rods or tetrahedra depending on which facet-area perturbations are amplified.
ER -