[Paper Review] Unveiling and quantifying the topology-dependent pre-melting of nanoparticles

Marthe Bideault, Arnaud Allera+3 more|arXiv (Cornell University)|Feb 18, 2026

nanoparticles nucleation surface interactions0 citations

TL;DR

The paper shows facet-dependent surface pre-melting in hexagonal close-packed Co nanoparticles using unsupervised machine-learning to identify facet-specific melting, linking facet temperatures to nanoparticle size via a two-dimensional Gibbs–Thomson relation, and defining a size-dependent critical liquid-layer thickness for global melting.

ABSTRACT

The melting of metallic nanoparticles is governed by surface pre-melting, a phenomenon traditionally modeled as the isotropic growth of a uniform liquid shell. Challenging this classical view, we report facet-dependent surface pre-melting in hexagonal close-packed Co nanoparticles, arising from the structural heterogeneity of the nanoparticle surface. Characterizing melting in molecular dynamics simulations (500 to 6000 atoms), we observe the onset of surface mobility, starting as low as $0.2 imes T_{M,\infty}$ (the bulk melting point), driven by the early disordering of stepped $\{01\bar{1}1\}$ facets. We found that these facets consistently melt at temperatures nearly 200 Kelvin lower than flat $\{0001\}$ facets, regardless of particle size, and relate facets melting temperatures to the nanoparticle size via a 2D extension of the Gibbs-Thomson relation. We determine a critical liquid layer thickness that triggers the melting of the entire nanoparticle, which is found to be size-dependent. Our results confirm the recent experimental observation of the surface pre-melting effect, and extend it to anisotropic particles with different facet orientations.

Motivation & Objective

• Motivate understanding of how nanoparticle surface topology affects pre-melting and melting behavior beyond isotropic models.
• Quantify facet-specific onset and progression of surface melting in hcp Co nanoparticles.
• Develop and apply a robust, descriptor-based analysis framework to classify atomic environments and track melting.
• Relate facet melting temperatures to nanoparticle size and extend Gibbs–Thomson concepts to two-dimensional facet systems.

Proposed method

• Perform molecular dynamics simulations of hcp Co nanoparticles (500–6000 atoms) using a machine-learned q-SNAP potential calibrated to DFT-PBE data.
• Construct hierarchical atomic-environment classes (bulk, facets, edges, vertices) with unsupervised Gaussian Mixture Models.
• Quantify melting by Mahalanobis-based distortion scores to classify atoms as in-distribution or outliers during heating.
• Extract global melting temperature from the maximum rate of outlier fraction increase and cross-validate with heat capacity maxima.
• Analyze facet-specific melting by fitting sigmoid functions to facet-atom populations to determine T_c for {01-11} and {0001} facets.
• Extend Gibbs–Thomson analysis to two-dimensional facet systems by relating facet characteristic temperatures to facet atom counts and particle size.

Experimental results

Research questions

• RQ1 How does surface topology (facet type) influence the onset and progression of pre-melting on cobalt nanoparticle surfaces?
• RQ2 Can a two-dimensional Gibbs–Thomson framework describe facet-specific melting temperatures as a function of nanoparticle size?
• RQ3 What is the relationship between the global melting point, surface melting, and the critical liquid-layer thickness in hcp nanoparticles?
• RQ4 How can machine-learning descriptors robustly classify complex, multimodal atomic environments and track melting without ad hoc thresholds?

Key findings

• {01-11} facets melt at temperatures nearly 200 K lower than {0001} facets, independent of particle size.
• Global melting temperature scales with size following a Gibbs–Thomson-type relation with T_m,NP ≈ T_m,∞ − a N^(−1/3).
• There exists a critical liquid-layer thickness (or equivalently, a critical fraction of outlier atoms τ_c) that triggers complete nanoparticle melting and this τ_c is size-dependent with a non-monotonic trend.
• For very small nanoparticles, global melting requires melting of the more stable {0001} facets, while larger particles exhibit early surface pre-melting forming a liquid layer that thickens with size.
• A two-dimensional Gibbs–Thomson extension accurately captures facet-specific characteristic temperatures T_c as functions of facet atom count n_(hkil), yielding T_c,∞ values around 0.60 T_m,∞ for {01-11} and 0.77 T_m,∞ for {0001} in the large-N limit.
• The distortion-score method provides robust, precise identification of atomic environments and outliers, improving over traditional metrics for surface melting analysis.