Unveiling and quantifying the topology-dependent pre-melting of nanoparticles

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 $0.2\times T_{M,\infty}$ (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.

Figures (13)

• Figure 1: Facet-dependent surface pre-melting in a 1483 atoms hexagonal close-packed cobalt nanoparticle during a heating simulation. Snapshots are taken at 0 K (A), 370 K (B), 750 K (C), 1000 K (D), 1260 K (E) and 1380 K (F), which is the melting point. Atoms belonging to $\{0001\}$ facet are colored in light blue, those from $\{01\bar{1}1\}$ facet in dark blue, edge atoms are yellow and vertices are brown. Atoms that does not belong to any class are colored in red: they are outliers.
• Figure 2: Percentage of outliers (plain red line) and its derivative (dotted blue line) as a function of temperature, for a 3009 atoms hcp nanoparticle. The melting temperature corresponds to the maximum of the derivative, which is 1450 K for this hcp nanoparticle. $\tau_c$ is the maximum percentage of outliers after which the entire nanoparticle melts. The gray dashed line correspond to potential energy of the system.
• Figure 3: Correlation between melting point from the present structural approach and from energetics, i.e., the maximum of the heat capacity.
• Figure 4: Linear regression of the melting points of nanoparticles as a function of $N^{-1/3}$, where $N$ is the number of atoms. The curve intersect the $y$ axis at 1771 K.
• Figure 5: Critical percentage of outliers after which the entire nanoparticle melts for nanoparticles of increasing size. The MD results are plotted with diamond symbols, and the model is an analytical function discussed in the next section.