Shape Stability of Metallic Nanoplates: Insights from Molecular Dynamics Simulations

Abstract

Metallic nanoplates exhibit remarkable functional versatility that is tightly linked to their morphology. Using atomistic molecular dynamics, we examined the shape stability of body‑centered‑cubic (bcc) nanoplates with low‑index surfaces. Our simulations reveal that (110) surfaces are intrinsically the most stable, while (111) and (001) nanoplates undergo temperature‑driven deformations. The (001) plate transforms into a saddle‑shaped structure composed of (110) facets before collapsing into an irregular particle. The evolution is governed by shear‑stress distribution, which depends on facet orientation. By modulating facet orientations, plate size (diameter and thickness), and material composition, we demonstrate tunable shape stability across several bcc metals (Fe, W, Nb, Mo, Cr). These findings provide an atomistic framework for controlling nanoplate morphology during synthesis and application.

Introduction

Metallic nanoplates are key functional nanomaterials with applications ranging from catalysis to optoelectronics. Their performance is dictated by surface area, facet chemistry, and overall shape. Although thermodynamics predicts a tendency toward spherical minimization of surface energy, kinetic barriers frequently stabilize anisotropic platelets. Thin plates (few atomic layers) possess high surface‑to‑volume ratios, making them especially sensitive to temperature and environmental stimuli. Previous in‑situ TEM studies have observed edge fragmentation and facet reorientation upon heating, yet quantitative atomistic insight remains limited. Here we use large‑scale molecular dynamics (MD) to capture the complete temperature‑dependent morphology evolution of bcc metallic nanoplates, focusing on the role of crystal orientation, size, and composition.

Methods

Fe nanoplates were constructed with a lattice constant a = 2.8665 Å and diameter d = 32a, each comprising three atomic layers. Initial surfaces were set to the (111), (001), or (110) orientations. Analogous structures were generated for W, Nb, Mo, and Cr. Models were built in LAMMPS and relaxed via conjugate‑gradient minimization. Subsequent heating was performed in an NVT ensemble, ramping temperature from 1 K to 300 K (or higher) in 1 K increments, with a 2 fs timestep and 200 ps equilibration per step. Potential energy and stress tensors were recorded; the last 8 ps of each step were averaged. Interatomic forces employed EAM potentials validated in prior MD studies. Local stress for atom i was computed using the standard virial expression:

σ_{αβ}=\frac{1}{2Ω_i}\sum_{j\ne i}F_{ij}^{α}R_{ij}^{β}

where Ω_i is the Voronoi volume of atom i.

Results and Discussion

Energetic hierarchy and shape evolution. The initial potential energies per atom were −2.833, −3.457, and −3.668 eV/atom for (111), (001), and (110) Fe plates, respectively, mirroring the surface energies of 2.58, 2.47, and 2.37 J/m². As temperature rises, (111) and (001) plates rapidly adopt curved, metastable shapes, whereas the (110) plate retains its flat geometry up to the highest simulated temperatures. The (001) plate develops a saddle shape dominated by (110) facets, as confirmed by fitting its mid‑layer to a quadric surface z = ax² + by² + cxy + d. Critical transitions occur at 8, 129, and 205 K, with corresponding changes in the fit coefficients and R² values > 0.8 indicating robust saddle geometry until 205 K.

Stress‑driven deformation. Shear‑stress maps reveal anisotropic distribution linked to facet orientation: positive stresses on red facets and negative on blue facets create opposing forces that drive bending. At 9 K, increased bending eliminates stress gaps, lowering potential energy. A secondary transition between 129–134 K corresponds to buckling of a central region, causing a sudden drop in R² and eventual collapse into an irregular particle.

Facet modulation and material dependence. A “modulated (110)” Fe plate, comprising four differently oriented facets, shows similar saddle formation at 1 K but transitions back to a disk at 179 K and finally collapses at 277 K. In contrast, the regular (110) plate remains stable until 552 K, underscoring the influence of facet design. Extending the study to W, Nb, Mo, and Cr plates of d = 32a demonstrates that saddle stability ranges from 62 K (Cr) to 582 K (W), correlating with the initial potential energy and structural stability of each element.

Size and thickness effects. Fe (001) plates with diameters 12a, 40a, and 50a display distinct stability windows: the 12a plate collapses by 84 K, the 40a plate holds the saddle up to 190 K, while the 50a plate only up to 134 K. Thickness variations reveal that 4‑layer plates maintain their shape up to 98 K before converting to (110) facets; thinner plates collapse earlier. Overall, larger plates improve baseline stability, but kinetic and entropy contributions can reduce saddle stability at very large diameters.

Conclusions

Our MD study elucidates the atomistic mechanisms governing shape evolution in bcc metallic nanoplates. (110) surfaces offer the highest structural stability, whereas (111) and (001) plates transform into saddle shapes composed of (110) facets before collapsing. Shear stress, tied to facet orientation, drives these deformations. By engineering facet orientations, plate dimensions, and selecting material composition, the stability of desired morphologies can be finely tuned. These insights lay a theoretical foundation for morphology control in the synthesis of metallic nanomaterials.

Availability of Data and Materials

All simulation data and analysis scripts are included within this publication.

Abbreviations

a

Lattice constant

bcc

Body‑centered‑cubic

d

Diameter

EAM

Embedded atom method

E_p

Potential energy

MD

Molecular dynamics

R²

Coefficient of determination

TEM

Transmission electron microscope