[Paper Review] The structure of binary Lennard-Jones clusters: The effects of atomic size ratio

Jonathan P. K. Doye, Lars Meyer|arXiv (Cornell University)|Apr 10, 2006

Supramolecular Self-Assembly in Materials5 citations

TL;DR

This study introduces a global optimization method to identify the most stable structures and compositions of binary Lennard-Jones clusters as a function of atomic size ratio and cluster size. It reveals that polytetrahedral structures—especially core-shell configurations with larger atoms on the surface and smaller atoms in the core—are significantly stabilized by size mismatch, reducing strain that would otherwise destabilize such geometries in monatomic clusters.

ABSTRACT

We introduce a global optimization approach for binary clusters that for a given cluster size is able to directly search for the structure and composition that has the greatest stability. We apply this approach to binary Lennard-Jones clusters, where the strength of the interactions between the two atom types is the same, but where the atoms have different sizes. We map out how the most stable structure depends on the cluster size and the atomic size ratio for clusters with up to 100 atoms and up to 30% difference in atom size. A substantial portion of this parameter space is occupied by structures that are polytetrahedral, both those that are polyicosahedral and those that involve disclination lines. Such structures involve substantial strains for one-component Lennard-Jones clusters, but can be stabilized by the different-sized atoms in the binary clusters. These structures often have a `core-shell' geometry, where the larger atoms are on the surface, and the smaller atoms are in the core.

Motivation & Objective

• To systematically map the most stable structures of binary Lennard-Jones clusters across cluster sizes (up to 100 atoms) and atomic size ratios (up to 30% difference).
• To investigate how size mismatch between two atom types stabilizes polytetrahedral and icosahedral structures that are strained or unstable in monatomic clusters.
• To identify the conditions under which core-shell geometries emerge as the global minimum energy configurations.
• To explore the implications of these findings for understanding local structure in metallic liquids and glass-forming ability.

Proposed method

• Develops a global optimization approach that treats composition as a variable, enabling direct search for the most stable structure-composition combination for each cluster size.
• Uses the Lennard-Jones potential with four effective interaction parameters: σ_AA, σ_BB, ε_AA, and ε_BB, with ε_AA = ε_BB to isolate size ratio effects.
• Applies a hybrid optimization algorithm capable of navigating the complex potential energy surface with multiple homotop isomers and compositional degrees of freedom.
• Analyzes structural motifs using geometric decomposition into tetrahedral units and identifies disclination lines and icosahedral symmetry.
• Maps the structural phase diagram at zero temperature, focusing on the stability of polytetrahedral vs. close-packed structures.
• Validates results against known monatomic LJ cluster behavior and compares with experimental glass-forming criteria.

Experimental results

Research questions

• RQ1 How does the atomic size ratio influence the stability of polytetrahedral structures in binary Lennard-Jones clusters?
• RQ2 What structural motifs—especially core-shell or icosahedral—are favored as the most stable configurations for binary clusters of varying size and size ratio?
• RQ3 To what extent can size mismatch stabilize strained polytetrahedral geometries that are energetically unfavorable in monatomic clusters?
• RQ4 How does the stability of polytetrahedral structures compare to close-packed or Mackay-type structures across the size and composition space?
• RQ5 What implications do these findings have for the local structure in metallic liquids and the nucleation of bulk glasses?

Key findings

• A substantial portion of the parameter space (up to 100 atoms, 30% size difference) is occupied by polytetrahedral structures, including both icosahedral and disclination-line-containing geometries.
• Core-shell structures with larger atoms on the surface and smaller atoms in the core are consistently among the most stable configurations, especially for size ratios near 1.2.
• The 13-atom icosahedron, which is highly strained in monatomic systems, becomes stable in binary clusters when the central atom is 9.79% smaller than surface atoms.
• The critical size ratio at which solid solutions become unstable is found to be 1.20, consistent with experimental glass-forming criteria.
• Temperature effects reinforce the stabilization of polytetrahedral structures, as vibrational entropy favors these geometries at higher temperatures.
• The results suggest that Frank-Kasper phases are unlikely to be ground states in the bulk limit, but may be stabilized in clusters of finite size, particularly in systems like Ni-Al, Ag-Cu, and Ag-Ni.