[Paper Review] Coexistence of close packed structures in large substrate-free Ar-Kr clusters according to THEED data

O. G. Danylchenko, O. P. Konotop|arXiv (Cornell University)|Jan 5, 2026

nanoparticles nucleation surface interactions0 citations

TL;DR

The paper analyzes Ar-Kr clusters formed by adiabatic expansion and shows large clusters exhibit a two-phase fcc-hcp structure with equal component concentrations, independent of composition, with the hcp fraction growing with size and peaking at equimolar composition.

ABSTRACT

A quantitative phase analysis of substrate-free single-component and binary clusters of the Ar-Kr system obtained by adiabatic expansion of gas into vacuum through a supersonic nozzle was performed. The studies were carried out in-situ using transmission electron diffraction technique (THEED) on clusters with an average size ranging from 2000 to 100000 atoms/cluster and across the entire range of component concentrations. The independence of the threshold size of clusters, corresponding to the beginning of the formation of the hcp phase, from the component composition was revealed. It was established that clusters larger than this threshold size have a two-phase fcc-hcp structure with an identical concentration of components in each phase. The fraction of the hexagonal phase increases with the size of the aggregations and depends on the component content, reaching maximum in clusters with an equimolar composition. Arguments are presented in favor of the formation of two-phase clusters in the supersonic jet, rather than separate single-phase fcc and hcp ones. These findings are in good agreement with the previously proposed thermally activated diffusion mechanism for the nucleation and growth of the hcp phase in rare gas clusters.

Motivation & Objective

• Determine whether cluster size threshold for hcp phase formation in Ar-Kr clusters is dependent on component composition.
• Characterize the structural coexistence and phase distribution (fcc and hcp) in large substrate-free Ar-Kr clusters.
• Assess whether two-phase clusters form in the supersonic jet rather than mixtures of single-phase fcc and hcp clusters.
• Correlate phase fractions with overall cluster size and composition to test thermally activated diffusion mechanisms for hcp nucleation.

Proposed method

• In-situ quantitative phase analysis using transmission electron diffraction (THEED) on substrate-free Ar-Kr clusters.
• Clusters produced by adiabatic expansion of gas into vacuum through a supersonic nozzle, size range 2000–100000 atoms per cluster.
• Systematic variation of overall component concentration across the entire range.
• Analysis focused on determining phase composition (fcc vs hcp) and its dependence on size and composition.

Experimental results

Research questions

• RQ1 Does the threshold cluster size for initiating the hcp phase depend on the Ar-Kr composition of the cluster?
• RQ2 Do large Ar-Kr clusters exhibit a two-phase coexistence of fcc and hcp with identical component concentrations in each phase?
• RQ3 How does the hexagonal (hcp) phase fraction depend on cluster size and Ar/Kr composition?
• RQ4 Are two-phase clusters in the supersonic jet more consistent with nucleation mechanisms than separate single-phase fcc and hcp clusters?

Key findings

• The threshold size for hcp formation is independent of the component composition.
• Clusters larger than the threshold show a two-phase fcc-hcp structure with identical concentrations of components in each phase.
• The hexagonal phase fraction increases with cluster size and depends on component content, reaching a maximum in equimolar clusters.
• Arguments support the formation of two-phase clusters in the supersonic jet rather than mixtures of single-phase fcc and hcp clusters.
• Results align with a thermally activated diffusion mechanism for hcp nucleation and growth in rare gas clusters.