First-principles melting of gallium clusters down to nine atoms: structural and electronic contributions to melting

Abstract

First-principles Born-Oppenheimer molecular dynamics simulations of small gallium clusters, including parallel tempering, probe the distinction between cluster and molecule in the size range of 7-12 atoms. In contrast to the larger sizes, dynamic measures of structural change at finite temperature demonstrate that Ga7 and Ga8 do not melt, suggesting a size limit to melting in gallium exists at 9 atoms. Analysis of electronic structure further supports this size limit, additionally demonstrating that a covalent nature cannot be identified for clusters larger than the gallium dimer. Ga9, Ga10 and Ga11 melt at greater-than-bulk temperatures, with no evident covalent character. As Ga12 represents the first small gallium cluster to melt at a lower-than-bulk temperature, we examine the structural properties of each cluster at finite temperature in order to probe both the origins of greater-than-bulk melting, as well as the significant differences in melting temperatures induced by a single atom addition. Size-sensitive melting temperatures can be explained by both energetic and entropic differences between the solid and liquid phases for each cluster. We show that the lower-than-bulk melting temperature of the 12-atom cluster can be attributed to persistent pair bonding, reminiscent of the pairing observed in α-gallium. This result supports the attribution of greater-than-bulk melting in gallium clusters to the anomalously low melting temperature of the bulk, due to its dimeric structure.

Superatomic Gallium Clusters in Dendrimers: Unique Rigidity and Reactivity Depending on their Atomicity

“…For example, gallium clusters shows significant change in melting temperature with a change in size by one atom. [32][33][34][35][36][37] It is theoretically revealed that the property change depends on the geometric structure for gallium clusters. [32,33] In the case of metal clusters with valence electrons, such properties are not determined only by the geometric structure.…”

Quantum Size Effects in the Size–Temperature Phase Diagram of Gallium: Structural Characterization of Shape‐Shifting Clusters

“…The naked gallium clusters have been studied theoretically in order to identify the structures6–8 and to compare the bonding patterns to that of the bulk α‐phase, with some success 9. Bare clusters of gallium have also been investigated in order to understand the anomalous paradigm of greater‐than‐bulk melting temperatures, which have been both experimentally and theoretically confirmed 10–12. Studies of the ground‐state structure alone are manifestly unable to describe the process of melting.…”

Two worlds collide: Image analysis methods for quantifying structural variation in cluster molecular dynamics

“…How, then, does one go about identifying isomerization in a simple, straight-forward manner without a priori or "library" structural data? In the process of analyzing molecular dynamics simulations for small gallium clusters (9-36 atoms), [15][16][17] we required methods allowing for the direct comparison of structural similarity over a range of isomers, across multiple cluster sizes and temperatures, without any a priori knowledge of cluster structure. We noted similarities to the challenges encountered in the field of remote sensing image analysis, where the analysis methods typically involve a large amount of data measured under dissimilar conditions.…”

“…Here, we present an overview of the PCA and PCC analysis techniques applied to small cluster MD, using representative examples from our simulations on small gallium clusters sized 9, 12, and 20 atoms. 15,16…”