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

Abstract

Finite temperature analysis of cluster structures is used to identify signatures of the low-temperature polymorphs of gallium, based on the results of first-principle Born-Oppenheimer molecular dynamics simulations. Pre-melting structural transitions proceed from either the β- and/or the δ-phase to the γ- or δ-phase, with a size- dependent phase progression. We relate the stability of each isomer to the electronic structures of the different phases, giving new insight into the origin of polymorphism in this complicated element.

Cluster melting: new, limiting, and liminal phenomena

“…The use of DFT based BOMD for these small gallium clusters has demonstrated the ability of these calculations to replicate the experimental findings, both with respect to the melting temperature variations and the nature of melting in those cases where multiple transitions are observed [51,52,83,84]. As expected, the complex phase diagram of gallium leads to many interesting features in the electronic structure as a function of temperature, and these have been isolated through statistical analysis of the dynamic structures [84] to provide evidence of the relative stability of different solid phases -related to the various low temperature polymorphs of gallium (β, δ, or γ ), but never to the dimeric standard (α) phase -at finite temperature [51].…”

“…As expected, the complex phase diagram of gallium leads to many interesting features in the electronic structure as a function of temperature, and these have been isolated through statistical analysis of the dynamic structures [84] to provide evidence of the relative stability of different solid phases -related to the various low temperature polymorphs of gallium (β, δ, or γ ), but never to the dimeric standard (α) phase -at finite temperature [51].…”

“…In this and subsequent work, a growing consensus has established that to a large extent, electronic effects are mediated through changes in preferred geometric structure, which of course must be involved in melting phenomena [21,50]. This complex relationship has been further elucidated in recent work by Steenbergen et al [51] on gallium clusters. BOMD simulations of melting allow for the relative stability of different phases -including competing solid phases, or geometric structures -to be quantified as a function of temperature.…”

“…Earlier work on the same system of gallium clusters had already demonstrated how geometric effects may sensitively affect the melting behaviour of a clusters [52]. However at temperatures just below the melting temperature, structures other than the ground state structure may be quite dominant: where this is the case, it is clear that ground state geometries may fail to explain melting temperature variations with size [51]. This point has been neglected in many studies of cluster structure that look to correlate ground state with melting properties (although in most cases the potential for solid-solid transitions to complicate the melting phase diagram is much less than for gallium, which is notoriously polymorphic) [53][54][55][56].…”

“…The phase diagram of these gallium clusters, and examples of the analysis of their electronic structure that can be achieved through BOMD simulations, explaining for example the one-atom differences Notes: For the top three the electron density is projected onto spherical harmonic functions to demonstrate the electronic shell structure, and the relation of the electronic structure of the δ-phase between cluster and bulk. Adapted in part from the work of Steenbergen et al [51].…”