Nanoscale melting: how size changes thermodynamic stabiility
The properties of nanomaterials change in a number of different ways, some of which are predictable, while others can be quite surprising! Nanoparticles usually melt at lower temperatures than the bulk material, due to the reduced stability of atoms at the surface. This paradigm – called melting point depression – has been challenged by experimental evidence, now confirmed by our calculations, that the melting temperatures can actually increase by hundreds of degrees1. These clusters of atoms are made out of gallium, a fascinating element sometimes referred to as a molecular metal, as it is built out of little gallium dimers. However the clusters transition at very small sizes – around 9 atoms – from a molecule-like structure to a more metal-like structure.2 This work was conducted by Dr Krista G. Steenbergen, now a postdoctoral fellow at Massey University in Auckland. In molecular-dynamics simulations, which we use to calculate the melting temperature based on a density functional theory description of the electronic interactions, we can identify numerous isomers, which exhibit features of different structures that bulk gallium is known to adopt when it is cooled to very low temperatures.3
Figure 2: From the structure of the cluster isomer we can calculate a pair distribution function at finite temperature (here about 260oC) which allows us to compare the cluster structures with the bulk polymorphs of gallium. The g phase is shown in red and the d phase in blue (of the two structures shown in each case, the one on the left is the 33-atom cluster, right is the unit cell depiction of the bulk structure). By seeing how clusters transform from one phase to another, and what temperatures they become stable at, we can improve our understanding of how bulk structures emerge from the interactions between individual atoms. We can also visualize those interactions in the form of the density of states – which shows the energies at which molecular orbitals exist, and how they broaden to form bands in the bulk phases.3
Figure 3: Molecular orbitals of S, P, and D character, occupied by the s and p valence electrons of the individual gallium atoms, delocalized over a cluster of 36 atoms. Size matters, for melting, but so does the material it is made of, and modifying that material – for example, through doping – can also have significant effects on the melting temperature. In subsequent work, Dr Udbhav Ojha studied the effect of mixing aluminium and gallium on the melting temperature of the nanoparticle. By considering how different the stability of individual atoms are, depending on whether they are at the centre or at the surface of the cluster, he was able to construct a model of how the melting temperature changes in a cluster of a given size, depending on composition, and in comparison to the bulk melting temperature of the relevant alloy.4
Figure 4: A first sketch of the phase diagram of Ga-Al clusters The most interesting thing to be learnt from studying thermodynamic stability and transitions between phases, is that in contrast to most ab initio calculations of the properties of nanomaterials, the entropy plays a significant role, and can even outweigh the energetic interactions in terms of importance. This is where most of the surprises have come from – and probably, where more surprises about the structures of nanomaterials still remain to be discovered. Gaston, Steenbergen, Ojha et al References
- K. G. Steenbergen, N. Gaston, Phys. Rev. B2013,88, 161402.
- K. G. Steenbergen, N. Gaston, Phys. Chem. Chem. Phys.2013, 15, 15325.
- K. G. Steenbergen, N. Gaston, Chem. Eur. J.2015, 21, 2862-2869.
- U. Ojha, N. Gaston, J. Phys. Chem. C 2015. DOI: 10.1021/acs.jpcc.5b04930