Schotky defects in a spherical gold nanoparticle.

A vacancy is the lack of an atom in the crystal lattice and defects like these are important for a material's electrical and mechanical characteristics. They also dictate how heat is transported in a structure. Engineers need to control how vacancies form as the size of particles become smaller, but this is no easy task – especially for nanoparticles.

To address this issue, Grégory Guisbiers of the Catholic University of Louvain has now developed a theoretical model that shows how vacancies are easier to form in nanoparticles compared to the bulk. The calculations also seem to imply that the concentration of vacancies in smaller particles increases dramatically as the temperature increases (see figure). The results will help shed light on how mechanical, electrical and thermal properties are modified on the nanoscale because of vacancies, he says.

The findings are not all that surprising, he adds, and are rather intuitive too. Vacancies are thought of as being related to the internal surface in a material, so the surface plays the same role as defects here. “It is therefore natural to expect that decreasing the size of a material will increase the concentration of vacancies in it thanks to an increasing surface area to volume ratio,” he told

“Theoretically, vacancy concentrations can be described by an Arrhenius equation – as the vacancy formation energy and entropy decrease with size, then the vacancy concentration increases.” The presence of vacancies in the crystal lattice also modifies the lattice structure around the defects, resulting in the lattice parameter decreasing and “lattice softening”.

The hardness and yield strength of a material typically increases with decreasing particle size, a phenomenon known as the Hall-Petch effect. Guisbiers' calculations also suggest that smaller particles become harder at temperatures well below their melting temperature. This occurs thanks to the bond lengths contracting and an accompanying increase in bond strength.

All in all, an increased number of vacancies leads to a decrease in the electrical and thermal conductivity in a nanomaterial thanks to scattering of electrons on vacancies and lattice softening, Guisbiers sums up. “Since vacancies are the source of future pores, my model will also help us to better understand how pores appear in nanomaterials. This is important since nanoporous structures themselves are particularly attractive as 'host' materials for a variety of nanotechnology applications.”

Next on his list: study interstitial defects and dislocations, and see how these affect nanomaterial properties.

The present work is described in the Journal of Physical Chemistry C.