Authors' response

— In their comment, Mathur, Sharma and Cammarata nicely summarize and clarify definitions of surface energies for single- and multicomponent systems. Surface energy for single-component systems is always positive, whereas for multicomponent systems it can become negative under certain conditions. It is an important conclusion from our density functional theory calculations that the surface energy of θ-alumina can become negative in the presence of water.

Mathur, Sharma and Cammarata go on to discuss whether the single- or multicomponent surface energy is the critical parameter. We agree that in idealized situations (like in an ultra-high vacuum experiment, for instance) the surface energy (or surface stress) without effects due to interactions with the surroundings is the quantity of interest, but for most conditions (including those where transition aluminas are synthesized) the effect of the surroundings is very important and cannot be neglected. Indeed, the other new result of our paper is that for such multicomponent systems a negative surface energy can lead to porous equilibrium structures or small stable nanoparticles.