Quantum mechanical study of the shape and stability of SnO2 nanocrystalline grains

The purpose of this study is to get insight into the instability which is observed, under operative conditions, in SnO2 nanocrystalline materials. To this purpose, the binding and fragmentation energies of SnO2 crystalline grains have been evaluated quantum mechanically at the semiempirical level using the extended Debye-Hu¨ckel approximation. The grain structure is assumed to be an unreconstructed rutile lattice, as in the parent solid. The grain size and shape are variable, and a parametric search has been carried out on both quantities. Ab initio calculations of the binding energies of small oxygen and tin clusters have been also performed in order to test the accuracy of the semiempirical Hamiltonian and to offer a simple description of the properties of O-O, Sn-Sn, and Sn-O bonds. It has been found that a primary role in the grain stability arises from the interplay of the grain composition and shape, rather than from its size. Furthermore, the functional dependence of each of the characteristic energies on these parameters is qualitatively similar. However, the quantitative differences are not secondary. These features represent a central difference with respect to the known properties of pure clusters whose energetics is uniquely dictated by the cluster size.