‘Madelung model’ prediction for dependence of lattice parameter on nanocrystal size

The competition between the long-range Coulomb attractive and the short-range repulsive interaction in ionic nanocrystals creates an effective negative pressure, which causes the lattice parameter a to increase with decreasing nanoparticle size d. A simple ‘Madelung model’ is used to predict the dependence of the lattice parameter for CeO2 and BaTiO3 on d, δa/a=α/d, for α=0.22 and 0.18 Å, respectively. The model predictions are compared with experimental results.