"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, delta a/a = alpha/d, for alpha = 0.22 A and 0.18 A respectively. The model predictions are compared with experimental results. 
Vasili Perebeinos, Siu-Wai Chan and Feng Zhang