Study of surface cell Madelung constant and surface free energy of nanosized crystal grain

Surface cell Madelung constant is firstly defined for calculating thesurface free energy of nanosized crystal grains, which explains the physicalperformance of small crystals and may be greatly beneficial to the analysisof surface states and the study of the dynamics of crystal nucleation andgrowth. A new approximative expression of the surface energy and relevantthermodynamic data are used in this calculation. New formula and computingmethod for calculating the Madelung constant α of any complexcrystals are proposed, and the surface free energies and surfaceelectrostatic energies of nanosized crystal grains and the Madelung constantof some complex crystals are theoretically calculated in this paper. Thesurface free energy of nanosized-crystal-grain TiO₂ and the surfaceelectrostatic energy(absolute value) of nanosized-crystal-grain α-Al₂O₃ are found to be the biggest among all the crystal grainsincluding those of other species.