In this paper we derived a new condition of formation and stability of all crystalline systems and we checked its validity andit is found to be in a good agreement with experimental data. This condition is derived directly from the quantum conditionson the free electron Fermi gas inside the crystal. The new condition relates both the volume of Fermi sphere VF andvolume of Brillouin zone VB by the valence electron concentration VEC as ;ð‘½ð‘ð‘½ð‘©= ð’ð‘½ð‘¬ð‘ªðŸfor all crystalline systems (wheren is the number of atoms per lattice point).
Higher Moments for Lattice Point Discrepancy of Convex Domains and Annuli
