Modified Born-Lande Equation to calculate Lattice Energy in a theoretical approach

Defects in ionic solid are very much common, which is increased with the rise in temperature. It causes the change in the value of many physical properties and varieties of physical parameters and the Lattice Energy is one such parameter to control the physical properties of the crystals. Considering the loss of ions from lattice points as random, the examination of each of the defects individually is going to be unpredictable, thus leading to almost nonattainment of the correct crystal structure with the theoretical calculations applying for available models. Here, in this present work, we have used some statistical methods and probabilistic approximation to introduce a novel idea of calculating the Madelung constant, and then Lattice Energy analytically. To make the understanding more lucid, we have taken one of the very common crystals, very popular in the crystallographic community, NaCl crystal having 6:6 co-ordination number, for which a significant number of Schottky defects are observed. During this study, we are bound to assume the random distribution of defects as Poisson distribution due to the fact that the number of defects is very less with respect to the total numbers of lattice points present in the crystal to calculate the Madelung Constant.