Modified Born-Lande equation to calculate the lattice energy: A theoretical treatise

Ionic defects are a common phenomenon in solid state chemistry, which increases with the rise in temperature. It causes the change in the attributes of many physical properties and different physical parameters, among them Lattice Energy is one of the important parameters to tune the physical properties of the crystals. The presence of defects in a crystal arises from the loss of ions from the respective lattice points, this loss is considered as random event, each occurrence of the defect cannot be analysed with precision, doing so it will lead to nonattainment of the correct crystal structure with the theoretical calculations applying for available models. In this attempt, the Poisson Distribution and probabilistic approximations are introduced to have a novel approach of quantitative estimation of the change in value of Madelung constant due to varying parameters, this in turn changes the Lattice Energy. Applying a limiting condition, such as lowering of temperature causes dramatic reduction in the number of defects, hitherto the equation of the modified Lattice energy equation converts its form into Born-Lande equation. To study the phenomenon, sodium chloride (NaCl) crystal is chosen, because of its very wellknown as well as structurally simple crystallographic identity. NaCl shows 6:6 co-ordination number, for which a significant number of Schottky defects are observed. The study leads to a turn of events, when it approaches a critical limit. Importantly, the increase in number of defects from a threshold value forces the crystal to exhibit a phase change, i.e. a crystal having defects greater than the threshold value shows melting and initiates the conversion from solid state to liquid state.