Lattice energy equation series#

Considering the loss of ions from lattice points as random, the examination of each of the defects. 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. The effects of modifying this model by addition of next nearest neighbor repulsion and by varying the ionic charge are considered: neither approach significantly improves theory-experiment agreement but the varying of the charge leads to the interesting effect of making the elastic properties and the Born model parameters of the oxides correlate more closely with those of the fluorides.ĭefects in ionic solid are very much common, which is increased with the rise in temperature.

Lattice energy equation series#

A simple (repulsion between nearest neighbors only) Born model for the cohesive energy is tested in both series of compounds and found to be less satisfactory for the oxides. In addition the pressure derivatives of these constants were measured with the results These results are combined with similar data for MgO and a detailed comparison is made between the elastic properties of the series MgO-CaO-SrO and the analogous alkali halide series NaF-KF-RbF. Results are, in units of 1012 dynes/cm2, Where the notation B = (C11 + 2C12)/3, C = C44, C′ = (C11 − C12)/2 has been used. Values for the elastic stiffness constants of CaO and SrO have been obtained at room temperature using the ultrasonic pulse-echo technique. 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. 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. 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.

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. Defects in ionic solid are very much common, which is increased with the rise in temperature.