Computation of Madelung Energies for Ionic Crystals of Variable Stoichiometries and Mixed Valencies and their application in Lithium-ion battery voltage modelling

Electrostatic energy (Madelung energy) is a major constituent of the cohesive energy of ionic crystals. Several physicochemical properties of these materials depend on the response of their electrostatic energy to a variety of applied thermal, electrical and mechanical stresses. In the present study, a method has been developed based on Ewalds technique, to compute the electrostatic energy arising from ion-ion interactions in ionic crystals like LixMn2O4 with variable stoichiometries and mixed valencies. An interesting application of this method in computing the voltages of lithium ion batteries employing spinel cathodes is presented for the first time. The advantages of the present method of computation over existing methods are also discussed.Comment: 15 page

A stochastic model on the mean time to recruitment for a two graded manpower system associated with a univariate policy of recruitment involving combined thresholds using same geometric process for inter-decesion times

In this paper, an organization with two grades subjected to loss of manpower due to the policy decisions taken by the organization is considered. A mathematical model is constructed and an appropriate univariate recruitment policy, based on shock model approach involving combined optional thresholds and combined mandatory thresholds for the loss of manpower in the organization is suggested. The expected time for recruitment is obtained for different cases on the distribution of the thresholds when (i) the loss of manpower forms a sequence of independent and identically distributed exponential random variables and (ii) the inter-decision times for the two grades form the same geometric process. The analytical results are substantiated by numerical illustrations and relevant conclusions are presented