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In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ionic solids.
The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound.In 1918 [1] Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
The initial stage A. of defect creation, until all excess kinetic energy has dissipated in the lattice and it is back to its initial temperature T 0, takes < 5 ps. This is the fundamental ("primary damage") threshold displacement energy, and also the one usually simulated by molecular dynamics computer simulations.
The Born–Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound.It is a refinement of the Born–Landé equation by using an improved repulsion term.
The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is [6] = +, ˙, where q is heat flux vector, −ρc p (∂T/∂t) is temporal change of internal energy (ρ is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and ˙ is the energy conversion to and from thermal ...
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known.
This results in typical lattice and free energy differences between polymorphs that are often only a few kJ/mol, very rarely exceeding 10 kJ/mol. [10] Crystal structure prediction methods often locate many possible structures within this small energy range. These small energy differences are challenging to predict reliably without excessive ...
The Ising model is given by the usual cubic lattice graph = (,) where is an infinite cubic lattice in or a period cubic lattice in , and is the edge set of nearest neighbours (the same letter is used for the energy functional but the different usages are distinguishable based on context).