Born–Mayer equation

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.{{cite web|url=http://alpha.chem.umb.edu/chemistry/ch370/CH370_Lectures/Lecture%20Documents/Ch07_2_LatticeEnergy.pdf|title=Lattice Energy}}

:$E\; =-\; \backslash frac\{N\_AMz^+z^-\; e^2\; \}\{4\; \backslash pi\; \backslash epsilon\_0\; r\_0\}\backslash left(1-\backslash frac\{\backslash rho\}\{r\_0\}\backslash right)$

where:

• N_A = Avogadro constant;
• M = Madelung constant, relating to the geometry of the crystal;
• z⁺ = charge number of cation
• z⁻ = charge number of anion
• e = elementary charge, 1.6022{{e|−19}} C
• ε₀ = permittivity of free space
• :4{{pi}}ε₀ = 1.112{{e|−10}} C²/(J·m)
• r₀ = distance to closest ion
• ρ = a constant dependent on the compressibility of the crystal; 30 pm works well for all alkali metal halides