Born–Mayer equation explained

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.^[1]

E =- (N ^{+ z} _{AMz} ^{-} e ^{2})/(\left( 1- 4 \pi \epsilon _{0} r _{0}) (\rho)/(r _{0}) \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 C
• ε₀ = permittivity of free space

4ε₀ = 1.112 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

See also

• Born–Landé equation
• Kapustinskii equation

Notes and References

1. Web site: Lattice Energy.