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.

$E=-\frac{N_{A}M{z}^{+}{z}^{-}{e}^2}{4\pi {ϵ}_0{r}_0}(1-\frac{\rho }{r_0})$

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, 1.6022Template:E C
• ε₀ = permittivity of free space

  4Template:Piε₀ = 1.112Template:E 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