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.^[1]

${\displaystyle E=-{\frac {N_{A}Mz^{+}z^{-}e^{2}}{4\pi \epsilon _{0}r_{0}}}\left(1-{\frac {\rho }{r_{0}}}\right)}${\displaystyle E=-{\frac {N_{A}Mz^{+}z^{-}e^{2}}{4\pi \epsilon _{0}r_{0}}}\left(1-{\frac {\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×ばつ10⁻¹⁹ C
• ε₀ = permittivity of free space

  4πε₀ = 1.112×ばつ10⁻¹⁰ 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

• Born–Landé equation
• Kapustinskii equation

• Eponymous equations of physics
• Solid-state chemistry
• Ions