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]

E =- \frac{N_AMz^+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, 1.6022×10⁻¹⁹ C
ε₀ = permittivity of free space
4 $π$ ε₀ = 1.112×10⁻¹⁰ C²/(J·m)
r₀ = distance to closest ion
ρ = a constant dependant on the compressibility of the crystal; 30 pm works well for all alkali metal halides

See also

References

↑ "Lattice Energy" (PDF).

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