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 = − N A M z + z − e 2 4 π ϵ 0 r 0 ( 1 − ρ r 0 ) {\displaystyle E=-{\frac {N_{A}Mz^{+}z^{-}e^{2}}{4\pi \epsilon _{0}r_{0}}}\left(1-{\frac {\rho }{r_{0}}}\right)}

where:

  • NA = 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
    4πε0 = 1.112×10−10 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

See also

References

  1. ^ "Lattice Energy" (PDF).