The Born–Mayer equation is an equation that is used to calculate the

lattice energy In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ...

of a crystalline

ionic compound In chemistry, an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. The compound is neutral overall, but consists of positively charged ions called cations and negatively charged i ...

. It is a refinement of the

Born–Landé equation The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice an ...

by using an improved repulsion term. :

E =- \frac\left(1-\frac\right)

where: *''N''_A =

Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...

; *''M'' =

Madelung constant The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges. It is named after Erwin Madelung, a German physicist. Because the anions and cations in an ionic soli ...

, relating to the geometry of the crystal; *''z''⁺ = charge number of cation *''z''⁻ = charge number of anion *''e'' =

elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...

, 1.6022 C *''ε''₀ =

permittivity of free space Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...

*:4''ε''₀ = 1.112 C²/(J·m) *''r''₀ = distance to closest ion *''ρ'' = a constant dependent on the compressibility of the crystal; 30 pm works well for all alkali metal halides

References

{{DEFAULTSORT:Born-Mayer Equation Solid-state chemistry Ions

See also

References