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Born–Landé equation : ウィキペディア英語版
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 and a repulsive potential energy term.
:E =- \frac\left(1-\frac\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 C
*''ε''0 = permittivity of free space
*:4π''ε''0 = 1.112 C2/(J·m)
*''r''0 = distance to closest ion
*''n'' = Born exponent, typically a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
==Derivation==
The ionic lattice is modeled as an assembly of hard elastic spheres which are compressed together by the mutual attraction of the electrostatic charges on the ions. They achieve the observed equilibrium distance apart due to a balancing short range repulsion.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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