How this calculator works
These ideal ionic-solid models estimate the positive energy required to separate a crystal into gaseous ions. Formation energies carry the opposite sign. Use effective ionic radii compatible with coordination number, or enter a measured nearest-neighbour separation. Six-coordinate presets are starting estimates and need custom values for other coordination environments. Born models require a structure-dependent Madelung constant; other structures can use a custom constant. Kapustinskii also needs the number of ions per formula unit. Inverse distance calculations use the larger-distance root when a repulsion correction produces two mathematical roots.
Formula
Electrostatic magnitude U0 = NA M |z+ z-| e^2/(4 pi epsilon0 r). Born-Lande U = U0(1 - 1/n); Born-Mayer U = U0(1 - rho/r). Kapustinskii U = 120200 nu |z+ z-| (1 - 34.5/r)/r kJ/mol with r in pm.
Worked example
For unit charges, two ions per formula unit and a 300 pm separation, Kapustinskii gives 120200 x 2/300 x (1 - 34.5/300) = 709.18 kJ/mol. At 200 pm, charge product 2 and three ions give 2983.965 kJ/mol.
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Frequently asked questions
Why do the methods disagree?
Their repulsion and structural approximations differ; none replaces measured thermochemical data for a real material.
Which sign is shown?
Positive lattice dissociation energy. Multiply by -1 for the ideal reverse formation process.
Can I solve an inverse parameter while comparing all models?
Choose a single approximation first; different models imply different inverse results.