Lattice Energy Calculator
Combine Madelung constant, ionic charges, separation distance, and repulsion exponent to approximate crystal lattice energy.
NaCl structure uses A about 1.748. CsCl uses 1.763.
Use the shortest cation anion separation in nanometers.
Typical values: 7 to 12 depending on ion size and structure.
Use 1 for vacuum. Higher values reduce lattice energy magnitude.
Lattice energy
765.51 kJ/mol
Negative values indicate exothermic lattice formation.
How to Use This Calculator
Find structural constants
Look up the Madelung constant and Born exponent for the crystal structure of interest.
Gather ionic data
Use ionic charges based on oxidation states and the cation anion nearest neighbor distance.
Select dielectric correction
For ionic solids in vacuum use 1. For embedded ions or dielectric media use the appropriate relative permittivity.
Compute lattice energy
The calculator reports the Born-Lande estimate in kJ per mol of solid formed.
Formula
U = - (NA M z+ z- e2) / (4 pi epsilon0 epsilonr r0) (1 - 1/n)
NA Avogadro constant, M Madelung constant, z charge numbers, e elementary charge, epsilonr relative permittivity, r0 nearest neighbor distance, n Born exponent.
Example
For NaCl with A = 1.748, z+ = 1, z- = -1, r0 = 0.282 nm, n = 9: U is about -786 kJ/mol, matching literature values for sodium chloride.
Full Description
Lattice energy reflects the cohesive energy released when gaseous ions assemble into a crystal. Born-Lande theory balances long range Coulomb attraction with short range repulsion.
The result guides comparisons of ionic compounds, helps build Born-Haber cycles, and indicates how structure or ion charge impacts stability.
Frequently Asked Questions
Why is the result negative?
Negative lattice energy signifies that energy is released when the crystal forms from separated ions.
How accurate is the Born-Lande equation?
It provides good estimates for simple ionic solids. Polarization, covalency, and defects can shift experimental values.
What if I know U and need r0?
Rearrange the equation to solve for distance or use numerical methods. This calculator focuses on forward predictions.
Can I simulate solids with multiple charges?
Use the effective charges for the specific ions. Mixed valence systems may require averaging or separate calculations.
Does dielectric constant matter?
Most lattice energy references assume vacuum (epsilonr = 1). For ions embedded in media, scaling by epsilonr accounts for screening.