Lattice Energy Calculator Formula

Understand the math behind the lattice energy calculator. Each variable explained with a worked example.

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Formulas Used

Lattice Energy (U)

lattice_energy = -(madelung * 1389.4 * z_cation * z_anion / (distance_pm / 100)) * (1 - 1 / born_exp)

Variables

VariableDescriptionDefault
z_cationCation Charge (z⁺)1
z_anionAnion Charge (z⁻)1
distance_pmInterionic Distance (r₀)(pm)281
madelungMadelung Constant (A)1.748
born_expBorn Exponent (n)8

How It Works

Born-Landé Equation for Lattice Energy

Formula

U = −(A × N_A × e² × z⁺ × z⁻) / (4πε₀ × r₀) × (1 − 1/n)

Simplified with constants combined: U = −(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 − 1/n)

Where r₀ is in angstroms (pm/100), and 1389.4 kJ·Å/mol combines N_A, e², and 4πε₀.

Where:

  • A = Madelung constant (depends on crystal structure)
  • z⁺, z⁻ = ion charges
  • r₀ = interionic distance
  • n = Born exponent (5-12 depending on electron configuration)

    • Worked Example

    NaCl: z⁺ = 1, z⁻ = 1, r₀ = 281 pm, A = 1.748, n = 8.

    z_cation = 1z_anion = 1distance_pm = 281madelung = 1.748born_exp = 8
    1. 01U = -(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 - 1/n)
    2. 02r₀ = 281 pm = 2.81 Å
    3. 03U = -(1.748 × 1389.4 × 1 × 1 / 2.81) × (1 - 1/8)
    4. 04U = -(864.2) × (0.875)
    5. 05U = -756 kJ/mol

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