Madelung Constant Formula:
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Definition: The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.
Purpose: It helps in calculating lattice energies of ionic crystals and understanding their stability and properties.
The calculator uses the Born-Mayer equation:
Where:
Details: The Madelung constant is crucial for understanding ionic crystal structures, calculating lattice energies, and predicting material properties like melting points and hardness.
Tips: Enter the lattice energy in J/mol, distance of closest approach in meters (default 6.0×10⁻⁹ m), cation and anion charges in elementary charge units (default 1), and compressibility constant in meters (default 6.044×10⁻⁹ m).
Q1: What's a typical value for the Madelung constant?
A: For NaCl structure it's about 1.748, for CsCl structure about 1.763, and for zincblende structure about 1.638.
Q2: Why is the distance of closest approach important?
A: It represents the equilibrium distance between cation and anion in the crystal lattice, affecting the electrostatic potential.
Q3: What is the compressibility constant (ρ)?
A: It accounts for the repulsive forces between electron clouds at short distances, typically around 30 pm for alkali metal halides.
Q4: How do I find the lattice energy?
A: Lattice energy can be calculated using Born-Haber cycles or measured experimentally via calorimetry.
Q5: Can this calculator be used for all ionic crystals?
A: Yes, but the compressibility constant may need adjustment for different crystal types.