Born Exponent Formula:
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Definition: The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
Purpose: It characterizes the repulsive potential between ions in a crystal lattice according to Born's model of ionic solids.
The calculator uses the formula:
Where:
Explanation: The formula calculates the exponent that describes how rapidly the repulsive force between ions decreases with distance.
Details: The Born exponent is crucial in solid-state physics for calculating lattice energies, elastic properties, and compressibility of ionic crystals.
Tips: Enter the repulsive interaction constant (B), repulsive interaction energy (ER), and distance of closest approach (r0). All values must be > 0.
Q1: What is the typical range for Born exponent?
A: The Born exponent typically ranges between 5 and 12 for most ionic solids.
Q2: How is the repulsive interaction constant determined?
A: It's usually determined experimentally from compressibility measurements or calculated from quantum mechanical principles.
Q3: What affects the distance of closest approach?
A: It depends on the ionic radii of the atoms involved and the crystal structure.
Q4: Why use logarithms in this formula?
A: The logarithms convert the multiplicative relationship into an additive one, making it easier to solve for the exponent.
Q5: Can this calculator be used for covalent bonds?
A: No, this model is specifically for ionic solids. Covalent bonds require different treatment.