1. What is Interplanar Spacing?

Interplanar spacing (d) is the distance between adjacent and parallel planes of atoms in a crystal lattice. It is a fundamental parameter in crystallography that helps characterize the structure of crystalline materials.

2. How Does the Calculator Work?

The calculator uses the interplanar spacing formula for cubic crystals:

Where:

• \( d \) — Interplanar spacing (m)
• \( a \) — Edge length of the unit cell (m)
• \( h \) — Miller index along x-axis
• \( k \) — Miller index along y-axis
• \( l \) — Miller index along z-axis

Explanation: This formula calculates the perpendicular distance between parallel crystal planes in a cubic lattice system using Miller indices and the unit cell edge length.

3. Importance of Interplanar Spacing

Details: Interplanar spacing is crucial in X-ray diffraction studies, material characterization, and understanding crystal properties. It helps determine atomic arrangements and identify crystalline phases.

4. Using the Calculator

Tips: Enter the edge length of the cubic unit cell in meters and the Miller indices (h, k, l) for the crystal plane. All values must be valid (edge length > 0).

5. Frequently Asked Questions (FAQ)

Q1: What are Miller indices?
A: Miller indices are a notation system in crystallography that represent the orientation of crystal planes using three integers (h, k, l).

Q2: Why is this formula specific to cubic crystals?
A: The simplified formula d = a/√(h²+k²+l²) applies only to cubic crystal systems where all axes are perpendicular and of equal length.

Q3: What happens if all Miller indices are zero?
A: The denominator becomes zero, making the result undefined. Miller indices (0,0,0) do not represent a valid crystal plane.

Q4: How is interplanar spacing measured experimentally?
A: Interplanar spacing is typically measured using X-ray diffraction techniques, where it can be calculated from diffraction angles using Bragg's law.

Q5: Can this calculator be used for non-cubic crystals?
A: No, this calculator is specifically designed for cubic crystal systems. Other crystal systems require more complex formulas.