1. What is Cubic Lattice Spacing?

The interplanar spacing (d-spacing) is the distance between adjacent parallel planes of atoms in a crystal lattice. For cubic crystals, it can be calculated from the lattice constant and Miller indices of the crystallographic plane.

2. How Does the Calculator Work?

The calculator uses the cubic lattice spacing formula:

Where:

• \( d \) — Interplanar spacing (Å)
• \( a \) — Lattice constant (Å)
• \( h, k, l \) — Miller indices of the plane (dimensionless integers)

Explanation: The formula accounts for the geometric relationship between the crystal planes and the unit cell dimensions in cubic crystals.

3. Importance of Lattice Spacing

Details: Lattice spacing is crucial for X-ray diffraction analysis, determining crystal structures, and understanding material properties at the atomic level.

4. Using the Calculator

Tips: Enter the lattice constant in Ångströms (Å) and Miller indices as integers. The lattice constant must be positive, and all Miller indices cannot be zero simultaneously.

5. Frequently Asked Questions (FAQ)

Q1: What are Miller indices?
A: Miller indices are a notation system in crystallography for planes in crystal lattices, represented by three integers (hkl).

Q2: Does this formula work for all crystal systems?
A: No, this simplified formula only works for cubic crystals. Other crystal systems require more complex formulas.

Q3: What are typical values for lattice constants?
A: For common cubic crystals: NaCl (~5.64 Å), Diamond (~3.57 Å), Copper (~3.61 Å), Iron (~2.87 Å).

Q4: Why can't all Miller indices be zero?
A: The (000) plane is undefined as it would represent an infinite plane spacing (division by zero in the formula).

Q5: How is this related to X-ray diffraction?
A: The d-spacing relates to diffraction angles through Bragg's Law: nλ = 2d sinθ.