1. What are Miller-Bravais Indices?

Miller-Bravais indices (hkil) are a 4-index notation system used to describe crystallographic planes in hexagonal crystal systems. The fourth index (i) is derived from the first two indices (h and k) through the relationship i = -h - k.

2. How Does the Calculator Work?

The calculator uses the Miller-Bravais equation:

Where:

• \( h \) — First Miller index
• \( k \) — Second Miller index
• \( i \) — Third Miller-Bravais index (calculated)
• \( l \) — Fourth Miller index (same as in 3-index system)

Explanation: The four-index system provides symmetry in the notation that matches the hexagonal crystal symmetry.

3. Importance of Miller-Bravais Indices

Details: The 4-index system is essential for properly describing crystallographic planes in hexagonal systems because it maintains the symmetry of the hexagonal lattice in the notation.

4. Using the Calculator

Tips: Enter the h, k, and l indices as integers. The calculator will automatically compute the i index and display the complete 4-index notation.

5. Frequently Asked Questions (FAQ)

Q1: Why use 4 indices instead of 3 for hexagonal systems?
A: The 4-index system maintains the symmetry of the hexagonal lattice in the notation, making equivalent planes easier to identify.

Q2: What's the relationship between Miller and Miller-Bravais indices?
A: The first three Miller indices (hkl) correspond to (hkil) where i = -h - k. The l index remains the same in both systems.

Q3: When should I use Miller-Bravais indices?
A: Always for hexagonal crystal systems. For cubic, tetragonal, and orthorhombic systems, the standard 3-index Miller notation is sufficient.

Q4: Can negative indices be used?
A: Yes, negative indices are common and are typically written with a bar over the number in crystallographic notation.

Q5: How do I visualize these planes?
A: Crystal visualization software can display planes using these indices, or you can plot them using the intercept method on hexagonal graph paper.