1. What is Miller Index along Z-axis?

Definition: The Miller Index along z-axis is a notation system in crystallography for planes in crystal (Bravais) lattices along the z-direction.

Purpose: It helps crystallographers and materials scientists describe the orientation of crystal planes.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Miller index along z-axis
• \( a \) — Weiss index along x-axis
• \( b \) — Weiss index along y-axis
• \( c \) — Weiss index along z-axis
• \( \text{lcm} \) — Least common multiple function

Explanation: The LCM of all Weiss indices is divided by the Weiss index along z-axis to get the Miller index along z-axis.

3. Importance of Miller Indices

Details: Miller indices are crucial for describing crystal planes, which affect material properties like cleavage, electronic properties, and surface reactivity.

4. Using the Calculator

Tips: Enter the Weiss indices along x, y, and z axes (must be positive integers). The calculator will compute the corresponding Miller index along z-axis.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Weiss and Miller indices?
A: Weiss indices are the reciprocals of intercepts with crystal axes, while Miller indices are the smallest integers having the same ratio.

Q2: Why do we use LCM in this calculation?
A: LCM helps find the smallest integers that maintain the same ratio as the Weiss indices.

Q3: Can Miller indices be negative?
A: Yes, negative indices are written with a bar over the number, but this calculator only returns positive values.

Q4: What's the physical meaning of the z-axis Miller index?
A: It describes how the crystal plane intersects the z-axis of the unit cell.

Q5: How are Miller indices used in materials science?
A: They're used to describe crystal planes for diffraction studies, surface analysis, and predicting material properties.