1. What Are Miller Indices for Directions?

Miller indices for directions, denoted as [uvw], are a notation system in crystallography to describe directions in crystal lattices. They represent the vector components reduced to the smallest integers.

2. How Does the Calculator Work?

The calculator uses the following method:

Where:

• \( x, y, z \) — Direction vector coordinates
• \( gcd \) — Greatest common divisor of the coordinates

Explanation: The direction vector is reduced to its smallest integer components by dividing all coordinates by their greatest common divisor.

3. Importance of Direction Indices

Details: Miller indices for directions are crucial in crystallography for describing crystal orientations, slip systems, and anisotropic properties of materials.

4. Using the Calculator

Tips: Enter the x, y, and z coordinates of your direction vector. The calculator will reduce them to smallest integers and display the proper [uvw] notation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between (hkl) and [uvw]?
A: (hkl) represents crystallographic planes, while [uvw] represents directions in the crystal lattice.

Q2: How are negative indices represented?
A: Negative indices are represented with a bar over the number, e.g., [1̄01] for [-1,0,1].

Q3: What does [uvw] = [000] mean?
A: [000] is not a valid direction as it has zero length. All three components cannot be zero.

Q4: Are fractional indices allowed?
A: No, Miller indices must always be reduced to smallest integers. Fractions are not permitted in the final notation.

Q5: How are equivalent directions represented?
A: Equivalent directions in cubic crystals are denoted by angle brackets, e.g., <100> represents [100], [010], [001], etc.