1. What Are Miller Indices?

Miller indices (hkl) are a notation system in crystallography for planes in crystal lattices. They are defined as the reciprocals of the fractional intercepts that the plane makes with the crystallographic axes.

2. How Does the Calculator Work?

The calculator uses the Miller indices formula:

Where:

• \( h \) — reciprocal of a-axis intercept
• \( k \) — reciprocal of b-axis intercept
• \( l \) — reciprocal of c-axis intercept

Explanation: The intercepts are first converted to their reciprocals, then multiplied by the least common multiple to get integers, and finally reduced to the smallest integers by dividing by their greatest common divisor.

3. Importance of Miller Indices

Details: Miller indices are crucial for describing crystal planes and directions in materials science, mineralogy, and solid-state physics. They help predict cleavage planes, diffraction patterns, and other important crystal properties.

4. Using the Calculator

Tips: Enter the intercepts on the a, b, and c crystallographic axes. The calculator will return the Miller indices in the standard (hkl) notation. None of the intercepts can be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if my plane is parallel to an axis?
A: If a plane is parallel to an axis, its intercept is at infinity and the corresponding Miller index is zero.

Q2: What do negative Miller indices mean?
A: A negative index is written with a bar over the number and indicates the plane intercepts the negative side of that axis.

Q3: How are Miller indices used in XRD?
A: In X-ray diffraction, Miller indices help index diffraction peaks to specific crystal planes.

Q4: What's the difference between (100) and [100]?
A: (100) denotes a plane, while [100] denotes a direction in the crystal lattice.

Q5: Can Miller indices be fractions?
A: No, Miller indices are always reduced to the smallest set of integers that maintain the same ratio.