Miller index

High school (ages 12+)
Science & Technology

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/miller-index

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the originator?William Hallowes Miller, introduced in 1839
2. What is the mathematical basis?Reciprocals of intercepts with crystallographic axes, reduced to smallest integers
3. What are Miller indices and why do they matter for crystals?They are a simple set of numbers that label flat surfaces inside a crystal. They let scientists talk about crystal shapes and how atoms are arranged.
4. How do you find the Miller indices for a crystal plane?Look where the plane meets the crystal axes, take the reciprocals of those distances, and turn any fractions into whole numbers. If a line goes the other way, write a bar over the number.

Crystallographic Axes: Reference directions defined by the repeating unit cell of a crystal's internal structure.
Reciprocal Lattice: A mathematical space where points correspond to the orientations and spacings of planes in the real crystal lattice.
Bragg's Law: The fundamental equation relating X-ray wavelength, crystal lattice spacing, and diffraction angle.
Unit Cell: The smallest repeating structural unit of a crystal lattice.