Which of the following best describes the Miller indices for a plane that intercepts the x-axis at 1, the y-axis at infinity, and the z-axis at infinity in a cubic unit cell?

• A. (0\,0\,1)
• B. (1\,0\,0)
• C. (0\,1\,0)
• D. (1\,1\,0)

Answer: (B)

Verified step by step guidance

1. Recall that Miller indices (hkl) are determined by taking the reciprocals of the intercepts of a plane with the crystallographic axes, then clearing fractions to get the smallest set of integers.
2. Identify the intercepts of the plane with the x, y, and z axes. Here, the plane intercepts the x-axis at 1, and the y- and z-axes at infinity (meaning it never intersects those axes).
3. Write the intercepts as (1, \infty, \infty).
4. Take the reciprocals of these intercepts: 1/1 = 1, 1/\infty = 0, and 1/\infty = 0, giving (1, 0, 0).
5. Express the Miller indices as integers without fractions, so the Miller indices for this plane are (1\,0\,0).