Which of the following sets of Miller indices corresponds to a plane that intersects the x-axis at 1, the y-axis at infinity, and the z-axis at 1 in a cubic unit cell?

• A. (111)
• B. (011)
• C. (101)
• D. (110)

Answer: (C)

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 axes: x-intercept = 1, y-intercept = infinity (meaning the plane is parallel to the y-axis), and z-intercept = 1.
3. Write the intercepts as fractions: x = 1, y = \infty, z = 1. The reciprocals are therefore: 1/1 = 1 for x, 1/\infty = 0 for y, and 1/1 = 1 for z.
4. Combine these reciprocals into the Miller indices (hkl) = (1, 0, 1). This means the plane cuts the x and z axes at 1 and is parallel to the y-axis.
5. Compare the calculated Miller indices with the given options to confirm that (101) matches the plane described.