English
Menu

Crystal structures and Miller indices

In a cubic crystal, a plane intercepts the x axis at 1a and the y axis at 2a, and is parallel to the z axis. What are its Miller indices?

  1. A(120)
  2. B(102)
  3. C(210)
Show answer and explanation

Answer: C. (210)

Miller indices are found by expressing the intercepts on each axis in units of the lattice parameter, taking their reciprocals and reducing to the smallest integer ratio. The intercepts are 1, 2 and ∞, so the reciprocals are 1, 1/2 and 0; multiplying by 2 gives (210). (120) is the mistake of listing the intercepts 1 and 2 without taking reciprocals. A plane parallel to the z axis has an infinite z intercept, so l = 0 always, and (102), whose third index is not zero, is also wrong. If the plane passes through the origin, move the origin to a neighboring lattice point before reading the intercepts.

Report an error

Practice this topic Back to topic

Related calculators

XRD Calculator (Bragg's Law and Extinction Rules)Calculate cubic interplanar spacings, 2θ angles and the peaks allowed by extinction rules

More Crystal structures and Miller indices questions

  1. Which correctly pairs the close-packed planes and close-packed directions of an FCC metal?
  2. Which value is closest to the interplanar spacing of the (111) planes of aluminum (FCC, lattice parameter 0.405 nm)?
  3. Which statement about the ideal hexagonal close-packed (HCP) structure is correct?
  4. In a cubic crystal, which value is closest to the angle between the [100] and [111] directions?
  5. At 912 °C, pure iron transforms from BCC α-iron (lattice parameter 0.2904 nm) to FCC γ-iron (lattice parameter 0.3647 nm). Which correctly describes the change in volume per atom? Both lattice parameters are values at 912 °C.