Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Lattice Planes and Miller Indices Questions
Lattice Planes and Miller Indices AimsBefore you startIntroductionHow to index a lattice planeParallel lattice planesHow to draw a lattice planeBracket ConventionsVectors and PlanesExamples of lattice planesDraw your own lattice planesPractical UsesWorked examplesSummaryQuestionsGoing further
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Questions

Game: Identify the planes

Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

  1. Which one of the following statements about the (241) and (241) planes is false?

    a They are perpendicular.
    b They are part of the same set of planes.
    c They are part of the same family of planes.
    d They are parallel.

  2. Does the [122] direction lie in the (301) plane?

    a Yes
    b No

  3. When writing the index for a set of symmetrically related planes, which type of brackets should be used?

    a (Round)
    b {Curly}
    c <Triangular>
    d [Square]

  4. Which of the <110> type directions lie in the (112) plane?

    a [110] and [110]
    b [101] and [101]
    c [011] and [101]
    d [110] and [110]

  5. What is the common direction between the (132) and (133) planes?

    a [310]
    b [310]
    c [410]
    d [410]

  6. Which set of planes in a cubic-close-packed structure (such as copper) is close packed?

    a {110}
    b {100}
    c {111}
    d {222}

Open-ended questions

The following questions are not provided with answers, but intended to provide food for thought and points for further discussion with other students and teachers.

  1. Practice sketching some lattice planes. Make sure you can draw the {100}, {110} and {111} type planes in a cubic system.

  2. Draw the trace of all the (121) planes intersecting a block 2 × 2 × 2 block of orthorhombic (a ≠ b ≠ c, α = β = γ = 90°) unit cells.

  3. Sketch the arrangement of the lattice points on a {111} type plane in a face centred cubic lattice. Do the same for a {110} type plane in a body centred cubic lattice. Compare your drawings. Why do you think the {110} type planes are often described as the "most close packed" planes in bcc?

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