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



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 of these is not a lattice type ?

    a H
    b F
    c I
    d C

  2. What is a lattice ?

    a A transforming matrix
    b A set of atoms
    c A group of symmetry elements
    d An infinite array of identical points repeated throughout space

  3. How many Bravais lattices (3D) are there ?

    a 36
    b 28
    c 14
    d 16

  4. How many point groups (3D) are there ?

    a 24
    b 32
    c 12
    d 19

  5. What is a unit cell ?

    a A unit of volume
    b Any parallelepiped with lattice points at its corners
    c A parallelepiped containing only one lattice point
    d The angle between lattice vectors

Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

  1. Construct a plan view of NaCl (sodium chloride).
    NaCl has a face-centred cubic lattice. The motif is:
    Cl @ (0,0,0);
    Na @ (0,0,1/2);
    Note 1: The motif coordinates are positions relative to each lattice point
    Note 2: In a face centred cubic structure the lattice points are located at:
    (0,0,0), (1/2,1/2,0), (1/2,0,1/2), (0,1/2,1/2)

  2. Diamond has a face centred cubic lattice. Its motif is
    C @ (0,0,0), (1/4,1/4,1/4)
    Construct a plan view of the diamond unit cell.
    Treating the carbon atoms as hard spheres calculate the packing efficiency of diamond.
    Note: In a face centred cubic structure the lattice points are located at:
    (0,0,0), (1/2,1/2,0), (1/2,0,1/2), (0,1/2,1/2)