Assignment 4

Rob Whittock

  1. (a). The unit cell is chosen by the crystallographer. It is usually chosen so that it contains the smallest number of lattice points and has cell angles as close to 90o, unless the cell angle is constrained by symmetry.

    2. 1 Mark

    (b). The crystal lattice - The atoms / molecules pack together in an ordered way forming a unit cell, which when repeated in three dimensions forms the crystal lattice.
    1 Mark

    (c). The origin in reciprocal space (where h = k = l = 0) is related to the symmetry of the diffracting crystal and is due to the packing of the atoms / molecules in the crystal.
    Comment: see model answer
    0 Marks

    (d). The origin in the crystal is an arbitrary point chosen by the crystallographer. It is often chosen at a point of high symmetry within the unit cell, i.e. it is often on an axis where two or more axes intersect.
    1 Mark

    (e). The space-group symmetry of the crystal is due to the ordered packing of the atoms / molecules in the crystal.
    1 Mark

  2. The term Laue Class describes 3D diffraction symmetry and consists of 11 centrosymmetric point groups. Low symmetry crystal systems (monoclinic, triclinic and orthorhombic) give rise to diffraction data, which has a single corresponding symmetry. The high symmetry crystal systems (tetragonal, trigonal, hexagonal and cubic) give rise to diffraction data, which has two possible corresponding symmetries.

    3. Comment: You need to give some point group examples of Laue classes in your answer
    3 + 0 Marks

  3. In the crystal structure of an enantiomorphic molecule all the molecules are either right or left handed molecules. For this reason the two symmetry operators (rotary-inversion and mirror / glide planes) cannot be present in a crystal structure of an enantiomorphic molecule, since their operation would generate the handed molecule which is not present in the crystal structure.

    4. Comment: Good clear answer, but a bit brief
    4 Marks

  4. I don't understand space group diagrams particularly the values of x, y and z after a symmetry operation has taken place.

    5. Comment: See model answer
    0 Marks

  5. Molecule point symmetry for 'View A but rotated 90o about Y is a four fold rotation. The 'view A but rotated 35o' ?????

    6. Comment: See model answer
    0 Marks

  6. (i). The three types of symmetry element present are

Overall comment: If you still don't understand space groups after seeing the model answers, then please send us questions via email on those points that you don't understand.