Lars-Erik Briggner, Assignment 4

1. a) The Unit Cell is chosen by the crystallographer (ii) in order to have the smallest number of lattice points and angels close to 90 °

b) The Crystal Lattice is determined by how the molecules or ions will pack (i)

c) The origin in the Reciprocal Space is determined by where the straight thrue X-ray beam will pass (iii)

d) The Origin in the Crystal is chosen to be convienient for having a unit cell with high symmetry (ii)

e) The Space-Group Symmetry of the Crystal describes how the molecules/ions are related symmetrically i.e. due to packing (i)
5 Marks

2. There are eleven centrosymmetrical point groups which descibes 3-D diffraction symmetry. Brings you information about the number of symmetry ekvivalent refections there are. E.g. -1 have symmetry operators (x,y,z) and (-x,-y,-z) i.e.multiplicity 2.  2/m have symmetry operators (x,y,z), (-x,y,-z), -x,-y,-z) and x,-y,z), i.e. multiplicity 4
Comment: Initial answer a bit brief
4 Marks

3. Of the 5 different groups of symetry operations only three can be found for an enantiomorphic molecule. The rotary inversion and the mirror/glide plane can not be found since they will alter the handedness of the molecules (giving the other enantiomorph).
Comment: Too brief
3 Marks

4. The coordinates for the central Co atom in an organometallic compound are 0.271,0.250,0.458 and the compound crystallises in space group P2₁/c. There are 4 two-one screw axes, glide planes and 8 points of inversion in this group. Anyone of this can be used to calulate the position of another Cowithin the unit cell (0<x,y,z<1). E.g. c-glide plane with operator (x,½-y,½+z) which gives the coordinates 0.271,1.250,0.958
Comment: I think you misunderstood what the question was about. See model answer.
0 Marks

The coordinates for the Co atom is not on a special position since it is not positioned on any point group symmetry element. Alternatively, can it be seen since all symmetry operators generate different symmetry ekvivalent positions.
2 Marks

5. The 1,2-dichloroethane seems to have three symmetry elements present: point of inversion in the C-C bond, twofold rotation axe perpendicular to the screen (view A) and a single mirror plane through the C and Cl atoms. The molecular point symmetry is then -1 2 m  i.e. 2/m
5 Marks

6. i) In the diagram there are twofold rotation axes (perpendicular to the screen), mirror planes (perpendicular to the screen, normal in the x direction) and glide plane (perpendicular to the screen, normal in the y direction)
Comment: You state type of glide plane (e.g. a)
2 Marks

ii-iii) B - lattice translation , same handedness (just "movement")

C - mirror and lattice transl, different handedness due to the mirror

F - two lattice translations, same handedness

G - twofold  rotation (0,½,z), same handedness (just "movement")

J - translation and glide plane, different handedness due to glide plane

K - twofold rotation (½,½,z), same handedness

Z - mirror, different handedness

c - lattice translation, same hanedness

d - twofold rotation (0,0,z), same handedness

g - glide plane, different handedness due to glide plane

h - twofold rotation (½,0,z), same handedness
Comment: Excellent, but the question said "within" (and italicised for emphasis too).
4 Marks

iv) The crystal class could be 2 m since it has twofold rotation and mirror plane and as such is belong to the monoclinic.
Comment: Wrong - see model answer
0 Marks