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)

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

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).

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

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.

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

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)

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

iv) The crystal class could be 2 m since it has twofold rotation and mirror plane and as such is belong to the monoclinic.