Assignment 4

Question 1.

a. The unit cell is the smallest repeating unit within the crystal lattice and is selected by the crystallographer

b. The crystal lattice is an array of unit cells in the same orientation and is due to the packing of the atoms/molecules in a crystal.

c. The origin in reciprocal space is selected by the crystallographer and is used to construct the reciprocal lattice.

d. The origin of the crystal is also selected by the crystallographer and is the point from which the unit cell can be calculated.

e. Space group symmetry is neither due to packing or the crystallographer, it is a combination of symmetry elements such as screw and/or rotation axes and the translational symmetry of the lattice.

Question 2.

Laue class is the symmetry of the reciprocal lattice or diffraction pattern.

A lattice with orthorhombic symmetry will have a laue class of 'mmm' which indicates the presence of 3 mirror planes.

A lattice with triclinic symmetry will have a laue class of -1 which shows only inversion symmetry.

Question 3.

An anantiomorphic molecule is triclinic with space group P1. Rotations (other than 1), rotary inversions, screw-rotations and mirror/glide planes do not exist due to such low symmetry. The only symmetry operations which do occur are lattice translations along the unit cell directions a, b and c.

Question 4.

Space group P2₁/c has four equivalent positions with co-ordinates xyz, -x-y-z, x1/2+y1/2-z, and x1/2-y1/2+z.

Including the central atom, x,y,z at 0.271,0.250,0.458, three other atoms exist within the unit cell at:-

i. -x-y-z = (-0.271),-(0.250),-(0.458) = -0.271,-0.250,-0.458

ii. x,1/2+y,1/2-z = 0.271,(0.5+0.250),(0.5-0.458) = 0.271,0.750,0.042

iii. x,1/2-y,1/2+z = 0.271,(0.5-0.250),(0.5+0.458) = 0.271,0.250,0.958

The central atom situated at 0.271,0.250,0.458 is not in a special position as it is not situated on a non-translational symmetry element.

Question 5.

A two fold rotation exists midway between the 2 carbon atoms perpendicular to the plane of the paper in view A..

The carbon and chlorine atoms all lie in a mirror plane.

The appropriate point group for this structure would be 2/m.

Question 6.

i. In the diagram supplied there are two-fold rotational axes parallel to the c-direction, mirror planes parallel to the c-direction and glide planes parallel to the a-direction. The glide is also parallel to the a-direction.

ii. & iii. See table below

iv. A primitive unit cell with two fold rotation, mirror and glide plane would have a space group of P2₁/c and hence would have a monoclinic crystal system.