Assignment 4

Question 1.

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

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.
1 Mark

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

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

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.
0 Marks
See model answer for two incorrect parts

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.
2 Marks

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.
Comment: Wrong. See model answer and URL: /pd01/symm2/enantio1.htm
0 Marks

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
Comment: This is outside the unit cell.

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.
Minor comment: The triple negative makes reading tricky!
2 Marks

Also please avoid the use of the underline tag (U) as the underlining doesn't print well (it is better to use italics or bold for emphasis).

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.
Comment: Correct, but you didn't mention the inversion centre.
4 Marks

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.
Comment: You should specify normals for plane directions and not parallels (not required here, but you could be penalised if it was required).
3 Marks

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.
Comment: see model answer.
0 Marks