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1. Question 1:
   1. The Unit Cell:
      chosen by the crystallographer.
      Actually, the crystallographer can choose an unit cell in an infinite number of ways. Off all possibilities, mostly the unit cell chosen contains the smallest number of lattice points. But also centered cells can be chosen when the centered cell displays the symmetry of the lattice better. In any case, an unit cell (3D) is characterised by three vectors (a, b and c) and the edges between the vectors are symbolised by a, b, g.

   2. The Crystal Lattice:
      due to the packing of atoms/molecules in a crystal.
      The Crystal Lattice is an infinite set of points that are equally spaced (each point has the same enviroment in the same orientation.) The points are a refelection of the repititive units in the structure. The origin of the lattice however is chosen by the crystallographer. When translation symmetry (the points, the lattice) is combined with rotation symmetry, seven possible crystal systems result: triclinic, monoclinic, orthorombic, tetragonal, trigonal, hexagonal and cubic.

   3. The Origin in Reciprocal Space:
      neither.
      The origin in reciprocal space is determined by the direction of the indicent X-ray beam. (The large spot in the pattern of single crystal diffraction.)

   4. The Origin in the Crystal:
      chosen by the crystallographer.
      Usually the origin is chosen so that the contents of the unit cell are easy to describe and frequently, this is a point of high symmetry within the unit cell. Furthermore, in polar space groups the origin cannot be uniquely fixed in space by symmetry elements of the space group.

   5. The Space-Group Symmetry of the Crystal:
      due to the packing of atoms/molecules in a crystal.
      It is the symmetry of the molecules and the way they are packed that determines the space group symmetry. Furthermore, some space groups occur more frequently than others. This is due to the fact that certain symmetry elements are preferred for molecular packing. As is illustrated by successively replacing a twofold rotation axis by a two-one axis in P 222:

      Symbol	No.	Frequency
      P222	16	18
      P2221	17	39
      P21212	18	847
      P212121	19	16256

   
   5 Marks

2. Question 2: The term Laue Class:

   In a diffraction experiment, the intensity of reciprocal lattice points is measured. Friedel's law states that the intensity of X-ray reflection from the planes (hkl) is the same as that from (-h-k-l) (In absence of anomalous dispersion effects). So the point group symmetry of the reciprocal lattice is centrosymmetric. There are eleven centrosymmetric point groups and these are known as the Laue Classes.

   Crystal System	Laue Classes
   Triclinic	-1
   Monoclinic	2/m
   Orthorhombic	mmm
   Tetragonal	4/m	4/mmm
   Trigonal	-3	-3m
   Hexagonal	6/m	6/mmm
   Cubic	m-3	m-3m

   In single crystal diffraction, it is possible to measure the intensity of the individual reflections, I(hkl). The point symmetry of the origin in reciprocal space is related to the symmetry of the diffracting crystal, thus in determining the crystal symmetry, the determination of its point group symmetry (one of the Laue Classes) is the first step. In powder diffraction generates only 1-dimensional data and therefore it is impossible to determine the laue class directly.
   two examples: 2/m (monoclinic) and 6/mmm (hexagonal)
   5 Marks

3. Question 3:

   An enantiomorphic molecule cannot posses improper rotations. Improper rotations are -1, m, -3, -4, -6. For example: When having an enantiomorphic molecule, like D-glucose, its mirror image will not be identical. In this case, the mirror image is L-glucose. So, symmetry operations that cannot be found in the crystal structure of an enantiomorphic molecule are rotary inversions and mirror/glide planes because they will change the handedness of the molecule (i.e. right handed versus left handed). Thus space groups possessing these operations cannot be enantiomorphic The change in handedness is indicated by placing a comma (,) in the open circle in the space group diagram.
   5 Marks

4. Question 4:

   symmetry element	symmetry operation	coordinates for Co	coordinate for Co within the unit cell (via translations)
   1	x,y,z	0.271,0.250,0.458	0.271,0.250,0.458
   i	-x,-y,-z	-0.271,-0.250,-0.458	0.729,0.750,0.542
   21	-x,1/2+y,1/2-z	-0.271,0.750,0.042	0.729,0.750,0.042
   c	x,1/2-y,1/2+z	0.271,0.250,0.958	0.271,0..250,0.958

   Co is not sited on a special position. Co would have been sited on a special position if it was located on one of the point group symmetry elements of the space group. In that case, the symmetry operators of the space group wouldn't generate 4 symmetry equivalent Co-atoms within the unit cell but less than 4.


Comment: A lovely clear table
5 Marks
5. Question 5:

   The symmetry elements present in 1,2-dichloroethane are: m, i and 2 (a mirror plane passing through the two C-atoms and the two Cl-atoms, an inversion point in the centre of the bound between the two C-atoms and a twofold axis perpendicular to the mirror plane and passing through the inversion point.)
   Via the diagram for point group determination I arrive at the crystallographic point group 2/m.
   5 Marks

6. Question 6:
   1. The symmetry elements present in the diagram are:
      mirror planes, twofold rotation axes and glide planes
      Minor comment: You should have specified the type of glide plane here. However, since you have specified it in the table below, no marks have been deducted.
      3 Marks
   2. 
      

      symmetry element	position
      1	object in red
      2	K
      m	Z
      a	J

      
      3 Marks
   3. 
      

      position	handedness	reason
      object in red	original
      K	original	a twofold rotation doesn't change handedness
      Z	changed	the used symmetry operator is a mirror plane This is an improper rotation (-2)
      J	changed	The used symmetry operator is a glide plane consisting of a reflection through a mirror plane (= improper rotation) followed by a translation

      
      2 Marks
   4. The crystal class is derived from the point group formed by the symmetry operators of the space group with the translational components set to zero. Working in the same manner as in the course, this gives for the crystal class mm2.
      

      Space group	Symmetry operators	Symmetry elements	Symmetry operators	Symmetry elements	Crystal class
      Pma2	x,y,z	1	x,y,z	1	mm2
      	-x,-y,z	2	-x,-y,z	2
      	1/2-x,y,z	m	-x,y,z	m
      	1/2+x,-y,z	a	x,-y,z	m

      Comment: Lovely answer (which is correct for the crystal class), but strictly speaking you were asked for the crystal system, and not crystal class.
      1 Mark

      Minor point re HTML above. The ALIGN=LEFT qualifier in the TABLE tag is in the wrong place: it can be used to qualify the TR, TH, or TD tags. LEFT is the default except for TH which uses CENTER as the default.