Question

consider space group Fdd2

1) What is point symmetry of an atom located at (0,0,Z)

2) give d-glides coordinates of Fdd2

3) what is multiplicity at a general position on Fdd2

4) Give a possible maximal non-isomorphic subgroup of Fdd2 that would be considered a translationengleiche group. What is the crystal system of this subgroup?

Answer 1

consider space group Fdd2

1) What is point symmetry of an atom located at (0,0,Z)

--> mm2, because it is having two fold symmetry along x , then y and then Z

2) give d-glides coordinates of Fdd2

--> glide plane is having reflection and translational symmetry oepration.The d glide is also called as diamond glide. As the name conveys it is having only diamond lattice so it can be translated as diagonal along diagonal i,e by 1 and by 4 only. So the d-glide coordiantes of fdd2 are : a+/- 1/4, b+/- 1/4, , c+/- 1/4.

The d-glide plane at z = 1/8, in this direction is along positive coordinate of a and b.

at z=3/8, the cordinate of d-glide are a=1/4 and b=-1/4

3) what is multiplicity at a general position on Fdd2.?

--> 16 is the multiplicity at general position of Fdd2 because it is having face centered space group. The coordination number of 12 plus 4 symmetry operation per lattice point contributes to multiplicity of 16. Also Fdd2 has no inversion point but has improper symmetry operation

4) Give a possible maximal non-isomorphic subgroup of Fdd2 that would be considered a translationengleiche group. What is the crystal system of this subgroup?

• --> A subgroup H < G is maximal subgroup if no Z exists for which H < Z < G holds. A subgroup H of a space group G is called a translationengleiche subgroup. The maximum non-isomorphic subgroup iof fdd2 can be written as

I [2[C1(P1) , +1

IIA [2]P1c1(Pc) 1;2

IIA [2]P1n1(Pc) 1; (2 + (1/2, 1/2, 0)

• Fdd2 has orthorhombic crystal system.