Question

In: Chemistry

consider space group Fdd2 1) What is point symmetry of an atom located at (0,0,Z) 2)...

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?

Solutions

Expert Solution

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.

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