Iron crystalizes in two bcc lattices, the alpha- from below 910^(@) and the gamma-form above 1400^(@)C, and in an fcc gamma-atom between these two temperatures. What is the symmetry of a face-centered void of a bcc unit cell?

Iron crystalizes in two bcc lattices, the alpha- from below 910^(@) an

1.	Iron crystalizes in two bcc lattices, the alpha- from below 910^(@) and the gamma-form above 1400^(@)C, and in an fcc gamma-atom between these two temperatures. What is the symmetry of a face-centered void of a bcc unit cell?
Answer» distored octahedral Linear Square planer Tetrahedral Solution : In bcc, the ATOM at the BODY center B is in contact with those at the corners, the corner atoms do not touch each other. The body diagonal `=sqrt(3)a=4r` thus, `a=((4)/sqrt(3))r` ....(i) From body center to body center (A-B)=a (figure above) ALSO, `a=2r_((Fe))+2r_(("void"))=(4r)/sqrt(3)` `thereforer_(Fe)+r_("void")=(2)/sqrt(3)r`. `THEREFORE (r_("void"))/(r_(Fe))=((2)/sqrt(3)-1)=0.155` The face diagonal are longer `(sqrt(2)a)` than the distance between body centers, so the geometry of the void is a shortened octagedron called distorted octahedron.