Question

predict the cubic crystal structure for CsCl when Cs is 0.170nm and Cl is 0.181nm. I think it is .170/.181 and that is <1 so it is FCC. but there is something I am missing because it was not right.

Answer 1

We first assume its BCC type and check the atomic packing fraction

In BCC type all Cs occupies at corners of cube while Cl is present inside

so overall we have 1Cs and 1Cl per 1 cube

volume of Cs = ( 4/3) pi x r^3 = ( 4/3) ( 3.14) ( 0.17 nm)^3 = 0.02057 nm^3

volume of Cl = ( 4/3) ( 3.14) ( 0.181nm)^3   = 0.024826 nm3

total volume of atoms inside cube = 0.02057+0.024826 = 0.0454 nm3

now we find unit cell i.e cube volume , in BCC atoms join along body diagonal

we have relation body dioagonal of cube ( whihc is 1.732a) = (2 x radius of two atoms)

1.732a = ( 2Cs atomic radius + 2Cl- atomic radius) = 2 ( 0.17+0.181)

a = 0.4053 nm isour cell edge length

cell volume = a^3 = 0.4053^3 = 0.06658 nm3

now atomic packing fraction = volume of atoms in cube / cube volume

         = 0.0454 nm3 / (0.06658 nm3) = 0.68

atomic packing fraction of 0.68 atches with BCC since BCC has atomic pakcing fraction of 0.68

Hence CsCl is BCC type structure where Cs occupies all edges of cube while Cl is center of cube.

( FCC has packing fraction of 0.74 , since we got 0.68 our CsCl is not FCC)