Question

Consider a cubic I crystal with a lattice parameter of 3 Å, and a single atom at each lattice point.  Calculate the structure factor (F) and its square magnitude |?|² for the primitive and conventional unit cells. Indicate for each the constraints on ℎ+?+? for systematic absences (|?|²=0).

Answer 1

1) Primitive cell -simple cubic

Atom coordinate -0,0,0

Structure factor is

so we get

and

2) Body Centerd cubic atom coordinates

0,0,0    ; 1/2,1/2,1/2

so,

so when h+k+l is even F is nonzero reflection

when h+k+l is odd F=0 no reflection

3) Face centered cubic

Atom coordinates

0,0,0 ; 1/2,0,1/2 ; 1/2,1/2,0 ' 0,1/2 ,1/2

so we get

so w

so when h,k,l are unmixed means all even or all odd

F= 4f

and

when h,k,l are mixed combination of odd or even

then

F=0