j

rgijg

jefF

2

The structure factor for copper

• fcc lattice with one atom in [000] relative to the lattice point.

• r1= [0,0,0], r2= [1/2,1/2,0], r3= [1/2,0,1/2], r4= [0,1/2,1/2]

j

rgijg

jefF

2

The structure factor for copper

• Result: • hkl even: F=fCu(1+1+1+1)=4fCu

• hkl odd: F=fCu(1+1+1+1)=4fCu

• h odd, k and l even: F=fCu(1-1+1-1)=0

• h and k odd, l even: F=fCu(1+1-1-1)=0

• Conclusion: hkl even or odd gives allowed reflections, hkl mixed gives forbidden reflections

)()()(1 lkilhikhiCuhkl eeefF

1

1)12(

2

in

in

e

e

The reciprocal lattice for bcc iron?

• Body centered cubic lattice • One atom per lattice point, [000] relative to the lattice

point• What is the reciprocal lattice?