Scattering by the unit cell Structure amplitude(factor)Fk:summation of the amplitude scattered by each atom in the unit cell with respect to Bragg's law. 下w=∑fe i=l Describes how atomic arrangement influences the intensity of the scattered beam. 11
Scattering by the unit cell 11 Structure amplitude(factor) Fhkl: summation of the amplitude scattered by each atom in the unit cell with respect to Bragg’s law. n j i hkl j j F f e 1 Describes how atomic arrangement influences the intensity of the scattered beam
S (hkI) S 12
rj 12 (hkl)
Structure factor FN=∑1f,exp(2πigw)=∑f,exp[2πi(hx,+y,+le,】 =∑=1f{cos[2π(hx,+y,+l,】+isin[2π(hx,+y,+lz,J} scattering intensity Ff=F-F-[∑￡exp[2(hx,+ky,+1a,门 The scattering intensity of the unit cell in terms of the intensity of the atom / 1。=Fw21。 13
c hkl e I F I 2 2 1 2 * exp[2 ( )] nj Fhkl Fhkl Fhkl fj i hx j ky j lz j 13 Structure factor scattering intensity 1 1 1 exp(2 ) exp[2 ( )] {cos[2 ( )] sin[2 ( )]} n n hkl j hkl j j j j j j j n j j jj j jj j F f ig r f i hx ky lz f hx ky lz i hx ky lz uuur ur The scattering intensity of the unit cell Ic in terms of the intensity of the atom Ie:
Discussion on structure factor Fk For a unit cell with one atom,F For a unit cell with more than one atom, there is structure extinction (0). 14
Discussion on structure factor Fhkl • For a unit cell with one atom, Fhkl =f. • For a unit cell with more than one atom, there is structure extinction ( Fhkl=0). 14
Fin for Simple Cubic Atom coordinate(s)u,v,w: -0,0,0 Fi fe2xi(oh+ok+oD)=f No matter what atom coordinates or plane indices you substitute into the structure factor equation for simple cubic crystals,the solution is always non-zero. Thus,all reflections are allowed for simple cubic(primitive)structures. 15
15