Diatomic line, consider a line of atoms ABAB. . . AB, with an A––B bond length of 1/2a, the form factors are fA, fB for atoms A, B, respectively. The incident beam of x-rays is perpendicular to the line of atoms. 

(a) Show that the interference condition is nλ = a cos θ, where θ is the angle between the diffracted beam and the line of atoms.

(b) Show the intensity of the diffracted beam is proportional to |f_A – f_B|2 for n odd, and to |f_A + f_B) 2 for n even.

(c) Explain what happens if f_A = f_B.

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(220) (311) 0.45 0.65 (400) 0.509 20 30° 45° 60° 75° Counter position 20