?The coordinates, as multiples of a, of the A atoms, with scattering factor \(f_{A}\)

Chapter 15, Problem P15B.7

(choose chapter or problem)

The coordinates, as multiples of a, of the A atoms, with scattering factor \(f_{A}\), in a cubic lattice are (0,0,0),(0,1,0),(0,0,1),(0,1,1),(1,0,0),(1,1,0), (1,0,1), and (1,1,1). There is also a B atom, with scattering factor \(f_{\mathrm{B}}\), at \(\left(\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right)\). Calculate the structure factors \(F_{h k l}\) and predict the form of the diffraction pattern when

(a) \(f_{\mathrm{A}}=f, f_{\mathrm{B}}=0\),

(b) \(f_{\mathrm{B}}=\frac{1}{2} f_{\mathrm{A}}\), and

(c) \(f_{\mathrm{A}}=f_{\mathrm{B}}=f\).

Text Transcription:

f_A

f_B(1/2, 1/2, 1/2

F_hkl

f_A=f, f_B=0

f_B=1/2 f_A

f_A=f_B=f