Q1(d). Why KCl diffracts like a simple cubic lattice

Answer in brief

K⁺ and Cl⁻ are isoelectronic (18 e each), so they scatter X-rays almost equally; the all-odd (hkl) lines cancel and KCl looks simple cubic with edge a/2.

Key points

• Both have the rock-salt structure: fcc lattice with basis M at (0, 0, 0) and Cl at (½, 0, 0); Z = 4.
• Structure factor: F = 4(fM + fCl) for h, k, l all even; 4(fM − fCl) for all odd; 0 for mixed.
• X-rays are scattered by electrons, f ∝ number of electrons; K⁺ (18 e) ≈ Cl⁻ (18 e) ⇒ F(odd) ≈ 0: (111), (311), (331) are absent in KCl.
• Remaining KCl lines have h² + k² + l² ∝ 1, 2, 3, 4, 5, 6: they index as simple cubic with edge a/2 = 3.15 Å.
• NaCl: Na⁺ (10 e) ≠ Cl⁻ (18 e), so the odd lines appear (weak): fcc, a = 5.64 Å.