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GATE 2019 MT – Question 38

Materials Science and Non-Metallic Materials · Crystal structures and bonding · 2 marks · Multiple choice

Which set correctly gives crystal structure, coordination number CN and packing fraction PF? FCC: face-centred cubic; BCC: body-centred cubic; DC: diamond cubic.

  1. FCC: CN12, PF0.74; BCC: CN8, PF0.68; DC: CN4, PF0.34
  2. FCC: CN8, PF0.74; BCC: CN4, PF0.68; DC: CN6, PF0.34
  3. FCC: CN8, PF0.52; BCC: CN12, PF0.68; DC: CN12, PF0.74
  4. FCC: CN12, PF0.74; BCC: CN8, PF0.68; DC: CN4, PF0.74

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Correct answer: (A) FCC: CN12, PF0.74; BCC: CN8, PF0.68; DC: CN4, PF0.34

Explanation

FCC close packing gives CN12 and PF≈0.74; BCC gives CN8 and PF≈0.68. Diamond cubic has tetrahedral CN4 and the more open PF≈0.34. Only A has all three pairs correct; D incorrectly gives diamond the FCC packing fraction.

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