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Diamond lattice can be considered as a combination of two fcc lattices displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure is
  • a)
    0.48
  • b)
    0.74
  • c)
    0.34
  • d)
    0.68
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Diamond lattice can be considered as a combination of two fcc lattices...
Explanation:

Packing fraction is defined as the fraction of the total volume of the unit cell that is occupied by atoms.

The diamond lattice can be considered as a combination of two face-centered cubic (fcc) lattices displaced along the body diagonal by one quarter of its length.

Each fcc lattice has a packing fraction of 0.74.

Therefore, the packing fraction of the diamond structure can be calculated as follows:

- The volume of the unit cell of the diamond structure can be calculated as the volume of the parallelepiped formed by the three vectors that define the unit cell.
- The length of the body diagonal of the unit cell can be calculated as a√3, where a is the length of the edge of the fcc unit cell.
- Therefore, the volume of the unit cell of the diamond structure is (a√3)3/4.
- Each fcc lattice contributes four atoms to the diamond structure, so there are eight atoms per unit cell.
- The volume of each atom can be approximated as a sphere with a radius of a/2.
- Therefore, the total volume of the eight atoms in the unit cell is 4/3π(a/2)3 x 8 = 8a3π/3.
- The packing fraction is the ratio of the volume of the atoms to the total volume of the unit cell:

packing fraction = 8a3π/3 / (a√3)3/4

packing fraction = 8π / (3√3)

packing fraction = 0.340

Therefore, the correct answer is option C, 0.34.
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Diamond lattice can be considered as a combination of two fcc lattices displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure isa)0.48b)0.74c)0.34d)0.68Correct answer is option 'C'. Can you explain this answer?
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Diamond lattice can be considered as a combination of two fcc lattices displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure isa)0.48b)0.74c)0.34d)0.68Correct answer is option 'C'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Diamond lattice can be considered as a combination of two fcc lattices displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure isa)0.48b)0.74c)0.34d)0.68Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Diamond lattice can be considered as a combination of two fcc lattices displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure isa)0.48b)0.74c)0.34d)0.68Correct answer is option 'C'. Can you explain this answer?.
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