The primitive translation vector of the face centre cubic (FCC) crystal structure may be as: 1 1 a₁ a; = — a(8 + 9); a¿ = ²a( + 2); az = = a(8 + 2) - Calculate: 1. The volume of the primitive unit cell. 2. The reciprocal translation vectors: ai, az, a3, of the primitive lattice. 3. The volume of the reciprocal unit cell. 4. Determine the crystal structure of the reciprocal lattice.

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Hi, please answer all these questions for me. Most importantly number 4, please don't skip steps on that one.
Question 1: (23%)
The primitive translation vector of the face centre cubic (FCC) crystal structure may be taken
as:
1
1
2)
āî = ¾a(8 + 9); ā¿ =
· + 9); āį = = a(9 + 2); ā3 = = a (x + ²
Calculate:
1. The volume of the primitive unit cell.
2. The reciprocal translation vectors: ai, a2, a3, of the primitive lattice.
3. The volume of the reciprocal unit cell.
4. Determine the crystal structure of the reciprocal lattice.
[3]
[9]
[5]
[6]
Transcribed Image Text:Question 1: (23%) The primitive translation vector of the face centre cubic (FCC) crystal structure may be taken as: 1 1 2) āî = ¾a(8 + 9); ā¿ = · + 9); āį = = a(9 + 2); ā3 = = a (x + ² Calculate: 1. The volume of the primitive unit cell. 2. The reciprocal translation vectors: ai, a2, a3, of the primitive lattice. 3. The volume of the reciprocal unit cell. 4. Determine the crystal structure of the reciprocal lattice. [3] [9] [5] [6]
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