Crystal structures & average number of atoms per unit cell - Material Science

Q.  Match the following group 1 items (crystal structures) with group 2 items (average number of atoms per unit cell) and select the correct option

1. Simple cubic crystal structure ----------------- A.  2
2. Body centered crystal structure --------------- B.  6
3. Face centered crystal structure ---------------- C.  1  
4. Hexagonal close packed structure ------------ D.  4
- Published on 05 Aug 15

a. 1 – A, 2 – C, 3 – D, 4 – B
b. 1 – C, 2 – A, 3 – D, 4 – B
c. 1 – B, 2 – A, 3 – C, 4 – D
d. 1 – D, 2 – A, 3 – B, 4 – C

ANSWER: 1 – C, 2 – A, 3 – D, 4 – B

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    Discussion

  • Raja   -Posted on 02 Dec 16
    Really a very good explanation/ tk u
  • Sravanthi   -Posted on 06 Oct 15
    1) Simple cubic structure has zero face atoms in an unit cell (Nf), zero interior atoms (Ni) and eight atoms representing eight corners (Nc)
    Average number of atoms per unit cell:
    (Navg) = (Nc / 8) + (Nf / 2) + (Ni / 1)
    (Navg) = (8/8) + (0/2) + (0/1) = 1

    Hence, average number of atoms per unit cell = 1

    2) In body centered crystal structure, one atom is present in the interior.
    Nc = 8, Nf = 0, Ni = 1

    Therefore, (Navg) = (8 / 8) + (0 / 2) + (1 / 1)
    (Navg)= 2

    3) In face centered crystal structure, six faces consist of six atoms, 8 atoms at eight corners and has no interior atom.

    (Navg) = (8 / 8) + (6 / 2) + (0 / 1)
    (Navg) = 4

    4) Hexagonal close packed structure consists of 12 corners i.e six at bottom and six at top, 2 atoms at centers and 3 interior atoms.

    (Navg) = (12 / 6) + (2 / 2) + (3 / 1)
    (Navg) = 6

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