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with the help of a labelled diagram ...

with the help of a labelled diagram show that there are four octahedral voids per unit cell in cubic close packed structure .

Text Solution

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cubic close packed structure contains one ato at each of eight corners of a unit cell and one atom at each of six faces which can be repesented below
As we known any atom surrounded by six atoms (hard sphere) creates an octahedral void, in case of fcc body centre is surrouded by six identical atoms present at face centre hence there is a octahedral void ay body centre of ech unit cell

Besside the body centre there is one octahedral void at centre each 12 edge as shoen below
since each void is shared by 4 unit cell threrefore , contricuttion of octahedral void to each edge of unit cell is `(1)/(4)`
Number of octahedral void at centre of 12 edge `=(1)/(4)xx12=3`
Number of octahedral at each ccp littice `=3+1=4`
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Knowledge Check

  • The number of octahedral voids in a unit cell of a cubical closest packed structure is:

    A
    1
    B
    2
    C
    4
    D
    8
  • The number of octahedral void(s) per atom present in a cubic close-packed structure is

    A
    1
    B
    2
    C
    3
    D
    4
  • The number of octahedral void(s) per atom present in a cubic close-packed structure is :

    A
    1
    B
    3
    C
    2
    D
    4
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