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Question

The vacant space in the bcc unit cell is -


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Solution

Body-Centered Cubic (BCC) Unit Cell

  • The Body-Centered Cubic (BCC) crystal structure is one of the ways for atoms to arrange themselves in metals.
  • The BCC crystal structure has one atom per lattice point at each corner of the cube and the center of the cube.
  • BCC is nearly close-packed and has great stability because of its high number of nearest neighbors and next-nearest neighbors.

Step 1: Packing efficiency of BCC unit cell

  • Packing efficiency of BCC unit cell is given by,

Packingefficiency= Volumeoccupiedbytwospheres×100Volumeofunitcell

= 2×43πr3×100a3

= 68%

  • The % volume occupied by atoms in a unit cell is 68%

Step 2: % Vacant space in BCC unit cell

  • % vacant space is given by,

% Vacantspace = 100 - % ofthevolumeoccupiedbyatoms

= 10068

=32%

  • %Vacant space is 32%

Therefore, the % vacant space in the BCC unit cell is32%.


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