Close Packing in Solids in Three Dimensions, Covering Tetrahedral Voids (For CBSE, ICSE, IAS, NET, NRA 2022)

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Covering Octahedral Voids

  • In this kind of close packing, the spheres of the third layer are not aligned with those of either the first or the second layer. Thus, if we name the first layer as ‘A’ and second as ‘B’ , then the third layer will be named as ‘C’ . This pattern of layers can be written as This crystal structure is called cubic close-packed (CCP) or face-centered cubic (FCC) structure.
  • In both of them, the coordination number is 12 as each sphere is in contact with twelve spheres. space in the crystal is filled in these kinds of close packing.
  • Only when the fourth layer is placed, its spheres are aligned with those of the first layer as shown. This pattern of layers is often written as ABCABC … This structure is called cubic close – packed (CCP) or face – centred cubic (FCC) structure. Metals such as copper and silver crystallize in this structure.
Covering Octahedral Voids

Characteristics of Hexagonal Close Packing

  • In these three-dimensional arrangements of the unit cells, spheres of the third layer are placed on triangular – shaped tetrahedral voids of the second layer.
  • The spheres of the third layer lie exactly above the spheres of the first layer.
  • The arrangement of the first layer and third layer are identical.
  • The arrangement of hexagonal close pacing is represented as ABAB type.
  • Packing efficiency is .


What is Close Packing in Solids?


  • Close packing in crystals is refers to space efficient arrangement of constituent particles in a crystal lattice.
  • For understand this packing more, we have to assume all particles atoms, molecules and ions are of the same spherical solid shape. So, the unit cell of a lattice is a cubic shape.

What is the Packing Efficiency?


The packing efficiency is the fraction of the crystal actually occupied by the atoms. It must always be less than because it is impossible to pack spheres (atoms are usually spherical) without having some empty space between them.

How Do You Calculate Packing Efficiency?


Packing Efficiency

  • First calculate the volume of the unit cell.
  • Second count how many atoms there are per unit cell.
  • Calculate the volume of a single atom and multiply by the number of atoms in the unit cell.
  • Divide this result by the volume of the unit cell.

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