voids in crystalline


A Crystalline Solid is characterized by the close packing and space lattices of their atoms. Nevertheless, there are some gaps present in between the structures in the arrangement of crystalline solids which are called “Voids”.

Literally, void means the gap in between constituent particles. A ‘void’ is also defined as the empty space or the unoccupied empty space in an unit cell. They are called the ‘holes’ in the unit cell. In a Close-Packed Structure, by voids present in the solid state, we mean that it’s the vacant space acting between constituent particles.


Usually, Close-Packing in solids is done in 3 ways:

  • One-dimensional Packing
  • Two-dimensional Packing
  • Three-dimensional Packing


Talking of the two-dimensional structures, atoms here are arranged in the form of hexagonal and square close packing, we could see unoccupied empty spaces which are left between the atoms.

In hexagonal packing, these voids are arranged in triangular shapes, which are called the “​trigonal or​ ​triangular voids”.

Voids are encircled by 3 particles/spheres in contact, which are called as trigonal or triangular voids. These spheres and the voids enclosing it, lies in the same plane. In trigonal void type, the radius of the small sphere is 0.155 times greater than the larger sphere which can fit. Therefore, regarding ionic crystals, the trigonal voids are occupied by the positively charged cations which are surrounded by negatively charges anions.


In constituent particle’s 3-D closed packing, two types of voids are seen:

1. Tetrahedral Voids:

Tetrahedral voids are formed when one particle or sphere are located in depression organized by 3 particles. The void or empty space present amongst 4 constituent particles which have the tetrahedral arrangement inside a crystal lattice, resulting in the tetrahedral void.

For the calculation of Tetrahedral Voids:

If the number of spheres that is unit cells = “n”, Then, the number of voids is equal to twice as many. Hence, the number of tetrahedral voids = ​“2n”.

Tetrahedral Voids Characteristics

  • Tetrahedral void’s co-ordination number is 4.
  • The presence of atom in tetrahedral void makes the contact with 4 atoms located on four corners of a tetrahedron.
  • This empty space is formed when triagonal void formed coplanar atoms are in contact with 4th atom, present above it or below it.
  • Void’s volume is very much small in comparison to the spherical particle
  • If R represents the constituent particle of sphere’s radius, then tetrahedral void’s radius will be equal to 0.225 R.


2. Octahedral Voids

Octahedral voids are formed when 3 Close-Packed spheres form an equilateral triangle, which are positioned on another three-spheres set up in opposite directions. The void or empty space present at atoms’ or six spheres’ centre results in the formation of the octahedral void. For the calculation of an octahedral void:

Octahedral Voids Characteristics

  • Tetrahedral void’s coordination number is 6 in this void.
  • In the octahedral void, the atom is in contact with 6 atoms positioned on the 6 corners of the octahedron.
  • This vacant space is formed on the condition, when 2 sets of the equilateral triangles are pointed in opposite direction having a number 6.
  • Void’s volume is small
  • If R represents the radius the constituent particle of sphere, then octahedral void’s radius will be equal to 0.414 R. If number of spheres in the structure = “n”,Then, the number of octahedral voids will exactly be same. Which is “n”.


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