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# Voids - Definition, Types, Location and Number of the voids, Formula of the compound

Let’s take a set of spherical balls and try to arrange them as closely as you can. Did you manage to arrange them closely without any gap? Well, I believe you must have tried all the possibilities but somehow you failed to avoid gaps between these balls. Now repeat the same exercise but this time instead of a spherical ball take a set of cubical boxes or you can simply look at a Rubik's cube. What did you find? Yes, there’s no gap between these cubical boxes. What do we observe from the above exercise? Flat surfaces can easily overlap with each other without any gap whereas spherical objects will leave some gaps or voids when arranged in a close packing. Particles in the crystals are also arranged in close packing leaving some vacant spaces or voids as particles are assumed to be spherical in shape. The study of voids in a crystal helps to know the properties of solids (Like solubility, density, shape, compressibility etc.) better, to make sure solids are used for appropriate applications.

Table of Content

## Definition of a Void

In a closely packed structure, void refers to the vacant space between the constituent particles (atoms, molecules or ions) of the crystal.

## Types of Voids

There are four types of voids:

• Triangular void
• Tetrahedral void
• Octahedral void
• Cubical void

Let’s discuss them all one by one.

## Triangular void

Take three atoms and arrange them in a plane as shown in the figure below. The vacant space between these atoms will be in the shape of a triangle. Thus the void generated due to the arrangement of three atoms is called a triangular void. The coordination number of triangular void is 3 as void is surrounded by 3 neighbouring atoms.

## Tetrahedral void

The void formed by 4 constituent particles (atoms, molecules and ions) is called tetrahedral void. Take 4 atoms and arrange three of them in one plane and one above the plane. The vacant space between these atoms will be in the shape of a tetrahedron. The coordination number of tetrahedral void is 4 as void is surrounded by 4 neighbouring atoms.

## Octahedral void

The void formed by 6 constituent particles (atoms, molecules and ions) is called an octahedral void. Take 3 atoms in one plane and arrange them in a triangular shape, then put another 3 atoms on top of the previous arrangement in opposite direction. The vacant space between them will be in the shape of an octahedron. The coordination number is 6 as void is surrounded by 6 neighbouring atoms.

## Cubical void

The void formed by 8 constituent particles (atoms, molecules and ions) is called a cubical void. Take 4 atoms in a plane and arrange the other 4 atoms just above them. The vacant space between them will be in the shape of a cube.The coordination number is 8 as void is surrounded by 8 neighbouring atoms.

## Number and Location of Voids in Cubic Closed Packing

Octahedral voids

One octahedral void is present at the body centre of the cube and 12 octahedral voids are

present on the centres of the 12 edges of the cube as shown in the figure below.. But each void

on the edge centre is shared by 4 unit cells. Hence its contribution in the unit cell

The effective number of octahedral voids in the CCP structure: .

Tetrahedral voids

The 8 tetrahedral voids in the CCP arise from the fact that there are 8 atoms present at the corners of the unit cell and each atom at the corner touches three other atoms present on the face centres of three adjoining faces, each giving rise to one tetrahedral void. These tetrahedral voids are found to be present on the body diagonals, two on each body diagonal at one-fourth of the distance from each end.

Thus, in CCP, total number of voids per unit cell is:

## Predicting Formula of the Compound

In the cubic close packed structure (CCP) there are two types of voids present in the lattice, i.e. tetrahedral and octahedral voids. It is found that:

• Number of octahedral voids = Number of particles present in the cubic close packed structure
• Number of tetrahedral voids = Number of octahedral voids

In case of ionic compounds, it is found that the bigger ions (usually anions) form CCP structure whereas smaller ions (usually cations) occupy the voids. Generally, if cations are smaller in size they occupy tetrahedral voids and if they are bigger in size then they occupy octahedral voids. It is not necessary that voids have to be fully occupied, sometimes fraction of the total voids may also be occupied.

## Practice problems

Q 1. Two elements, and , combine to form a compound. The atoms of element forms , while the atoms of element fill all of the octahedral voids. The formula of the compound is:

a.
b.
c.
d.

Suppose the number of atoms of element in

As, number of octahedral voids Number of atoms in

∴ Number of octahedral voids

As all the octahedral voids are occupied by atoms of element .

∴ Number of atoms of element in the compound

Ratio of atoms of elements in the compound

Hence, the formula of the compound is .

Q 2. In a crystal lattice, oxygen particles form cubic close packed (CCP) structure. fraction of octahedral voids are occupied by aluminium ions and fraction of tetrahedral voids are occupied by magnesium ions, the values for m and n are:

a.
b.
c.
d.

In arrangement:

No. of oxygen atoms = 4 (∵ Effective number of atoms in )

No. of octahedral holes effective no. of atoms in

No. of tetrahedral holes effective no. of atoms in

No. of ions

No. of ions

Since the molecule is neutral, the sum of the total charge on all the atoms would be .

By hit and trial method, clearly by putting  and  , the equation itself satisfies.

So, option (A) is the correct answer.

Q 3. If the structure can be described as a cubic closed packed array of oxide ions with titanium present in half of the octahedral voids.

What is the mass percentage of titanium in rutile structure, a mineral that contains Titanium and oxygen?

What is titanium's oxidation number?

If the number of oxide ions , then;

Number of octahedral voids Number of atoms in

∴ Number of octahedral voids

And hence, titanium ions (∵ titanium ions are present in half of the octahedral voids only)

So,

Hence, formula of the oxide is .

Molar mass of

Hence, mass percentage of

Let’s assume the oxidation state of be

As, is neutral. So, the the sum of the oxidation states of all the atoms in would be .

So,

Hence, the oxidation state of in .

Q 4. In a crystal lattice, oxide ions are arranged in a cubic closed packing array. One-sixth of the tetrahedral voids are occupied by cations and one-third of the octahedral voids are occupied by cations . What is the formula of the compound?

a.
b.
c.
d.

Suppose ions in the crystal lattice

Then, octahedral voids in the crystal lattice and Tetrahedral voids in the crystal lattice

No. of cations

No.of cations

Ratio of

Hence, the formula of the compound is .

## Frequently Asked Questions- FAQs

Q 1. What do you understand by close packing in solid structures?

Answer: The packing is done in such a way that the constituent particles will leave minimum empty space between them by occupying maximum available space. This type of packing is called closed packing.

Q 2. Is there any difference between voids and interstitial sites?

Answer: We see empty spaces between the atoms in 2-D structures when the atoms are arranged in square close packing and hexagonal close packing. These empty spaces are referred to as voids. A position between the regular arrangements of atoms or ions in a crystal that can be occupied by other atoms or ions is referred to as an interstitial site. Hence, both terms are nearly identical to each other.

Q 3. Is compressibility of solid affected by voids?

Answer: Compressibility is the property of being compressed by pressure into a smaller space. The size of voids will determine the degree of compressibility. The greater the size of the voids in a crystal, the greater will be the degree of compressibility. Hence, the compressibility of a solid crystal is hugely affected by the voids.

Q 4. Do amorphous solids have voids between their particles?

Answer: Amorphous solids have voids between them but due to the irregular arrangement of the particles in amorphous solids, the shapes of these voids can’t be defined properly.

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