Relation Between Lattice Constant and Density

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Consider a cubic crystal of lattice constant ‘a’.

The density of the crystal = ρ

Volume of the unit cell = a³

Eqn 1

Mass in each unit cell = ρa³

 \left(\because \text { Density }=\frac{\text { Mass }}{\text { Volume }}\right)

The number of atoms per unit cell = n

The atomic weight of the material = M

Avogadros number = N

(number of molecules per kg mole of the substance)

Mass of each molecule  =\frac{M}{N}

where, M is atomic weight

Eqn 2

Mass in each unit cell  =\mathrm{n} \times \frac{\mathrm{M}}{\mathrm{N}}

(for n atoms)

From equations (1) and (2), we have

 \rho a^3=\frac{n M}{N} \quad \text { or } \quad \rho=\frac{n M}{N a^3}

 \rho=\frac{(\text { Number of atoms per unit cell }) \times(\text { Atomic weight })}{(\text { Avogadros number }) \times(\text { Lattice cons } \tan t)^3}

From the above equation, the value of lattice constant ‘a’ can be calculated.

Read More Topics
Face centred cubic (FCC) structure
Important parameters in crystal structure
Classification of solids – crystal physics

Santhakumar Raja

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