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
[latex] \left(\because \text { Density }=\frac{\text { Mass }}{\text { Volume }}\right) [/latex]
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 [latex] =\frac{M}{N} [/latex]
where, M is atomic weight
Eqn 2
Mass in each unit cell [latex] =\mathrm{n} \times \frac{\mathrm{M}}{\mathrm{N}} [/latex]
(for n atoms)
From equations (1) and (2), we have
[latex] \rho a^3=\frac{n M}{N} \quad \text { or } \quad \rho=\frac{n M}{N a^3} [/latex]
[latex] \rho=\frac{(\text { Number of atoms per unit cell }) \times(\text { Atomic weight })}{(\text { Avogadros number }) \times(\text { Lattice cons } \tan t)^3} [/latex]
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 |
