The coefficient of linear expansion of crystal in one direction is α 1 and that in the other two directions perpendicular to it is α 2 . The coefficient of cubical expansion is

Step-by-step solution

V = V 0 1 + γ Δ θ or L 3 = L 0 1 + α 1 Δ θ L 0 2 1 + α 2 Δ θ 2 ⇒ L 3 = L 0 3 1 + α 1 Δ θ 1 + α 2 Δ θ 2 Since L 0 3 = V 0 , hence 1 + γ Δ θ = 1 + α 1 Δ θ 1 + α 2 Δ θ 2 ≅ 1 + α 1 Δ θ 1 + 2 α 2 Δ θ ≅ 1 + α 1 Δ θ + 2 α 2 Δ θ ∴ γ = α 1 + 2 α 2