The coefficient of linear expansion of crystal in one direction is α1 and that in every direction perpendicular to it is α2. The coefficient of cubical expansion is

V = V0(1+γ∆θ)  L3 = L0(1+α1∆θ)L20(1+α2∆θ)2       = L30(1+α1∆θ)(1+α2∆θ)2Since L30 = V0 and L3 = VHence 1+γ∆θ = (1+α1∆θ)(1+α2∆θ)2                         = (1+α1∆θ)(1+2α2∆θ)                          = (1+α1∆θ+2α2∆θ)⇒γ = α1+2α2