Assume $a=bc.$ The tetragonal distortion is Use the Taylor expansion formula to the

first orderf$(x+h)=f(x)+h{f}^{\text{'}}(x)$ in Eq$.2$ to obtain the new expression of $\frac{1}{d^2}$ as a function of a and $.$

Hint:

$(\frac{1}{d^2}{)}_T=(\frac{1}{d^2}{)}_C+\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{c}}(\frac{1}{d^2}{)}_c=ac$

with $c=a$

Please show that:

$(\frac{1}{d^2}{)}_T=\frac{h^2+k^2+l^2(1-2)}{a^2}$