Getting an “index” of 7 for a Set of Powder Diffraction Data
I think:
$$\frac{1}{d^{2}} =\frac{\frac{h^{2}\sin^{2} \alpha }{a^{2}} +\frac{k^{2}\sin^{2} \beta }{b^{2}} +\frac{l^{2}\sin^{2} \gamma }{c^{2}} +\frac{2hk}{ab}(\cos \alpha \cos \beta -\cos \gamma ) +\frac{2kl}{bc}(\cos \beta \cos \gamma -\cos \alpha ) +\frac{2lh}{ac}(\cos \gamma \cos \alpha -\cos \beta )}{1+2\cos \alpha \cos \beta \cos \gamma -\cos^{2} \alpha -\cos^{2} \beta -\cos^{2} \gamma }$$
Have you explored the case where $a\neq c$ such as tetragonal?
$$\frac{1}{d^{2}} =\frac{h^{2} +k^{2}}{a^{2}} +\frac{l^{2}}{c^{2}}$$