# Calculate the void fraction for the structure formed by A and B atoms such that A form hexagonal closed packed structure and B occupies 2/3 of octahedral voids. Assuming that B atoms exactly fitting into octahedral voids in the HCP formed by A

Total volume of A atom =$\large\frac{6\times 4}{3}$$\pi r_A^3 Total volume of B atoms =4\times \large\frac{ 4}{3}$$\pi r_B^3=4\times \large\frac{ 4}{3}$$\pi (0.414r_A^3) Since \large\frac{r_A}{r_B}$$=0.414$ as B is in octahedral void of A
Volume of HCP = 24$\sqrt 2r_A^3$
Packing fraction =$\large\frac{\Large\frac{6\times 4}{3}\pi r_A^3+4\times \Large\frac{ 4}{3}\pi (0.414r_A^3)}{24\sqrt2r_A^3}$