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Determine the packing efficiency of the unit cell in hexagonal close-packed (hcp) structure of particles. |
Answer» Solution :The unit cell in an hcp structure of particles is a hexagonal unit cell as shown in the given figure. The number of particles in the hexagonal unit cell = 6. If radius of each the  particles MAKING up the unit cell is = r, then total volume for 6 particles = `6xx4/3pir^(3)`. The area of the BASE of a hexagonal unit cell = `=6xxsqrt3/4xx4r^(2)=6sqrt3r^(2)`. The height of this unit cell = `4rsqrt(2/3)` Therefore, the volume of unit cell = area of the base `xx` height = `6sqrt3r^(2)xx4rsqrt(2/3)=24sqrt2r^(3)` `therefore" "` Packing efficiency of the hexagonal unit cell `=("Volume of 6 particles")/("Volume of unit cell")xx100=(6xx4/3pir^(3))/(24R^(3)sqrt2)xx100` = 74.01% |
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