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Calculate packing efficiency in HCP and CCP structures. |
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Answer» Solution : LET edge length be "a" and face DIAGONAL AC = b In `triangleABC`, `AC^2 = b^2 = BC^2 + AB^2` `= a^2 + a^2 = 2a^2` `b = sqrt(2)a` If r is the radius of the sphere We get `b = 4r = sqrt(2)a` OR `a = (4r)/(sqrt2) = 2sqrt(2)r` The number of spheres per unit CELL in CCP structure is 4. Hence total volume of four spheres is equal to `4 xx (4/3 pi r^3)` and the volume of cube is equal to `a^3` ` implies a^3 = (2sqrt(2)r)^3` % Packing EFFICIENCY =`("Volume occupied by four spheres in unit cell" xx 100)/("Volume of the unit cell")` `=(4xx(4/3pir^3)xx100)/(2sqrt2r)^3` =74% |
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