Saved Bookmarks
| 1. |
Calculate the packing efficiency in Face Centred Cubic (FCC) structure. |
Answer» Solution : The edge length `=.a.` Radius of sphere = r Face diagonal AC = b = 4r In `DeltaABC , AC^(2) = b^(2) =AB^(2) + BC^(2)` `=a^(2)+ a^(2) = 2a^(2)` `:. b=SQRT(2)a " But " b = 4r = sqrt(2) a ` ` a= (4r)/(sqrt(2)) = 2 sqrt(2) r ` VOLUME of sphere `= ((4)/(3))pir^(3)` Volume of cube `=a^(3) = (2sqrt(2)r)^(3)` Number of particle per unit CELL in FCC = Z = 4 spheres . Packing efficiency `=("Volume OCCUPIED by four spheres in the unit cell " xx 100)/("Total volume of the unit cell ") or ` Packing efficiency `=(ZV_("sphere") xx 100)/(a^(3))` `=(4 xx (4)/(3) pir^(3) xx 100)/((2sqrt(2)r)^(3))=(16 pi r^(3)xx 100)/( 48 sqrt(2) r^(3))` ` (pi xx 100)/(3 sqrt(2)) = 74%` |
|