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Calculate packing efficiency in face-centred cubic (fee) structure. |
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Answer» Solution :Face-centred cubic (Fee) structure: In this UNIT CELL, there are 8 atoms at 8 corners and 6 atoms at 6 face centres. Number of atoms due to 8 corner `= 8 XX (1)/(8) = 1` Number of atoms due to 6 face centres `= (1)/(2) xx 6 = 3` `THEREFORE` Total number of atoms in the unit cell= 1 + 3 = 4 If a is the edge length ofthe unit cell and ris theradius of the atom, the in fcc structure, `r = (a)/(2sqrt(2))`. Hence `a= 2sqrt(2)r` Volumeof unit cell `=a^(3) = (2sqrt(2r))^(3) = 16 sqrt(2r)^(3)` Volumeof 1 atom ` = (4)/(3) pir^(3)` Packingfraction `=("VOLUME occupiedby 4 atoms")/("Volumeof unit cell")` `=(4((4)/(3)pir^(3)))/(16 sqrt(2)r^(3)) = (16//3pir^(3))/(16sqrt(2)r^(3))=(pi)/(3sqrt(2))` `=(3.142)/(3xx 1.414) = 0.74` `therefore` Packing efficiency= 0.74 `xx` 100 = 74 % `therefore` % of void space = 100 - 7 4 = 26 % . |
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