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Calculate packing efficiency in face centred cubic (fcc) structure. |
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Answer» Solution : Face centred cubic (fcc) 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 corners `=8xx(1)/(8)=1` Number of atoms due to 6 face centres `=(1)/(2)xx6=3` `therefore` TOTAL number of atoms in the unit cell =1+3=4 If a is the edge length of the unit cell and r is the radius of the atom, then in fcc structure, `r=(a)/(2sqrt2)`. Hence `a=2sqrt2r` Volume of unit cell `a^(3)=(2sqrt2r)^(3)=16sqrt2r^(3)` Volume of 1 atom `=(4)/(3)pir^(3)` `"Packing FRACTION"=("Volume occupied by 4 atoms")/("Volume of unit cell")` `=(4((4)/(3)pir^(3)))/(16sqrt2r^(3))` `=(16//3pir^(3))/(16sqrt2r^(3))` `=(PI)/(3sqrt2)` `=(3.142)/(3xx1.414)` `=0.74` Packing efficiency=`0.74xx100=74%` `therefore ` % of void space=100-74=26% |
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