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Calculate packingefficieny in the crystal of facecentred cubic (fcc) sturcture. |
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Answer» Solution :Face - centred cubic (FCC) structre: In the unit cell, there are 8 atoms at 8 cornersand 6 atoms at 6 facecentres. NUMBEROF atoms due to 8 corners `= 8 xx (1)/(8) = 1` Number of atomsdue to 6 facecentre `= (1)/(2) xx 6 = 3` `therefore` Totalnumberof atoms in the unit cell = 1+3=4 If a is the edge lenghtof the unit cell and r is the radius OFTHE atoms , then in fccstructure, `r = (a)/(2sqrt(2))`. Hence `a = sqrt(2)` Volumeof unit cell `= a^(3) = (2sqrt(2r))^(3) = 16 sqrt(2r)^(3)` Volumeof unit cell`=a^(3) = (2qrt(2r))^(3) = 16 sqrt(2r)^(3)` Volumeof 1 atom `= (4)/(3)pir^(3)` Packing FRACTION `= ("Volume occupiedby 4 atoms")/("Volumeof unit cell")` `=(4((4)/(3)pir^(3)))/(16sqrt(2)pir^(3))` `=(16//3pir^(3))/(16sqrt(2)r^(3))` `=(pi)/(3sqrt(2))` `=(3.142)/(3xx1.414)` ` = 0 .74` `therefore` Packingefficiency `= 0.74 xx 100 = 74%` `therefore` of void SPACE= 100 - 74 = 26% |
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