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Find the size of largest sphere that will fit in octahedral void in an ideal FCC crystal as a function of atomic radius 'r'. The insertion of this sphere into void does not distort the FCC lattice. Calculate the packing fraction of FCC lattice when all the octahedral voids are filled by this sphere. |
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Answer» Solution : If RADIUS of shpere is r Radius of LARGEST sphere that will fit in the octahedral void is 0.414 r 2[r + 0.414 r] = a 2.828 r = a Volume of spheres `=4XX(4)/(3)PIR^(3)+3xx(4)/(3)pi(0.414r)^(3)` `(16)/(3)pir^(3) [1+0.071]` Volume of unit cell=`a^(3)=(2sqrt(2)r)^(3)=16sqrt(2)r^(3) phi` `((16)/(3)pir^(3)xx1.071)/(16sqrt(2)r^(3))=(pixx1.071)/(3xx1.414)=0.793implies79.3%` |
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