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Calculate packing efficiency in BCC lattice. |
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Answer» Solution :Diagram Relationship between .a. and .r. `a = 4/SQRT3 r` OR `r = (sqrt3a)/4` Packing efficiency formula Substitution and answer Detailed Answer: In `DeltaABC`, `b^2 = a^2 + a^2 :.b^2 = 2a^2`, In, `Delta ABC`  `C^2 = a^2 + b^2= a^2 + 2a^2 :. C = sqrt 3a` Radius of the atom `=r`. Length of the body diagonal ` C =4r` `sqrt 3a = 4r` `a = ( 4r)/(sqrt3)` EDGE length of the CUBE`= a = (4r)/sqrt(3)` Volume of the cubic unit cell `= a^3 = ((4r)/sqrt(3))^3` Volume of one particle (sphere) `= 4/3 pi r^3` The number of particles PER unit cell of a bcc = 2 Total volume occupied by two spheres `= 2 xx 4/3 pi r^3` Packing efficiency `= ("Total volume occupied by the two spheres")/("VOlume of a cubic unit cell") xx 100` `(4/3pir^3xx2)/((4/sqrt3r)^3) xx100 =(8/3pir^3)/(64/(3sqrt3)r^3)xx100 =68%` (1) A face CENTRED cube contains 8 lattice points at the eight corners and 6 lattice points at the centres of six faces. (2) A particle present at the corner shares `1/8` of that particle to each unit cell. (3) A particle present at the centre of a face provdes a share of `1/2` of that particle to each unit cell. |
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