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# Assign1Solution - CMPE 103 Electronic Materials Assignment...

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CMPE 103 Electronic Materials Assignment 1 Solution 1.5 Find the maximum fractions of the unit cell volume that can be filled by hard spheres in the sc, bcc and diamond lattice. Simple Cube [2 marks] No. of atoms in 1unit cell = (1/8 x 8) = 1 atom Radius of each atom = a / 2 where a is the lattice constant Volume of 1 atom (sphere) = 4/3 π r 3 = 4/3 x π x (a / 2) 3 = π /6 x a 3 Total volume taken up by atoms in 1 unit cell = No. of atoms in 1 unit cell x Volume of 1 atom = 1 x π /6 x a 3 Volume of unit cell = a 3 Fraction of unit cell filled = Total volume taken up by atoms in 1 unit cell / Volume of unit cell = (1 x π /6 x a 3 ) / a 3 = π /6 = 0.52 Body Centered Cube [2 marks] No. of atoms in 1unit cell = (1/8 x 8) + 1 = 2 atoms Radius of each atom = 3 a/4 where a is the lattice constant Volume of 1 atom (sphere) = 4/3 π r 3 = 4/3 x π x ( 3 a/4) 3 = 3 π a 3 / 16 Total volume taken up by atoms in 1 unit cell = No. of atoms in 1 unit cell x Volume of 1 atom = 2 x 3 π a 3 / 16 Volume of unit cell = a 3

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Assign1Solution - CMPE 103 Electronic Materials Assignment...

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