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Homework01_solution - Homework 1 Solution Problem#1 Simple...

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Homework # 1 - Solution Problem #1 Simple cubic structure: The distance between nearest-neghbor atoms is a . Therefore the radius r of the touching spheres located at lattice sites is / 2 = r a . Since in the simple cubic structure there is one atom in the unit cell, the volume coved by the spheres is 3 3 4 4 3 3 2 π π ° ± = = ² ³ ´ µ sc a V r , whereas the total volume of the unit cell is 3 = cell V a . The packing ratio is, therefore, 3 3 4 3 2 0.52 6 π π ° ± ² ³ ´ µ = = = sc sc cell a V p V a . Bcc structure: The distance between nearest-neghbor atoms is 3 / 2 a and therefore 3 / 4 = r a . In the bcc structure there are 2 atoms in the conventional unit cell so that the volume coved by the spheres is 3 4 3 2 3 4 π ° ± = ² ³ ² ³ ´ µ bcc a V . The packing ratio is 3 0.68 8 π = = bcc bcc cell V p V . Fcc structure: The distance between nearest-neghbor atoms is 2 / 2 a , so that 2 / 4 = r a . In the fcc structure there are 4 atoms in the conventional unit cell, and therefore the volume coved by the spheres is 3 4 2 4 3 4 π
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