hw1_solutions - iECE 440 1 Homework I Solutions Due...

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iECE 440 Homework I Solutions Spring 2005 Due: Wednesday, January 26, 2005 1. How many atoms are found inside a unit cell of a simple cubic (sc), body-centered cubic (bcc), face-centered cubic (fcc), diamond structure, and zinc-blende structure crystal? Find the maximum fractions of the unit cell volume that can be filled by hard sphere in the sc, bcc, fcc and diamond lattices. If all unit cells have the same lattice constants, i.e. the unit cell dimension, which structure among sc, bcc, fcc, diamond and zincbelnde has the largest atomic density (atoms/cm 3 )? Which of them has the highest packing density, i.e. highest volume fraction being occupied by hard spheres? Simple Cubic (SC) 1/8 of each of the atoms on the corners is within the unit cell. Since there are 8 corners, 1/8 x 8 atoms = 1 atom. To find the maximum fraction of the unit cell volume we must follow the procedure outlined on page 6 of Streetman. Assuming the atoms touch one another (maximum packing without the spheres intersecting) the radius of each atom equals a/2. The ratio of volume filled to total volume is the number of atoms multiplied by the volume of one atom divided by the volume of the unit cell.
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