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lecture11

# lecture11 - 16 Lecture 11 February 8 2008 4 The density of...

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16 Lecture 11, February 8, 2008 4. The density of the unit cell is usually expressed in g/cm 3 , and can be calculated in a similar manner; but in this case, the mass of the atoms (g atoms ) in the unit cell is divided by the total volume (V cell ). Ex : Calculate the density of Al, which crystallizes in an fcc unit cell. The atomic radius of Al is 1.423 Å, and its molar mass is 26.98 g/mol. V cell = 64 r 3 2 2 = 64 1.423 " 10 # 8 cm ( ) 3 2 2 = 6.52 " 10 # 23 cm 3 g atoms = 4 atoms " 1 mol 6.023 " 10 # 23 atoms " 26.98 g mol = 1.79 " 10 # 22 g density = g atoms V cell = 1.79 " 10 # 22 g 6.52 " 10 # 23 cm 3 = 2.75 g / cm 3 E. Non-close packed structures 1. body-centered cubic: the atom in the center of the cube is the same as the atoms on the corners. Packing density = 68%. 2. primitive cubic: there are no atoms in the cell other than the ones on the corners. Packing density = 52%. F. Alloys: solid solutions 1. Substitutional (one metal substitutes for another on the lattice sites) a. Their atomic radii must be within 15% of each other. If the substituting atom is too large, it will significantly distort the overall lattice structure.

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