1. Calculate the bond angle between atoms in a diamond lattice. Use the position of atoms in the FCC lattice, with the second atom in the basis at d = a/4 (x + y + z) and a third atom on a nearby face, where x, etc. are Cartesian unit vectors. Use vector properties and dot products to get the angle theta.
2. Calculate the ideal c/a ratio for the hcp lattice, by considering stacked layers of hard spheres of radius r. An atom in the second layer will lie above 3 spheres in the lower layer, where the lattice constant a is the distance between 2 spheres (i.e. a = 2r).
3. At a temperature of 23 K, metallic sodium transforms from BCC to HCP (Martensitic transformation). The mass density is constant, and the cubic lattice constant acubic = 0.423 nanometer. Calculate the new hexagonal lattice constant ahex.
4. How many atoms are there in the unit cell of the Silicon lattice?
(a) verify that there are 4.994 x 1022 atoms /cm3
in Si at room temperature. (hint, use the value for the lattice constant
a)
(b) determine the center to center distance between nearest neighbors
in the Si lattice..
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