2. Calculate the density of forsterite (Mg2SiO4) two ways:

a. based on the Mg2+O2 distance and (20 points)

b. on the Si4+O2 distance. (20 points)

c. Compare your results to the published density, forsterite = 3.21 g/cm3. Do so by commenting on which bonds (i.e., SiO or MgO) do more to dictate the density and offer an explanation of why this is the case. (10 points)

Two important considerations:

For your calculations, assume that the O2 sublattice for forsterite has a hexagonal-close-packed (hcp) structure. The density of the hcp packing of spheres is the same as that of the face-centered-cubic (fcc) arrangement of the same spheres (in this case, O2 anions). The halite & fluorite crystal lattices also has a fcc structure.

Also, something youll need to consider when you work on this: where are the Mg cations (tetrahedral or octahedral sites)? Likewise, where are the Si cations? How many of each of them are there in the unit cell? Your approach to this part should be pretty similar to what you did for Q1