Consider the three types of cubic units cells. (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cubes edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)r3, where r is the radius of the sphere.) (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?

Which solid phase that is, which allotrope of carbon is more stable, graphite or diamond? You should consult some of the tables in the thermodynamics section of this text.. Both solid phases exist under normal conditions of pressure and temperature. Explain why this is so, given that one solid phase is more thermodynamically stable than the other. Do their unit cells provide any suggestion for their relative stabilities?

Lithium hydride (LiH) has the sodium chloride structure, and the length of the edge of the unit cell is 4.086 108 cm. Calculate the density of this solid.

Outline a two-dimensional unit cell for the pattern shown here. If the black squares are labeled A and the white squares are B, what is the simplest formula for a compound based on this pattern?