Mg has a hexagonally close packed $($HCP$)$ crystal structure $($with $a=3\mathrm{.}20927$ and $c=$

$5\mathrm{.}21033.$ Use space group $\frac{P_3}{m}mc$ with $Mg$ atoms at $(\frac{2}{3},\frac{1}{3},0\mathrm{.}25).$

a$.$ Draw several unit cells, showing the bonds that connect the $Mg$ atoms.

b$.$ Compare the $Mg$ coordination with that of $Cu.$ Specify both number of neighbors and

their geometric arrangement.

c$.$ Which is the close$-$packed plane in this material?

d$.$ How does the stacking sequence of close$-$packed planes differ for HCP and FCC

metals?