$($a$)$ Figure $3,$ below, shows a mineral structure named Cooperite, PtS:

Find coordination numbers for the chemical elements Pt and S$.$

ii$.$ How many atoms of the two chemical elements are in the unit cell?

$[4$ marks$]$

$($b$)$ Find the mirror symmetry elements in the unit cell $($number and orientations$).$

$[3$ marks$]$

$($c$)$ Explain the type of rotational symmetry $($if any$)$ along the horizontal and vertical arrows in the figure.

$[2$ marks$]$

$($d$)$ Give two other common crystal structures adopted by AB compounds and draw unit cells for each.

$[3$ marks$]$

$($e$)$ Compare the structure in Figure $3$ with your other AB structures in terms of symmetry, including the Bravais lattice they may be derived from, their crystal system and inversion symmetry.

$[4$ marks$]$

$($f$)$ Comment on which features influence the choice of $AB$ structures by various chemical elements $($referring to coordination, size difference, and bond type$).$

$[4$ marks$]$

SECTION B over page $-$ CONTINUED