= Solution
Use <mass density> $\rho=ZM/(N_Aa^3)$, with $M=74.55\,\mathrm{g\,mol^{-1}}$. The <rock salt structure> has $Z=4$ <formula units> per conventional cell; the <CsCl structure> has $Z=1$. In <pressure> order the densities are approximately
$$
\boxed{2099,\ 2172,\ 2208,\ 2527,\ 2571,\ 2614\ \mathrm{kg\,m^{-3}}}.
$$
The increase across the transition is approximately $14.5\%$, much greater than the smooth compression within either branch. Comparing $a^3$ directly without correcting the different $Z$ would create a fictitious <volume> discontinuity.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1-kcl-density.png]
{title=KCl density calculated separately for the two crystal structures}
{description=Original calculation from cell mass and volume. The narrow gap brackets the transition; separate lines avoid implying a continuous single-phase density through the jump.}
Back to article page
