The pseudo$-$binary phase diagram of $H{g}_{x}C{d}_{(1-x)}Te$ is shown below. The thermal

expansion coefficient of $aH{g}_{0\mathrm{.}3}C{d}_{0\mathrm{.}7}Te$ crystal is $5\mathrm{.}05{10}^{-6}{K}^{-1}$ and the lattice parameter

of the cubic crystal is $6\mathrm{.}36.$ The precision with which the length of a typical $($e$.$g$.,$

approximately $1cm$ long$)$ crystal can be measured by interferometry at high temperatures

is about $+-1nm,$ and the precision of $x-$ray diffraction is about $+-0\mathrm{.}00002.$ Can the

dilatation technique, applied to a $H{g}_{0\mathrm{.}3}C{d}_{0\mathrm{.}7}Te$ crystal heated from room temperature, be

used to experimentally test the reported value of $G_V^{\text{'}}=0\mathrm{.}81eV$ obtained from first$-$

principles simulations? Support your answer with calculations.