Past exam of the condensed matter physics major option course of the University of Oxford / 2019 / 4 / d / Solution

The low-temperature bond-length difference is ${ϵ}_0=2.05-1.98=0.07\text{A˚}$. With the question's thermal criterion,Use $\alpha =\beta {ϵ}_0$ and $E_{\mathrm{JT}}=\beta {ϵ}_0^2/2$ to obtainIn SI units these are about $7.89\times 10^{-10}\mathrm{N}$ and $113\mathrm{N}{\mathrm{m}}^{-1}$, respectively. They are estimates within the stipulated energy criterion; a cooperative transition also involves interactions and entropy, so its temperature is not in general exactly an isolated-ion stabilization energy divided by $k_B$.