Measurement of diamond nucleation rates from hydrocarbons at conditions comparable to the interiors of icy giant planets

We present measurements of the nucleation rate into a diamond lattice in dynamically compressed polystyrene obtained in a pump-probe experiment using a high-energy laser system and in situ femtosecond x-ray diffraction. Different temperature-pressure conditions that occur in planetary interiors were probed. For a single shock reaching 70 GPa and 3000 K no diamond formation was observed, while with a double shock driving polystyrene to pressures around 150 GPa and temperatures around 5000 K nucleation rates between ${10}^{29}$ and ${10}^{34}\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}$ ${\mathrm{s}}^{\ensuremath{-}1}$ were recorded. These nucleation rates do not agree with predictions of the state-of-the-art theoretical models for carbon-hydrogen mixtures by many orders of magnitude. Our data suggest that there is significant diamond formation to be expected inside icy giant planets like Neptune and Uranus.