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For most planets in the range of radii from 1 to 4 R$_{\oplus}$, water is amajor component of the interior composition. At high pressure H${}_{2}$O can besolid, but for larger planets, like Neptune, the temperature can be too highfor this. Mass and age play a role in determining the transition between solidand fluid (and mixed) water-rich super-Earth. We use the latest high-pressureand ultra-high-pressure phase diagrams of H${}_{2}$O, and by comparing themwith the interior adiabats of various planet models, the temperature evolutionof the planet interior is shown, especially for the state of H${}_{2}$O. Itturns out that the bulk of H${}_{2}$O in a planet's interior may exist invarious states such as plasma, superionic, ionic, Ice VII, Ice X, etc.,depending on the size, age and cooling rate of the planet. Different regions ofthe mass-radius phase space are also identified to correspond to differentplanet structures. In general, super-Earth-size planets (isolated or withoutsignificant parent star irradiation effects) older than about 3 Gyr would bemostly solid.

The effect of temperature evolution on the interior structure of H${}_{2}$O-rich planets