Recently, it has been revealed that a supercooled liquid below the melting point has intrinsic structural heterogeneity due to local structural ordering as a manifestation of many-body correlations. The impact of such preordering on crystal nucleation has recently attracted considerable attention. In this work, by extensive molecular dynamics simulations of TIP5P water, we find a two-step homogeneous nucleation of a ferroelectric ice crystal: the first step is spontaneous dipolar ordering, i.e., paraelectric-to-ferroelectric transition, in a supercooled liquid state and the second step is the nucleation of the ferroelectric ice crystal selectively in the preordered regions. We reveal that in this system the dipole-dipole correlation grows rapidly with an increase in pressure, eventually leading to spontaneous dipolar ordering at a certain condition (e.g., at 2000 bars and 227 K). This result is obtained by simulations of TIP5P water with a simple cutoff of Coulomb interactions. By comparing this result with those of the particle-mesh Ewald and reaction field treatments of the Coulomb interactions, we find that the potential cutoff significantly enhances the dipole-dipole correlation, resulting in the fast ice nucleation to the ferroelectric cubic form. Despite the unrealistic enhancement of dipolar correlation in this model, this work provides an intriguing physical scenario of two-step crystal nucleation in polar molecules assisted by dipolar orientational ordering, which may be relevant to crystallizations, e.g., under an external electric field, on a charged surface, or under extreme conditions.

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