Investigation of Solidification in Supercooled Water Drops using Large Data Sets of Synchronized Optical Images and X-ray Diffraction Patterns

The freezing of supercooled water drops is a complex example of rapid nonequilibrium solidification that includes dendritic crystal growth, changes in volume leading to mechanical deformation and fracture, and the formation of metastable crystal phases. It is also an important natural phenomenon that occurs in clouds and can trigger precipitation.<br/><br/>We investigated the freezing of water drops cooled by evaporation in vacuum. We imaged optically the freezing drops at high magnification with short light exposures, and we probed them simultaneously with ultrashort X-ray laser pulses. This approach provided a snapshot of a drop’s state at both the micron scale and at the molecular scale, and had the temporal resolution needed to resolve a freezing process that is completed in approximately one millisecond. Since the X-ray lasers are pulsed and have sufficient energy to damage the drops, only one multiscale data point can be collected from a drop.<br/><br/>A major challenge in investigating a spontaneously freezing system with high resolution is the randomness of nucleation. Our experiment reduced greatly the range of nucleation times by using very rapid cooling, but even so the spread of nucleation times was comparable with the duration of solidification, and the nucleation statistics averaged the details of the freezing dynamics. We therefore collected large data sets of drops freezing at several average time delays, which each set containing a distribution of drops at different elapsed times after ice nucleation. The data contains more than 10000 simultaneous optical and X-ray measurements from single drops, and additional optical data from more than 40000 drops. At each average time delay, we had available thousands of data points to measure the distribution of the stages of freezing that could be observed experimentally.<br/><br/>Seven distinct stages of freezing were identifiable from the optical images, from supercooled liquid drops to drops that shattered due to the strain accumulated during solidification. We developed a kinetic model of freezing based on these stages, and we determined all the model properties (nucleation rate, stage durations, probability of shattering, etc.) though a complex fitting procedure that used the experimental distributions of freezing stages.<br/><br/>Using the optical images and the seven-stage freezing model, we sorted the X-ray diffraction data by the time elapsed from nucleation. Sorting improved substantially the temporal resolution of diffraction, and the resolution was sufficient to observe the increase in the intensity of high-index diffraction peaks, which indicated that long-range crystalline order in ice was largely formed in approximately one millisecond. The diffraction patterns also showed that during the first millisecond after freezing the ice had a hexagonal crystal structure with inhomogeneous strain and a grain size on the order of 100 nm.