Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å −1 , which covered the principal doublet of the x-ray structure factor of water. The oxygen-oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen-oxygen structure factor (q 2 ). We found that q 2 exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q 2 shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen-oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling.

In this paper, we study the nonlinear interaction of a laser beam with a periodic lattice of nanoparticles in the presence of a planar magnetostatic wiggler. The static magnetic field of the wiggler can couple with the electric field of the laser wave and change the electric field intensity of the pumped wave, leading to the formation of a nonlinear force. In consequence, the nonlinear force enhances plasmonic oscillations of the electronic cloud of each nanoparticle causing electron density modulation, which improves self-focusing property of the laser beam propagating through a periodic lattice of nanoparticles. By manipulating a classical microscopic approach into plasmonic oscillations of electronic clouds of the nanoparticles and the well–known perturbative method, a nonlinear dispersion relation describing the evolution of the laser amplitude propagating through the nanoparticle lattice has been obtained. The effect of the wiggler magnetic strength on the evolution of the laser transverse profile has been discussed. It was found that by increasing the wiggler strength, the transverse profile bandwidth shrinks and laser focusing is enhanced. In addition, further numerical results indicated that by increasing the wiggler field strength, the cut-off frequency of the body waves increases.