  We report a new experimental approach for observing mesoscopic fluctuations
underlying the thermodynamic anomalies of ambient liquid water. In this
approach, two sound velocity measurements with different frequencies, namely
inelastic X-ray scattering (IXS) in THz band and ultrasonic (US) in MHz band,
are required to investigate the relaxation phenomenon with the characteristic
frequency between the two aforementioned frequencies. We performed IXS
measurements to obtain the IXS sound velocity of liquid water from the ambient
conditions to the supercritical region of liquid-gas phase transition (LGT) and
compared the results with the US sound velocity in the literature. We found
that the ratio of the two sound velocities, Sf, which corresponds to the
relaxation intensity, exhibits a simple but significant change. Two distinct
rises were observed in the high-temperature and low-temperature regions,
implying that two relaxation phenomena exist: in the high-temperature region, a
peak was observed near the LGT critical ridge line, which was linked with
changes in the density fluctuation and isochoric and isobaric specific heat
capacities; in the low-temperature region, Sf increased toward the
low-temperature region, which was linked with the change in the isochoric heat
capacity. We concluded that these two relaxation phenomena are originated from
critical fluctuations of liquid-gas phase transition (LGT) and liquid-liquid
phase transition, respectively. The linkage between Sf and isochoric heat
capacity in the low-temperature region proves that the relaxation is the cause
of the well-known heat capacity anomaly of ambient liquid water. In this study,
both LGT and LLT critical fluctuations were observed, and the relationship
between thermodynamics and the critical fluctuations was comprehensively
discussed.
