Mysteries of water and other anomalous liquids: “slow” sound and relaxing compressibility and heat capacity (brief review)

Reasons for the existence of “fast” sound at terahertz frequencies in various liquids have been analyzed. It has been shown that the fast sound speed is described well by the conventional formula from the theory of elasticity $V_l = ((B(\omega)+4/3G(\omega))/\rho)^{1/2}$, where $\rho$ is the density of a liquid and $B(\omega )$ and $G(\omega )$ are the bulk and shear moduli at the frequency $\omega$, respectively. The excess of the speed of fast sound over the speed of normal sound in “normal” liquids is 10–20% and is almost completely determined by the contribution of the shear modulus $G(\omega )$ at high frequencies, and vanishes on the Frenkel line. At the same time, the huge excess (50–120%) of the fast speed of sound over the speed of normal sound in some liquids (called “anomalous”), such as water and tellurium melt, is due mainly to the strong frequency dependence of the bulk modulus $B(\omega)$. Anomalously low relaxing bulk moduli were studied in our previous works for many oxide and chalcogenide glasses near smeared pressure-induced phase transitions. In anomalous liquids, smeared phase transitions also occur in a wide temperature and pressure region, which sharply reduces the bulk moduli and speeds of sound. Thus, the record large difference between speeds of fast and normal sound in anomalous liquids is due not to anomalously fast sound but to the fact that normal sound in such liquids is anomalously “slow” and bulk moduli are anomalously low. Ultrasonic studies of low- and high-density amorphous water ices show that their bulk moduli are indeed a factor of 4–5 higher than the bulk modulus of water. In addition, because of smeared phase transitions, the heat capacities of water and tellurium melt are a factor of 1.5–2 higher than those for normal liquids; i.e., anomalous liquids are characterized not only by an anomalous (nonmonotonic) behavior but also by anomalous magnitudes of physical quantities for most of the available measurement methods. A similar anomalous increase in the compressibility and heat capacity is observed for all fluids in the close vicinity of the liquid–gas critical point. In this case, anomalously fast sound is observed at terahertz frequencies, which is also due to a sharp increase in the bulk modulus $B(\omega )$ at high frequencies. At the same time, high compressibility and heat capacity, as well as a large excess of the speed of fast sound over the speed of normal sound, for anomalous liquids and glasses near smeared phase transitions are not necessarily due to the proximity of critical points and occur in any scenario of the smeared phase transition.