Analysis of inelastic x-ray scattering spectra of low-temperature water

We analyze a set of high-resolution inelastic x-ray scattering (UCS) spectr a from H2O measured at T = 259, 273, and 294 K using two different phenomen ological models. Model I, called the "dynamic cage model," combines the sho rt time in-cage dynamics described by a,a generalized Enskog kinetic theory with a long-time cage relaxation dynamics described by an alpha relaxation . This model is appropriate for supercooled water where the cage effect is dominant and the existence of an alpha relaxation is evident from molecular -dynamics (MD) simulation data of extended simple point charge (SPC/E) mode l water. Model II is essentially a generalized hydrodynamic theory called t he "three effective eigenmode theory" by de Schepper et al. [1]. This model is appropriate far normal liquid water where the cage effect is less promi nent and there is no evidence of the alpha relaxation from the MD data. We use the model I to analyze IXS data at T = 259 K (supercooled water). We su ccessfully extract the Debye-Waller factor, the cage relaxation time from t he long-time dynamics, and the dispersion relation of high-frequency sound from the short time dynamics. We then use the model II to analyze IXS data at all three temperatures, from which we are able to extract the relaxation rate of the central mode and the damping of the sound mode as well as the dispersion relation for the high-frequency sound. It turns out that the dis persion relations extracted from the two models at their respective tempera tures agree with each other giving the high-frequency sound speed of 2900 /- 300 m/s. This is to be compared with a slightly higher value reported pr eviously, 3200 +/- 320 m/s, by analyzing similar IXS data with a phenomenol ogical-damped harmonic oscillator model [2]. This latter model has traditio nally been used exclusively for the analysis of inelastic scattering spectr a of water. The k-dependent sound damping and central mode relaxation rate extracted from our model analyses are compared with the known values in the hydrody- namic limit.