Phase transition other ices

Figure 9.9 Exceptional physical properties of liquid water (solid lines) temperature dependences (upper diagrams) of the density d (45) and isothermal compressibility Xt (adapted from Refs. (45 7)) pressure dependences (lower drawings) of the shear viscosity 7] at various temperatures (adapted from Ref. (48)) and of the isothermal diffusion coefficient Z) at 0 (adapted from Ref. (49)). Dashed lines sketch typical dependences displayed by almost all other liquids. Note that at —15 °C no value is given for 17 at/ > 300MPa, because of a phase transition towards ice V (Figure 8.5).

From our data, obtained above for the temperatures —7°C, —30°C, and 100 K, we show in Fig. 38a that the bandwidth AvT ban(i decreases with cooling of ice. However, at very low temperature this parameter practically does not change with T. Our estimates show that at a given pressure the criterion (A36) roughly corresponds to the phase transition of ice Ih to other ice modification. 

In both cases the density p(r) depends on the local pressure pit) and temperature T(r). In sufficiently large satellites the density of ice may change stepwise on certain levels corresponding to p, T conditions of phase transitions in ice. In particular, in water ice at about 200 K the phase equilibrium levels for I => II and II => VI transitions are about 0.2 GPa and 0.6 GPa, respectively. On the other hand, the pressure in the interiors of the smallest icy satelhtes combined with their low internal temperature allow for only very slow creep (slow rheology) of the material forming the satellite. So, if a small satellite have been formed as a porous body it is quite possible that the internal porosity has survived imtil the present time. 

The variation of the phase transition temperature with pressure can be calculated from the knowledge of the volume and enthalpy change of the transition. Most often both the entropy and volume changes are positive and the transition temperature increases with pressure. In other cases, notably melting of ice, the density of the liquid phase is larger than of the solid, and the transition temperature decreases... 

Some physical properties of water are shown in Table 7.2. Water has higher melting and boiling temperatures, surface tension, dielectric constant, heat capacity, thermal conductivity and heats of phase transition than similar molecules (Table 7.3). Water has a lower density than would be expected from comparison with the above molecules and has the unusual property of expansion on solidification. The thermal conductivity of ice is approximately four times greater than that of water at the same temperature and is high compared with other non-metallic solids. Likewise, the thermal dif-fusivity of ice is about nine times greater than that of water. 

Calorimeters of Historical and Special Interest Around 1760 Black realized that heat applied to melting ice facilitates the transition from the solid to the liquid stale at a constant temperature. For the first time, the distinction between the concepts of temperature and heat was made. The mass of ice that melted, multiplied by the heal of fusion, gives the quantity of heal. Others, including Bunsen, Lavoisier, and Laplace, devised calorimeters based upon this principle involving a phase transition. The heat capacity of solids and liquids, as well as combustion heats and the production of heat by animals were measured with these caloritnelers. 

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

At very high pressures (0.3-2.1 GPa), gas hydrates undergo structural transitions to other hydrate phases and filled ice phases. Guests can multiply occupy the large cages of these high-pressure hydrate phases. 

The vapor-water phase transition occurs when classically determined action (A8) approaches to the minimal vallue h due to too short lifetime Tq of longitudinally vibrating dipoles. On the other hand, the transition of ice Ih to other ice modification occurs when the translational bandwith Av—t-band approaches to classically estimated limit (A36) (A38). 

---