Phase transitions in ice

Appendix V. Classically Estimated Minimal Action and Phase Transitions in Ice and Water... 

APPENDIX V. CLASSICALLY ESTIMATED MINIMAL ACTION AND PHASE TRANSITIONS IN ICE AND WATER... 

Keywords. Icy satelhtes, kinetics of phase transitions in ices, porous ices, theology of ices... 

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. 

In Fig 1.10, Riehle shows log J (J = nuclei per time and volume) as a function of the temperature of the phase transition water - ice different pressures of 1 and 2100 bar. At 2100 bar, J is comparable with J at an approximately 35 °C higher temperature. Under pressure, water can be subcooled further, with a delayed formation of nuclei. 

The second type is simple phase transitions in which one phase transforms into another of identical composition, e.g., diamond graphite, quartz coe-site, and water ice. This type sounds simple, but it involves most steps of heterogeneous reactions, including nucleation, interface reaction, and coarsening. 

Our approach based on experimental fact that in conditions enough fast cooling at T < 133K water is able to form amorphous phases [1-4], There is polyamorphism of ice, but for all that ice has only two essentially different amorphous forms. In the field of low pressure the amorphous phase of low density is formed, and at increase of pressure there is an amorphous phase of higher density. Qualitative scheme of this polyamorphic transition in ice is shown on Fig. 1. At change of pressure or temperatures in amorphous phases occur more then 20% jumps of density. 

The temperature dependence of Tj (Fig. 13) points to a noticeable effect of the nature of adsorbent (phenolic oligomer) on the properties of adsorbed water. Firstly, the value of Ti (1-1.2 s) is nearly half that of free water (in 0.5 1). Secondly, relaxation curves sharply differ in 20- and 400-oersted fields. In the 20-oersted field the dependence Ti = f (T) is stepwise and the steepest part is observed near temperatures corresponding to the phase transition water - ice . The authors suggest that the minimum observed between 0 to -2 °C is connected with the dispersion of the relaxation time distribution. In order to confirm this assumption a classical relaxation analysis using deuterated water and the temperature dependence of longitudinal relaxation time is required. 

Because structural phase transitions are often ferroelastic or coelastic in character it is essential to have a well-defined stress applied to the crystal at high pressures. In effect, this means that a hydrostatic pressure medium must be used to enclose the crystal. A 4 1 mixture by volume of methanol ethanol remains hydrostatic to just over 10 GPa (Eggert et al. 1992) and is convenient and suitable for many studies. If the sample dissolves in alcohols, then a mixture of pentane and iso-pentane which remains hydrostatic to 6 GPa (Nomura et al. 1982), or a solidified gas such as N2, He, or Ar can be employed. Water appears to remain hydrostatic to about 2.5 GPa at room temperature, just above the phase transition from ice-VI to ice-VII (Angel, unpublished data). The solid pressure media such as NaCl or KCl favoured by spectroscopists are very non-hydrostatic even at pressures below 1 GPa and have been shown to displace phase transitions by at least several kbar (e g. Sowerby and Ross 1996). Similarly, the fluorinert material used in many neutron diffraction experiments because of its low neutron scattering power becomes significantly non-hydrostatic at -1.3 GPa. Decker et al. (1979) showed that the ferroelastic phase transition that occurs at 1.8 GPa in lead phosphate under hydrostatic conditions is not observed up to 3.6 GPa when fluorinert was used as the pressure medium. At pressures in excess of the hydrostatic limit of the solidified gas and fluid... 

M. Benoit, D. Marx, and M. Parrinello (1998) Quantum effects on phase transitions in high-pressure ice. Comp. Mat. Set. 10, p. 88... 

As a result we have obtained frozen C02-hydrate-saturated samples. The analysis of the thermo-baric changes in the pressure chamber during the process of hydrate and ice formation allows us to localized any phase transition in the soil samples as well as to calculate the water content, the volumetrical hydrate content (Hy) and the hydrate coefficient Kh (fraction of liquid water transformed into hydrate). 

Tajima, Y., Matsuo, T. and Suga, H. (1984). Calorimetric study of phase transition in hexagonal ice doped with alkali hydroxides. J. Phys. Chem. Solids 45, 1135-1144. 

In the laboratory we normally carry out unidirectional changes, that is, either ice to water or water to ice. We can calculate entropy change in each case using the equation AS = AH/T as long as the temperature remains at 0°C. The same procedure can be applied to the water-steam transition. In this case AH is the heat of vaporization and T is the boiling point of water. Example 18.5 examines the phase transitions in benzene. 

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. 

Some initial experiments on frozen solutions of theiron(II) salts FeCl2.4H20 [Fe(H20)6](C104)3, [Fe(H20)6]S04-H20, and [Fe(H20)6](NH4)2(S04)2, showed that the iron species in each matrix was identical and unaffected by the anion [63]. Very unusual behaviour was detected at about 190 K due to a phase transition in the ice [64], amd this was later confirmed [65]... 

Apart from the protein matrix, where it is possible for protons to move effectively in keeping with a mechanism somewhat similar to that proposed for the motion of protons in ice there is another path for protons through hydrophobic barrier of which the membrane is an example. This transition is based on the observations of phase transitions in a bilayer by X-ray diffraction methods. In this mechanism developed for mitochondria the main role falls to cardiolipin, which accounts for 33% of the total amount of lipids in the mitochondrial membrane.146 The protonation of the head groups of cardiolipin contained in the membranes of mitochondria caused a phase transition of the bilayer into an inverted hexagonal phase.147 This process is promoted by calcium ions whose reactions with the head groups of lipids favor neutralization of the membrane charge and effective dehydration of the polar heads. 

Name the phase transition in each of the following situations and indicate whether it is exothermic or endothermic (a) When ice is heated, it turns to water, (b) Wet clothes dry on a warm siunmer day. (c) Frost appears on a window on a cold winter day. (d) Droplets of water appear on a cold glass of heer. 

Chapter 5 is the scientific core of the book. It begins with familiar phase transitions of ice-to-water and water-to-vapor, both of which demonstrate increased disorder with increased temperature. It then brings in the unique phase transitions of the two-component system, model proteins in water, in which the protein... 

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