Phase Transitions and the Effects of Pressure

In summary, we calculate that the low clinoenstatite is not stable under hydrostatic conditions and enstatite has a comparatively small stability field. The energy differences are so small that they are within the reliability of the simulations and thus the precise positions of the phase boundaries are not well located. The primary reason for this problem is the reliability of the potential models. Hence, calculating phase relationships represents the most difficult challenge for free energy minimization techniques. However, the simulations do provide valuable insights into the mechanisms of phase transitions and the effect of pressure and/or temperature on the crystal structures and the relative phase stabilities. 

Plot the enthalpy, entropy, and chemical potential of water as a function of temperature at some pressure P using the Steam Tables, and identify the discontinuities occuring at the phase transition. Neglect the effect of pressure on the enthalpy and entropy of the liquid. 

The effects of pressure on the phase transition of liquid water to ice (and within the ice phase itself) are complicated by the formation of several pressure-dependent ice polymorphs (Chaplin, 2004 Franks, 1984, 2000 Kalichevsky et al., 1995 Ludwig, 2001). Thirteen crystalline forms of ice have been reported to date Ih (hexagonal or normal or regular ice), Ic (cubic... 

Neutral NIPA gel is the most extensively studied among known gels from the standpoint of phase transition, and thus, various physical properties around the transition have been reported. These include the shear and bulk modulus [20, 24], the diffusion constant of the network [25], spinodal decomposition [26], specific heat [21], critical properties of gels in mixed solvents [8] and the effect of uniaxial [27] and hydrostatic [28] pressures on the transition, and so... 

The effects of pressure on the properties of perovskite fes and rls are manifestations of the influence of pressure on the soft fe mode frequency of the host lattice [14,24], This frequency is determined by a delicate balance between short-range and long-range forces, and these forces exhibit markedly different dependences on interatomic separation, or pressure. Specifically, pressure increases the soft-mode frequency at constant temperature, which reduces the polarizability of the host lattice, thereby reducing Ac. The result is a shift of the transition temperature, Tc (or Tm), to lower temperatures and a suppression of the e (T) response in the high temperature paraelectric phase [14,24],... 

Inversion of phase relationships induced by spin-pairing in Fe2+ ions provides one mechanism for possibly enriching this transition element in the Lower Mantle. Other, more general mechanisms influencing element fractionations, are the effects of pressure on relative sizes, crystal field stabilization energies, bond-types and oxidation states of the cations. 

We determined further thermodynamic parameters for the reversible phase transition between the crystalline (high temperature) and gel (low temperature) phases by studying the effect of hydrostatic pressure on the phase transition at c = 0.1 M. A swollen gel was loaded into a quartz cell as described above, and on this occasion the quartz cell was contained in a Zircal pressure cell designed for pressures up to 2 kbar [25],... 

For instance, Raman spectroscopy was used to study the effect of pressure and temperature on the phase composition of fluoranil crystals. Figure 2 shows the Raman spectra obtained at a series of increasing pressures, where the changes in band frequency indicate the existence of pressure-induced phase transitions. It was deduced from sharp discontinuities in the Raman spectra that a phase transition took place at a temperature of around 180 K if the pressure was 1 atm, but that this transition shifted to 300 K if the pressure was increased to 0.8 GPa. Other work indicates that this particular phase transition does not entail a change in the crystal space group, but involves displacement within the unit cell. 

Values of the Helmholtz energy estimated as a function of pressure at constant temperature on the basis of equation (2.9.22) are shown in fig. 2.11. These plots are reasonably linear in the logarithm of the pressure at low pressures. This is to be expected, since the density is proportional to the pressure under these conditions, and the effects of non-ideality are relatively unimportant. However, at higher pressures the value of A, starts to rise sharply due to non-ideality. Eventually, one reaches positive values of A, indicating that the fluid is not stable. It has been shown that the hard-sphere system undergoes a phase transition from fluid to solid when = 0.943. For the system considered in fig. 2.11, this... 

Very little is known about the motions of lipid bilayers at elevated pressures. Of particular interest would be the effect of pressure on lateral diffusion, which is related to biological functions such as electron transport and some hormone-receptor interactions. Pressure effects on lateral diffusion of pme lipid molecules and of other membrane components have yet to be carefully studied, however. Figure 9 shows the pressure effects on the lateral self diffusion coefficient of sonicated DPPC and POPC vesicles [86]. The lateral diffusion coefficient of DPPC in the liquid-crystalline (LC) phase decreases, almost exponentially, with increasing pressure from 1 to 300 bar at 50 °C. A sharp decrease in the D-value occurs at the LC to GI phase transition pressure. From 500 bar to 800 bar in the GI phase, the values of the lateral diffusion coefficient ( IT0 cm s ) are approximately constant. There is another sharp decrease in the value of the lateral diffusion coefficient at the GI-Gi phase transition pressure. In the Gi phase, the values of the lateral diffusion coefficient ( 1-10"" cm s ) are again approximately constant. 

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