Critical Phase Transitions Under Pressure

Indentation techniques were widely used for a long time to investigate the plasticity of silicon at low temperature. However, a difficulty arises because silicon shows a phase transition from diamond-cubic structure to p-Sn metallic Si at a pressure of about 12GPa [49]. As the shear stress increases during an indentation test, the hydrostatic component simultaneously increases and the critical pressure for the phase transition can be reached. In such conditions, the hardness values and dislocation microstructures cannot be representative of dislocation-induced plasticity mechanisms. Indeed, the occurrence of the phase transition under indentation was found to explain the observed saturation of hardness values below 400 °C ([50,51] see also Fig. 8). Dislocations were nevertheless observed after indentation at temperatures lower than 400 °C, but their possible connection with the phase transition was not investigated. 

There are many other examples in the literature where sealed-vessel microwave conditions have been employed to heat water as a reaction solvent well above its boiling point. Examples include transition metal catalyzed transformations such as Suzuki [43], Heck [44], Sonogashira [45], and Stille [46] cross-coupling reactions, in addition to cyanation reactions [47], phenylations [48], heterocycle formation [49], and even solid-phase organic syntheses [50] (see Chapters 6 and 7 for details). In many of these studies, reaction temperatures lower than those normally considered near-critical (Table 4.2) have been employed (100-150 °C). This is due in part to the fact that with single-mode microwave reactors (see Section 3.5) 200-220 °C is the current limit to which water can be safely heated under pressure since these instruments generally have a 20 bar pressure limit. For generating truly near-critical conditions around 280 °C, special microwave reactors able to withstand pressures of up to 80 bar have to be utilized (see Section 3.4.4). 

The explosive phenomena produced by contact of liquefied gases with water were studied. Chlorodifluoromethane produced explosions when the liquid-water temperature differential exceeded 92°C, and propene did so at differentials of 96-109°C. Liquid propane did, but ethylene did not, produce explosions under the conditions studied [1], The previous literature on superheated vapour explosions has been critically reviewed, and new experimental work shows the phenomenon to be more widespread than had been thought previously. The explosions may be quite violent, and mixtures of liquefied gases may produce overpressures above 7 bar [2], Alternative explanations involve detonation driven by phase changes [3,4] and do not involve chemical reactions. Explosive phase transitions from superheated liquid to vapour have also been induced in chlorodifluoromethane by 1.0 J pulsed ruby laser irradiation. Metastable superheated states (of 25°C) achieved lasted some 50 ms, the expected detonation pressure being 4-5 bar [5], See LIQUEFIED NATURAL GAS, SUPERHEATED LIQUIDS, VAPOUR EXPLOSIONS... 

We re all used to seeing solid/liquid and liquid/gas phase transitions, but behavior at the critical point lies so far outside our normal experiences that it s hard to imagine. A gas at the critical point is under such high pressure and its molecules are so close together, that it becomes indistinguishable from a liquid. A... 

Theoretical approaches to total energy as a function of volume predict a phase transition to the rock salt structure under high pressure [11,12], The transition is calculated to occur at a pressure of about 245 GPa and an experimental value of 230 GPa [13] has been quoted [9], but other workers quote 10 -14 GPa [14]. The critical volume ratio [11] is V/V0 = 0.83, equivalent to a molecular volume reduction from 31 to 27 A3. 

The effects of such precipitation conditions as pressure, temperature, and solute and solvent concentrations are listed in Table 2. These effects are related to the behavior of the maximum attainable supersaturation 5 m, as described by Equation (51) and also to the phase transition at the mcp between the jet mixing and droplet dispersion mechanisms. As follows from our earlier discussions in Sections 2 and 5, the most uniform particles can be produced under conditions very close to the mcp (practically, just above P ), where the supercritical properties are most pronounced, local values of supersaturation are high, and the constants Cgq, Tn, and tq are the smallest. Figure 19a shows that particles produced below the mixture critical pressure are more agglomerated than to the individual and separate crystal particles obtained at high pressure. This is because the nuclei confined within the droplets at P < Pm coalesce and fuse during further growth. In this respect,... 

Coexistence of FM order and superconductivity under pressure The experimental phase diagram of FM collapse under pressure and simultaneous appearance of superconductivity is shown in fig. 43. The critical pressure for disappearance of FM order is pc2 = 16-17 kbar. The SC phase appears between pc = 10 kbar and pc2 = 16 kbar which is also the critical pressure for the FM-PM transition. The critical temperature Tx p) of the jc-phase hits the maximum of Tdp) at the optimum pressure pm = 12.5 kbar. As mentioned before the nature of the order parameter in the jc-phase remains elusive. The coincidence of maximum Tc with vanishing jc-phase order parameter suggests that the collective bosonic excitations of the X-phase which supposedly become soft at pm mediate superconductivity and not quantum critical FM spin fluctuations which are absent due to the persisting large FM... 

In P-r space, we see only two remarkable features the vapor pressure curve, indicating the conditions under which the vapor and liquid coexist, and the critical point, at which the distinction between vapor and liquid disappears. We indicate in this figure the critical isotherm 7 = Tc and the critical isobar P = Pc. If the liquid is heated at a constant pressure exceeding the critical pressure, it expands and reaches a vapor-like state without undergoing a phase transition. Andrews and Van der Waals called this phenomenon the continuity of states. 

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