Higher order phase change

These results were ascribed to higher-order phase changes in water solutions containing chloride. The inflection in the temperature dependence shown in Figure 8 occurs at 42°C. It was postulated that the higher-order phase change for water in the presence of chloride at this temperature may be related to the inability of advanced forms of life to survive temperatures above this value. 

The shape of the curve, similar to the Greek letter lambda, has led to the term lambda transition. This is preferable to the term higher-order phase change, which presupposes the correctness of the theory as outlined above. Indeed, the occurrence of such transitions seems really to imply a breakdown, or at least a limitation, in the usual concept of phase. This concept is based on the idea that there exist entirely distinct forms of a substance, and for each of them there is a, p suriace which may be thought of as being continued into an unstable region, as in Fig. 20. The... 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

The formation and dissolution of 2D Me UPD phases can involve positive and negative 2D nucleation and growth steps, respectively. 2D nucleation and growth represent a first order phase transition where an expanded overlayer is transformed into a condensed one (or vice versa) by a discontinuous change of r. Additionally, higher order (order-disorder) phase transitions, characterized by 7" = constant, but with a discontinuity in its partial derivative (dr / dE), may also take place within 2D Meads overlayers in the UPD range. However, clear experimental evidence for higher order phase transitions in Me UPD overlayers does not yet exist. 

In these approximations, as well as in higher ones, one finds that when w < 0 (attraction) there exists a critical temperature below which a first order phase change will be observed—a sudden condensation, as the equilibrium gas pressure is increased, from a dilute localized monolayer to a relatively condensed localized monolayer. For a plane square surface lattice of sites, the Bragg-Williams approximation gives — w/kTc = 1 and the quasi-chemical approximation — w/kTc = 1.386. 

Time-resolved spectroscopy has become an important field from x-rays to the far-IR. Both IR and Raman spectroscopies have been adapted to time-resolved studies. There have been a large number of studies using time-resolved Raman [39], time-resolved resonance Raman [7] and higher order two-dimensional Raman spectroscopy (which can provide coupling infonuation analogous to two-dimensional NMR studies) [40]. Time-resolved IR has probed neutrals and ions in solution [41, 42], gas phase kmetics [42] and vibrational dynamics of molecules chemisorbed and physisorbed to surfaces [44]- Since vibrational frequencies are very sensitive to the chemical enviromnent, pump-probe studies with IR probe pulses allow stmctiiral changes to... 

Observe how in each of these four events, H is zero until, at some critical Ac (which is different for different cases), H abruptly jumps to some higher value and thereafter proceeds relatively smoothly to its final maximum value i max = log2(8) = 3 at A = 7/8. In statistical physics, such abrupt, discontinuous changes in entropy are representative of first-order phase transitions. Interestingly, an examination of a large number of such transition events reveals that there is a small percentage of smooth transitions, which are associated with a second-order phase transition [li90a]. 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

MnAs exhibits this behavior. It has the NiAs structure at temperatures exceeding 125 °C. When cooled, a second-order phase transition takes place at 125 °C, resulting in the MnP type (cf. Fig. 18.4, p. 218). This is a normal behavior, as shown by many other substances. Unusual, however, is the reappearance of the higher symmetrical NiAs structure at lower temperatures after a second phase transition has taken place at 45 °C. This second transformation is of first order, with a discontinuous volume change AV and with enthalpy of transformation AH. In addition, a reorientation of the electronic spins occurs from a low-spin to a high-spin state. The high-spin structure (< 45°C) is ferromagnetic,... 

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