First-order transition, occurrence

Another important aspect of phase transitions in solids is the presence of soft modes. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In second-order transitions, the soft mode frequency goes to zero at Tc, but in first-order transitions, the phase change occurs before the mode frequency goes to zero. Soft modes have been found to accompany a variety of solid-state transitions, including those of superconductors and organic solids.2,5 Occurrence of soft modes in phase transitions can be inferred from Landau s treatment wherein atomic displacements may themselves be considered to represent an order parameter. 

The combined DSC and x-ray analysis of PorAA-n with n > 12 revealed the occurrence of two first-order transitions at temperatures T and T2 separating three structurally distinct phases [40], Both transition temperatures and small-angle x-ray spacings characteristic of the phases decrease steadily with the number of methylenes in the side chain (Figure 12). 

Are there additional effects, beyond the shift of the transition temperature, on the smectic-d smectic-C phase transition in chiral-racemic systems The transition is, in the vast majority of compounds, of the second-order type, the first examples for a first-order smectic-d-smectic-C transition were found in chiral compounds possessing large Pg values [7], [8]. It has been even observed, that a weakly first-order transition in the chiral enantiomer becomes continuous in the racemate [79], However, it seems that chirality and/or large spontaneous polarization are not the primary reasons for the occurrence of first-order smectic-d-smectic-C transitions, since first-order transitions were also found in racemic or nonchiral compounds [80], [81] (the above-mentioned second-order transition in a racemate results probably from an increased width of the smectic-d temperature range in the racemate compared to the chiral enantiomer). One relevant factor for a first-order... 

The occurrence of a structural transition in the liquid and the crystalline states, in addition to the two amorphous structures which mimic the 2D-3D transition observed by Shimada, suggest that a first order transition between two liquids GeSe2 with different densities could be possible. Furthermore, measurements based on high pressure Raman spectroscopy on glassy GeSc2 [78] showed that the Raman spectra are reversible. In addition no structural transition was reported up to 9 GPa and only a change in the sample color was noticed. 

Another interesting limit is the quasistatic limit r 0. Based on the numerical solution of the saddle point equations (160)-(162), it was suggested in Ref. 117 that T q) converged to a constant value over a finite range of work values. Figure 15a shows the results obtained for the heat distributions, whereas the path temperature is shown in Fig. 15b. A more detailed analysis [134] has shown that a plateau is never fully reached for a finite interval of heat values when r 0. The presence of a plateau has been interpreted as the occurrence of a first-order phase transition in the path entropy s q) [134]. 

Alphen (dHvA) effect every cycle of the magnetic oscillations is accompanied by a first-order phase transition, and by the appearance of a domain structure. Figure 1, taken from [29], illustrates the splitting of the NMR frequency of Ag109 in metallic silver under the condition of the dHvA effect, which unambiguously testifies to the occurrence of diamagnetic domains. 

Besides fine-structure splitting, the occurrence of spin-forbidden transitions is the most striking feature in which spin-orbit interaction manifests itself. Radiative spin-forbidden transitions in light molecules usually take place at the millisecond time scale, if the transition is dipole allowed. A dipole- and spin-forbidden transition is even weaker, with lifetimes of the order of seconds. Proceeding down the periodic table, spin-forbidden transitions become more and more allowed due to the increase of spin-orbit coupling. For molecules containing elements with principal quantum number 5 or higher (and the late first-row transition metals Ni and Cu), there is hardly any difference between transition probabilities of spin-allowed and spin-forbidden processes. 

We have also examined a two-sublattice model, where the displacement on one sublattice is opposite to that on the other, but this model shows only second-order spin-state transitions. In order to explain the occurrence of both first- and second-order spin-state transitions, we have explored a two-sublattice model where the spin states are coupled to the cube of the breathing mode displacement This model predicts first- or second-order transitions but only zero high-spin-state population at low temperatures. The most general model that predicts nonzero high-spin-state population at low temperatures, a first- or a second-order transition, and other features appears to be one where the coupling of the spin states to a breathing mode is linear and that to an ion-cage mode is quadratic. Nonetheless, spin-state transitions in extended solids need to be further explored to enable us to fully understand the mechanism of these transitions. 

Adsorption isotherm of surfactant vacancies in foam bilayers. As discussed above, the investigation of the stability of foam bilayers at different temperatures allow determination of the binding energy Q of a surfactant molecule in the bilayer. At the highest temperatures of 30°C the Q value for a NaDoS molecule in the foam bilayer (Q 6kT) is high enough to ensure the occurrence of 2D first-order phase transition in the bilayer. Theoretically Q > 8kT is known to be the condition for such a transition in the most frequently encountered 2D lattices [423],... 

The temperature dependence of the thickness of foam bilayers shows the occurrence of a first-order phase transition of melting of hydrocarbon tails of the phospholipid molecules. This melting is realised at a temperature very close to the temperature of the corresponding phase transition in fully hydrated water dispersions of phosphatidylcholines. This result is in agreement with the theoretical considerations of Nagle [436] for the decisive role of van der Waals attractions between hydrocarbon chains of phospholipid molecules for the chainmelting phase transition in bilayer systems. 

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