Phase transitions hysteresis

Phase transition hysteresis takes place within T range depends on the G expansion coefficients (Equation 27)... 

More recently, studies of the hysteresis of these phase transitions have illuminated the importance of kinetic factors in solid-solid phase transitions [224]. The change between crystal stmctures does not occur at the same point when pressure is increasing, as when it is decreasing the difference between this up-stroke and down-stroke pressure... 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

The small effects and the progressive evolutions observed seem to be in agreement with a second order phase transition. The lack of coexistence of the low- and high-temperature phases in the temperature range close to the transition temperature and the apparent lack of thermal hysteresis confirm this conclusion. 

First-order phase transitions exhibit hysteresis, i.e. the transition takes place some time after the temperature or pressure change giving rise to it. How fast the transformation proceeds also depends on the formation or presence of sites of nucleation. The phase transition can proceed at an extremely slow rate. For this reason many thermodynamically unstable modifications are well known and can be studied in conditions under which they should already have been transformed. 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

For solid nitrogen five modifications are known that differ in the packing of the N2 molecules. Two of them are stable at normal pressure (transition temperature 35.6 K) the others exists only under high pressure. At pressures around 100 GPa a phase transition with a marked hysteresis takes place, resulting in a non-molecular modification. It presumably corresponds to the a-arsenic type. Electrical conductivity sets in at 140 GPa. 

A hysteresis cycle in the molar susceptibility measurements has been observed for [Ni2(Medpt)2(N3)2(/r-N3)2] (883). This has been ascribed to a phase transition caused by an asymmetrization process of the rhombus-like centrosymmetric [Ni-(N3)2-Ni] core that occurs with falling temperature. The asymmetrization transition can be explained in terms of a second-order Jahn-Teller distortion, taking into account the local symmetry of the dinuclear [Ni-(N3)2-Ni] entity (D2h, rhombic symmetry) before the arrangement.2128... 

Also known for some time is a phase transition at low temperature (111K), observed in studies with various methods (NQR, elasticity measurement by ultrasound, Raman spectrometry) 112 temperature-dependent neutron diffraction showed the phase transition to be caused by an antiphase rotation of adjacent anions around the threefold axis ([111] in the cubic cell) and to lower the symmetry from cubic to rhombohedral (Ric). As shown by inelastic neutron scattering, this phase transition is driven by a low-frequency rotatory soft mode (0.288 THz 9.61 cm / 298 K) 113 a more recent NQR study revealed a small hysteresis and hence first-order character of this transition.114 This rhombohedral structure is adopted by Rb2Hg(CN)4 already at room temperature (rav(Hg—C) 218.6, rav(C—N) 114.0 pm for two independent cyano groups), and the analogous phase transition to the cubic structure occurs at 398 K.115... 

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

In Figure 8.5, w is the distance between the heating and cooling curves at the point where a = 0.5 is called the hysteresis width. This temperature may be quite small, or it may amount to several degrees depending on the nature of the phase transition and the heating rate. Many substances exhibit this type of behavior as a result of a phase change. 

Fe(btr)2(NCS)2]-H20 undergoes a complete ST centred at 134 Kwith a hysteresis loop of width 21 K. This derivative represents the first example of a 2D ST compound and has become a model material in SCO research. The presence of a crystallographic phase transition to account for the observed hysteresis was first proposed since crystal cracking was regularly observed when the sample was cooled through the temperature region of the spin transition [59]. Recent X-ray data recorded at 95 K, where the com-... 

When we compared the viscosities of solutions of natural rubber and of guttapercha and of other elastomers and later of polyethylene vs.(poly)cis-butadiene, with such bulk properties as moduli, densities, X-ray structures, and adhesiveness, we were greatly helped in understanding these behavioral differences by the studies of Wood (6) on the temperature and stress dependent, melting and freezing,hysteresis of natural rubber, and by the work of Treloar (7) and of Flory (8) on the elasticity and crystallinity of elastomers on stretching. Molecular symmetry and stiffness among closely similar chemical structures, as they affect the enthalpy, the entropy, and phase transitions (perhaps best expressed by AHm and by Clapeyron s... 

Reconstructive phase transitions occur when major changes are made in the topology, i.e. when the bond graph is reorganized. The transitions usually observed in structures with lattice-induced strain are displacive and often second order (no latent heat). Reconstructive transitions arise when two quite different structures with the same composition have similar free energies. Unlike the displacive transitions they involve the dissolution of one structure and the recrystallization of a quite different structure. These phase transitions possess a latent heat and often display hysteresis. 

A similar study by O Brien and coworkers utilized bilayers composed of a shorter chain diacetylenicPC (9) and DSPC or DOPC [37]. Phase separation was demonstrated in bilayers by calorimetry and photopolymerization behavior. DSC of the 9/DSPC (1 1) bilayers exhibited transitions at 40 °C and 55 °C, which were attributed to domains of the individual lipids. Polymerization at 20 °C proceeded at similar rates in the mixed bilayers and pure 9 bilayers. A dramatic hysteresis effect was observed for this system, if the bilayers were first incubated at T > 55 °C then cooled back to 20 °C, the DSC peak for the diacetylenicPC at 40 °C disappeared and the bilayers could no longer be photopolymerized. The phase transition and polymerizability of the vesicles could be restored simply by cooling to ca. 10 °C. A similar hysteretic behavior was also observed for pure diacetylenicPC bilayers. Mixtures of 9 and DOPC exhibited phase transitions for both lipids (T = — 18 °C and 39 °C) plus a small peak at intermediate temperatures. Photopolymerization at 20 °C initially proceeded at a similar rate as observed for pure 9 but slowed after 10% conversion. These results were attributed to the presence of mixed lipid domains... 

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