Phase transformation coexistence

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

The isotherms represented in Fig. 1 give a general idea of the equilibria in the Pd-H system under different p-T conditions. Most experimental evidence shows, however, that the equilibrium pressure over a + /3 coexisting phases depends on the direction of the phase transformation process p a-p > pp-a (T, H/Pd constant). This hysteresis effect at 100°... 

The Nematic - Isotropic Phase Transition. For nematic solutions kept free from moisture, the phase transformations described in the preceding were not observed, but the nematic phase could be reversibly transformed to the isotropic phase over a temperature interval Tj - Tj lOK. For the sample with w = 0.041, this transition occurred over the range T = 92 C to Tj = 101 0. For temperatures between T and Tj, the sample was biphasic, with the isotropic and nematic phases coexisting. This behavior is similar to that observed in previous studies, in which Tj - Tj is observed to be independent of w over a range of w for which Tj increases with increasing w (3,4). 

Three-Phase Transformations in Binary Systems. Although this chapter focuses on the equilibrium between phases in binary component systems, we have already seen that in the case of a entectic point, phase transformations that occur over minute temperature fluctuations can be represented on phase diagrams as well. These transformations are known as three-phase transformations, becanse they involve three distinct phases that coexist at the transformation temperature. Then-characteristic shapes as they occnr in binary component phase diagrams are summarized in Table 2.3. Here, the Greek letters a, f), y, and so on, designate solid phases, and L designates the liquid phase. Subscripts differentiate between immiscible phases of different compositions. For example, Lj and Ljj are immiscible liquids, and a and a are allotropic solid phases (different crystal structures). 

To check the phase transformation isotropic -> nematic, the validity of the Clausius Clapeyron equation is examined. It has been shown 38), that within the experimental error the results fulfill Eq. 1 in analogy to the low molar mass l.c. The phase transformation isotropic to l.c. is therefore of first order with two coexisting phases at the transformation point. Optical measurements on the polymers confirm these thermodynamical measurements (refer to 2.3.1.3). 

From the measurements of the birefringence in Fig. 12a further important aspect has to be mentioned. With increasing temperature An does not continuously tend to zero at the phase transformation temperature Tc but vanishes discontinuously. At the phase transformation the nematic phase, having a finite birefringence, coexists... 

The phase rule(s) can be used to distinguish different types of equilibria based on the number of degrees of freedom. For example, in a unary system, an invariant equilibrium (/ = 0) exists between the liquid, solid, and vapor phases at the triple point, where there can be no changes to temperature or pressure without reducing the number of phases in equilibrium. Because / must equal zero or a positive integer, the condensed phase rule (/ = c — p + 1) limits the possible number of phases that can coexist in equilibrium within one-component condensed systems to one or two, which means that other than melting, only allotropic phase transformations are possible. Similarly, in two-component condensed systems, the condensed phase rule restricts the maximum number of phases that can coexist to three, which also corresponds to an invariant equilibrium. However, several invariant reactions are possible, each of which maintains the number of equilibrium phases at three and keeps / equal to zero (L represents a liquid and S, a solid) ... 

Decrease in purity of crystal structure. Since larga single crystals are easily obtained, the amount impurity in a crystal can be reduced. However, in the case of consecutive phase transformations (6), the possibility of coexisting crystal... 

Some special attention should be placed on the p (bulk) phase as well. Although this form is often reported as being non-crystalline, it gives rise to sharp Bragg reflections commensurate with lamellar order with a long period of 12.3 A [74] and fiber periodicity of 16.6 A (which corresponds to two monomer units) [67]. Thus, it differs from real crystals in the sense that it is mesomorphic. This phase also includes the presence of absorbed solvent and may be obtained by extended exposure to solvent vapor or solvent (cf., the solvent section). In particular, it has been found to appear as an intermediate step in the transformation from the solvent induced clathrate-like structure to the solvent-free well-ordered a phase [74], The a and fi (bulk) phases may coexist and are closed related to one another but are still structurally incompatible. 

In general, any substance that is above the temperature and pressure of its thermodynamic critical point is called a supercritical fluid. A critical point represents a limit of both equilibrium and stability conditions, and is formally delincd as a point where the first, second, and third derivatives of the energy basis function for a system equal zero (or, more precisely, where 9P/9V r = d P/dV T = 0 for a pure compound). In practical terms, a critical point is identifled as a point where two or more coexisting fluid phases become indistinguishable. For a pure compound, the critical point occurs at the limit of vapor-Uquid equilibrium where the densities of the two phases approach each other (Figures la and lb). Above this critical point, no phase transformation is possible and the substance is considered neither a Uquid nor a gas, but a homogeneous, supercritical fluid. The particular conditions (such as pressure and temperature) at which the critical point of a substance is achieved are unique for every substance and are referred to as its critical constants (Table 1). 

The conditions for equilibrium discussed in Section 1.1.3 are applied here to the problem of phase equilibria. These conditions are that, in order for two or more phases to coexist at equilibrium, they must have the same temperature and pressure and the chemical potential of each component must be equal in all the phases. The chemical potential is not a measurable quantity and is not intuitively related to observable physical properties. Applying the conditions of equilibrium to real fluids involves a transformation to more practical terms and the utilization of fluid models such as equations of state. 

In this chapter we have summarized the fundamentals and recent advances in thermodynamic and kinetic approaches to lithium intercalation into, and deintercalation from, transition metals oxides and carbonaceous materials, and have also provided an overview of the major experimental techniques. First, the thermodynamics oflithium intercalation/deintercalation based on the lattice gas model with various approximations was analyzed. Lithium intercalation/deintercalation involving phase transformations, such as order-disorder transition or two-phase coexistence caused by strong interaction oflithium ions in the solid electrode, was clearly explained based on the lattice gas model, with the aid of computational methods. 

First-order phase transitions are characterized by a coexistence region and thermal hysteresis. The kinetics of the overall phase transformation is a mixed process of nucleation, and growth of the different phase boundaries upon complete completion of the process, which occur more or less simultaneously. 

The hypothesis on the phase transformation under heating of CdSe Tei.x nanoparticles is consistent with the phase diagram of this system well known for the bulk compounds this system includes the narrow two-phase region in which sphalerite and wurtzite CdSCxTcj-x coexist at 0.8[Pg.394]

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