Location of phase boundary

Sample phase diagrams collected using the two gradient methods are presented in Fig. 9 and 11. It is important to realize that in both cases only the location of phase boundaries are shown, while in fact, phase identification and structural characterization is available continuously along each isotherm and isopleth in the respective plots. 

Although any of the designs mentioned above will provide the location of phase boundaries (versus temperature and pressure), it is also important to know the compositions of the two phases in equilibrium. Note that while tie lines (lines connecting phases in equilibrium on T-x or p-x diagrams) are horizontal for simple binary mixtures, this is not true for phase separation in multicomponent systems (most notably polymer-fluid systems where the polymer sample contains chains of various lengths). Consequently, ports which allow withdrawal of samples following phase separation and equilibration are an important feature of view cells. Such ports also allow for the measurement of partition coefficients of solutes between, for example, aqueous and CO2 phases. 

The study of simple liquids can be said to be the beginning of Molecular Dynamics and Monte Carlo in the 1950s and 60s. Although the scope of molecular simulation, as a field or discipline, has widened dramatically since then, there is nevertheless a continual interest in simple liquids. In fact, this is partly due to the fact that the so-called simple liquids are far from simple One of the motivations for the continual interest in the simple liquids is that, because of the basic nature of the interparticle interactions, an improved understanding of these systems should lead to better theoretical models, which can be extended to more complex molecular liquids. Also, the rapid growth of interest in colloids and polymers (so-called complex liquids) in recent years has provided new areas where the theories of simple liquids can be applied, especially those associated with local structure and thermodynamics. In the latter case, phase equilibria and the location of phase boundaries feature prominently. In this section, some of the recent advances in our understanding of simple liquids are covered. 

Differential thermal analysis (DTA) is a commonly used method to determine the location of phase boundaries. Figure 8.3 shows a hypothetical binary phase diagram and the DTA curves that would be expected for several compositions within the system. The endothermic melting and solidi-solid2 first-order transformations during heating are clearly evident. These peaks are due to the temporary... 

From Table 9.1, it is seen that at a reduction of the interdiffusion coefficient in the ternary y phase, the growth rate constant of the binary phase decreases, the concentration in the P phase at the fi-y interphase boundary approaches the boundary concentration the concentration in the y phase at the same interphase boundary becomes more and more different from Cgg(OO), and the coefficient S, which characterizes the diffusivity of the phase, decreases. Thus, as the interdiffusion coefficient in the ternary y phase diminishes (which is achieved due to introduced Pt or other additions), the possibility of growth suppression of the binary intermediate p phase becomes evident. At that, the magnitudes of the boundary concentrations at the fi-y interphase boundary correspond to the conode, which shifts along the phase diagram toward eg" , and the respective value determines the concentration interval of the phase, which allows one to find that the effective diffusivity of the phase is less than the maximal one D, by 1/5. The concentration distributions and locations of phase boundaries yr and y obtained from the calculations for the model Si-Ni-Pt system are given in Figure 9.7. 

The determination of the character and location of phase transitions has been an active area of research from the early days of computer simulation, all the way back to the 1953 Metropolis et al. [59] MC paper. Within a two-phase coexistence region, small systems simulated under periodic boundary conditions show regions of apparent thermodynamic instability [60] simulations in the presence of an explicit interface eliminate this at some cost in system size and equilibration time. The determination of precise coexistence boundaries was usually done indirectly, through the... 

Figure 6. Relative stabilities of native mercury, Hg°, HgzSO/, schuctteite, Hgfio Oj, and montroydite, HgO in a chloride-free system in which the activity of the predominant dissolved sulfur species is O.OIM. Stippled zones represent estimated uncertainty in locations of phase dominance boundaries.

One important point is that the phase boundary which separates the dilute phase from the dense phase is somewhat arbitrary to define and is located with difiiculty. Instead of defining the phase boundary, it might be more reasonable to place a transition zone between the above two phases. In what follows, however, the concept of phase boundary has been... 

The phase diagrams of two quaternary mixtures made of sodium dodecylsulfate (SDS)-water-dodecane and hexanol (system A) or pentanol (system B) have been investigated in detail [22,23]. In both cases, sections of the three-dimensional diagram with constant water/surfactant ratio have been examined. These cuts were chosen because they allow a good description of the oil region and also because the water/SDS ratio, termed X in the following, fixes the size of the droplets in the inverse microemulsion phase and the thickness of the bilayers in the oil-rich lamellar phase. In the description of the quaternary mixtures, we emphasize the details of the evolution of the phase equilibria as X is varied. We have focused our attention not only on the characterization and the location of the boundaries of the various phases but also on the equilibria between the phases. 

Most substances have a phase diagram similar to that of Fig. 1.17. They differ in their triple point and critical point locations, and of course in the location of the boundaries between phase pairs. 

Criticism of the phase diagrams The phase diagrams appear consistent with expectations from die theory of mixtures, and reversibility experiments show that their boundaries are equilibrium boundaries. Still, the locations of these boundaries may be inaccurate for 2 reasons. First, the two-phases (sol and floe) may not separate properly and one of them may take an excessive amount of one component. We have checked this by making sols located at the boundary through direct mixing, and we have found that the location of the "sol" boundary is accurate. Second, the volume mesured for the floes may not reflect their concentrations. Indeed, the floes are turbid, which indicates that they must be heterogeneous, i.e. made of lumps and voids. 

Special experiments have established no influence of small amounts of NaCl on the location of the boundary of the phase separation region. The role of NaCl is in elimination of kinetic hindrances and letting new-phase particles form. The mechanism of such an action is not clear as yet, but work in this direction is promising. We note that with an equal volume of the secend phase (an equal concentration of the precipitated polymer), the sizes of the new-ph2isc particles have been found to depend on the NaCl concentration, which points to a new way of optimization of STT of polymer solutions (see subsection 3.2.3). 

When a (solid) surface moves in a liquid, or vice versa, there is always a layer of liquid adjacent to the surface that moves with the same velocity as the surface. The distance from the surface over which this stagnant liquid layer extends or, in other words, the location of the boundary between the mobile and the stationary phases, the so-called plane of shear or slip plane, is not exactly known. For smooth surfaces, the plane of shear is within a few liquid (water) molecules from the surface (see Figure 9.4), that is, well within the electrical double layer. The stagnant layer is probably somewhat thicker than the Stern layer, so that the plane of shear is located in the diffuse part of the electrical double layer. It follows that the potential at the plane of shear, that is, the electrokinetic potential or the zeta potential is somewhat lower than the Stern potential /j. Because the largest part of the potential drop in the... 

There are some limitations to the use of DSC in phase studies in addition of its inability to identify phases [5], They are that (1) there are difficulties in locating very steep phase boundaries in heterogeneous systems from DSC data alone because heat capacity depends strongly on the slope of phase boundaries and so the heat capacity jumps are small [10] and (2) the determination of phase boundaries in systems with slow nucleation rate, interfacial transport problems, or inherently slow phase changes may not be possible [11], This is why it is hard to discover a liquid miscibility gap by DSC measurements. 

Unlike Sn-Pb joints, which have a dual phase structure and block the path of corrosion due to the existence of phase boundaries, the SAC305 joint is basically pure Sn with coarse islands of A n and CueSns intermetallic precipitate (Fig. 5). A corrosion crack can propagate and lead to additional corrosion along the way, without interruption from the Sn phase structure. Although both materials show strong resistance to corrosion, the localized nature of the corroded area at critical locations causes significant degradation in Sn-Ag-Cu solder joints[40]. 

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