Four-phase model

FIGURE 14.2 Phase distribution of organic contaminants in the vadose zone. The solid arrows in the three-and four-phase models represent the equilibria taken into consideration in the equations of Table 14.3. 

For analytical purposes, the fiber composites are conveniently modeled using axisymmetric three-phase (i.e. fiber-interlayer-matrix), four-phase (i.e. fiber-interlayer-matrix-composite medium) cylindrical composites, or in rare cases multi-layer composites (Zhang, 1993). These models are schematically presented in Fig. 7.9. The three-phase uniform interphase model is typified by the work of Nairn (1985) and Beneveniste et al. (1989), while Mitaka and Taya (1985a, b, 1986) were the pioneers in developing four-phase models with interlayer/interphase of varying stiffness and CTE values to characterize the stress fields due to thermo-mechanical loading. The four phase composite models contain another cylinder at the outermost surface as an equivalent composite (Christensen, 1979 Theocaris and Demakos, 1992 Lhotellier and Brinson, 1988). 

Using a four-phase model consisting of ambient/simple grade/film/ substrate, we fit the data to obtain the dispersion of optical constants for each films in the range of 1.55-6.53 eV. The Cauchy model was used as a model for the substrate and fixed during the fitting. The Cody-Lorentz (CL) model [14] was used as a model for the film. 

With a four-phase model, the results are shown in Table 7.1 where the mean square error (MSE) represents the goodness-of-fit parameter. The uncertainties of the film thickness listed in Table 7.1 were obtained with a 90% confidence limit. To verify that the dispersion in the experimental spectral range (1.55-6.53 eV) is correct, we used the data inversion to obtain its pseudo-optical constants (< n ) and ). Theseconstants are calculated from the measured 4 and A using the film thickness obtained from the fitting. 

Hidi, S and Renninger, BLA (2006) The Four-Phase Model of Interest Development. Educ Psychol 41(2) 11 l-fa . 

Hidi S, Renninger KA (2006) The four-phase model of interest development. Educ Psychol,... 

Fig. 18. Calculated difference spectra in AJJ/JJ, based on the four-phase model. Angle of incidence, 70°. 1-0.5% H20.

In the spectroelectrochemical experiment, the simulation of reflectivity responses can become quite complicated owing to the multiple interfaces and phases through which the optical beam must pass [104]. However, the models employed have gained in sophistication over the years as they have been needed to assist in the design of cells and optical systems and in the interpretation of spectra [23, 80, 104, 189-193]. An expanded discussion of the computational approach and its application to a four-phase model of the infrared spectroelectrochemical experiment was presented by Pettinger and coworkers recently [104]. An example of its use and the type of detailed structural information that can be gained is described for the case of pyridine adsorption on an Au electrode [103]. 

Leddy has now developed an exact treatment of a four-phase model quartz/ metal electrode/lilm/solution, where it is assumed that the redox species are located at the film/solution interface and heat transport in all phases is diffusion controlled. Details will be published elsewhere [95]. This will be discussed further in Sec. V.E. 

See also the widely used four-phase model mitigation-preparedness-response-recovery, developed by the US Federal Emergency Management Agency (fema). 

Double films formed on InP were studied by applying ex situ ellipsometry after successive etching steps of the thermally formed oxide by an HF solution. From calculations based on a four-phase model (see Appendix A1 for treatment of two and more layers), the existence of an easily etched outer layer with smaller refractive index and a more durable inner layer with larger index was shown, which is consistent with XPS analysis. In the same work, in situ ellipsometry data was shown to be explained by the presence of a liquid layer when a microscopic model based on the Lorentz-Lorenz relation was used. Other ellipsometric studies of double films, such as double films of Si02 and Si3N4 on Si, have been reported. 

Fig. 8.13. Four-phase model of highly oriented semicrystalline fiber, (a) crystalline lamellae, (b) fully extended tie segments, (c) non-extended tie segments, (d) matrix (folds, ciliae, broken chains).

The relevant Hamiltonian for the gas-phase solute molecules can be treated by the same three-orbitals four-electron model used in Chapter 2. Since the energy of 3 is much higher than that of , and d>2 (see Table 2.4), we represent the system by its two lowest energy resonance structures, using now the notation fa and fa as is done in eq. (2.40). The energies of these two effective configurations are now written as... 

Shiga and Kurauchi have predicted that the swelling deformation of a gel in an electric field is caused by an increase in Flory s osmotic pressure. In order to prove this mechanism, the change in the osmotic pressure under an electric field has been calculated using a simple model for ion transport. The gel and the surrounding solution have been divided into four phases, the A phase (solution at the anode), B phase (gel at the anode), C phase (gel at the cathode), and D phase (solution at the cathode). A mobile cation in a dc field moves toward the... 

For convenience of presentation, model building can be divided into four phases (1) problem definition and formulation, (2) preliminary and detailed analysis, (3) evaluation, and (4) interpretation application. Keep in mind that model building is an iterative procedure. Figure 2.2 summarizes the activities to be carried out,... 

FIGURE 5.22 (See color insert following page 280.) Perspective four-cell view snapshots of various stationary-phase models, which illustrate the contrasting surface topography with bonding density and alkyl chain length. (Adapted from Lippa, K.A., et al., Anal. Chem., 11, 7852, 2005.)... 

Fig. 1.2 Model of a four-phase system consisting of two liquid phases (e.g., an aqueous and an organic phase) in equilibrium with a gas phase and a solid phase. 

Janssen-Jurkovicova et al. (1994) presented a conceptual model for CCB weathering, which breaks the process into four phases. Figure 2 illustrates their model for weathering of alkaline fly ash (i.e., fly ash producing alkaline water extracts defined as fly ash having Ca/S > 2.5 by Ainsworth Rai 1987), modified using observations of Warren Dudas (1984). In phase 1, oxides and soluble salts present on ash particle surfaces dissolve in contact with water. Hydrolysis of metal oxides (especially CaO) results in a rapid rise of pH to values of approxi-... 

To describe the phase diagram of cuprates, where we observe four phase separations, we consider a Poole model with three different anisotropic interactions yi, y2, and y3 giving rise to three different intermediate phases with preferential volume VyI, Vy2 and Vys respectively. 

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