Topology multiphase

In Q the non-topological structure parameters of the material s nanostructure are combined. For multiphase systems this fact can be deduced by application of the Fourier-slice theorem and the considerations which lead to Porod s law. In particular, for a two-phase system it follows64... 

For a multiphase structure this information is made from both some direction-dependent topological information, and the non-topological information that is collapsed in the scattering power. 

Figure 8.17. The topological information on the structure of a multiphase system that is related to one-dimensional projections / 1 (sj) in different directions. The demonstration shows two directions indicated by arrows and the related chords. From /jj ( ) the distributions of the chord segments between domain edges are retrieved. Long periods are indicated by broken lines...

After we have discussed the composition parameters of the SAXS of a multiphase material, we now start with the investigation of the topology. The most simple access to the arrangement of domains in the material is the discussion of long period... 

Quantitative Analysis of Multiphase Topology from SAXS Data... 

The quantitative analysis of a multiphase topology comprises the formulation of structure models and the fitting of measured data. Fitting is discussed in Chap. 11. In this section the setup of topological models is discussed. The problem arises from the fact that most structural models of particle correlation are anisotropic and the visualization of structure in anisotropic materials by means of the CDF shows that suitable models must be rather complex. Thus a direct fit of anisotropic data would require fitting of a measured 3D or 2D function by a complex model. Both the effort to setup such models, and the computational effort to fit the data are very high. 

A schematic representation of the phase diagram for pure H20 (not to scale) is shown in Fig. 7.1. Let us examine the topological features of this diagram in terms of increasing complexity from single- to multiphase character. 

The microstructure of the multiphase media is often the product of phase transitions, e.g. (i) capillary condensation in the porous media, (ii) phase separation in polymer/polymer and polymer/solvent systems, (iii) nucleation and growth of bubbles in the porous media, (iv) solidification of the melt with a temporal three-phase microstructure (solid, melt, gas), and (v) dissolution, crystallization or precipitation. The subject of our interest is not only the topology of the resulting microstructured media, but also the dynamics of its evolution involving the formation and/or growth of new phases. 

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