Polk model

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

Polk model calculated for the case of neutron scattering and with the constituents having the isolated H2O molecule shape and size. The oscillatory behavior for large R, with period 3.7 A, corresponds to the peak in the structure function at 1.7 A-1. 

Figure 2.08 Early test of Polk model (1971) via a comparison of its distribution function with that of amorphous silicon.

Alben and Boutron suggest that the peak in the X-ray and neutron scattering functions at 1.7 A-1 is indicative of an anisotropic layer structure extending over at least 15 A in Polk type continuous random network models. To show this better Fig. 52 displays the radial distribution function of the Alben-Boutron modified... 

The reader should recall that the fitting of a structure to diffraction data is not unique. We have shown that both the constructed modified random network model of Polk, as well as the network simulated by allowing Gaussian distributions of atom-atom distances can fit the observed structure functions for low density H20(as), and the latter, with modification to include small OOO... 

Several cluster models have been tested to account for patterns of small clusters (p = 1 or 2 bar in Fig. 18). First, clathrate models have been examined. The most popular of these consists of a regular dodedecahedron with one H2O molecule at each of the 20 vertices and possibly one additional molecule at the center. In this model, HjO molecules form regular pentagons with a molecular angle HOH of 108°, which is intermediate between 104.5°, the value for the free molecule, and 109.5°, that for tetrahedral bonding in the diamond cubic structure. Such a clathrate model, stabilized by an additional proton, accounts well for mass spectrometry results, but is found to be far too symmetrical to account for the structure of neutral clusters. An amorphous model,derived from Polk s random dense packing, has been tested. This... 

In the literature several models have been described in which amorphous alloys are, considered to be relatively stable if certain requirements are fulfilled. In many of the alloys Aj that can be obtained in the amorphous state there is a substantial difference in size between the metallic radii of the components (r > rg). In addition, the composition of many amorphous alloys made by means of liquid quenching is close to X = 0.2. This led Polk (1970) to propose a stability criterion for amorphous alloys in which the size difference in atomic radii and the asymmetry in composition is of prime importance. This stability criterion is based on the possibility of obtaining a higher packing density when the holes available in the dense random packing of the larger A atoms are filled by the smaller B atoms. In recent years it has... 

Polk s random network model confirmed many essential features of the Grigorovici-M aila continuous network model Uke the mixing of merged 5-and 6-fold rings in about the same ratio, the overlap of correlation layers on the r scale, the possibility to extend the model without limits, etc. Due to the peculiarities of the ball-and-spoke units he used, the increase in the... 

Fig. 2.35. The histogram of an ideal random continuous network model of a-Ge or a-Si (after Polk (1971)). Horizontally shaded area - first correlation layer diagonally shaded area - second correlation layer vertically shaded area - third- and higher order correlation layers. Full curve - RDF of a-Si (after Moss and Graczyk (1969)).

The aim of these studies is to find the parameters which yield the tetrahedral films in the form of a voidfree random network structure similar to the model constructed by Polk (1971). 

The random network model was established by Polk [36,37] in sp systems (Si and Ge). It was supported by the calculations of Henderson and Herman [42]. Polk proposed to keep the same coordination as in a crystal but introduce small variations in interatomic distances and bonding angles (Figure 1.21). In this model, the minimum entity is only the atom corresponding to the amorphous state (see Section 1.1.2.4, Figure 1.3). 

FIGURE 1.21 Random network model of an amorphous material. (From D.E. Polk. Structural model for amorphous metallic alloys. Scripta Metallurgica 4, 117-122 (1970). With permission.)... 

It can be concluded that as-deposited carbon films are initially amorphous but become organized under the weakest stress. Because such films initially do not contain coherent scattering domains, they are amorphous and conform to a random network model similar to that of Polk [36,37]. The occurrence of a persistent halo near 0.2 A favors the hypothesis of sp bonds initially being present, possibly replaced by sp bonds when the metastable amorphous stage really... 

D.E. Polk. Stractural model for amorphous metallic alloys. Scripta Metallurgica 4, 117-122(1970). 

D.E. Polk. Stmctural model for amorphous silicon and germanium. J. Non-Cryst. Solids 5, 365-376 (1971). 

A verification case for Aspen Plus [34] modeling is provided by McDaniel [70] and has been chosen for the present study. The data is given in Table 6.10. All design configurations for the GE coal gasification process (see Table 6.8) have been modeled based on that verification case from the Polk IGGC plant [70,71]. 

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