Broken-bond model

Broken Bond Model were developed to describe the process of ionization of ionic compounds, especially under primary oxygen-ion bombardment - or gas admission ("O2... 

Using the broken-bond model of surface enrichment one derives (36)... 

The surface energy of dense-packed faces (111) of Si and diamond will be estimated taking as a reference value that for Ge at its melting point and applying the expression (1.15) of [Pg.395]

For an FCC structure one gets a truncated octahedron (see Fig. 1) that we generally call a Wulff polyhedron. It contains only (111) and (100) faces. At OK and for a simple broken-bond model, the ratio between the surface energies <7(100)/<7(111) is 2/v, which fixes the relative extensions of these facets. However, when the temperature increases, the surface-energy anisotropy decreases, disappearing at the melting point. 

Simple criteria for surface segregation in alloys (relative melting points, enthalpies of sublimation, metal atom radii, surface free energies of the pure metals) all indicate that surface segregation of titanium should occur on Pt/Ti alloys in vacuo. However, this is inadequate because of the large departures from ideality in Pt/Ti alloys. Analysis (11) of a broken bond model of the system, especially with the use of data directly determined with Pt/Ti alloys, gives a more reliable result. 

The theoretical analysis (11) of surface segregation in PtjTi, on the same basis as the analysis of dilute solid solutions, predicts no surface segregation at exact stoichiometry. The broken bond model of surface segregation is also successful in the prediction of surface segregation in some other non-ideal platinum alloys (17). 

Figure 12. For a fee erystal (from Ref. 32) (a) eontour lines of the surfaee free energy y based on the nearest-neighbor broken-bond model and (b) and (e) eorre-sponding y plots—the horizontal axis is sealed taking into aeeount the angular distanees between the faees the free surfaee energy relative to the (210) faee is plotted on the vertieal axis.

For this matter, Mackenzie et al. [14] developed a systematic way to calculate surface energies based on the broken bond model. The basic idea is that, since all the bonds to be broken for opening a surface should lie in the same direction of the surface normal, the total number of such bonding vectors, normalized by the area of the unit cell of the surface, is equal to the product, NS-NB. For pure metals with the fee symmetry, the energy of the (hkl) surface is given as ... 

Although the discussion on the broken bond model has been mainly focused on pure metallic surfaces, the extension can be easily made simply by replacing the binding energy term Ej, in Eq. (1) with the interaction energies among different atoms in the case of metallic alloys [15-17]. However, in the case of ceramic materials the... 

Table 11.1 A sample calculation of relative surface energies in a simple fee crystal based on the broken bond model when the first and second nearest-neighbor interaction are considered.

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