Universal binding energy relation

FIG. 7 Total energy per cross-sectional area as a function of interfacial separation between Fe and A1 surfaces for the clean interface and for monolayer interfacial impurity concentrations of B, C, N, O, and S. Graph (a) is for the case where the impurity monolayer is applied to the free A1 surface prior to adhesion, while graph (h) has the impurity monolayer applied to the free Fe surface prior to adhesion. The curves fitted to the computed points are from the universal binding energy relation. (From Ref. 28. Copyright 1999 hy the American Physical Society.)... 

A relationship between the bonding in diatomic molecules and in solids has been demonstrated. It follows from the so-called Universal Binding Energy Relation (UBER), applicable to both metals and covalent diatomic molecules. The energy and the interatomic separation are scaled in the following way ... 

Fig. 4.8. Universal binding energy relation (adapted from Rose et al. (1984)).

One of the cleanest routes to determining embedding functions is by invoking the universal binding energy relation (UBER) (Rose et al. 1984). On the basis of a vast collection of experience with first-principles calculations of a range of materials, it was found that the total energy as a function of lattice parameter may be fitted to... 

Baneijea, A., Smith, J.R. Origins of the universal binding-energy relation. Phys. Rev. B 37, 6632 (1988)... 

Several approaches have been used for determining functional forms for the pair sum Eq. [12]. Once the Hamiltonian matrix elements had been specified, Chadi, for example, used a near-neighbor harmonic interaction for covalent materials where the force constants and minimum energy distances were fit to bulk moduli and lattice constants, respectively. This expression was then used to predict energies and bond lengths for surfaces and related structures. More recently. Ho and coworkers have fit the pair sum to the universal binding energy relation. This reproduces not only lattice constant and bulk modulus, but also ensures reasonable nonlinear interatomic interactions that account for properties like thermal expansion. 

The symmetry-preserving bulk de-cohesion obeys a remarkably simple scaling relationship arising from a universal binding-energy relation demonstrated by Rose et al. (1983) to be given, for uniaxial tension, simply by... 

That this form does indeed hold had been demonstrated for the cavitation of glassy polypropylene (Mott et al. 1993) in a computational study furnishing the validity of this extension of the universal binding-energy relation to symmetrical bulk response. The additional attraction of this expression is that it points out directly that application of a pressure produces symmetrical elastic compaction in an isotropic solid. However, more interestingly, one notes that, when dilatation is imposed, the bulk modulus monotonically decreases and eventually, at a dilatation of 1 /p, vanishes. This also leads to the observation that, if dilatation results from thermal expansion in response to a temperature increase, the bulk modulus also decreases. This simple observation represents the essence of the temperature dependence of all other elastic constants in anisotropic solids, beyond the mere effect on the bulk... 

Fig. 11.1 A comparison of behaviors of the mean normal-stress (negative-pressure) response to dilatation predicted, from top to bottom, by the universal binding-energy relation (UBER), and from the responses of the 1.815-nm-sized cubical simulation cell, the 2.615-nm-sized cubical cell, and the 3.396-nm-sized cubical cell (from Mott et al. (1993a) courtesy of Taylor Francis).

Figure 5.7. Fit of calculated total energies of various elemental solids to the Universal Binding Energy Relation the calculations are based on DFT/GGA.

For the purpose of the present chapter, a comment on the interpretation of oxygen Is binding energies in oxides seems appropriate. The contribution of the surface terminating layer and of a possible adsorbate to the total O Is spectrum of an oxide catalyst is low (an estimated 15% for laboratory XPS) as in oxides the depth of information [33] is commonly larger than estimated from the universal relation between kinetic energy and escape depth, which is vahd for metals only. 

Table 6.4 shows some variation in the actual binding energies, which can be partly related to different materials and partly to the lack of universality applied to aligning the Eg scale. The reference point is typically the C Is line at somewhat arbitrary energies (284.4—285 eV) and some publications do not indicate their referencing procedure at all. However, there are clearly some obvious tendencies to observe in Table 6.4. For example, most materials contain vanadium in mainly the 4-e formal oxidation state molybdenum is usually fitted to obtain two (6-1- and 5-i-) components, that is, its peak maximum is observed between the position of these two oxidation states the Ep values of niobium are somewhat lower, and those of...

In an alternative microscopic model,a universal relation between binding energy and interatomic distance is presumed. The validity of this assumption was demonstrated for interfaces between metals, gases absorbed on metals and finally pure metals. The interdependence of binding energy ii(a) and distance a can be decomposed into a product of a function E a) and the cohesion energy Eq at equilibrium distance oq-... 

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