First-neighbor interactions

It turns out that for some systems the GPM yields the pair interactions, particularly those between first neighbors, which do not correspond to experimental phase diagrams. It is the purpose of the present work to show some of these cases and make a comparison with results obtained by other methods, particularly by the CWIS. 

In order to check the consistency and mutual relations of ECIs calculated by various methods, as well as to compare them with experimental data, we have performed calculations for several alloy systems, as diverse as Cu-Nl, Al-Li, Al-Ni, Ni-Pt and Pt-Rh. Here we present the results for Al-Ni, Pt-Rh and Ni-Pt alloys in some detail, because the pair interactions between the first neighbors are dominant in these alloys which makes the interpretation relatively simple. On the other hand, the pair interactions between more distant neighbors and also triplet interactions are important for Al-Li and Cu-Ni. The equilibrium atomic radii, bulk moduli and electronegativities of A1 and Ni are rather different, while Pt and Rh are quite similar in this respect. The Ni and Pt atoms differ mainly by their size. 

To conclude this section it may be worthwhile to remark that, although the L-J-D method is generally applied to a face-centered cubic lattice (z = 12), it is equally valid for the cavities in a clathrate (z = 20—28), as long as one restricts oneself to first-neighbor interactions. 

It will be observed that entropies of dilution (as indicated by i) are highly variable from one system to another. This is contrary to the theory developed from consideration of lattice arrangements, according to which pi should be approximately 1/2 and nearly independent of the system. For polystyrene in methyl ethyl ketone, the entropy of dilution is nearly zero i.e., this solvent is a poor one not because of an adverse energy of interaction but because of the low entropy. First neighbor interactions apparently contribute to the entropy as well as to the energy, a point which was emphasized in Chapter XII. It will be noted also that cyclic solvents almost without exception are more favorable from the standpoint of the entropy than acyclic ones. 

Parameter expressing the first neighbor interaction free energy, divided by kTj for solvent with polymer (Chap. XII et seq.). 

Fig. 3. Formal potentials of oligo(dihexylferrocenylene)s 13 (O) (60,76), those calculated from the first neighboring site interaction (A) with u, = 15 kJ mol-1 and u2 = 4.5 kJmol-1, and those calculated from both first and second neighboring-site interaction (V) with u, = 15kJmol u2 = 4.5 kJ mol 1, and oxr = -3.8 kJ mol-1 (77).

Consider a diatomic chain in which the atoms, of distinct masses mi and m2, are positioned at distance a (figure 3.6). The repetition distance of the chain is 2a, and the Brillouin zone falls between —irlla and i lla. If only the interactions between first neighbors are significant, the equation of motion for atom r at position ja is given by... 

Figure 11 Simulated voltammogram (top) and adsorption isotherm (bottom) for the model with first neighbor shell exclusion and second neighbor shell interaction. Adsorption with an attraction of —0.5 kgT (dotted line) and a repulsion of +0.5 ksT (dashed line) compared to the case without second neighbor shell interaction (solid line)...

A lattice model for an electrolyte solution is proposed, which assumes that the hydrated ion occupies ti (i = 1, 2) sites on a water lattice. A lattice site is available to an ion i only if it is free (it is occupied by a water molecule, which does not hydrate an ion) and has also at least (i, - 1) first-neighbors free. The model accounts for the correlations between the probabilities of occupancy of adjacent sites and is used to calculate the excluded volume (lattice site exclusion) effect on the double layer interactions. It is shown that at high surface potentials the thickness of the double layer generated near a charged surface is increased, when compared to that predicted by the Poisson-Boltzmann treatment. However, at low surface potentials, the diffuse double layer can be slightly compressed, if the hydrated co-ions are larger than the hydrated counterions. The finite sizes of the ions can lead to either an increase or even a small decrease of the double layer repulsion. The effect can be strongly dependent on the hydration numbers of the two species of ions. 

The first difficulty could be explained by observing that water is not homogeneous at a molecular scale [34], The interactions with remote dipoles are screened by the intervening water molecules, because the effective dielectric constant of their interaction is comparable with the macroscopic dielectric constant (a—80). In contrast, the interaction between neighboring dipoles is much less screened, because there is no intervening medium between than. While assuming a constant e for all interactions would predict a vanishing electric field near the surface, the local value of an effective e leads to a net electric field, which can polarize the water molecules above the surface. 

It was reported [53] that the LP influences the molecular and electronic distortions observed in [Cr(C6H6)(CO)3] and related carbine and carbene complexes. The mutual orientation of the first-neighboring CO groups in these species reflects more the balance between the molecular shape and the tendency of the molecules to lie as close as possible (close-packing principle), rather than an electronic requirement of the CO-CO intermolecular interactions. 

Large differences in Pd LMH XANES between Si02 and y-Al203 supported PdO catalysts and PdO crystal are evidence for structural disorder of the first neighbor shell in the former and for PdO-substrate interaction (73a). 

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