Self-consistency of the lattice-gas model

The parameters of the models, which include the equilibrium constants, the rate constants of elementary processes, and the interaction potentials, differ when the same experimental data are described by using different approximations. This is why the description of complicated processes requires that all the subsystems be considered with one level of accuracy, i.e., with the employment of the same approximation. For this purpose, it is essential that the physical and chemical fundamentals introduced into a mathematical model correspond to the real conditions within a broad range of variations of the external conditions. Now the parameters of models found from an analysis of individual subsystems can also be used when describing a process as a whole. 

The developed theory allows to construct mathematical models that would satisfy different limiting states of a system and the joint influence of real factors with an identical accuracy of their consideration. This point of view in a certain sense is opposite to the traditional situation when a single factor is taken as the basis, and the contributions of all other factors are ignored. To take into account the real properties of surface systems, the competition of the contributions of various factors must be considered. 

An importance of the self-consistent description of the equilibrium and kinetic properties demonstrated two examples, which based on explicit taking into account the correlation effects between desorbed species with their changing the phase states. 

As shown in previous subsection, the activation energy of desorption coincides with the adsorption heat if there is no lateral interaction of the activated desorption complex and its surrounding, e — 0. This is the model that Jones and Perry invoked [144,145] to describe thermal desorption in the Hg/W(100) system. They were able to reproduce the experimental data, taking K(l(d)=K() — const, and Eej(6)=Q(6) the adsorption heat Q(6) was calculated with the quasi-chemical approximation for a homogeneous surface. The calculated and experimental spectra were found to be in a 

this is an example of such theoretical treatment when thermodynamic and kinetic characteristics are not self-consistent with each other. The theoretical failure above occurred due to the desorption equation used, that does not allow for the real distribution of the Hg atoms, i.e., the macroscopic equation used does not describe the two-dimensional adspecies condensation appearing in the experiment. It should be taken into account that adspecies are in two coexisting phases, so the total desorption rate is a sum of the desorption rates from these phases [146,152]. 

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