Equilibrium of the crystallization process

In the case of equilibrium of the crystallization process, equilibrium equations of reactions (8.6a-c) can be used to define the probabilities. Equilibrium means equilibrium of the surface processes. The equilibria are, if the following is restricted to ions of equal charge 

These equilibrium reactions can be compared to the equilibrium reaction between reactants and transition state in the kinetic theory of homogeneous reactions. The kink site position in this model is comparable to the transition state of the reactants. 

The concentrations of the newly formed kink site positions Eqs. (8.10a)-(8.10d). can be deduced from 

Substituting the surface densities of kink site positions by equilibrium constants and ion concentrations in the electrolyte bath one obtains 

From the finite Markov chain theory, it follows that the atomic fiactions x and x ) of atoms A and B in the alloy can be calculated with the probabilities and the following equations 

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The entire network structure is divided into several components, so-called molecular budding-blocks or tectons, which consist of core parts and interaction parts. The geometrical shape of the core part controls the direction of the interaction. The interaction parts are substituents such as carboxylic acid groups for hydrogen bonds and carboxylates for coordination bonds, which control the interaction strength and affect the equilibrium of the crystallization process. By choosing appropriate molecular building blocks, we can construct the desired molecular networks and frameworks. 

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