The Markov chain theory for ternary systems

Similar to the binary system, one can define probabilities for the formation of new kink sites. For equilibrium conditions one can use the equilibria of the reactions, Eqs. (8.65)-(8.67). For kinetic control one can formulate probabilities with the rate equations. 

For equilibrium conditions, the probabilities for the reactions with the kink site atom A are given by the equations 

The probabilities for reactions with the kink site position B are 

The components of the Eigen vector a of the (3X3) probability matrix, a, and c give the equations for the mole fractions of the components in the alloy 

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