CALCULATION OF INTERACTION CONSTANTS FOR Cu AND Ag CHALCOGENIDES BASED ON BIOCOMPONENTAL THREE-ATOM LINEAR CHAIN MODEL
In this paper we propose a mathematical model to calculate interaction constants for crystalline Cu- and Ag-chalcogenides in a three-atom chain. Each molecule makes a linear three-atom chain of ions, one of which, i.e. the chalcogen ion, has a deformed electronic shell and the other two are metals (for instance, Cu and Ag). This simple model enables us to determine the relationship between physical properties of ions entering the crystalline lattice and the occurrence of superionic conductivity and is helpful in understanding the nature of superionic conductivity. An especially important point is that there is still no more or less satisfactory microscopic theory despite the growing number of data in support of the presence of superionic states in a large class of compounds, and major factors conducive to the formation of such states are far from clear. Moreover, it is known that a relatively simple classical approximation taking into account the discreteness of the lattice often gives the results reflecting essential peculiarities of elastic oscillations and waves in crystals. Our model can also be used for superionic conductors with the MexChy structure, although this may lead to greater mathematical complexity. It is interesting that very low numerical values of the interaction constants occur even in a non-superionic state of compounds having superionic properties. This peculiar feature is typical for the interaction constants of chalcogen ions and their electronic shells as well as for the interaction constants of chalcogen and metal ions. The results of our calculations show that force constants of superionics, already in a non-superionic state, are lower than those of the compounds with no superionic properties. This makes itself evident both in the interaction constants of chalcogen ions and their electronic shells and in the interaction constants of chalcogen and metal ions.