On the glass transition temperature in covalent glasses

We give a simple demonstration of the formula relating the glass transition temperature, $T_g$, to the molar concentration $x$ of a modifier in two types of glasses: binary glasses, whose composition can be denoted by $X_n{Y}_m+x{M}_p{Y}_q$, with ^$X$ an element of III-rd or IV-th group (e.g. B, or Si, Ge), while $M_p{Y}_q$ is an alkali oxide or chalcogenide; next, the network glasses of the type $A_x{B}_{1-x}$, e.g. $G{e}_{x}S{e}_{1-x}$, $S{i}_{x}T{e}_{1-x}$, etc. After comparison, this formula gives an exact expression of the parameter $\beta$ of the modified Gibbs-Di Marzio equation.