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 $X_nY_m+xM_pY_q$, with ^$X$ an element of III-rd or IV-th group (e.g. B, or Si, Ge), while $M_pY_q$ is an alkali oxide or chalcogenide; next, the network glasses of the type $A_xB_{1-x}$, e.g. $Ge_xSe_{1-x}$, $Si_xTe_{1-x}$, etc. After comparison, this formula gives an exact expression of the parameter $\beta$ of the modified Gibbs-Di Marzio equation.