Ergodicity breaking of an inorganic glass in aging near $T_g$ probed by elasticity relaxation

We performed a series of aging experiments of an inorganic glass (As${}_2$Se${}_3$) at a temperature $T_2$ near the glass transition point $T_g$ by first relaxing it at $T_1$. The relaxation of Young’s modulus was monitored, which was(almost if not ideally) exponential with a $T_1$-dependent relaxation time $\tau (T_1)$. We demostrate the Kovacs’ paradox for the first time in an inorganic glasses. Associated with the divergence of $\tau$, the quasi-equilibrated Young’s modulus $E_{\mathrm{\infty }}$ does not converge either. An elastic model of relaxation time and a Mori-Tanaka analysis of $E_{\mathrm{\infty }}$ lead to a similar estimate of the persistent memory of the history, ergodicity breaking within the accessible experimental time. Experiments with different $T_2$ exhibits a critical temperature ${T_p \sim T_g}$,i\mathrm{.}e\mathrm{.},when${T_2 > T_p}$,both${\tau}$and${E_\infty}$ converge.