Activation Entropy as a Key Factor Controlling the Memory Effect in Glasses

As opposed to the common monotonic relaxation process of glasses, the Kovacs memory effect describes an isothermal annealing experiment, in which the enthalpy and volume of a preannealed glass first increases before finally decreasing toward equilibrium. This interesting behavior has been observed for many materials and is generally explained in terms of heterogeneous dynamics. In this Letter, the memory effect in a model Au-based metallic glass is studied using a high-precision high-rate calorimeter. The activation entropy ($S^{*}$) during isothermal annealing is determined according to the absolute reaction rate theory. We observe that the memory effect appears only when the second-annealing process has a large $S^{*}$. These results indicate that a large value of $S^{*}$ is a key requirement for observation of the memory effect and this may provide a useful perspective for understanding the memory effect in both thermal and athermal systems.

Figure 1

Enthalpy changes for a Au-based MG during annealing. (a) The enthalpy change $\mathrm{\Delta }h$ at $T_1=383\mathrm{K}$ versus annealing time $t_1$. Inset is the thermal protocol of single-step annealing treatment. Solid curve is for guiding eyes. (b) The enthalpy change of sample preannealed at $T_1=383\mathrm{K}$ for $t_1=50\mathrm{s}$ and then annealed at $T_2=373\mathrm{K}$ for $t_2=0.1–100000\mathrm{s}$. Inset is the thermal protocol. Solid curve is for guiding eyes. (c) The enthalpy change of sample preannealed at $T_1=373\mathrm{K}$ for $t_1=50\mathrm{s}$ and then being annealed at $T_2=383\mathrm{K}$ for $t_2=0.1–2000\mathrm{s}$. Inset is the thermal protocol. Solid curve is the TNM model fitting result. (d) Two-dimensional contours of the relaxation heat flows ($\dot{Q}$) at $T_1=383\mathrm{K}$. (e) Two-dimensional contours of the relaxation heat flows at $T_2=373\mathrm{K}$ for the sample preannealed at $T_1=383\mathrm{K}$ for $t_1=50\mathrm{s}$. (f) Two-dimensional contours of the relaxation heat flows at $T_2=383\mathrm{K}$ for the sample preannealed at $T_1=373\mathrm{K}$ for $t_1=50\mathrm{s}$.

Figure 2

Enthalpy changes for two-step annealing experiments, with fit results from TNM model (solid lines). (a) The enthalpy change following annealing at $T_2=383\mathrm{K}$ for the sample preannealed at $T_1=348\mathrm{K}$ for $t_1=0.1$, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100 s. (b) The enthalpy change following annealing at $T_2=383\mathrm{K}$ for the sample preannealed at $T_1=363\mathrm{K}$ for $t_1=0.1$, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100 s. (c) The enthalpy change when being annealed at $T_2=383\mathrm{K}$ for the sample preannealed at $T_1=373\mathrm{K}$ for $t_1=0.1$, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100 s. (d) The strength of memory effect ($\mathrm{\Delta }{h}_{\mathrm{peak}}$) versus enthalpy evolution ($\mathrm{\Delta }h$) during the first annealing step at $T=348$, 363, 373 K. $\mathrm{\Delta }{h}_{\mathrm{peak}}$ is obtained by subtracting the initial enthalpy from the peak enthalpy. The memory effect appears only for $\mathrm{\Delta }h$ greater than about $0.4\mathrm{kJ}/\mathrm{mol}$. The solid symbols represent experimental data in which the memory effect was observed. The dashed lines are for guides for the eyes.

Figure 3

Absolute rate theory analysis of annealing kinetics. (a) The peak temperature and heating rate are used to extract the activation enthalpy $H^{*}$ for various annealing times during annealing at 383 K. (b) The evolution of $H^{*}$ and the activation entropy $S^{*}$ with annealing time at 383 K. (c) $S^{*}$ as a function of enthalpy change for single-step annealing at $T=348$, 363, 373, 383 K. The arrow shows that the memory effect appears only if the glass jumps from low temperature (with a small $S^{*}$) to high temperature (with a big $S^{*}$).

Figure 4

Schematic map of enthalpy changes during glass annealing. As the enthalpy decreases during isothermal annealing at low temperature, the as-cooled glass first experiences a small $S^{*}$ stage and then transitions into a large $S^{*}$ stage. When the preannealed glass jumps to higher temperature, the enthalpy continues to decrease if the jump reaches a relaxation stage with small $S^{*}$, but there is a memory effect if the jump reaches a relaxation stage with large $S^{*}$. The color map represents the value of $S^{*}$. Open blue squares: the sample preannealed at $T=348\mathrm{K}$ for 1 s does not exhibit the memory effect at 383 K. Filled pink circles: the sample preannealed at $T=348\mathrm{K}$ for 20 s exhibits memory effect at 383 K. Filled green pentagons: the sample preannealed at $T=348\mathrm{K}$ for 100 s exhibits memory effect at 383 K.