Thermometer Effect: Origin of the Mixed Alkali Effect in Glass Relaxation

Despite the dramatic increase of viscosity as temperature decreases, some glasses are known to feature room-temperature relaxation. However, the structural origin of this phenomenon—known as the “thermometer effect”—remains unclear. Here, based on accelerated molecular dynamics simulations of alkali silicate glasses, we show that both enthalpy and volume follow stretched exponential decay functions upon relaxation. However, we observe a bifurcation of their stretching exponents, with $\beta =3/5$ and $3/7$ for enthalpy and volume relaxation, respectively, in agreement with Phillips’s topological diffusion-trap model. Based on these results, we demonstrate that the thermometer effect is a manifestation of the mixed alkali effect. We show that relaxation is driven by the existence of stressed local structural instabilities in mixed alkali glasses. This driving force is found to be at a maximum when the concentrations of each alkali atom equal each other, which arises from a balance between the concentration of each alkali atom and the magnitude of the local stress that they experience.

Figure 1

Relative variation of the (a) enthalpy and (b) volume of the sodium (Na), potassium (K), and mixed alkali ($\mathrm{Na}+\mathrm{K}$) silicate glasses with respect to the number of stress perturbation cycles applied. The insets show the final absolute relative variations of (a) the enthalpy and (b) volume. Lines serve as a guide for the eye.

Figure 2

Relaxation function $f$ of the enthalpy, volume, and internal stress in the mixed sodium potassium silicate glass, with respect to the number of stress perturbation cycles $N$. The data are fitted with stretched exponential decay functions $f(N)=\exp [-(N/N_0{)}^{\beta }]$ with a stretching exponent $\beta =3/5$ and $3/7$ for the stress or enthalpy and volume, respectively (see text). The inset shows $\log [-\log (f)]$ with respect to $\log (N/N_0)$ for the enthalpy, stress, and volume, whose slope yields $\beta$. Dashed lines corresponding to the slopes $\beta =3/5$ and $3/7$ are added for comparison.

Figure 3

(a) Shift of the coordination number of Na (K) atoms, using the binary sodium (potassium) silicate glass as a reference, with respect to the composition of the glass. (b) Average stress per Na and K atoms. A positive (negative) stress denotes a local compression (tension). (c) Total cumulative stress experienced by all Na and K atoms. (d) Difference between the total cumulative stresses experienced by Na and K atoms, which acts as the driving force for relaxation. Lines serve as guides for the eye.