Atomistic structural mechanism for the glass transition: Entropic contribution

A popular Adam-Gibbs scenario has suggested that the excess entropy of glass and liquid over crystal dominates the dynamical arrest at the glass transition with exclusive contribution from configurational entropy over vibrational entropy. However, an intuitive structural rationale for the emergence of frozen dynamics in relation to entropy is still lacking. Here we study these issues by atomistically simulating the vibrational, configurational, as well as total entropy of a model glass former over their crystalline counterparts for the entire temperature range spanning from glass to liquid. Besides confirming the Adam-Gibbs entropy scenario, the concept of Shannon information entropy is introduced to characterize the diversity of atomic-level structures, which undergoes a striking variation across the glass transition, and explains the change found in the excess configurational entropy. Hence, the hidden structural mechanism underlying the entropic kink at the transition is revealed in terms of proliferation of certain atomic structures with a higher degree of centrosymmetry, which are more rigid and possess less nonaffine softening modes. In turn, the proliferation of these centrosymmetric (rigid) structures leads to the freezing-in of the dynamics beyond which further structural rearrangements become highly unfavorable, thus explaining the kink in the configurational entropy at the transition.

Figure 1

Glass transition and excess total entropy. (a) Temperature dependence of the volume of a glass-forming liquid during cooling, the discontinuity in slope indicates the glass transition temperature, $T_{\mathrm{g}}=695$ K. (b) Temperature dependence of total entropy in disordered phase and crystal. (c) Temperature dependence of excess total entropy $\mathrm{\Delta }{S}_{\mathrm{tot}}$.

Figure 2

Phonon of glass-forming liquid and crystal. (a) Phonon DOS of glass and liquid over wide temperature range. (b) Comparison of phonon DOS between simulation and experiment at 600 K. (c) Phonon DOS of three crystal phases including orthorhombic ${\mathrm{Cu}}_{10}{\mathrm{Zr}}_7$, Laves ${\mathrm{CuZr}}_2$, and B2 ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$.

Figure 3

Vibrational entropy of (a) glass-forming liquid and (b) crystal as a function of temperature. The simulations are calibrated to the experiments. (c) Temperature dependence of excess vibrational entropy of glass and liquid over crystal. The error bars in (c) stand for the standard deviation of the entropy in five statistically independent configurations.

Figure 4

Panorama of excess total and vibrational entropy over entire temperature range. The excess total entropy experiences abrupt increase upon glass transition with dominating contribution from its configurational component. The simulations are calibrated by experiments.

Figure 5

Shannon entropy of local structures across the glass transition as a microscopic measure of configurational entropy. (a) Distribution and variation of 30 most frequent Voronoi polyhedra at 10 K and 1200 K, respectively. (b) Distribution of Voronoi polyhedra in crystals. (c) Temperature dependence of Shannon entropy which is extracted from the distribution of local structures. The fractions of specific Voronoi polyhedra $〈0,3,6,4〉$, $〈0,0,12,0〉$, and $〈0,2,8,2〉$ are also shown for comparison. Each data point is an average of five independent inherent structures, with error bars in (c) denoting the standard deviation of entropy in five statistically independent configurations. (d) Temperature dependence of excess configurational entropy of glass-forming liquid, which is extracted from the difference between total entropy and the vibrational entropy as plotted in Fig. 4. The error bars in (d) stand for the standard deviation of entropy in five statistically independent configurations.

Figure 6

Composition dependence of the Shannon entropy about Voronoi structures. The data of four different metallic glass systems, i.e., ${\mathrm{Cu}}_{46}{\mathrm{Zr}}_{54},{\mathrm{Cu}}_{55}{\mathrm{Zr}}_{45},{\mathrm{Cu}}_{64}{\mathrm{Zr}}_{36}$ and $\mathrm{Cu}50\mathrm{Zrso}$, include 32000 atoms, are listed for comparison. Even if the composition varies, the remarkedly change of Shannon entropy on glass transition is clearly seen and is general for all the compositions.

Figure 7

Size dependence of the Shannon entropy about Voronoi structures. Three independent large, medium and small systems include 31 250, 21 296 and 10 976 atoms, respectively. As the size becomes larger, the Shannon entropy is bigger with increase in structural diversity. But the data of Shannon entropy convergence to a fixed value if the system size is approximately of the large system. Therefore, the present model with 31 250 atoms is believed to yield reliable statistics on Voronoi polyhedra.

Figure 8

Ensemble average of the centrosymmetry parameter for systems with different number of atoms. As the size becomes larger, the centrosymmetry parameter changes slightly (the kink becomes more pronounced) with the increase of structural diversity. There is no clear size effect on this parameter, compared with Shannon entropy as shown in Fig. 7.