Revealing the relationship between liquid fragility and medium-range order in silicate glasses

Despite decades of studies, the nature of the glass transition remains elusive. In particular, the sharpness of the dynamical arrest of a melt at the glass transition is captured by its fragility. Here, we reveal that fragility is governed by the medium-range order structure. Based on neutron-diffraction data for a series of aluminosilicate glasses, we propose a measurable structural parameter that features a strong inverse correlation with fragility, namely, the average medium-range distance (MRD). We use in-situ high-temperature neutron-scattering data to discuss the physical origin of this correlation. We argue that glasses exhibiting low MRD values present an excess of small network rings. Such rings are unstable and deform more readily with changes in temperature, which tends to increase fragility. These results reveal that the sharpness of the dynamical arrest experienced by a silicate glass at the glass transition is surprisingly encoded into the stability of rings in its network.


Linear MRD -SiO2 mol% correlation of 27 CAS glasses
Room-temperature (RT) neutron total-scattering patterns were collected for 27 CAS glasses, with their XRF-analyzed compositions being listed in Supplementary Table 2. There are many ways to group these 27 glasses and search for correlations between structural parameters and SiO2 mol% content. Here, we explore the evolution of the MRD structural parameter along both vertical and horizontal joins in the CAS ternary phase diagram.

MRD of vertical compositional line with constant NBO/T
As shown in Fig. 1a, five vertical lines are drawn in the CAS phase diagram. This is motivated by the fact that the glass compositions on each vertical join feature a constant NBO/T value but different SiO2 mol% values. The NBO/T ratio is here defined as the amount of non-bridging oxygen (NBO) per glass-former tetrahedron (T) and is calculated by: for CAS glasses. It is noted that two glasses contain more Al2O3 than CaO, which results in negative values of NBO/T according to the

MRD of horizontal compositional lines with constant SiO2 content (mol%)
Seven horizontal lines are drawn in the CAS phase diagram (Fig. 2a). The glass compositions on each join have the same SiO2 mol% values but different NBO/T ratios. Seven plots with SiO2 mol% values ranging from 40 to 80 are shown in Fig. 2, b to h, respectively.
In each plot, the F(Q)-FSDPs are labeled by their NBO/T values. For the glass groups with SiO2 mol%  65 ( Fig. 2, e to h

No inverse correlation between m-SiO2 mol% for the non-CAS glasses
To further confirm that m depends on MRD but not on SiO2 mol%, we plot both the m-MRD and m-SiO2 mol% correlations in Fig

CAS fragility measurement by an isothermal equilibrium viscosity method
Equilibrium three-point beam-bending viscosity measurements were conducted for four charge-balanced CAS glasses xCaO-xAl2O3-

FEAR simulation of CAS glasses and ring-size quantification
We simulated the structure of three CAS silicate glasses by combining neutron-diffraction experiments and force-enhanced atomic refinement (FEAR) [1]. All simulations were carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator packages [2]. Three CAS glass models, CAS40, CAS50 and CAS70, were computed by molecular-dynamics (MD) simulations with each model comprising around 3000 atoms. We applied the interatomic potential parametrized by Jakseas it has been found to yield some structural and elastic properties that are in good agreement with experimental data for CAS [3]. A cutoff distance of 8.0 Å was used for the short-range interactions. The Coulombic interactions were calculated by adopting the Fennell damped shifted force model with a damping parameter of 0.25 Å -1 and a global cutoff of 8.0 Å. These three glasses were first simulated by MD simulations using a conventional melt-quench method, as described in the following. First, the atoms were randomly placed in a cubic box using PACKMOL [4] while ensuring the absence of any unrealistic overlap. The systems were then subjected to an energy minimization, followed by some 100 ps relaxations in the canonical (NVT) and isothermal-isobaric (NPT) ensembles at 300 K, sequentially. These models were then fully melted at 3000 K for 100 ps in the NVT and, subsequently, NPT ensemble to ensure the loss of the memory of the initial configurations and to equilibrate the system. Then these liquids were cooled from 3000 K to 300 K in the NPT ensemble at zero pressure with a cooling rate of 1K/ps. For all simulations, we adopted the Nosé-Hoover thermostat and a fixed time step of 1 fs.
We then assessed the ability of the FEAR [5] (force-enhanced atomic refinement) method to offer an improved description of the atomic structure of glassy silica as compared to those generated by MD or reverse Monte Carlo (RMC). To this end, we adopted the FEAR methodology introduced by Drabold et al. [6]. In contrast to MD simulations (which solely uses the knowledge of the interatomic potential) and RMC [7] simulations (which solely uses the knowledge of experimental data), the FEAR approach leverages all the available information. FEAR presents two key advantages: (i) it is more computationally efficient, since the energy does not need to be computed at every RMC step, and (ii) it does not rely on any assumption regarding the weights associated with the structural and energy terms in the cost function. In detail, we first started from a "randomized" structure generated by RMC while using a very high effective temperature, namely, = 5000 K. Following the original implementation of the FEAR method, the system was then iteratively subjected to a combination of RMC refinements and energy-minimization steps, wherein each FEAR iteration consists of: (i) 3600 RMC steps and (ii) an energy minimization (conducted with the conjugate-gradient method). We found that 16 of such iterations were sufficient to achieve a convergence of the potential energy and for the CAS glasses. During the refinement, we dynamically adjusted the average acceptance probability of the Metropolis algorithm by linearly decreasing the effective temperature from 10 2 down to 10 −3 during the FEAR refinement. These parameters were found to yield a glass structure exhibiting minimum and potentialenergy values.
We then explored the structure of the glass structures generated by FEAR. To this end, we computed the neutron structure factor for each of the simulated glasses. Fig. 5 shows the reduced structure factor, F(Q), predicted by FEAR and MD, which are compared with experimental neutron-diffraction data. We observe that the FEAR-derived structure factors exhibit an excellent agreement with the experimental data over the entire Q range-which is not unexpected, since the neutron PDFs were used as input for the FEAR simulations. In contrast, the MD-derived structure factors present some notable discrepancies with the experimental data.
Especially, FEAR predicts a sharper FSDP than MD, suggesting that the glass refined using FEAR exhibits a more ordered mediumrange structure than its MD-based counterpart This echoes the fact that glass structures generated by FEAR tend to exhibit an increased thermodynamic stability (i.e., lower energy) as compared to structures generated by MD. We then computed the ring-size distribution from the FEAR-simulated structures using the RINGS code [8]. The Guttman's ring definition was used for ring-counting since it is the most relevant to describe the ring distribution derived from the FSDP of scattering patterns in terms of the probed length scale [1]. The relative ring-size distributions derived from the direct ring counting of the FEAR structure models were compared with the RingFSDP results and are shown in Fig. 6

Inaccuracy of DSC-measured fragility data does not affect m-MRD correlation
Since it is not possible to obtain and measure every single glass in this study, we also used data from the literature. Unfortunately, some of them had to be calorimetric measurements due to the limited viscosity data in the literature. Considering the possible accuracy problems in the calorimetric data, we employed the empirical relationship of Zheng et al [24] obtained from the study of various oxide glass systems, including borates, aluminosilicates, and vanadium tellurites. Even though Zheng et al. did not prove that it was a universal empirical relationship, it can be used as a method to improve the accuracy of calorimetric fragility-index data in silicates considering the diversity of oxide glass systems used in that empirical study.
In addition, our goal is to understand and explain the relationship between the structure and the fragility of glasses, but we are not trying to propose a universal empirical model for MRD and m. Thus, the small inaccuracies in the m data do not lead to a change in our observations or the conclusion. In order to demonstrate the effect of the inaccuracy of fragility-index data based on calorimetric measurements, we plot the same dataset without using the correction used in the plot in the manuscript. The comparison of the two plots ( Fig. 7) clearly shows that the general trend and correlation between the two parameters do not change when we use the calorimetric data as reported in the cited references without employing the correction. The linear fit quality is slightly worse than the original case, but the difference between the two fits can be considered negligible.