Composition – structure – property relationships in alkali aluminosilicate glasses: A combined experimental – computational approach towards designing functional glasses

Journal of Non-Crystalline Solids 505 (2019) 144–153

Contents lists available at ScienceDirect

Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol

Composition – structure – property relationships in alkali aluminosilicate glasses: A combined experimental – computational approach towards designing functional glasses

T

Mengguo Rena, Justin Y. Chengb, Siva Priya Jaccanic, Saurabh Kapoorb, Randall E. Youngmand, ⁎ ⁎ Liping Huangc, Jincheng Dua, , Ashutosh Goelb, a

Department of Materials Science and Engineering, University of North Texas, Denton, TX 76203, USA Department of Materials Science and Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854-8065, USA Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA d Science and Technology Division, Corning Incorporated, Corning, NY 14831, USA b c

ABSTRACT

A set of 12 glass compositions with distinct structural features have been designed over a broad composition space in the per-alkaline region of the Na2O – Al2O3 – SiO2 ternary system. As expected from a per-alkaline system, aluminum has been found to be tetrahedrally coordinated in all the glasses using 27Al magic angle spinning – nuclear magnetic resonance (MAS-NMR) spectroscopy and from structure models generated using molecular dynamic (MD) simulations. The physical properties of glasses, for example, density, coefficient of thermal expansion (CTE), glass transition, elastic moduli and Vickers hardness and brittleness have been measured experimentally and their trends have been explained based on the atomic structure of glasses, from both simulations and experiments. A reasonable agreement has been observed between the composition – structure – property relationship trends obtained experimentally when compared with those predicted by MD simulations. This demonstrates that MD simulation is a promising technique for predictive modeling and designing novel glass compositions for functional applications.

1. Introduction Aluminosilicate glasses have been at the helm of some of the most recent technological innovations which include the development of chemically durable, scratch resistant, high strength display glasses for electronic and automobile industries [1,2]. At present, the toughest glasses being produced in industry are designed in Na2O-Al2O3-SiO2 (NAS) [3] and Ca2O-Al2O3-SiO2 (CAS) [4] systems that exhibit hardness of 5 GPa, density of 2.40–2.80 g⋅cm−3 and Young's modulus of 60–103 GPa [5]. Most of these glasses have been traditionally designed empirically using a trial-and-error approach. However, with an everincreasing demand for lighter and tougher damage resistant glasses, it is becoming difficult to design novel glass compositions using the same conventional approach. Although glasses and transparent glass-ceramics with elastic and mechanical properties much higher than multicomponent aluminosilicates have been reported in literature, for example glasses in Al2O3 – SiO2 binary system [6] or glass-ceramics in La2O3-Al2O3 binary system [7], their narrow glass forming regions and high processing temperatures (≥1800 °C) limit their manufacturing under existing industrial settings. Therefore, a new level of conceptual understanding about the composition – structure – property

⁎

relationships in aluminosilicate glass systems is required that can be applied to attain a significant leap in hardness and fracture toughness [5]. Some recent efforts in this direction use temperature dependent topological constraint theory [8] to predict hardness of borates [9], borosilicates [10], phosphosilicates [11], and aluminoborosilicate [12] glasses. Although interesting, research on this topic is still in its nascent stage as it is difficult to apply this theory on complex, multicomponent glass systems [13]. The other approach towards design of novel multicomponent functional glasses is through the combination of experimental and computational approaches wherein predictive modeling is used to design glass compositions with desired properties, while rigorous experimental data is required to validate these models [14]. With a reliable interaction potential model, MD simulations can provide comprehensive insights into the short/medium-range structure features that are hard to derive from experiments [15–19]. This approach is highly promising considering the significant advancement in the field of computational modeling as we can now easily model multicomponent silicate glasses for their structure, and predict their physical properties. However, it is difficult to find a rigorous and comprehensive experimental dataset in existing scientific literature to validate these models

Corresponding author. E-mail addresses: [email protected] (J. Du), [email protected] (A. Goel).

https://doi.org/10.1016/j.jnoncrysol.2018.10.053 Received 7 August 2018; Received in revised form 25 October 2018; Accepted 31 October 2018 0022-3093/ © 2018 Published by Elsevier B.V.

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

due to several reasons mainly related with inconsistencies in synthesis and processing conditions of glasses and variations in methods of characterizing their properties. Therefore, it is necessary to generate an experimental dataset pertaining to the structure – property relationships in oxide glasses and use it to validate the models predicting their structure and various physical properties. In this paper, an attempt has been made to combine the strengths of experimental studies with MD simulations to understand the composition – structure – property relationships over a comprehensive range of glass compositions in per-alkaline (Na/Al > 1) Na2O-Al2O3-SiO2 system. The computational models have been used to predict the thermal and elastic properties of the studied glasses and comparison with their corresponding experimental dataset has been presented. The emphasis has been laid upon addressing the concerns pertaining to previous composition – structure – property relationship studies reported in literature such that our work not only helps in understanding the macroscopic properties of these glasses from the fundamentals of their atomic structure, but also forms the baseline for development of non-empirical models to design functional glasses with novel applications.

2.2. Structural analysis 27

Al magic-angle spinning (MAS) NMR experiments on aluminosilicate glasses were conducted at 16.4 T using a commercial spectrometer (VNMRs, Agilent) and a 1.6 mm MAS NMR probe (Agilent) with spinning speeds of 25 kHz. MAS NMR data were acquired using radio frequency pulses of 0.6 μs (equivalent to a π/12 tip angle), relaxation delays of 2 s, and signal averaging of 1000 acquisitions. MAS NMR data were processed using commercial software, without additional apodization and referenced to aqueous aluminum nitrate at 0.0 ppm. A weak background signal from the zirconia MAS rotors was detected by 27Al MAS NMR of an empty rotor and subsequently subtracted from the MAS NMR data of the glass samples. This signal, at approximately 16 ppm, is clearly distinct from the Al peaks in the glasses, but nonetheless has been removed to ensure higher accuracy in the 27Al MAS NMR experiments. 2.3. Density and thermal analysis Archimedes' method was employed to measure the apparent density of the monolith glass samples at room temperature. D-Limonene was used as the immersion liquid and a digital balance of sensitivity 10−4 g was employed to weigh the glass samples. A minimum of five samples per composition were used to obtain the density values. The standard deviation in all the density values is ≤0.009 g/cm3. The glass transition temperature (Tg) of the annealed glasses was obtained by differential scanning calorimetry (DSC, STA8000, Perkin Elmer Inc.). The glass powders (particle size < 120 μm) weighing ~50 mg were contained in a platinum pan and scanned in air from 30 °C to 1000 °C at a heating rate (β) of 20 K min−1 in flowing N2 environment. The Tg values and standard deviation reported in this paper are an average of at least three scans per glass composition. Coefficient of thermal expansion (CTE) of all the glasses (dimensions: 5 mm × 15 mm, parallel surfaces) was measured using a horizontal dilatometer (L75HS1400C Platinum Series, Linseis Inc.) in the temperature range of 100–400 °C at a heating rate of 5 °C/min.

2. Experimental and computational methodologies 2.1. Synthesis of the glasses Table S1 in the Supplemental Material presents the batched glass compositions. High-purity powders of SiO2 (Alfa Aesar; > 99.5%), Na2CO3 (Sigma Aldrich; > 99%), and Al2O3 (Sigma Aldrich; ≥99%) were used as glass precursors. Homogeneous mixtures of batches (corresponding to 75 g oxide composition), obtained by ball milling, were melted in PteRh crucibles at temperatures varying between 1550 and 1650 °C for 2–3 h in air. The glass melts were quenched on a metallic plate followed by annealing at temperature corresponding to (Tg⁎ - 50) °C for 1 h, where Tg⁎ is the predicted glass transition temperature obtained from SciGlass database. The amorphous nature of glasses was confirmed by X-ray diffraction (XRD) analysis (PANalytical – X'Pert Pro; Cu Kα radiation; 2θ range: 10°–90°; step size: 0.007° s−1). Table 1 presents the experimental glass compositions as analyzed by inductively coupled plasma – optical emission spectroscopy (ICP – OES; PerkinElmer Optima 7300 V), and flame emission spectroscopy (PerkinElmer Flame Emission Analyst 200). The content of Al2O3 and SiO2 in synthesized glasses was determined by ICP – OES, while sodium concentration in glasses was determined by flame emission spectroscopy.

2.4. Mechanical property measurements Glass samples with dimensions of about ~12 × 12 × 3 mm3 were cut and the flats were ground and polished in water using SiC adhesive disks with increasing grit size. The final steps of polishing were carried out in a water-free diamond suspension on a polishing cloth in order to prevent surface hydration. Vickers hardness (HV) of glasses was measured using a Vickers micro-indenter (Leco LM-248AT). The measurements were performed in air at room temperature with a dwell time of

Table 1 Analyzed glass compositions, experimental density, molar volume (VM) and atomic packing factor (APF), Glass transition temperature (Tg) and Coefficient of thermal expansion (CTE). Label

1–1 1–2 1–3 BL 1–4 2–1 2–2 2–3 BL 2–4 3–1 3–2 BL 3–3

Composition (mol%) Na2O

Al2O3

SiO2

31.0 31.4 30.8 32.9 31.1 47.5 41.3 37.1 32.9 25.7 41.9 36.0 32.9 25.6

0 5.5 10.6 15.8 21.0 0 5.5 10.6 15.8 21.4 15.7 15.9 15.8 15.9

69.0 63.1 58.7 51.3 47.9 52.5 53.2 52.3 51.3 52.9 42.4 48.1 51.3 58.5

Na/Al

Density (g/cm3)

– 5.71 2.91 2.08 1.48 – 7.51 3.50 2.08 1.20 2.67 2.26 2.08 1.61

2.393 2.408 2.429 2.435 2.436 2.467 2.471 2.446 2.435 2.414 2.467 2.450 2.435 2.407

± ± ± ± ± ± ± ± ± ± ± ± ± ±

145

0.005 0.007 0.005 0.003 0.001 0.004 0.004 0.004 0.003 0.003 0.002 0.005 0.003 0.003

VM (cm3/mol)

APF

Tg (°C)

25.324 26.038 26.678 27.474 28.325 24.686 25.455 26.533 27.474 28.542 27.199 27.347 27.474 27.752

0.43 0.45 0.46 0.47 0.47 0.45 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.46

490.0 520.5 549.4 601.6 665.0 431.7 481.0 535.3 601.6 722.2 562.4 584.8 601.6 618.6

CTE (10−5 K−1) ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1.8 0.7 0.8 0.6 1.8 4.6 5.6 0.6 0.6 2.6 2.21 2.5 0.6 0.4

1.58 1.48 1.41 1.34 1.34 2.30 1.91 1.59 1.34 1.19 1.64 1.52 1.34 1.19

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.01 0.02 0.01 0.02 0.02 0.00 0.03 0.01 0.02 0.00 0.03 0.00 0.02 0.02

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

10 s. Ten indentations at each load (0.98, 2.9, 4.9, 9.8, and 19.6 N) were performed. Samples were spaced according to ASTM standard C1327–15, after crack length was established with a test indent. The indentation feature measurement was performed digitally on images of indents at 50× magnification using an OMAX A35140U3 14.0MP camera and its associated software, TopView. Nominal indents were judged as such provided that indentation sites were symmetric (indents too close to sample edges displayed lateral gouging indicating probable shifting of the diamond tip). Indentation corner cracks that ran out of field of view were measured via a crosshair in the eyepiece of the indentation machine and digital calipers installed in the sample stage of the indentation machine. The indentation diagonals were taken as 2a, and were averaged for each glass. The length of longest crack, if present, at each corner of the indents were taken as c and then averaged for each indent. Eq. 1 was used to calculate the Vickers hardness HV, where P is the indentation load (N) for median cracking, α is a shape parameter (2 for Vickers indenter), and a is the half-diagonal length of the indent.

Hv =

P a2

Table 2 Si and Al coordination number distributions of the simulated glasses (%) and percentage of [5]Al derived from NMR.

H = P Kc

1/4

c a

3/2

C44 = VT2

(4)

E = C44

B=

3C11 C11

3C11

4C44 C44

4C44 3

=

E 2G

(5) (6) (7)

G = C44 1

100 100 100 100 100 100 100 100 100 100 100 100 100 100

[4]

[5]

Al

– 99.90 99.60 99.60 99.70 – 99.60 99.80 99.60 99.70 100 99.70 99.60 99.40

± ± ± ±

0.08 0.31 0.16 0.09

± ± ± ±

0.31 0.25 0.16 0.21

± 0.20 ± 0.16 ± 0.22

[5]

Al

– 0.10 0.42 0.39 0.29 – 0.36 0.24 0.39 0.25 0 0.27 0.39 0.52

± ± ± ±

0.08 0.31 0.16 0.17

± ± ± ±

0.31 0.25 0.16 0.11

± 0.20 ± 0.16 ± 0.26

Al exp.

– 1.1 0.6 0 0 – 0 0 0 0 0 0 0 0

(9)

C /r 6

where r is the distance between the two atoms and A, C, and ρ are parameters. The parameters for this potential (as shown in Table S2 in the Supplemental Material) were initially fitted to both structure and physical properties of various minerals [25,26]. In the original form of Buckingham potential, the energy diverges to negative infinity at small distances. To solve this problem, a repulsion function V(r) = B/rn + Dr2 for the r values smaller than rc was introduced to replace the original potential to maintain repulsion at short distances. Here, rc is defined as the r value where the third derivative of potential energy was zero and B, n and D are fitted parameters that make the potential, force (first derivative of potential) and first derivative of force continuous from both functions at rc hence the potential and force functions are smooth after the corrections. Simulation boxes with a total number of ~6000 atoms were used in the MD simulations. The initial structure of each glass composition was generated by randomly putting atoms, with an experimental measured density and shortest distance constraints to avoid atoms being too close to each other, in a cubic simulation box. The glass structures were derived by a simulated melt and quench process (with a time step of 1 fs) as described here. Firstly, the whole system was energy minimized at 0 K for 60 ps, and then relaxed at 300 K for 60 ps under canonical ensemble (NVT). In the second step, the system was melted at 6000 K for 60 ps, relaxed at 5000 K for 100 ps, and then gradually cooled down to 300 K using NVT ensemble with a cooling rate of 5 K/ps. At 300 K, the glass went through a step of the isothermal and isobaric ensemble (NPT) simulation under ambient pressure for 60 ps and then was further relaxed under microcanonical ensemble (NVE) for another 60 ps. In order to maintain statistical rigor, the melt-quench process for each glass composition was simulated three times starting from different initial configurations. Mechanical properties were obtained by calculating the second derivatives of the internal energy respect to strain, from which the components of elastic constant (C) and elastic compliance (S), defined

where, γ is a function of Young's modulus and hardness. For most inorganic glasses, γ varies within ± 5% of 2.39 N1/4 μm1/2 [21]. Thus, at a constant load the c/a ratio gives an estimate of brittleness. Elastic properties of glasses were measured by Brillouin light scattering (BLS). Glass samples were cut and optically polished to 100–200 μm in thickness with parallel top and bottom surfaces using 600 grit SiC sand paper and cerium oxide slurry. The refractive index of the glass sample so polished was measured using a Metricon Model 2010/M Prism Coupler with an accuracy of ± 0.0002. A 532 nm Verdi V2 DPSS green laser was used as the probing light source for the refractive index measurements as well as the BLS measurements. A sixpass high contrast Fabry–Perot interferometer from JSR Scientific Instruments was used to carry out BLS experiments in the emulated platelet geometry (EPG) to measure both longitudinal (VL) and transverse sound (VT) velocities [22]. From the sound velocities measured in BLS, together with the density (ρ), the Young's modulus (E), bulk modulus (B), shear modulus (G), and the Poisson's ratio were calculated using the following equations: (3)

1–1 1–2 1–3 BL 1–4 2–1 2–2 2–3 BL 2–4 3–1 3–2 BL 3–3

Si

V (r ) = A exp ( r / )

(2)

C11 = VL2

[4]

to −1.2, 2.4, 1.8 and 0.6, respectively. Short range potentials acting between pairs of atoms include repulsive (due to electron cloud overlap) and attractive terms (due to Van der Waals or dispersion interaction). The short-range interactions of the potentials have the Buckingham form,

(1)

Brittleness was calculated using the formula proposed by Sehgal et al. [20] given in Eq. 2.

B=

Label

(8)

2.5. Molecular dynamics simulation details and property calculations

as Cij =

Sodium aluminosilicate glasses were studied by using classic MD simulations that were performed using the DL-POLY program [23]. A set of partial charge pair-wise potentials has been used in all the simulations of this work, which are similar to the widely used BKS and TTAM potentials for silica glass but with additional parameters for multicomponent glasses [24]. The charges of O, Si, Al, Na are assigned

1 V

( ) and S = C 2U i

j

−1

, respectively, were calculated. The bulk

(B) and shear (G) moduli were then calculated based on the elements of the elastic constant [27,28]. Voigt, Reuss and Hill are three commonly used methods for bulk and shear moduli calculation. Voigt method is based on the assumption of uniform strain or deformation in the aggregate, where the bulk and shear modulus can be calculated from Eqs. 10 and 11. Reuss method is based on the assumption of uniform stress 146

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

or pressure in the aggregate, where Eqs. 12 and 13 are used for the bulk and shear modulus calculation, respectively [29]. The elastic moduli reported in this work were the Hill values, which are defined as the average of Voigt and Reuss results. The Young's modulus was calculated using Eq. 14.

BVoigt =

1 (C11 + C22 + C33 + 2(C12 + C13 9 (10)

+ C23)) GVoigt =

Table 3 O coordination number distributions of the simulated glasses (%).

1 (C11 + C22 + C33 + 3(C44 + C55 + C66) 15

C12

C13 (11)

C23)

BReuss = (S11 + S22 + S33 + 2(S31 + S21 + S32))

1

(12)

GReuss =

4(S11 + S22 + S33

S12

15 S13

NBOTheory

NBO

BO

1–1 1–2 1–3 BL 1–4 2–1 2–2 2–3 BL 2–4 3–1 3–2 BL 3–3

35.30 28.60 22.20 16.40 10.50 58.10 42.40 28.60 16.40 5.10 28.60 22.20 16.40 10.50

35.30 ± 0.00 28.60 ± 0.01 22.30 ± 0.08 16.70 ± 0.18 11.90 ± 0.10 57.8 ± 0.06 42.3 ± 0.07 28.6 ± 0.10 16.7 ± 0.18 7.71 ± 0.22 28.70 ± 0.11 22.50 ± 0.03 16.70 ± 0.18 11.50 ± 0.28

64.70 71.40 77.50 82.70 86.70 42.10 57.70 71.20 82.70 89.70 71.00 77.20 82.70 87.40

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.00 0.05 0.19 0.33 0.23 0.03 0.03 0.16 0.33 0.44 0.24 0.16 0.33 0.51

TBO

FO

0 0 0.17 0.56 1.43 0 0 0.13 0.56 2.64 0.22 0.34 0.56 1.06

0 0 0 0 0 0.13 ± 0.03 0 0 0 0 0 0 0 0

± 0.09 ± 0.15 ± 0.14 ± ± ± ± ± ± ±

0.08 0.15 0.22 0.13 0.11 0.15 0.24

fraction of five-fold coordinated Al with the calculated concentrations < 0.5% for all the samples. Hence, both experiments and MD simulations reveal that Al in these per-alkaline glasses tends to be predominantly in four-fold coordination along with a very small amount of high coordinated Al. Fig. 1 shows a snapshot of the final structure of sodium aluminosilicate glass from MD simulation where the network structure made up of corner sharing SiO4 and AlO4 trahedrons are shown in dark and light blue, respectively. The appearance of higher coordinated Al, especially [5]Al, is known to depend on the Na/Al ratio, pressure and thermal history of glasses [30,31]. Although higher coordinated aluminum species are commonly found in per-aluminous glasses, these species have also been observed to exist sporadically in per-alkaline systems (as in the present study) in minor quantities [32]. The details about partial pair distribution function (PDF) and bond angle distribution (BAD) in the investigated glasses, as calculated from MD simulations, have been provided in Table S3 in the Supplemental Material. Since experimental and computational aluminum speciation in glasses are in good agreement, the glass structure derived from MD simulations can be considered as reasonable and reliable. For the oxygen speciation analysis, the fraction of three-bonded oxygen (TBO), bridging oxygen (BO), non-bridging oxygen (NBO) and free oxygen (FO) which are defined as oxygen atoms connected to three, two, one and none glass forming cations (Si or Al), have been derived from MD simulation for each glass composition (Table 3). As a comparison, the theoretical NBO concentration in glasses was calculated based on a simple stoichiometry argument used by Ganster [33] on calcium aluminosilicate glasses, where the glass system was assumed to be made of perfect tetrahedra with only two-fold oxygen atoms. Since the glasses in this study are per-alkaline in nature (Na2O/ Al2O3 > 1), the theoretical number of NBO atoms should be:

S23) + 3(S44 + S55 + S66 ) (13)

E =

Label

9BG 3B + G (14)

3. Results and discussion 3.1. Structural analysis of the glasses – Computational vs. Experimental Fig. S1 (in the Supplemental Material) presents the 27Al MAS NMR spectra of the studied glasses, while Table 2 presents the comparison between experimental (using MAS NMR) and computational aluminum speciation in glasses. The 27Al MAS NMR spectra are characterized by an intense peak centered around 60 ppm corresponding to four-fold coordinated aluminum [4]Al. In addition to [4]Al groups, there is some evidence for higher coordination sites ([5]Al) in some of these as-prepared glasses with glass 1–2 and 1–3 showing 1.1% and 0.6% five-coordinated Al, respectively (Table 2). For all the other samples, Al is 100% four-coordinated. In agreement with the MAS NMR results, the simulation results indicate the presence of small but non-negligible

NNBO = NNa

NAl

(15)

where NNa and NAl are number of Na and Al atoms in the system, respectively. As expected, the concentration of NBOs depends on Na2O/ Al2O3 ratio in the glasses (Table 3). An increase in Na2O/Al2O3 ratio results in higher concentration of NBOs and vice-a-versa. A comparison between percentages of theoretically calculated NBOs and those obtained from MD simulations reveals a good agreement between the two values for glasses with higher Na/Al ratio (> ~3). However, as the ratio of Na/Al decreases (< ~3), the difference between theoretically calculated and simulated NNBO results increases. For glass samples with lower Na/Al ratio (such as samples 1–4, 2–4, 3–3), NBO fraction calculated by MD simulation is higher than theoretically calculated value, indicating there exist some excess NBOs in the simulated glass structure. Stebbins reported NMR evidence for excess NBO in CaAl2Si2O8 glass in 1997 [34]. After that, many other experiments on alkali/alkaline-earth aluminosilicate glasses with Na/Al ≈ 1 have also revealed

Fig. 1. Snapshot of the structure of sodium aluminosilicate glass (Sample BL, 5940 atoms with cell size of 43.24 Å) from MD simulations. 147

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

Fig. 2. Comparison of experimental and simulated density for glass Series I (a), Series II (b) and Series III (c).

the presence of excess NBOs in their structures [34,35]. It is proposed that the excess number of NBOs could be compensated by oxygen triclusters [34,35]. As listed in Table 3, TBO with varying concentration (0.2% - 2.6%) showed up in ternary glasses as the ratio of Na/Al decrease below ~3. We evaluated the TBO percentage and compared it with the amount of excess NBOs (the NBO percentage calculated from MD simulation minus the theoretical percentage of NBO), and found that these two values agree well with each other. In other words, there exists a linear dependence between the formation of TBO and the growth of excess NBO in the studied glasses. The distribution of TBO environment is another consideration that is worth paying attention to. From Fig. S2 (in the Supplemental Material), the quantification of three types of triclusters (OAl3, OAl2Si and OAlSi2) can be clearly seen and OSi3 is not found in any of these glasses. OAl3 and OAl2Si are dominant triclusters types as compared to OAlSi2.

Fig. 2 presents the glass density variation in simulation vs. experimental results as a function of batched Al2O3 (Series I, Fig. 2a and Series II, Fig. 2b) and SiO2 (Series III, Fig. 2c) concentration. For all the investigated compositions, density of simulated glasses was always found to be higher than the experimental values, indicating that the volume of the simulation box shrank ~2% during the last NPT run at 300 K. However, a good agreement was observed in experimental and simulations results pertaining to the composition vs. density variation trends for all the glasses. In order to calculate the CTE of simulated glasses, the glasses in Series I were melted under NPT ensemble and then gradually cooled down to 300 K. The volume changes during glass cooling process were recorded and have been presented in Fig. S3 in the Supplemental Material. The CTE values were calculated based on the volume changes in the glass system in the 300–1500 K temperature range and have been presented in Fig. 3. The CTE decreased from 2.68 × 10−5 K−1 to 1.94 × 10−5 K−1 with an increasing Al2O3/SiO2 ratio, as was also observed in the experimental dataset. This demonstrates the ability of MD models to successfully predict the composition – structure – property trends in aluminosilicate glasses. However, the CTE values obtained from simulations are higher than their experimental analogues. This difference may be attributed to the different thermal histories of the simulated vs. experimental glasses owing to the significantly higher melting temperatures and higher quenching rates in simulated glasses.

3.2. Correlation between structure and thermal properties of glasses – Experimental vs. Computational Table 1 presents the apparent density, molar volume (Vm), coefficient of thermal expansion (CTE) and glass transition temperature (Tg) of the studied glasses. Since the density of a glass is a strong function of its composition and is sensitive to both the volume occupied by the atoms and to their mass, molar volume (Vm) is often used to obtain structural information about glasses. The molar volume increases with increasing Al2O3 content in Series I (varying Al2O3/SiO2 ratio) and Series II (varying Na2O/Al2O3 ratio), while it decreases with increasing Na2O/SiO2 ratio in Series III. The observed molar volume trends for all three series of glasses can be correlated with their structure, which will be explained below.

3.3. Correlation between structure and elastic properties of glasses – Experimental vs. Computational Table 4 presents the experimental values of elastic properties – Young's modulus (E), bulk modulus (B), and shear modulus (G) – of the studied glasses along with their Poisson's ratio (ν) as measured using BLS technique. The compositional dependence of refractive indices of glasses in the present study has been presented in Fig. S4 in the Supplemental Material. The APF and elastic moduli increased with increasing Al2O3/SiO2 ratio in Series I, while the Poisson's ratio remained constant (0.244 ± 0.002) for the whole series of glasses. For glasses with varying Na2O/Al2O3 ratio (Series II), the values of E and G showed an increase with increasing Al2O3 content, while the value of B remained constant (45.22 ± 0.45 GPa). The values of APF varied between 0.45 and 0.47 and Poisson's ratio decreased from 0.265 to 0.228 with decreasing Na2O/Al2O3 ratio. In case of glasses with varying Na2O/SiO2 ratio (Series III), the values of APF (0.468 ± 0.005), E (70.14 ± 0.57 GPa) and G (28.17 ± 0.45 GPa) remained constant, while the values of B and ν decreased from 47.68 GPa to 44.04 GPa and 0.26 to 0.23, respectively, with increasing SiO2 content. Elastic moduli reflect the stiffness of the glass network which is mostly governed by the bond strength (bond energy) and the atomic packing density [37–39], and to some extent by the intermediate range order of glass [40]. Here we focus on the effects of the bond strength and the atomic packing density on the elastic moduli of glasses studied in this work. In Series I (Na2O content remains roughly constant) and II

i. Glasses with varying Al2O3/SiO2(Series I) and Na2O/Al2O3(Series II) ratio: In per-alkaline aluminosilicate glasses, alkali cations preferentially act as charge compensator for [AlO4]− units [36]. In the glasses under investigation, aluminum exists in four coordination as elucidated by 27Al MAS NMR and MD simulations (Table 2). Therefore, increasing Al2O3 content in these glasses will attract the Na+ from silicate network leading to its re-polymerization and increase in Si–O–Si and Si–O–Al linkages. This leads to an increase in molar volume (Table 1) of these glasses along with an increase in glass transition temperature (Tg), and decrease in CTE, as shown in Table 1. ii. Glasses with varying Na2O/SiO2ratio (Series III): An increase in SiO2 (network former) content at the expense of Na2O (network modifier) will decrease the concentration of non-bridging oxygens (NBOs) in glasses. Since the decrease in the NBO concentration in glasses will decrease the asymmetry of the bond to the neighboring silicon, or other network cation, decrease in Na2O/SiO2 ratio will not only increase the molar volume (due to higher number of directional bonds), but will also lead to higher Tg and lower CTE values (Table 1). 148

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

vs. BO reveals the changes in network connectivity with composition, with a higher ratio of BO to NBO implying a higher network connectivity. Table 3 shows that this ratio increases in all three Series with Series II showing the largest increase, followed by Series I and then Series III. In Series I, with increasing Al2O3 content, an increase in the atomic packing density combined with an increase in the network connectivity have an opposite effect on Poisson's ratio, resulting in little change with composition in this series. In Series II, a small increase in the atomic packing density combined with a large increase in the network connectivity ensures that the connectivity has a higher impact on the trend in Poisson's ratio, hence resulting in its overall decrease as Al2O3 content increases. In Series III, a decrease in the atomic packing density together with an increase in the network connectivity results in the decrease of Poisson's ratio as SiO2 content increases in this series. Fig. 4 presents a comparison of the experimental elastic properties with their computationally calculated counterparts. Overall, a good agreement was observed in the experimental and simulated elastic properties. In case of Series I with varying Al2O3/SiO2 ratio, a good correlation was observed in the experimental and computationally obtained elastic properties, where, all the three – Young's, bulk and shear – moduli increased linearly with increasing Al2O3 concentration in glasses (Fig. 4a). For the other two series, Young's and shear moduli from simulations agree well with experiments but the bulk moduli exhibit some differences. In glasses with varying Al2O3/Na2O ratio (Series II), the bulk modulus from simulations shows a linear increase with Al2O3 concentration, while the experimental values remain almost constant (Fig. 4b). However, the computational values converged with the experimental results at higher Al2O3 concentration. Similarly, in glasses with varying Na2O/SiO2 ratio (Series III), the experimental values reveal a slight decrease in bulk moduli from 47.68 GPa to 44.04 GPa with increasing SiO2, while the MD simulations suggest an increasing trend starting from 37.89 GPa and converging into experimental values at 42.34 GPa with decreasing Na2O/SiO2 ratio (Fig. 4c). With respect to a comparison between experimental and computational values of Poisson's ratios of the studied glasses, a good qualitative agreement was observed in the composition – property trends in the series of glasses under investigation (Fig. 5). However, a quantitative comparison between the experimental and computational values reveal significantly higher experimental values of Poisson's ratio than their computational analogues, which may be due to the deficiency of the pair-wise potentials.

Fig. 3. Comparison of experimental and simulated coefficient of linear thermal expansion for glasses in Series I. Table 4 Young's modulus (E), shear modulus (G), bulk modulus (B) and Poisson's ratio (v) of the investigated glasses measured using Brillouin light scattering technique. Glass Label

E (GPa)

1–1 1–2 1–3 BL 1–4 2–1 2–2 2–3 BL 2–4 3–1 3–2 BL 3–3

60.01 63.74 67.96 70.08 72.55 … 64.20 66.89 70.08 72.71 69.88 69.66 70.08 70.97

B (GPa)

± ± ± ± ±

0.10 0.33 0.22 0.50 0.17

± ± ± ± ± ± ± ±

0.33 0.42 0.50 0.22 0.21 0.23 0.50 0.21

39.01 41.75 43.91 45.66 46.81 … 45.45 45.12 45.66 44.63 47.68 46.33 45.66 44.04

G (GPa)

± ± ± ± ±

0.18 0.24 0.22 0.30 0.16

± ± ± ± ± ± ± ±

0.26 0.34 0.30 0.17 0.20 0.10 0.30 0.17

24.13 25.59 27.36 28.16 29.22 … 25.38 26.69 28.16 29.59 27.83 27.88 28.16 28.82

v

± ± ± ± ±

0.06 0.19 0.13 0.28 0.10

± ± ± ± ± ± ± ±

0.18 0.24 0.28 0.13 0.12 0.12 0.28 0.13

0.244 0.246 0.242 0.244 0.242 … 0.265 0.253 0.244 0.228 0.256 0.249 0.244 0.231

± ± ± ± ±

0.001 0.003 0.002 0.003 0.001

± ± ± ± ± ± ± ±

0.003 0.003 0.003 0.002 0.002 0.001 0.003 0.002

(SiO2 content remains roughly constant), the atomic packing density increases with increasing Al2O3 content, but the change is smaller in Series II. On the other hand, since the addition of Al2O3 converts NBO to BO, as seen in Table 3, an increase in the BO concentration in Series II is more dramatic than in Series I due to the fact that Al2O3 content is increased at the expense of Na2O to maintain the constant concentration of SiO2. Thus, elastic moduli increase with increasing fraction of BO in both Series I and II, more obvious increases are seen in the latter than the former. In the case of Series III, where Al2O3 content remain constant, the atomic packing density decreases slightly, but the fraction of BO increases as the SiO2 content increases, to less extent than those in Series I and II. These two competing factors result in the smaller increases in elastic moduli as the SiO2 content increases in Series III compared to the changes in Series I and II with the increase of Al2O3. As is evident from the above-discussed results, the fraction of BO plays a dominant role in determining the elastic moduli as a function of glass composition. The seminal work by Greaves et al. [41] on Poisson's ratio in glass systems revealed that it is intimately linked to glass structure, especially the atomic packing and the overall network connectivity (dimensionality). It was found that Poisson's ratio decreases when (i) the atomic packing density decreases and (ii) when the network connectivity increases. Let us now consider both factors together to understand the trends in Poisson's ratio. Table 1 shows that a significant increase in the atomic packing density is seen in Series I, a smaller extent of increase is seen in Series II and a small decrease in Series III. The fraction of NBO

3.4. Correlation between structure and hardness (and brittleness) of glasses The indentation experiments on the Na2O-Al2O3-SiO2 glasses provide an insight into the resistance to elastoplastic deformation quantified as hardness (HV). In case of aluminosilicate glasses, HV has been correlated to the number of NBOs with varying Na/Al ratio, where the reduction in the number of NBOs increases the rigidity of the network, which in turn decreases the ability of the glass to deform under stress [42]. Fig. 6 presents the hardness of glasses investigated in the present study at 4.9 N as a function of number of non-bridging oxygens per tetrahedrally coordinated cation (NBO/T). In general, the HV of the glasses decreases with increase in NBO/T in the investigated glasses. This decrease in HV is attributed to the decrease in rigidity of the network with increase in NBO concentration in glasses [8]. It is noteworthy that the Tg of the glasses scales positively with the HV values, thus indicating that glasses with low NBO/T are more rigid in nature in comparison to glasses with high NBO/T. In addition, Bechgaard et al. [42], related the NBO/T to the plastic compressibility of the glasses, where glasses with lowest NBO/T are least compressible. Therefore, being more resistant to deformation under indentation thereby shows high hardness. Further, the stresses generated due to penetration of an indenter tip into the glass surface can result in crack initiation, which has been attributed to the stresses that originate from the mismatch between the 149

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

Fig. 4. Comparison of experimental and simulated glass elastic modulus for glass Series I (a), Series II (b) and Series III (c) (E–Young's modulus; B–Bulk modulus; G–Shear modulus).

assumed coordination numbers (2 for O, 4 for Si and AlIV, 5 for AlV, and 6 for Na) along with the corresponding effective ionic radii of Shannon [44] have been used to calculate the minimum theoretical volume occupied by the ions. The glasses with low values of APF (i.e., glasses with significant voids in their structure), such as vitreous silica, are prone to densification as they can be compacted by mechanical loading [45,46]. On the other hand, denser glasses with higher APF, for example, sodalime silicates, tend to primarily deform through an isochoric shear-flow mechanism, as the interstices in the glassy network are occupied by modifier cations hindering densification [45]. In the present case brittleness of glasses increase with increase in APF values for all the three series of glasses (Fig. 7). Owing to the decrease in free volume of the

plastically deformed volume and the surrounding elastically deformed material. According to Sehgal and Ito [20,43], crack initiation is related to the brittleness of the glass. i.e., the higher the brittleness, the easier the initiation of cracks upon application of stress. Also, the brittleness of glass is known to depend on the ease of densification and shear flow. Interestingly, glasses having a balance of densification and shear flow have been reported to exhibit a low brittleness index in comparison to glasses with only densification and shear flow contribution [43]. The ability of a glass to densify under pressure depends mainly on the atomic packing factor (APF) (Table 1). APF is the ratio between the minimum theoretical volume occupied by the ions (assumed to be spherical) and the corresponding molar volume of the glass. The

Fig. 5. Comparison of Poisson's ratio from experimental and MD simulations for glass Series I (a), Series II (b) and Series III (c). 150

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

(a) 5.4

(b) 5.4

5.2

5.2 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6

HV (GPa)

HV (GPa)

5.0 4.8 4.6 4.4 4.2 4.0 3.8 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75

NBO/T (-)

NBO/T (-)

(c) 5.4

5.3

HV (GPa)

5.2 5.1 5.0 4.9 4.8 4.7 4.6 0.2

0.3

0.4

0.5

0.6

0.7

NBO/T (-) Fig. 6. Hardness (HV) of the investigated glasses at 500 gf with variation in NBO/T in (a) Series I, (b) Series II and (c) Series III (The dashed line is a guide to the eye.)

glasses, shear flow becomes the predominant mode to accommodate the indentation-induced stresses, while densification becomes more difficult [46], which leads to an increase in residual stresses around the indent and hence, results in formation of cracks.

overestimates their elastic moduli, and the Morse potential slightly underestimates them [47]. Further, majority of the current potential fittings used in MD simulation of oxide glasses have been performed on crystalline systems based on the structure and mechanical properties under ambient temperature and pressure. Temperature dependent properties such as melting temperature, CTE and heat capacity are not commonly used in the fitting. Due to notable differences of the crystalline and glassy systems, fine tuning the parameters for glass and melt to correctly describe a wide temperature range is highly desirable for the simulation of glasses, yet only very few sets of potentials in the literature address this issue [26]. In understanding the composition – structure – property relationships in simulated glasses, it is thus important to keep these limitations in mind and extract critical information such as composition effect on elastic or other properties and structural origin of certain behaviors in glasses. With respect to the impact of melt cooling rate on structure – property relationships in the studied glasses, although several orders of magnitude higher cooling rates of glass melts in MD simulations in comparison to their experimental analogues are usually criticized (e.g., much higher Tg in simulated glasses), we do not anticipate this to be a major reason for differences in experimental vs. computational results in the current investigation [48]. Recent systematic studies of cooling rate and system size effect on the structure and properties of borosilicate glasses show that some structural aspects such as boron coordination are more sensitive while others such as silicate network structures are much less sensitive. [49] Interestingly, the structural features and properties converge at different cooling rates and, for these systems, a convergence test in terms of cooling rate is thus recommended in simulations of these glasses. [49] Similarly, phosphorus speciation in silicate glasses is highly sensitive to their thermal history,

3.5. Challenges associated with predictive modeling of composition – structure – properties in glasses using MD simulations and future directions Despite significant progress in modeling the structure of glasses at atomistic level along with predicting thermal and elastic properties of oxide glasses, MD simulations still face a number of challenges in studying the composition – structure – property relationships in multicomponent glasses. These challenges include reliable and transferable potentials for multicomponent systems, the cooling rate effect during simulated glass formation, and the system size effect on certain properties and concentration effect on the simulations of minor components. Although these challenges have been discussed in detail elsewhere [26], below we have provided a brief summary of some of these issues which in our opinion are important to understand the reasons behind the differences in the experimental and computational results observed in the present study. One major reason for the discrepancy in computational vs. experimental values of physical properties may be attributed to the accuracy and availability of empirical potentials. Despite the fact that significant progress has been made in developing potentials for common oxides that include most of the glass components, a major issue pertains to potential transferability. There exist potentials of various oxides in the literature but in most of the cases they are not compatible with each other. For example, it has been shown that while predicting the elastic properties of aluminosilicate glasses, Buckingham potential slightly 151

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

(b)

(a) 7.5

7.00

Brittleness (µm-0.5)

Brittleness (µm-0.5)

6.75 7.0 6.5 6.0 5.5 5.0

6.50 6.25 6.00 5.75 5.50

4.5 5.25 0.43

0.44

0.45

0.46

0.46

0.47

0.45

0.48

0.46

0.46

0.47

APF (-)

APF (-)

(c)

0.46

7.4

Brittleness (µm-0.5)

7.2 7.0 6.8 6.6 6.4 6.2 0.46

0.46

0.47

0.48

APF (-) Fig. 7. Brittleness index (B) of the investigated glasses at 1 kgf (a) Series I, (b) Series II and (c) Series III.

especially when they exist as minor components (as has also been shown by Stone-Weiss et al.) [49,50] However, the distribution of Qn units in the silicate or aluminosilicate network is fairly insensitive to the cooling rate effect. [51] It is thus expected in the aluminosilicate glasses studied in this work, the usual simulation cooling rate should not affect these structural features to a large extent. Although a few thousand atoms are sufficient to study structure, physical and elastic properties of glasses, a much large simulation size is needed to study their indentation behavior [52,53], thus hardness and brittleness, in order to avoid the influence of boundary conditions on the complex stress state under an indenter, and to reduce the indentation size effect on hardness. Experimental measurements also have similar limitations. Depending on the method of measurements, certain properties can have large variations. For example, elastic constants measured by different methods can show large variations. [54] By knowing the limitations of simulations and experiments, we can then focus on the essential information that can be extracted in these studies and the chemical and physical nature of the composition – structure – property relations. An intelligently informed design of novel glass compositions can then be achieved by integrated experimental and simulation studies.

expansion and elastic moduli) calculated by MD simulations also present similar variation trends as compared to corresponding experimental results. For glasses with varying Al2O3/SiO2 (Series I) and Na2O/Al2O3 (Series II) ratio, the increase of Al2O3 content in these glasses will attract sodium ions from silicate network leading to its re-polymerization and increase in directional bonds (Si–O–Si and Si–O–Al), which results in an increase in Vm and Tg, and a decrease in CTE. For glasses with varying Na2O/SiO2 ratio (Series III), an increase in SiO2 (network former) content at the expense of Na2O (network modifier) will decrease the concentration of non-bridging oxygens (NBOs) in glasses, which also leads to higher Vm and Tg, and lower CTE values. Other properties such as hardness and brittleness were experimentally investigated as well. In general, the HV of the glasses decreases with increase in NBO/T ratio in the investigated glasses, which is attributed to the decrease in network connectivity of the glass-forming network with increase in NBO concentration in glasses. In addition, brittleness of glasses increases with increase in APF values for all three series of glasses, confirming that the ability of a glass to densify under pressure depends mainly on the atomic packing factor. The insights of the composition – structure – property relation obtained in this work by an integrated computational and experimental approach will facilitate understanding of observed glass properties and new composition design for technological applications.

4. Conclusions

Acknowledgement

Experimental studies combined with MD simulations were used to understand the composition – structure – property relationships over a large range of glass compositions (Series I, II and III) in per-alkaline (Na/ Al > 1) Na2O-Al2O3-SiO2 system. Reasonable glass structures were generated by MD simulations with most of the Al (> 99%) in four-fold coordination, which is in good agreement with 27Al NMR results. These MD simulations clearly show that Na+ ions preferentially charge compensate [AlO4]− units, and then the excess Na+ ions were used to create NBO on Si. Various glass properties (such as density, coefficient of thermal

The material is based on upon work supported by the National Science Foundation under Grant No. 1507131, 1508001, 1255378, and 1508410. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jnoncrysol.2018.10.053. 152

Journal of Non-Crystalline Solids 505 (2019) 144–153

M. Ren et al.

References [29] [30]

[1] D. Käfer, M. He, J. Li, M.S. Pambianchi, J. Feng, J.C. Mauro, Z. Bao, Ultra-Smooth and Ultra-strong Ion-Exchanged Glass as Substrates for Organic Electronics, Adv. Funct. Mater. 23 (2013) 3233–3238. [2] A. Ellison, I.A. Cornejo, Glass substrates for liquid crystal displays, Int. J. Appl. Glas. Sci. 1 (2010) 87–103. [3] S. Yoshida, A. Hidaka, J. Matsuoka, Crack initiation behavior of sodium aluminosilicate glasses, J. Non-Cryst. Solids 344 (2004) 37–43. [4] A. Pönitzsch, M. Nofz, L. Wondraczek, J. Deubener, Bulk elastic properties, hardness and fatigue of calcium aluminosilicate glasses in the intermediate-silica range, J. Non-Cryst. Solids 434 (2016) 1–12. [5] L. Wondraczek, J.C. Mauro, J. Eckert, U. Kühn, J. Horbach, J. Deubener, T. Rouxel, Towards ultrastrong glasses, Adv. Mater. 23 (2011) 4578–4586. [6] G.A. Rosales-Sosa, A. Masuno, Y. Higo, H. Inoue, Crack-resistant Al2O3-SiO2 glasses, Sci. Rep. 6 (2016) 23620. [7] A. Rosenflanz, M. Frey, B. Endres, T. Anderson, E. Richards, C. Schardt, Bulk glasses and ultrahard nanoceramics based on alumina and rare-earth oxides, Nature 430 (2004) 761–764. [8] M.M. Smedskjaer, J.C. Mauro, Y. Yue, Prediction of glass hardness using temperature-dependent constraint theory, Phys. Rev. Lett. 105 (2010) 115503. [9] M.M. Smedskjaer, J.C. Mauro, S. Sen, J. Deubener, Y. Yue, Impact of network topology on cationic diffusion and hardness of borate glass surfaces, J. Chem. Phys. 133 (2010) 154509. [10] M.M. Smedskjaer, J.C. Mauro, R.E. Youngman, C.L. Hogue, M. Potuzak, Y. Yue, Topological principles of borosilicate glass chemistry, J. Phys. Chem. B 115 (2011) 12930–12946. [11] H. Zeng, Q. Jiang, Z. Liu, X. Li, J. Ren, G. Chen, F. Liu, S. Peng, Unique sodium phosphosilicate glasses designed through extended topological constraint theory, J. Phys. Chem. B 118 (2014) 5177–5183. [12] M.M. Smedskjaer, Topological model for boroaluminosilicate glass hardness, Frontiers in Materials. 1 (2014) 23. [13] O.L. Alderman, M. Liska, J. Macháček, C.J. Benmore, A. Lin, A. Tamalonis, J. Weber, Temperature-Driven Structural Transitions in Molten Sodium Borates Na2O–B2O3: X-ray Diffraction, Thermodynamic Modeling, and Implications for Topological Constraint Theory, J. Phys. Chem. C 120 (2015) 553–560. [14] J.C. Mauro, A. Tandia, K.D. Vargheese, Y.Z. Mauro, M.M. Smedskjaer, Accelerating the design of functional glasses through modeling, Chem. Mater. 28 (2016) 4267–4277. [15] A. Cormack, J. Du, Molecular dynamics simulations of soda–lime–silicate glasses, J. Non-Cryst. Solids 293 (2001) 283–289. [16] A. Cormack, J. Du, T. Zeitler, Alkali ion migration mechanisms in silicate glasses probed by molecular dynamics simulations, Phys. Chem. Chem. Phys. 4 (2002) 3193–3197. [17] J. Du, A. Cormack, The medium range structure of sodium silicate glasses: a molecular dynamics simulation, J. Non-Cryst. Solids 349 (2004) 66–79. [18] J. Du, A. Cormack, The structure of erbium doped sodium silicate glasses, J. NonCryst. Solids 351 (2005) 2263–2276. [19] J. Du, L.R. Corrales, Understanding lanthanum aluminate glass structure by correlating molecular dynamics simulation results with neutron and X-ray scattering data, J. Non-Cryst. Solids 353 (2007) 210–214. [20] J. Sehgal, Y. Nakao, H. Takahashi, S. Ito, Brittleness of glasses by indentation, J. Mater. Sci. Lett. 14 (1995) 167–169. [21] J. Sehgal, S. Ito, A New Low-Brittleness Glass in the Soda-Lime-Silica Glass Family, J. Am. Ceram. Soc. 81 (1998) 2485–2488. [22] M. Guerette, L. Huang, A simple and convenient set-up for high-temperature Brillouin light scattering, J. Phys. D 45 (2012) 275302. [23] W. Smith, T. Forester, DL_POLY_2. 0: a general-purpose parallel molecular dynamics simulation package, J. Mol. Graph. 14 (1996) 136–141. [24] B. Van Beest, G. Kramer, R. Van Santen, Force fields for silicas and aluminophosphates based on ab initio calculations, Phys. Rev. Lett. 64 (1990) 1955. [25] J. Du, A.N. Cormack, Molecular dynamics simulation of the structure and hydroxylation of silica glass surfaces, J. Am. Ceram. Soc. 88 (2005) 2532–2539. [26] J. Du, Challenges in Molecular Dynamics Simulations of Multicomponent Oxide Glasses, Anonymous Molecular Dynamics Simulations of Disordered Materials, Springer, 2015, pp. 157–180. [27] A. Pedone, Properties calculations of silica-based glasses by atomistic simulations techniques: a review, J. Phys. Chem. C 113 (2009) 20773–20784. [28] M. Ren, L. Deng, J. Du, Bulk, surface structures and properties of sodium

[31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

[43] [44]

[45] [46] [47] [48] [49] [50] [51] [52] [53] [54]

153

borosilicate and boroaluminosilicate nuclear waste glasses from molecular dynamics simulations, J. Non-Cryst. Solids 476 (2017) 87–94. J. Gale, GULP manual, GULP manual, (1998). M. Edén, Chapter Four-27Al NMR Studies of Aluminosilicate Glasses, Annual Reports on NMR Spectroscopy. 86 (2015) 237–331. S. Kapoor, L. Wondraczek, M.M. Smedskjaer, Pressure-induced densification of oxide glasses at the glass transition, Frontiers in Materials. 4 (2017) 1. A. Deshkar, J. Marcial, S.A. Southern, L. Kobera, D.L. Bryce, J.S. McCloy, A. Goel, Understanding the structural origin of crystalline phase transformations in nepheline (NaAlSiO4)-based glass-ceramics, J. Am. Ceram. Soc. 100 (2017) 2859–2878. P. Ganster, M. Benoit, W. Kob, J. Delaye, Structural properties of a calcium aluminosilicate glass from molecular-dynamics simulations: a finite size effects study, J. Chem. Phys. 120 (2004) 10172–10181. J.F. Stebbins, Z. Xu, NMR evidence for excess non-bridging oxygen in an aluminosilicate glass, Nature 390 (1997) 60–62. M. Benoit, S. Ispas, M.E. Tuckerman, Structural properties of molten silicates from ab initio molecular-dynamics simulations: Comparison between CaO−Al2O3−SiO2 and SiO2, Phys. Rev. B 64 (2001) 224205. H. Maekawa, T. Maekawa, K. Kawamura, T. Yokokawa, Silicon-29 MAS NMR investigation of the sodium oxide-alumina-silica glasses, J. Phys. Chem. 95 (1991) 6822–6827. T. Rouxel, Elastic Properties and Short-to Medium-Range Order in Glasses, J. Am. Ceram. Soc. 90 (2007) 3019–3039. A. Makishima, J. Mackenzie, Direct calculation of Young's moidulus of glass, J. NonCryst. Solids 12 (1973) 35–45. A. Makishima, J.D. Mackenzie, Calculation of bulk modulus, shear modulus and Poisson's ratio of glass, J. Non-Cryst. Solids 17 (1975) 147–157. L. Huang, F. Yuan, M. Guerette, Q. Zhao, S. Sundararaman, Tailoring structure and properties of silica glass aided by computer simulation, J. Mater. Res. 32 (2017) 174–182. G.N. Greaves, A. Greer, R. Lakes, T. Rouxel, Poisson's ratio and modern materials, Nat. Mater. 10 (2011) 823–837. T.K. Bechgaard, A. Goel, R.E. Youngman, J.C. Mauro, S.J. Rzoska, M. Bockowski, L.R. Jensen, M.M. Smedskjaer, Structure and mechanical properties of compressed sodium aluminosilicate glasses: Role of non-bridging oxygens, J. Non-Cryst. Solids 441 (2016) 49–57. J. Sehgal, S. Ito, Brittleness of glass, J. Non-Cryst. Solids 253 (1999) 126–132. R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta crystallographica section A: crystal physics, diffraction, theoretical and general crystallography, Vol. 32 (1976), pp. 751–767. S. Yoshida, J. Sanglebœuf, T. Rouxel, Quantitative evaluation of indentation-induced densification in glass, J. Mater. Res. 20 (2005) 3404–3412. R. Limbach, A. Winterstein-Beckmann, J. Dellith, D. Möncke, L. Wondraczek, Plasticity, crack initiation and defect resistance in alkali-borosilicate glasses: from normal to anomalous behavior, J. Non-Cryst. Solids 417 (2015) 15–27. Y. Xiang, J. Du, M.M. Smedskjaer, J.C. Mauro, Structure and properties of sodium aluminosilicate glasses from molecular dynamics simulations, J. Chem. Phys. 139 (2013) (044507). L.R. Corrales, J. Du, Thermal Kinetics of Glass Simulations, Physics and Chemistry of Glasses, Vol. 46 (2005), pp. 420–424. L. Deng, J. Du, Effects of system size and cooling rate on the structure and properties of sodium borosilicate glasses from molecular dynamics simulations, J. Chem. Phys. 148 (2018) 024504. N. Stone-Weiss, E.M. Pierce, R.E. Youngman, O. Gulbiten, N.J. Smith, J. Du, A. Goel, Understanding the structural drivers governing glass–water interactions in borosilicate based model bioactive glasses, Acta Biomater. 65 (2018) 436–449. J. Du, Y. Xiang, Effect of strontium substitution on the structure, ionic diffusion and dynamic properties of 45S5 Bioactive glasses, J. Non-Cryst. Solids 358 (2012) 1059–1071. Y. Yang, J. Luo, L. Huang, G. Hu, K.D. Vargheese, Y. Shi, J.C. Mauro, Crack initiation in metallic glasses under nanoindentation, Acta Mater. 115 (2016) 413–422. F. Yuan, L. Huang, Brittle to ductile transition in densified silica glass, Sci. Rep. 4 (2014) 5035. W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (1992) 1564–1583.