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Journal of Non-Crystalline Solids

journal homepage: www.elsevier.com/locate/jnoncrysol

The effect of TiO2 on the structure of Na2O-CaO-SiO2 glasses and itsimplications for thermal and mechanical properties

René Limbacha, Stefan Karlssona,b,⁎, Garth Scannella, Renny Mathewc, Mattias Edénc,Lothar Wondraczeka

a Otto Schott Institute of Materials Research, University of Jena, Fraunhoferstraße 6, D-07743 Jena, Germanyb RISE Research Institutes of Sweden, RISE Glass, SE-351 96 Växjö, Swedenc Physical Chemistry Division, Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden

A B S T R A C T

Titania represents an important compound for property modifications in the widespread family of soda limesilicate glasses. In particular, such titania-containing glasses offer interesting optical and mechanical properties,for example, for substituting lead-bearing consumer glasses. Here, we provide a systematic study of the effect ofTiO2 on the structural, thermal, and mechanical properties for three series of quaternary Na2O–CaO–TiO2–SiO2

glasses with TiO2 concentrations up to 12 mol% and variable Na2O, CaO, and SiO2 contents. Structural analysesby Raman and magic-angle spinning 29Si NMR spectroscopy reveal the presence of predominantly four-foldcoordinated Ti[4] atoms in glasses of low and moderate TiO2 concentrations, where Si–O–Si bonds are replacedby Si–O–Ti[4] bonds that form a network of interconnected TiO4 and SiO4 tetrahedra, with a majority of the non-bridging oxygen ions likely being located at the SiO4 tetrahedra. At higher TiO2 contents, TiO5 polyhedra arealso formed. Incorporation of TiO2 strongly affects the titanosilicate network connectivity, especially when itsaddition is accompanied by a decrease of the CaO content. However, except for the thermal expansion coeffi-cient, these silicate-network modifications seem to have no impact on the thermal and mechanical stability.Instead, the compositional dependence of the thermal and mechanical properties on the TiO2 content stems fromits effect on the network energy and packing efficiency.

1. Introduction

Soda-lime silicate glasses are used in a wide range of applications,e.g., windows, containers, display and cover glasses or in automotiveglazing. Their technical relevance originates from a unique set ofproperties, most prominently transparency in the visible spectral range,high hardness and chemical durability, a good forming ability (as thebasis for low-cost manufacture) and the possibility of recycling. Thehigh hardness of glassy materials is related to the nature and alignmentof bonds in the vitreous network. However, of the same origin is themain drawback of glasses, their brittle fracture behavior [1]. Alongwith low resistance against surface defects, the high brittleness tre-mendously reduces the practical strength of commercially availableglass products. Therefore, various attempts have been made in the pastyears to increase the defect resistance of silicate glasses, which are inprinciple based on two different concepts: post-processing of the re-sulting glass sheets by chemical [2–4] or thermal [1] strengthening, andoptimization of the chemical composition [1,5]. Recently, the latter

approach has received a renewed interest, as it has been demonstratedthat the mechanical performance of silicate glasses can be significantlyimproved by a proper adjustment of the pre-existing components withinthe glass network [6–10], or the implementation of additional networkformer oxides, such as B2O3[11–16] and Al2O3[17,18].

In this regard, considerable attention has been paid to the relationshipbetween chemical composition and the properties of glasses, especiallytowards the development of predictive tools. That is, modeling of glassproperties such as Young's modulus has historically been a key interest ofboth industry and academia. First attempts in this field were made byWinkelmann and Schott [19] who introduced empirical (linear) mixingmodels. Although this approach clearly lacks a physical basis, is has beenadopted and further refined [20–22]. A semi-empirical approach for pre-dicting the elastic properties of glasses was proposed by Makishima andMackenzie [23]. In their model, the Young's modulus is estimated from thevolume density of bond energy in a glass network. Although this modelhas been proven as a useful tool for describing the compositional depen-dence of Young's modulus in a variety of simple silicate glasses [23–25], it

http://dx.doi.org/10.1016/j.jnoncrysol.2017.04.013Received 6 February 2017; Received in revised form 22 March 2017; Accepted 16 April 2017

⁎ Corresponding author.E-mail address: stefan.karlsson@ri.se (S. Karlsson).

Journal of Non-Crystalline Solids 471 (2017) 6–18

Available online 14 July 20170022-3093/ © 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

MARK

fails in estimating the elastic properties of more complex glass networks[17,26–28], since topological aspects of the short- and medium rangeorder are usually not considered. With this in mind, large effort was putinto the refinement of the Makishima and Mackenzie model. For example,to account for the change from trigonal to tetragonal coordinated boron inborate glasses upon the addition of network modifying oxides [23–25,29],the influence of the double-bonded oxygen ions in phosphate glasses [24],or the introduction of fluorine [26,27] and nitrogen into the glass network[30,31]. However, the particular behavior of TiO2 bearing glasses is stillnot fully understood [32–34]. Very recently, Scannell et al. [32] suggestedthat the discrepancy between the predicted and experimentally obtainedresults stems mainly from the complex bonding environment of Ti, i.e., theoccurrence of four-, five- and six-fold coordinated Ti atoms, which de-pends not only on the TiO2 content, but also on the concentrations andspeciation of the other cations of the glass network.

In the past years, TiO2 has become an interesting component forincorporation in silicate glasses. Some unique properties have beengenerated in titania-containing silicate glasses, for example, almost zerothermal expansion at room temperature in binary TiO2–SiO2 glassescontaining 7.5 wt% TiO2 (ULE, Corning code 7972) [35–37]. On alarger scale, titania has been used in lead-free tableware and otherconsumer glasses, which rely on its impact on optical properties, suchas Abbe number (optical dispersion) and refractive index [38–45].However, only a limited number of studies on the influence of TiO2 onthe mechanical properties of silicate glasses exists and most of them arefocused on the binary Na2O–SiO2 glass system [24,32,45–50]. Little tonothing has been reported about the effects of TiO2 in the technologi-cally more relevant Na2O–CaO–SiO2 glass system [34,51,52].

On that account, the present report provides a comprehensive in-sight into the effects of TiO2 additions on the structure of ternary soda-lime silicate glasses and corresponding relations to thermal and me-chanical properties. For this purpose, three series ofNa2O–CaO–TiO2–SiO2 glasses with increasing amounts of TiO2 anddifferent Na2O:CaO:SiO2 molar ratios were prepared and analyzed withrespect to their glass transition temperature, thermal expansion coef-ficient, elastic-plastic deformation, defect resistance, and brittlenessusing differential scanning calorimetry (DSC), ultrasonic echography,

nano- and micro-indentation. By correlating these results with struc-tural information derived from Raman and magic-angle spinning (MAS)29Si Nuclear Magnetic Resonance (NMR) spectroscopic analyses, wedescribe the compositional dependence of the thermal and mechanicalproperties within this complex glass system.

2. Materials and methods

2.1. Glass preparation and compositional analysis

Starting from the ternary Na2O–CaO–SiO2 system, three glass serieswith increasing amounts of TiO2 were prepared using the raw materialsand procedure given in detail in Ref. [38]. Precursors of silica sand(MAM1S) and reagent grade NaNO3, Na2CO3, CaCO3, and TiO2 weremelted in Pt/Rh10 crucibles at 1450 °C for 18 h, followed by a homo-genization for 1 h at the same temperature and a conditioning step of2 h at 1500 °C. The homogenization consisted of stirring the melts witha Pt/Rh10 flag at 8 rpm (about 48–50 Nm). At the employed meltingtemperature, we did not visually observe any platinum or rhodiumdissolution in the glasses, which otherwise would generate a char-acteristic violet-brownish coloration. The melts were poured into non-tempered stainless steel molds and then annealed for 1 h at tempera-tures of 550–580 °C, depending on the respective composition, beforethe melts were cooled, first to temperatures between 400 and 430 °C ata rate of 0.5 °C/min, followed by a more rapid cooling of approximately2 °C/min to room temperature.

The chemical compositions of the as-prepared glasses were analyzedby means of laser ablation inductively coupled plasma mass spectro-metry (LA-ICP-MS), without an internal standard. The laser ablationwas conducted with a LSX-213 G2+ unit (Teledyne CETACTechnologies Inc.). For analysis, an X-series II ICP-MS (Thermo FischerScientific Inc.) was employed. The measured chemical compositionswere averaged over five independent analyses per sample, with thestandard deviations representing the uncertainty of this method being≤0.3 mol% for Na2O, ≤0.3 mol% for CaO, ≤0.2 mol% for TiO2, and≤1.3 mol% for SiO2. The normalized glass compositions are given inTable 1.

Table 1Normalized glass compositions (in mol%) as analyzed by LA-ICP-MS and theoretical considerations on the silicate network connectivity NBO

Si a, atomic packing density Cg and volumedensity of bonding energy<U0/V0> of the Na2O–CaO–TiO2–SiO2 glasses. The values of<U0/V0> and Cg were estimated according to the model of Makishima and Mackenzie [23]using Eqs. (1) and (2). The density ρ was evaluated via the Archimedes' principle in distilled water.

Sample Na2O CaO SiO2 TiO2 N (A)BOSi =N N (B)BO BO

Si N (C)BOSi ρ (g/cm3) Cg <U0/V0> (kJ/cm3)

Series 11.1 15.0 11.2 73.9 0.0 3.29 3.29 3.29 2.514 0.499 68.01.2 14.8 9.8 73.9 1.4 3.33 3.35 3.26 2.503 0.497 67.61.3 15.6 5.5 75.6 3.4 3.44 3.47 3.27 2.478 0.494 66.91.4 15.6 0.6 78.3 5.5 3.59 3.61 3.30 2.443 0.490 66.4

Series 22.2 14.6 14.0 69.8 1.7 3.18 3.20 3.08 2.560 0.499 67.72.3 14.6 14.0 68.3 3.0 3.16 3.20 2.99 2.566 0.502 68.42.4 15.0 13.3 67.0 4.7 3.15 3.21 2.87 2.594 0.505 69.42.5 15.0 13.2 65.8 6.0 3.14 3.21 2.78 2.605 0.505 69.52.6 15.1 13.9 62.8 8.2 3.08 3.18 2.55 2.638 0.507 69.92.7 15.0 13.8 61.3 9.9 3.06 3.19 2.42 2.661 0.509 70.5

Series 33.2 14.5 12.1 71.6 1.8 3.26 3.27 3.15 2.519 0.497 67.53.3 15.0 10.1 71.5 3.4 3.30 3.33 3.11 2.520 0.495 67.13.4 15.4 7.3 72.3 5.1 3.37 3.41 3.09 2.526 0.497 67.63.5 15.7 5.1 71.9 7.3 3.42 3.48 3.02 2.525 0.497 67.83.6 16.3 2.5 71.6 9.7 3.48 3.54 2.94 2.535 0.500 68.83.7 16.3 0.4 71.3 12.0 3.53 3.60 2.86 2.535 0.497 68.4

Uncertainty ± 0.3 ± 0.3 ± 1.3 ± 0.2 ± 0.03 ± 0.03 ± 0.03 ± 0.2% – –

a NBOSi was calculated from the analyzed glass compositions with each of the following assumptions (see Section 3.1.2): Ti solely present as TiO4 groups and all NBO at the SiO4

tetrahedra (scenario A); Ti solely as TiO4 and NBO evenly distributed among SiO4/TiO4 (scenario B); Ti exclusively acting as a network modifier (scenario C). Scenario A agrees overallbest with the 29Si NMR data, thereby offering the best description of the silicate network connectivity [53]. However, the most relevant parameter to compare with trends in physicalproperties is the connectivity of the titanosilicate network, which corresponds to the number of BO atoms per network-forming (Si4+ and Ti4+) cation [53]: NBO = 2[4–nO/(nSi + nTi)],where nE is the stoichiometric coefficient for element E. Note that the values of N Nare equal to those for (B)BO BO

Si .

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

7

In series 1, CaO was substituted for TiO2 and minor amounts ofSiO2. In series 2, SiO2 was gradually replaced for TiO2, whereas in series3, CaO was reduced at the expense of TiO2 but in contrast to series 1,the SiO2 content remained unchanged (Table 1). Noteworthy, the Na2Ocontent in all three glass series studied changes only within a narrowrange of 14.5–16.3 mol%. Therefore, the Na2O–CaO–TiO2–SiO2 qua-ternary is transformed into a ternary [Na2O + CaO]–TiO2–SiO2 glasssystem, as illustrated in Fig. 1. This simplification enables a morecomprehensive analysis of the structural modifications upon the var-iation of the CaO, TiO2 and SiO2 content.

2.2. Atomic packing density and bonding energy

The atomic packing density Cg is defined as the theoretical molarvolume occupied by the ions divided by the effective molar volume ofthe glass [23]:

=∑∑

C ρf Vf Mg

i i

i i (1)

where Vi = 4/3πN(xrA3 + yrB3) represents the molar volume of anoxide AxBy with the molar fraction fi and molar mass Mi. The symbol Ndenotes the Avogadro constant and rA as well as rB are the radii of thecorresponding cations and oxygen (rO = 135 pm), respectively, as ta-bulated in Ref. [54]. With respect to the current series of quaternaryNa2O–CaO–TiO2–SiO2 glasses, the values of Cg were calculated as-suming a prevalent tetrahedral coordination for Si4+ (rSi = 26 pm) andTi4+ (rTi = 42 pm, see Section 3.1 and 3.2 for details) and an octahe-dral coordination for Ca2+ (rCa = 100 pm) [55,56] and for Na+

(rNa = 102 pm) [56–58]. The density ρ was determined via Archimedes'principle (ASTM C693-93) using distilled water as the immersion li-quid.

The volume density of bonding energy<U0/V0> of a multi-com-ponent glass is estimated using the following Eq. [59]:

=∑∑

UV

f Hf M ρ

Δi ai

i i i

0

0 (2)

where ρi and ΔHai are the density and molar dissociation enthalpy, re-spectively, of each constituent inside the glass. The values of ΔHai werecalculated from the molar heats of formation ΔHf of the correspondingoxides AxBy in their crystalline state and the respective atoms in theirgaseous state, according to Eq. (3)[24]:

= + −H x H A y H B H A BΔ Δ ( , gas) Δ ( , gas) Δ ( , crystal)ai f f f x y (3)

using the values of ΔHf from Ref. [60].

2.3. Thermal analysis

The glass transition temperature Tg was determined by DSC using aNETZSCH STA 449 F1 Jupiter (NETZSCH-Gerätebau GmbH). Thesamples were mounted in Pt/10Rh crucibles and heated up to 700 °C ata rate of 20 °C/min in N2 atmosphere. The uncertainty of the mea-surements was estimated to be± 2 °C based on the precision specifi-cations given by the manufacturer of the instrument. The thermal ex-pansion coefficient α was analyzed by means of a NETSCH DIL 402 EPdilatometer (NETZSCH-Gerätebau GmbH) using fused silica as thesample holder and platinum as the reference material. Here, measure-ments were conducted in air atmosphere at a heating rate of 4 °C/minand the values of α were cumulated across the interval of 25–300 °C.The error of the measurements was estimated to be± 0.1·10−6/Kbased on the standard deviation of 27 calibration measurements of areference glass.

2.4. Mechanical testing

Elastic constants were determined by ultrasonic echography on co-planar, optically polished glass plates with thickness d ~ 2–3 mm. Anechometer 1077 (Karl Deutsch GmbH& Co KG), equipped with a pie-zoelectric transducer (f = 8–12 MHz) was applied to record the long-itudinal tL and transversal tT sound wave propagation times with anaccuracy of± 1 ns. The longitudinal, cL = 2d/tL, and transversal wavevelocities, cT = 2d/tT, were calculated from the exact thickness of theglass specimen, which was measured with an accuracy of± 2 μm usinga micrometer screw, and the time separating two consecutive echoes.On that basis, the shear G, bulk K and Young's modulus E as well as thePoisson ratio ν were calculated according to Eqs. (4)–(7)[61]:

=G ρcT2 (4)

= ⎛⎝

− ⎞⎠

K ρ c c43L T

2 2(5)

= ⎡⎣⎢

−−

⎤⎦⎥

E ρc c

c c3 4

( ) 1L T

L T

2 2

2 (6)

=−

−ν

c cc c

22( )

L T

L T

2 2

2 2 (7)

Young's modulus and hardness H were investigated through in-strumented indentation testing using a nanoindenter G200 (AgilentInc.) on co-planar, optically polished glass specimen. For each glasssample, at least 15 indents with a maximum depth of 2 μmwere createdat a constant strain-rate ε ̇ of 0.05 s−1. Meanwhile, the values of E and Hwere recorded as a function of the indenter displacement by applying aweak oscillation (Δh= 2 nm, f= 45 Hz) to the three-sided Berkovichdiamond tip used [62]. The tip area function and the instrument's framecompliance were calibrated prior to the measurements on a fused silicareference glass sample (Corning code 7980, Corning Inc.) following theprocedure proposed by Oliver and Pharr [63].

A nanoindentation strain-rate jump test, as described in detail inRef. [62], was performed to study the indentation creep behavior. Inthis test, the indenter tip initially penetrates the glass surface to a depthof 500 nm at a constant strain-rate of 0.05 s−1. During the further pe-netration the strain-rate is changed in intervals of 250 nm and thecorresponding change in the hardness is determined with the CSMequipment (Δh = 5 nm, f = 45 Hz). Ten strain-rate jump tests withstrain-rates of 0.05, 0.007 and 0.001 s−1 were performed on each glassspecimen and the strain-rate sensitivity m was derived from the slope ofthe logarithmic plot of the hardness versus the indentation strain-rateεi̇[64,65]:

= ∂∂

m lnHln εi̇ (8)

Fig. 1. Compositions of the quaternary Na2O–CaO–TiO2–SiO2 glasses investigated in thepresent study (series 1: squares, series 2: triangles, series 3: circles). The numbers denotethe Na2O molar fraction of each glass composition analyzed according to Ref. [38].

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

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with =ε ε˙ ˙ 2i for materials with a depth-independent hardness [66].A Duramin-1 microhardness tester (Struers GmbH) was used to

determine the Vickers hardness HV. On each glass specimen, 15 indentswith a maximum load of P = 981 mN (100 g) were generated, with aloading duration of 15 s and 10 s dwell-time at maximum load. Theresidual Vickers hardness imprints were analyzed using an AxioLab A1optical microscope (Carl Zeiss Microscopy GmbH) and the values of HV

were calculated according to Eq. (9):

= = š

H PA

sin Pd

Pd

2 (136 2) 1.8544V 2 2 (9)

where d stands for the length of the projected indentation diagonals.A Vickers indentation test, as proposed by Anstis et al. [67], was

used to estimate the indentation fracture toughness Kc:

⎜ ⎟= ⎛⎝

⎞⎠

K EH

Pc

0.016 ,cV

1 2

3 2 (10)

In the above equation, c denotes the length of a half-penny shapedmedian-radial crack with c/a > 2.5, where the parameter a is equal toone half of the indentation diagonals. For statistical relevance, at least25 indents with loads of 19.62 N (2 kg) were generated on each glassspecimen. Following this, the empirical brittleness parameter B, whichreflects the interplay between plastic deformation, HV, and fracture, Kc,was derived by means of Eq. (11)[68].

=B HK

V

c (11)

The crack resistance CR was analyzed through Vickers indentationtesting, according to Kato et al. [69]. Indents with stepwise increasingloads, ranging from 98.1 mN (≡ 10 g) to 9.81 N (≡ 1 kg), were createdand the number of median-radial cracks emanating from the corners ofthe residual Vickers hardness imprints were counted. In total, 25 in-dents were performed per load. On that basis, the probability of crackinitiation PCI, which is defined as the number of corners with cracksdivided by the total number of corners, was calculated and plottedagainst the applied load. The experimental results were fitted to a sig-moidal function and the crack resistance CR was derived from the loadat which on average two radial cracks (PCI= 50%) appeared.

2.5. Raman spectroscopy

Raman spectra were collected from co-planar, optically polishedglass specimen with an inVia dispersive confocal Raman Microscope(Renishaw plc.). All spectra were recorded for wavenumbers rangingfrom 100 to 2000 cm−1 at step widths of 2 cm−1 using the 514.5 nmlaser excitation line. For every glass specimen three scans were col-lected and accumulated, with a 10 s exposure time for each in-dependent scan. All spectra were first corrected regarding the frequencyand temperature following the procedure of McMillian et al. [70]. Thebands were then deconvoluted using Fityk [71]. Referring to the

Na2O–CaO–SiO2 base glass, individual peaks were fitted at 340, 460,490, 540, 600, 630, 800, 950, 1080 and 1100 cm−1 as presented inFig. 2, while in the TiO2 containing glasses additional peaks appeared at720, 840, 900 and 980 cm−1.

2.6. Solid-state 29Si NMR spectroscopy

All 29Si MAS NMR data were acquired at 9.4 T with a BrukerAvance-III spectrometer (Bruker BioSpin Inc.) operating at a 29SiLarmor frequency of 79.47 MHz. Glass powders were packed in 7 mmzirconia rotors and spun at 7.00 kHz. The NMR acquisitions utilized adirect “single-pulse” excitation with flip angles of 70° at a radio-fre-quency nutation frequency of 55 kHz, and 2500 s relaxation delays.Depending on the Si content of the glass, 108–144 signal transientswere accumulated for each specimen. On the basis of the slow 29Si spin-lattice relaxation encountered in all glasses, the presence of non-neg-ligible (> 0.2 at.%) paramagnetic Ti3+ species may be excluded. Nosignal apodization was employed in the data processing. Chemical shiftsare quoted relative to neat tetramethylsilane (TMS).

3. Results and discussion

3.1. 29Si MAS NMR spectroscopy

3.1.1. Structural role of TiSolid-state 29Si NMR spectroscopy was employed for qualitatively

probing the speciations of bridging oxygen (BO) atoms and non-brid-ging oxygen (NBO) ions around Si for glasses with variable TiO2 con-tents. Fig. 3 displays the 29Si MAS NMR spectra recorded from a se-lection of Na2O–CaO–TiO2–SiO2 glasses with increasing TiO2 contentfrom top to bottom. As expected, all spectra only reveal signals fromtetrahedrally coordinated 29Si species, where Qn onwards denotes aSiO4 tetrahedron with n BO atoms (and 4−n NBO ions) [72]. We firstconsider the results for the Na2O–CaO–SiO2 base glass, which revealstwo resonances, involving a major signal centered around −92 ppmand a minor one around −105 ppm that stem from Q3 and Q4 silicategroups, respectively. The average chemical shifts and widths of thesepeaks are typical for Na2O–CaO–SiO2 glasses [72–75], whereas therelative peak intensities are consistent with a mean number of BOspecies per Si4+ cation of NBO

Si = 2(4–nO/nSi) = 3.29, as calculatedfrom the stoichiometric coefficients of O (nO) and Si (nSi) obtained fromthe analyzed glass composition of Table 1 and the procedure of Ref.[53]. Note that in the literature, the parameter NBO

Si —i.e., the averagenumber of BO atoms per SiO4 tetrahedron in the glass network—is oftenreferred to as the silicate network connectivity; see Refs. [53,72,75] foradditional information.

As TiO2 is introduced in the glass structure, no significant changesoccur in the NMR peak position from the Q3 or Q4 species (except forthe Ti-richest glasses discussed below). The relative peak intensities,and hence the fractional Q3 and Q4 populations, merely redistribute

Fig. 2. Deconvoluted Raman spectrum of the Na2O–CaO–SiO2 baseglass investigated in the present study. The black dots display thecorrected spectrum, the blue lines show the individual fitted peaksand the red line represents the sum of all fitted peaks. (For inter-pretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

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when the TiO2 content of the glass is increased. When SiO2 is replacedby TiO2 (Fig. 3; series 2), the silicate network depolymerizes slightly, asmirrored in a reduced NMR peak intensity from the Q4 groups, ac-companied by a progressively increased center-of-gravity chemicalshift, δCG. In contrast, the reverse scenario of an increased silicate-network polymerization stemming from a concurrent growth of the Q4

population occurs when CaO is replaced either by TiO2 (Fig. 3; series 3)or a combination of TiO2 and SiO2 (Fig. 3; series 1).

The trends observed in the 29Si NMR spectra from glasses with lowor moderate TiO2 contents are most consistent with the Ti4+ cationsprimarily entering the glass structure as fully polymerized TiO4/2 tet-rahedra (i.e., as Q4 moieties) [76–79], where they may either replace Sivia Si–O–Ti bridges (scenario I), aggregate in clusters or form a separatephase (scenario II) [76,78,79], or a combination of both [77]. This may

be understood as follows: if a majority of the Ti ensemble would beinterlinked with Si, then Ti must predominantly be present as TiO4

groups (i.e., scenario I applies), owing to the insignificant changes ofthe 29Si chemical shift expected for a 29Si–O–Si → 29Si–O–Ti[4] bondreplacement and its accompanying negligible alteration of the O charge[80]. A similar situation applies for Si → B[3] substitutions (as opposedto Si → B[4]) in borosilicate glasses [81,82]. On the other hand, theeffective charge of O alters for any 29Si–O–Si → 29Si–O–Ti[p] conver-sion with p = {5, 6}; hence, a significant chemical-shift increase of6–9 ppm is then anticipated, as observed previously in 29Si NMR spectrafrom crystalline titanosilicates [80,83]. Consequently, the introductionof even minor amounts (< 5 mol%) of TiO2 in a silicate glass is ex-pected to markedly deteriorate its 29Si NMR spectral resolution wheneither Si–O–Ti[5] or Si–O–Ti[6] bonds are formed. This is in starkcontrast with the gross trends in Fig. 3, which are readily reconciledwith variations of the relative BO/NBO amounts at the SiO4 groupswhen the TiO2 content of the glass grows: these effects are responsiblefor the observed decrease and increase of the NMR-peak intensity fromQ4 moieties in glass series 2 and 3, respectively.

Yet, the 29Si NMR spectra of the Ti-richest Na2O–CaO–TiO2–SiO2

glass specimens (3.6 and 3.7) manifest unresolved resonances from theQ3 and Q4 groups (see Fig. 3). This is most evident when comparing theresults between the 1.4 (5.5 mol% TiO2) and 3.7 (12.0 mol% TiO2)specimens that should reveal very similar NMR spectra with nearlyequal contributions from the Q3 and Q4 groups (see Table 1 and Section3.1.2). Ti-free sodium silicate glasses are known to provide resolvedNMR signals among the various Qn groups [72], i.e., as indeed alsoobserved for the 1.4 glass comprising 5.5 mol% TiO2, whose structure isdominated by Ti[4] coordinations. In contrast, the poor NMR signaldiscrimination from the Ti-richer glass is attributed to the deshieldingeffects associated with a significant Si–O–Ti[5] bond formation [80,83].Another potential explanation for the distinct NMR responses is thepresence of distinct (average) numbers of Na+ and Ca2+ cations in thesecond coordination sphere of Si in the 1.4 and 3.7 glass structures[76–79]. However, this possibility is precluded by the minute CaOcontents in both glasses that effectively make them members of theternary Na2O–TiO2–SiO2 system (see Table 1). Hence, we conclude thatSi–O–Ti[5] bonds are responsible for the NMR peak-broadening ob-served in Fig. 3 for the Na2O–CaO–TiO2–SiO2 glass with 12.0 mol%TiO2 (specimen 3.7), and to a lesser extent also for 3.6 that comprises9.7 mol% TiO2.

While the precise coordination numbers of Ti4+ species present inmodified silicate glasses is still under debate [84–87], the herein ad-vocated structural role of Ti4+ supports the suggestions of Hendersonand Fleet [85] of a dominance of TiO4 tetrahedra in M(2)O–TiO2–SiO2

glasses with low or moderate TiO2 contents up to around 10 mol%.TiO5 polyhedra form when the amount of TiO2 is increased further, andthey dominate the Ti4+ speciation at high TiO2 contents (> 15 mol%)[85,88].

3.1.2. NBO partitioning among Si and TiHere we discuss the constraints on the NBO distribution among the Si

and Ti species available from 29Si NMR. Table 1 lists the predicted NBOSi

value of each glass, as obtained from its respective composition by thesplit network procedure of Ref. [53] (using Eqs. (13)–(18) therein) andassuming different NBO partitioning scenarios among Si and Ti. Westress that since the NMR data itself do not admit the extraction of thequantitative BO/NBO partitioning, we only consider categorical/lim-iting scenarios, for which the gross trends of the calculated NBO

Si valuesmay be evaluated qualitatively against the experimental constraints.Scenario A, which we promote as the closest description of theNa2O–CaO–TiO2–SiO2 glass structures that incorporate up to ~9 mol%TiO2, involves a titanosilicate network of interconnected SiO4 and TiO4/

2 tetrahedra (that possibly co-exist with a separate network of TiO4/2

groups), with all NBO species located at the SiO4 groups and the Na+

and Ca2+ cations assuming their usual role of glass network modifiers.

Fig. 3. 29Si MAS NMR spectra of selected Na2O–CaO–TiO2–SiO2 glasses. The number ateach rightmost spectral portion represents the center-of-gravity 29Si chemical shift δCG,while the dotted lines indicate the approximate peak maxima of the resonances from Q3

and Q4 SiO4 groups.

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

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Fully consistent with the qualitative 29Si NMR trends of Fig. 3, thepredicted silicate network connectivity increases from NBO

Si = 3.26 toNBO

Si = 3.53 for the glasses of series 3 when their TiO2 content is in-creased up to 12.0 mol%, whereas glass series 2 manifests the reversetrend, where NBO

Si is reduced (slightly) from 3.18 to 3.06. Note thatglasses with TiO2 contents above around 9 mol% involve an unknownbut non-negligible contribution of TiO5 groups.

Notwithstanding that the relative peak intensities from the Q3 andQ4 moieties constrain the number of permissible Ti–NBO contacts,owing to the overall low Ti content of each glass (i.e., low nTi/nSi molarratio), an even NBO-partitioning among Si and Ti (scenario B;Table 1)cannot be excluded. However, a scenario “C” of Ti acting solely as anetwork modifier (i.e., as the electropositive Na+ and Ca2+ species)may safely be excluded from the resulting NBO

Si data listed in Table 1,because this case predicts a decreased silicate network polymerization,in contradiction with the experimental observations for glass series 3;see Fig. 3. Moreover, the members of series 2 would manifest low sili-cate network connectivities (NBO

Si < 3) that require significant con-tributions from Q2 (or Q1) moieties, which is clearly inconsistent withthe negligible 29Si resonance-intensity observed in the spectral regionof< 84 ppm that is expected from such structural groups [72,73,75].We conclude that the Ti species do not markedly perturb the networkconnectivity, meaning that a Ti-bearing glass manifests a similar NBO

Si

value as its Na2O–CaO–SiO2 analog.We comment that the TiO5 and TiO6 polyhedra most likely assume a

similar structural role as their AlO5 and AlO6 counterparts in alumi-nosilicate glasses, which reveal a strong propensity for Al[5]–BO (asopposed to Al[5]–NBO) contacts [89,90]. Consequently, we avoid usingthe “network modifier” term for such moieties, because the relativelystrong Al–O (and Ti–O) bonds and their accompanying cross-linking ofdistinct glass-network fragments strengthen the structure rather thanweakening it. Indeed, as recently demonstrated for rare-earth basedaluminosilicate glasses, there is a strong correlation between the Alaverage coordination number and the glass microhardness [89,91].

Whereas the 29Si NMR spectra of the Ti-richest glasses (specimens3.6 and 3.7) suggest some Si–O–Ti[5] bonds in their networks, a solepresence of TiO5 species is less likely, because the associated calculatedNBO

Si value appears rather high (NBOSi = 3.7) to be consistent with the

experimental data of Fig. 3. Yet, this case cannot unambiguously beruled out, because a part of the NMR signal intensity in the spectralregion that we attribute to Q3 groups in the Ti-poor structures may infact correspond to Q4 groups with Si–O–Ti[5] bonds in the Ti-richcounterparts (see Section 3.1.1). Nonetheless, structural scenarios ofpredominantly TiO5 polyhedra with (on the average) at least one NBOion per polyhedron in the 3.7 structure—as well as any scenario ofsolely TiO6 species, regardless of their average number of NBO—aresafely precluded from the associated (unreasonably) high silicate net-work connectivities of NBO

Si ≥ 3.9 (data not shown).In summary, our 29Si MAS NMR data are most consistent with a

majority of the Ti ensemble entering a titanosilicate network with Ti[4]

coordinations dominating throughout, except for the Ti-richest glasseswith> 9 mol% TiO2, for which a non-negligible fraction of TiO5

polyhedra may coexist with the TiO4 species. Yet, the invariance of the29Si chemical shifts for 29Si–O–Si→ 29Si–O–Ti[4] bond substitutionsimplies that 29Si NMR spectroscopy cannot exclude that most Ti sitesare present in clusters or a separate phase that is isolated from the si-licate network: this ambiguity applies notably for the glasses of low Ticontents for which we propose a dominance of Ti[4] coordinations.

3.2. Raman spectroscopy

The further structural analysis of the Na2O–CaO–TiO2–SiO2 glasseswas conducted by Raman spectroscopy. Spectra from glasses of thethree different series are presented in Fig. 4. Regarding theNa2O–CaO–SiO2 base glass (1.1) first, a broad band at around1100 cm−1 exists in the high-frequency range, which has previously

been assigned to Si–O– stretching vibrations in Q3 groups [77]. How-ever, this peak obviously exhibits a non-Gaussian shape, see spectra inFig. 4, indicating an overlapping of more than one band. In a formerstudy, Mysen and Neville [77] proposed a deconvolution into threeindividual bands centered at around 1150, 1100 and 1050 cm−1, whichcorrespond to Si–O stretching vibrations in fully polymerized SiO4 tet-rahedral units, Si–O– stretching vibrations of Q3 groups and Si–Ostretching vibrations of BO in SiO4 tetrahedral units of at least one NBO,respectively. If the 1150 cm−1 peak would be related to the populationof Q4 units, an increasing intensity with decreasing network modifierconcentration would be expected. Instead, a strong intensity increase isvisible only on the left side of the 1100 cm−1 peak in series 2, whereTiO2 is increased at the expense of SiO2, while little to no changes in thepeak intensities occur when the CaO content is decreased for eitherTiO2 (series 3) or a combination of TiO2 and small amounts of SiO2

(series 1).We therefore suggest to deconvolute the peak at around 1100 cm−1

into two separate bands, a broader one located at 1080 cm−1 and

Fig. 4. Raman spectra of the Na2O–CaO–TiO2–SiO2 glasses investigated in the presentstudy.

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11

second narrow one at 1100 cm−1. Interestingly, both the peak positionand intensity of the 1100 cm−1 peak are controlled predominantly bythe CaO content, rather than by the total amount of TiO2. That is, shiftsto higher wavenumbers occur when CaO is substituted by TiO2 (series3) or a combination of TiO2 and small amounts of SiO2 (series 1), whilethe progressive replacement of SiO2 by TiO2 (series 2) has only smallimpact. Meanwhile, the intensity of the 1100 cm−1 band rapidly di-minishes when the CaO content is reduced at the expense of TiO2 and/or SiO2 (series 1 and 3), which implies that a decrease in the totalnumber of NBOs inside the glass network has a strong effect on thepopulation of this band.

Slightly different trends are visible for the neighboring band at1080 cm−1. When the TiO2 content is increased a much larger peakshift to lower wavenumbers is observed. The magnitude of this effectstrongly depends on the respective glass series, with the highest shiftdetermined for series 2 and the lowest one for series 1. Similar peakshifts have also been reported by Mysen et al. [77] or Osipov et al. [86],though for bands in the 1100 cm−1 region, and were related to a partialsubstitution of tetrahedrally coordinated Si[4] atoms by Ti[4] atoms ofthe same coordination. As SiO2 is replaced by TiO2 (series 2), the in-tensity of the 1080 cm−1 band increases considerably. A steady in-crease in peak intensity is observed when CaO is substituted for eitherTiO2 alone (series 3) or TiO2 and small amounts of SiO2 (series 1), in-dicating that both bands located at around 1080 and 1100 cm−1 areconnected to the population of NBOs. We may speculate that a pro-portion of the NBOs related to Q3 units are more rigid with a narrowselection of rotation angles (i.e., the narrow band at 1100 cm−1). TheseNBOs are most likely created by the Ca atoms inside the glass network,whereas the presence of Na atoms results in more flexible NBO ions(i.e., the broader band at 1080 cm−1) [92]. Likewise, the monotonicshift of the 1080 cm−1 band to lower wavenumbers in series 2 origi-nates from the replacement of the strong and rigid Si−O bonds by theweaker and more flexible Ti−O bonds.

With the addition of TiO2, a new band at around 900 cm−1 de-velops. This band has frequently been observed in TiO2 containing si-licate glasses [76,77,85,86], but its correct assignment is still underdebate. Reynard and Webb [93] attributed the 900 cm−1 band to thepresence of titanyl bonds Ti=O in TiO5 polyhedra, while Mysen et al.[77] discussed this band in terms of Ti−O bridging oxygen vibrationsassociated with Ti atoms in tetrahedral coordination, but also Si−O−

stretching vibrations in Q1 units, have been supposed as its origin.However, the peak intensity has been demonstrated to increase almostlinearly with the TiO2 content [76,85], which makes an assignment toQ1 units unlikely. Moreover, the 29Si NMR data precludes the presenceof significant amounts of Q1 groups (see Section 3.1). The assignment totitanyl oxygen vibrations, on the other hand, is well supported byprevious reports [93–95], although the population of TiO5 polyhedrashould be limited in glasses of low TiO2 concentrations up to around10 mol%, as discussed in Section 3.1. With increasing TiO2 content atthe expense of CaO (series 1 and 3) the position of the 900 cm−1 peakshifts to higher wavenumbers, but when TiO2 replaces SiO2 (series 2) ashift to lower wavenumbers is observable. Henderson et al. [92] arguedthat a more flexible network structure promotes the formation of TiO4

tetrahedra, whereas in rigid glass networks TiO2 is implemented mainlyin form of TiO5 polyhedra. Therefore, we would like to point out thatthe band at around 900 cm−1 might be composed of two individualbands representing different Ti coordinations, and hence the peak shiftto higher wavenumbers for lower amounts of CaO (series 1 and 3) anddecreasing SiO2 concentration (series 2) should rather be interpreted interms of changes in their relative intensities as a result of differentpopulations of TiO4 tetrahedra and TiO5 polyhedra.

Additionally, in the Na2O–CaO–SiO2 base glass, a band centered at950 cm−1 is observed, which has previously been assigned to Si–O–

stretching vibrations in Q2 units [77,85]. With the addition of evensmall amounts of TiO2, this band immediately disappears and is re-placed by a new band at 980 cm−1. The position of the 980 cm−1 band

is almost independent on compositional variations, except for a slightshift to lower wavenumbers for the two compositions of the highestTiO2 concentrations in series 3. In the past years, the 980 cm−1 bandhas been described by either Si–O– stretching vibrations of Q2 units[77,86] or Ti–O–Si antisymmetric bridging oxygen vibrations [96].However, the insensitivity of the peak position on the compositiondisproves an assignment to Q2 units, at least for the current series ofNa2O–CaO–TiO2–SiO2 glasses. Instead, the positive correlation betweenthe peak intensity and the TiO2 content supports the argumentation ofTi–O–Si antisymmetric bridging oxygen vibrations. For the latter case,the peak shift for large amounts of TiO2 in the third glass series maycorrespond to the formation of TiO5 polyhedra, as mentioned above.

In the mid-frequency range three bands at 720, 800, and 840 cm−1

exist and all of them increase in intensity almost linearly with in-creasing TiO2 concentration. The band at 800 cm−1 occurs in all glassesstudied, while the band at 720 cm−1 appears at around 3–5 mol% TiO2

and the band at 840 cm−1 forms at slightly higher TiO2 concentrationof around 5–7 mol%. Inoue et al. [78] and Osipov et al. [86] related theband at 720 cm−1 to the presence of TiO6 octahedra. On the contrary,Reynard and Webb [93] associated this band to Si–O–Ti and Si–O–Sibridging oxygen vibrations in both Q2 and Q3 units. However, the latterargumentation would imply a decrease of the peak intensity when CaOis progressively replaced by TiO2 (series 3), rather than its continuousincrease. In this regard, Scannell et al. [97] suggested that the720 cm−1 most likely arises from Ti–O bridging oxygen vibrations offully polymerized TiO4 tetrahedra units. Owing to the low intensity ofthis signal, as well as also of the two other bands at 800 and 840 cm−1

relative to the neighboring bands in the low- and high-frequency re-gions, fits of the peak positions show a significant scatter. Nonetheless,the latter two bands at 800 and 840 cm−1 seem to shift to higher wa-venumbers at very low CaO concentrations (series 1 and 3), while thereis only little response to even large variations of the SiO2 content (series2). The strong increase of the peak intensities upon TiO2 implementa-tion, in particular the band at 840 cm−1, supports its previous assign-ment to Ti−O symmetric stretching vibrations of TiO4 tetrahedra [85]or TiO5 polyhedra [85,86].

The band at 630 cm−1 is located in-between the low- and mid-fre-quency region of the Raman spectra. Its intensity exhibits a negativecorrelation with the SiO2 content (series 1 and 2), but modifications inthe peak position are not clearly distinguishable. This band is mostlikely part of the low-frequency bridging oxygen vibrations [98]. Itpossibly originates from the formation of different local structures ofsmaller bond angles when TiO2 is introduced into the glass network.

The low-frequency region is composed of several broad overlappingbands, located at 340, 460, 490, 540 and 600 cm−1. The two smallbands at 490 and 600 cm−1 are known as the defect bands D1 and D2

and correspond to oxygen breathing vibrations in four- and three-membered silica rings, respectively [14,15]. The D1 band at 490 cm−1

shifts to lower wavenumbers as the CaO concentration is lowered(series 1 and 3), while its intensity does not change consistently withthe glass composition. The position of the D2 band at 600 cm−1, on theother hand, depends mainly on the SiO2 concentration, i.e., with in-creasing SiO2 content (series 1 and 2) a shift to lower wavenumbers isobservable, while the substitution of CaO by TiO2 (series 3) has little tono effect on the band position. The D2 band continuously diminishes inintensity as the total amount of TiO2 is raised at the expense of SiO2

(series 2) or CaO (series 3) and then fades at above 6–7 mol% TiO2,reflecting a reduced population of three-membered silica rings [86],whereas in series 1, this phenomenon is counterbalanced by the parallelincrease of the SiO2 content with increasing TiO2 concentration and inaddition the overall lower TiO2 concentrations as compared to series 2and 3.

The band at 540 cm−1 is related to delocalized Si–O–Si bridgingoxygen vibrations [99]. It is increasing in intensity and shifting tohigher wavenumbers as the SiO2 gets reduced (series 1 and 2). A minorshift to lower wavenumbers is also visible when CaO is exchanged with

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

12

TiO2 (series 3), whereas the intensity remains almost the same.Finally, two broad bands at 340 and 460 cm−1 occur in all spectra.

The latter band has also been noticed in ternary soda-lime silicateglasses and corresponds to symmetric Si–O–Si bridging oxygen vibra-tions [97]. Its intensity monotonically increases with increasing TiO2

content, indicating either an increased population of Si–O–Si bonds ortheir progressive substitution by Si–O–Ti bonds. The band at 340 cm–1

has tentatively been described by Ti–O antisymmetric bending vibra-tions in TiO6 octahedra [100]. Similar to the neighboring band at460 cm−1, the intensity of the 340 cm−1 band strongly increases withincreasing TiO2 content, while compositional variations seem to haveno influence on the peak position. It should be noted that this bandappears not only in the quaternary Na2O–CaO–TiO2–SiO2 glasses, butalso in the ternary Na2O–CaO–SiO2 base glass. Moreover, as discussedin Section 3.1.2, the population of TiO6 octahedra is expected to benegligible in our glasses, which makes the band assignment of Kusa-biraki [100] questionable.

Based on our Raman spectroscopic data, we conclude that for lowTiO2 concentrations up to around 10 mol% the majority of Ti is tetra-hedrally coordinated and occupies the positions of Si, leading to thecreation of a titanosilicate network of interconnected TiO4 and SiO4

tetrahedra. At higher TiO2 concentrations, TiO5 polyhedra may alsoform. Apart from this, our results further indicate that the addition ofTiO2 at the expense of CaO (series 1 and 3) results in an increaseddimensionality of the glass network, whereas the partial substitution ofSiO2 by TiO2 (series 2) does not markedly influence the degree ofcrosslinking.

3.3. Thermal and mechanical properties of quaternaryNa2O–CaO–TiO2–SiO2 glasses

The results of the thermal analysis by DSC and dilatometry are listedin Table 2. The glass transition temperatures were derived from theonset of the endothermic event in the corresponding DSC curves and thecorresponding values of Tg are plotted in a [Na2O + CaO]–TiO2–SiO2

ternary contour diagram in Fig. 5a. In series 1 (Fig. 5a; squares), whereCaO was reduced at the expense of TiO2 and minor amounts of SiO2, theTg of the ternary Na2O–CaO–SiO2 base glass continuously decreases

from 587 to 560 °C at 5.5 mol% TiO2. As opposed to this, when SiO2 issubstituted for TiO2 (Fig. 5a; triangles), Tg tend to increase from 586 to610 °C at 9.9 mol% TiO2. The same observations were also made byTakahashi et al. [47] and Scannell et al. [32] in the ternaryxNa2O–yTiO2–(100–x–y)SiO2 glass system, while no distinct variationof Tg has been observed by Villegas et al. [42] in a series of ternary40CaO–xTiO2–(60–x)SiO2 glasses, irrespective of the TiO2/SiO2 ratio.Noticeably, the latter findings appear to be more compatible with thescattering of Tg in series 3 of our quaternary Na2O–CaO–TiO2–SiO2

glasses (Fig. 5a; circles), where CaO was again exchanged with TiO2,but unlike series 1 the SiO2 content was kept constant. At a first glance,no clear trend can be deduced for the Tg of these glasses, i.e., with theintroduction of TiO2 the Tg fluctuates in a limited range of 579–587 °C,except for the composition containing the highest amount of 12.0 mol%TiO2, which exhibits a Tg of 598 °C.

Similar trends were detected for the thermal expansion coefficient.In series 1 (Fig. 5b; squares) α of the Na2O–CaO–SiO2 base glass con-tinuously decreases with the addition of up to 5.5 mol% TiO2 from 10.0to 8.55·10−6/K. On the contrary, the partial replacement of SiO2 byTiO2 in series 2 (Fig. 5b; triangles) results in a marginal increase of α upto a maximum of 10.3 ∗ 10−6/K at 9.9 mol% TiO2. Referring to thebinary TiO2–SiO2 glass system, α is well-known to initially decrease forlow amounts of TiO2, with a narrow compositional region of almostzero thermal expansion [101,102], and then to increase as the TiO2

concentration is further raised [37]. The origin of this unique behavioris still under debate. Henderson et al. [92] suggested that the in-troduction of low amounts of TiO2 initially breaks up the SiO2 glassstructure via the formation of TiO5 polyhedra. This mechanism subse-quently allows additional TiO2 to be incorporated as TiO4 tetrahedralunits, which effectively stiffen the depolymerized glass network and asa consequence, decreasing its thermal expansion. However, for an im-plementation of large amounts of TiO2 the titanosilicate network has tobe further disrupted and hence the former benefits are reversed. Movingto ternary glass systems, the effect of TiO2 on α becomes less obvious.Takahashi et al. [47] determined a local minimum also in the thermalexpansion of xNa2O–yTiO2–(100–x–y)SiO2 glasses when SiO2 is gra-dually replaced by TiO2 and the Na2O content is kept constant, while nosuch minimum was noticed by Strimple and Giess [50] or Scannell et al.

Table 2Thermal and mechanical properties of the investigated Na2O–CaO–TiO2–SiO2 glasses. The glass transition temperature Tg and thermal expansion coefficient α were analyzed via DSC anddilatometry, respectively. The elastic constants, including the shear G, bulk K and Young's modulus E, as well as the Poisson ratio ν, were characterized by ultrasonic echography. TheYoung's modulus, hardness H and strain-rate sensitivity m were investigated through instrumented indentation testing using a nanoindenter, while the Vickers hardness HV, indentationfracture toughness Kc, brittleness B and crack resistance CR were studied by means of a microhardness tester.

Sample Tg

(°C)α(10−6/K)

G(GPa)

K(GPa)

E(GPa)a

v E(GPa)b

H(GPa)

m HV

(GPa)Kc

(MPa m1/2)B(μm−1/2)

CR(N)

Series 11.1 587 10.0 30.1 45.0 73.8 0.227 77.3 6.92 0.0134 5.64 0.69 8.3 1.221.2 576 9.4 29.7 43.9 72.6 0.224 76.5 6.75 0.0182 5.37 0.71 7.6 1.551.3 568 8.8 29.6 41.9 71.9 0.214 74.4 6.49 0.0171 5.02 0.74 6.8 1.851.4 560 8.6 28.4 39.5 68.8 0.210 71.2 6.10 0.0209 4.84 0.75 6.5 2.24

Series 22.2 590 9.5 30.3 46.5 74.6 0.233 79.7 7.12 0.0147 5.67 0.68 8.4 0.982.3 594 9.8 30.7 47.4 75.7 0.234 81.4 7.31 0.0174 5.78 0.67 8.6 0.772.4 600 9.9 31.1 48.3 76.8 0.235 82.8 7.44 0.0173 5.88 0.65 9.2 0.742.5 604 10.0 31.6 49.1 78.0 0.235 83.3 7.62 0.0181 5.98 0.63 9.5 0.592.6 607 10.3 32.4 50.8 80.1 0.237 85.3 7.62 0.0178 6.10 0.63 9.8 0.632.7 610 10.3 32.8 52.1 81.3 0.240 87.2 7.73 0.0180 6.35 0.61 10.4 0.51

Series 33.2 579 9.7 30.0 45.1 73.8 0.228 77.9 6.91 0.0159 5.59 0.72 7.8 1.013.3 579 9.2 29.9 44.5 73.4 0.225 77.8 6.87 0.0180 5.59 0.71 7.9 1.173.4 585 9.1 30.1 44.4 73.6 0.224 78.5 6.92 0.0180 5.60 0.68 8.3 1.113.5 584 9.0 30.0 44.4 73.5 0.224 78.0 6.85 0.0186 5.57 0.68 8.2 1.103.6 587 8.9 30.0 44.7 73.6 0.226 77.8 6.72 0.0182 5.51 0.67 8.3 1.033.7 598 8.6 30.1 43.7 73.5 0.219 76.4 6.69 0.0196 5.48 0.67 8.2 1.03

Uncertainty ± 2 ± 0.1 ± 0.2 ± 0.8 ± 1.3 ± 0.006 ± 0.5 ± 0.06 – ± 0.15 ± 0.06 ± 0.6 –

a Values of E were determined by ultrasonic echography.b Values of E were determined through nanoindentation.

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[97]. Instead, the thermal expansion of their xNa2O–yTiO2–(100–x–y)SiO2 glasses remains almost unaffected even for large variations in theTiO2/SiO2 ratio. On the other hand, substituting Na2O for TiO2 tre-mendously lowers α[50]. Likewise, the substitution of CaO by TiO2 inseries 3 of the present work (Fig. 5b; circles) reduces α from 10.0.10−6/K for the Na2O–CaO–SiO2 base glass to 8.6 ∗ 10−6/K for the quaternaryNa2O–CaO–TiO2–SiO2 glass containing the largest amount of TiO2

(12.0 mol%). This trend is explained as follows: With the addition ofTiO2 at the expense of CaO, the weak Ca−O interatomic bonds(F = 0.36 Å−2) are replaced by Ti−O bonds (F= 1.28 Å−2) of notablyhigher strength (as approximated by the field strength F, which is de-fined as the charge z divided by the sum of the ionic radii squared(rA + rB)2[103]). Besides, NBO is increased (see Table 1), leading to anenhanced rigidity of the glass structure and the improved resistanceagainst a thermally induced contraction of the glass network [97]. Thesame effects are also responsible for the reduction of α in series 1. Incontrast, the increase of α in series 2 stems mainly from the substitutionof the strong Si−O interatomic bonds (F = 1.28 Å−2) by weaker Ti−Obonds (F= 1.54 Å−2) and to a minor extent from the minor reductionof −NBO.

Regarding the compositional dependence of Tg, not only the averagestrength of the interatomic bonds but also the bond density in the glassnetwork need to be taken into account. The combination of bothparameters reflects the volume density of bonding energy [59]. How-ever, in this context we highlight the large discrepancy between theaverage Ti4+ coordination environments in rutile (Ti[6][92]) and ourglasses (Ti[4], see Sections 3.1 and 3.2 for details), as well as the ac-companied differences in the interatomic distances and angles, whichare not considered by this approach and may result in a significantoverestimation of the packing efficiency of the atoms in the glass. Onthat account, it was recently proposed to modify Eq. (2) and esti-mate<U0/V0> by means of the actual glass density rather than thoseof the crystalline compounds [32,104], according to:

=∑

∑UV

ρf H

f MΔi ai

i i

0

0 (12)

The results of these calculations are summarized in Table 1 andreveal the expected positive correlation between Tg and<U0/V0> forseries 1 and 2 of the quaternary Na2O–CaO–TiO2–SiO2 glasses underinvestigation. Moreover, the invariance of<U0/V0> on the TiO2/CaOratio in series 3 provides a reasonable explanation for the observedabsence of any distinct compositional variation of the Tg of theseglasses.

The compositional dependence of selected mechanical properties,including the Young's modulus and Poisson ratio as determined by ul-trasonic echography, are visualized in Fig. 6a and b. For theNa2O–CaO–SiO2 base glass, values of E= 73.8 GPa and ν= 0.227 were

obtained, which are in a good agreement with previous investigationson equivalent glass compositions, i.e., E = 69.3–75.0 GPa[10,13,51,105,106] and ν = 0.189–0.240 [7,13,51,105,106]. With theaddition of TiO2 both E and ν continuously decrease from E= 73.8 GPaand ν= 0.227 to E= 68.8 GPa and ν = 0.210 at 5.5 mol% TiO2 inseries 1 (Fig. 6a and b; squares), while the elastic constants in series 2(Fig. 6a and b; triangles) monotonically increase with the incorporationof TiO2 up to E= 81.3 GPa and ν = 0.240 at 9.9 mol% TiO2. In series 3(Fig. 6a and b; circles), E as well as ν are almost unaffected by thereplacement of CaO for TiO2 (E = 73.4–73.8 GPa, ν= 0.224–0.228),except for a sudden drop of ν from 0.226 (9.7 mol% TiO2) to 0.219(12.0 mol% TiO2) between the two compositions of the highest TiO2

concentrations. To explain these trends, we need to consider the dif-ferent structural aspects that may influence the elastic properties ofglasses, i.e., the volume density of bonding energy (<U0/V0>) andatomic packing density (Cg) in the short-range order and the topologyof the glass network in the medium-range order. In this regard, weinitially focus on the relationship between the elastic properties and thenetwork dimensionality. Note, that ν is nowadays widely applied as anindicator for the degree of network polymerization in glasses, i.e., lowvalues of ν are accompanied by a high degree of crosslinking, whilehigh values of ν are usually found for strongly depolymerized glassnetworks [32,59,62,104,107]. Indeed, in series 1 ν is reduced for in-creasing NBO, whereas in series 2, ν grows while NBOis decreasedslightly (see Table 1). In series 3, on the other hand, the values of νremain almost constant despite a predicted increase of the titanosilicatenetwork polymerization, which clearly demonstrates the limitations ofthis simplistic approach. Apart from the network dimensionality, thePoisson ratio is strongly correlated with the atomic packing density[25,59]. In agreement with Ref. [59], ν is directly related to Cg and incontrast to the influence of NBO on ν discussed above, the invariance ofCg in series 3 also reflects the negligible changes of ν upon the gradualreplacement of CaO by TiO2, demonstrating the dominant role of theatomic packing efficiency on the elastic properties of our glasses. Ad-ditional support for this conclusion is provided by the compositionalvariation of E, e.g., although NBO (see Table 1) in series 2 is decreasedmarginally upon the partial substitution of SiO2 by TiO2, E raises owingto the increase of Cg, while in series 3 the values of E remain almostconstant, irrespective of the increase in network polymerization (seeTable 1), because of the insignificant differences of Cg. However, itshould be noted that the effect of Cg in series 1 and 2 is superimposedby the parallel decrease (or increase) of<U0/V0> , which also con-tributes to the herein observed trends of E.

The further evaluation of the mechanical properties was conductedby nano- and microindentation. First of all, the investigation of Young'smodulus through nanoindentation confirms the preceding composi-tional trends, which were derived from the measurements of the

Fig. 5. Compositional dependence of the glass transition temperature Tg (a) and thermal expansion coefficient α (b) of the Na2O–CaO–TiO2–SiO2 glasses investigated in the present study(series 1: squares, series 2: triangles, series 3: circles). The ternary contour diagrams of Tg and α were derived by interpolating the experimental results presented herein.

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14

ultrasound velocities (Table 2), though there is a large discrepancybetween the absolute values of E from both experimental techniques.The latter phenomenon has previously been assigned to the pile-up ofmaterial at the periphery of the indenter tip, which causes an under-estimation of the contact area between the indenter tip and the materialtested and thus an overestimation of E[108]. Referring to the plasticdeformation, the Vickers hardness, which was estimated using a mi-crohardness tester, displayed the same behavior that was seen in theglass transition and Young's modulus. That is, the substitution of CaOby TiO2 and minor amounts of SiO2 (Fig. 6c; squares) results in an in-creased plasticity, which reflects in a monotonic decrease of HV from5.64 to 4.84 GPa at 5.5 mol% TiO2, while in series 2 (Fig. 6c; triangles),where TiO2 was added at the expense of SiO2, an increased resistance

against plastic deformation was detected, which mirrors in an increaseof HV from 5.64 up to 6.35 GPa for the glass containing 9.9 mol% TiO2.In series 3 (Fig. 6c; circles), where CaO was gradually replaced by TiO2,HV remains relatively constant and scatters only slightly within anarrow interval, ranging from 5.48 to 5.64 GPa. To validate thesefindings, the hardness was also characterized by means of a na-noindenter and although the absolute values of H differ significantlyfrom HV, the results from the nanoindentation testing clearly corrobo-rate the trends determined by microindentation (Table 2). Apart fromthis, the aforementioned mismatch between HV and H most likely ori-ginates from the large contribution of elastic deformation to the in-dentation response of glasses, leading to marked differences betweenthe contact area under load, which determines H, and the size of the

Fig. 6. Compositional dependence of the Young's modulus E (a), Poisson ratio ν (b), Vickers hardness HV (c), strain-rate sensitivity m (d), brittleness B (e) and crack resistance CR (f) of theNa2O–CaO–TiO2–SiO2 glasses investigated in the present study (series 1: squares, series 2: triangles, series 3: circles). The ternary contour diagrams of E, ν, HV, m, B and CR and werederived by interpolating the experimental results presented herein.

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

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residual hardness imprint after unloading, which is used to evaluateHV[108]. The plastic deformation of glasses is basically governed bytwo competing mechanisms, i.e., a congruent densification of the glassnetwork, on the one hand, and a volume conservative shear flow, on theother hand [109]. Considering silicate glasses, a permanent compactionis achieved via a reduction of the average silicate ring size (from largerfive- and six- membered to smaller three- and four-membered silicaterings) and a decrease of the Si–O–Si bond angles [14,15]. Introducingadditional network modifier ions usually diminishes the ability ofglasses to densify, by breaking up the glass network and inducing amore efficient packing [110], whereas the weak ionically bonded in-terfaces in the network modifier-rich region of the glass allows for theinitiation of a shear-mediated plastic flow [111]. In this regard, thedecreasing plasticity (increasing HV) with increasing TiO2 content inseries 2 most likely originates from the parallel increase of Cg, whichlimits the ability of these glasses for compaction, and<U0/V0> ,which enhances their resistance against shear. The reverse effects arevisible in series 1, where the decrease of Cg in combination with thereduction of<U0/V0> indicates the creation of more open glass net-works of lower resistance against both densification and shear (redu-cing HV) as compared to the TiO2-free Na2O–CaO–SiO2 base glass. Onthe contrary, no variations of HV are expected in series 3, owing to thenegligible changes of Cg and<U0/V0> .

The time-dependent indentation response as represented by thestrain-rate sensitivity (Fig. 6d) shows some deviations from the com-positional trends observed so far. For the ternary Na2O–CaO–SiO2 baseglass a value of m= 0.0134 was determined, which corresponds againquite well with previously obtained results on very similar composi-tions [13,62]. However, with the addition of TiO2 an overall increase ofm is observable in all glasses studied, whereas equivalent values weredetected even for compositions with large differences in the CaO andSiO2 contents but equivalent TiO2 concentrations (e.g., m= 0.0180 forglass specimen 2.7 with 13.8 mol% CaO, 9.9 mol% TiO2 and 61.3 mol%SiO2, by contrast with m= 0.0182 for glass specimen 3.6 containing2.5 mol% CaO, 9.7 mol% TiO2 and 71.6 mol% SiO2). These findingsindicate that the time-dependent indentation response is governedprimarily by the TiO2 content and to a minor extent by the remainingcomponents present in the glasses. Surprisingly, there appears to be nodirect correlation between m and NBO (see Table 1) or<U0/V0> ,which is completely contradictory to the strong influence of the net-work dimensionality and the strength of the interatomic bonds on thetime-dependence of the indentation deformation that has previouslyseen, e.g., in borate [112], fluoride-phosphate [26] or chalcogenideglasses [113]. Instead, the current trends are more comparable to themonotonic increase of m in ternary Na2O–B2O3–SiO2 glasses upon theprogressive substitution of SiO2 by B2O3 and the accompanied transi-tion from a silicate towards a borate glass network [13]. Although thefundamental mechanisms controlling the strain-rate sensitivity ofmixed network forming glasses still remain unresolved, the presentfindings in combination with our earlier observations on borosilicateglasses [13], indicate that with increasing TiO2 or B2O3 concentration,the time-dependent indentation deformation of the corresponding ti-tanosilicate and borosilicate glasses becomes progressively dominatedby atomic rearrangements related to the titanate and borate sub-net-works rather than a structural response of the silicate sub-network.

The results on the indentation fracture toughness are summarized inTable 2. Note that a comparison between the results obtained in thecurrent work and previous investigations is not straightforward, sincecrack initiation and propagation, and hence Kc, strongly depend on theloading conditions [114] as well as the testing environment [17,115].For example, a Kc of 0.69 MPa m1/2 was determined for theNa2O–CaO–SiO2 base glass for which values ranging from 0.68 to0.88 MPa m1/2 can be found in the literature [8,10,51,105]. Further-more, because of the complex residual stress field in the vicinity of asharp loaded indenter tip and the multiple different crack pattern thatmay occur during indentation, the indentation fracture toughness does

not represent the fracture toughness, KIc, of a glass, which is commonlyderived from more standardized methods [116]. As a consequence, Kc

can only be employed as an indicator for the compositional variationsof the fracture resistance of soda-lime silicate glasses upon the in-corporation of TiO2. The more relevant parameter in this context is thebrittleness illustrated in Fig. 6f, which constitutes the competition be-tween plastic deformation, HV, and fracture, Kc. The values of B followthe previously observed trends in the elastic-plastic deformation.Moreover, in accordance with Ref. [117], a direct correlation between Band ρ respectively Cg exists. With the addition of up to 5.5 mol% TiO2 inseries 1 (Fig. 6e; squares) the values of B decrease from 8.3 to 6.5 μm-1/

2, due to the enhanced capability for a congruent densification of theglass network (reducing Cg), which diminishes the surface tensilestresses responsible for the initiation of radial cracks and reflects in anincrease of Kc[107]. The opposite trend is noticed in series 2 (Fig. 6e;triangles). When SiO2 is partially replaced by up to 9.9 mol% TiO2, amore compact glass network is achieved (increasing Cg). This effect isaccompanied by a monotonic increase of the driving force for radialcrack formation and the apparent reduction of Kc[107]. By extension,the Na2O–CaO–SiO2 base glass become more brittle, i.e., B increasesfrom 8.3 to 10.4 μm-1/2. Besides that, the absence of any clear compo-sitional variation of B in series 3 (Fig. 6e; circles) is related to the in-significant changes of Cg, notwithstanding the large variations in theTiO2/CaO ratio.

An alternative approach for evaluating the brittleness of glasses isthe resistance against median-radial crack initiation, defined as thecrack resistance. In principle, glasses with lower values of Kc, and thushigher values of B, are also characterized by a low CR and vice versa[18,69,104,107]. In agreement with these findings the abovementionedincrease of Kc and decrease of B in series 1 (Fig. 6f; squares) is ac-companied by an increase of CR from 1.22 up to 2.24 N as well, while inseries 2 (Fig. 6f; triangles) CR decreases from 1.22 down to 0.51 N forthe glass containing 9.9 mol% TiO2. In series 3 (Fig. 6f; circles), on theother hand, the changes of CR are negligible with respect to the ex-perimental uncertainty of this method (1.01≤ CR ≤ 1.22 N).

4. Conclusions

In the present work, we studied the effects of TiO2 on the structural,thermal, and mechanical properties of Ti-bearing soda-lime silicateglasses. For this purpose, three series of quaternaryNa2O–CaO–TiO2–SiO2 glasses were prepared with TiO2 concentrationsup to 12 mol% and varying Na2O, CaO, and SiO2 molar ratios. Thestructural analysis by Raman and 29Si MAS NMR spectroscopy revealedthe presence of predominantly four-fold coordinated Ti atoms in glassesof low and moderate TiO2 contents up to around 10 mol%, where Tireplaces Si to form a titanosilicate glass network of interconnected TiO4

and SiO4 tetrahedra. For higher TiO2 contents, a significant fraction ofthe Ti speciation involves TiO5 polyhedra. Moreover, the incorporationof Ti strongly affects the network connectivity, especially when theaddition of TiO2 is accompanied by a decrease of the CaO content.

Apart from the thermal expansion coefficient, alterations of theglass network connectivity have essentially no impact on the thermaland mechanical stability of these glasses. Instead, the compositionaldependence of the thermal and mechanical properties on the TiO2

content stems from its effect on the network energy and packing effi-ciency. Replacing SiO2 by TiO2 monotonically raises the volume densityof bonding energy and atomic packing density and accompanied by thisalso the glass transition temperature, Young's modulus and hardnessincreases, while the crack resistance and indentation fracture toughnesscontinuously decreases, resulting in glasses of higher brittleness incomparison to the TiO2-free Na2O–CaO–SiO2 base glass. The reverseeffect is visible, when the CaO content is reduced at the expense of TiO2

and minor amounts of SiO2, while the progressive substitution of CaOby TiO2 have only a marginal influence on the thermal and mechanicalproperties. In contrast to this, the strain-rate sensitivity appears to be

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

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determined by the overall TiO2 content and to a lesser extent by theother components present in these glasses, which indicates that thestrain-rate dependence of the indentation deformation becomes moreand more controlled by atomic rearrangements in titanate sub-networkas the TiO2 concentration increases.

Acknowledgements

This work was partially supported through the priority program SPP1594 of the German Science Foundation (grant no. WO1220/10-1). LWwould like to thank the European Research Council for further support(ERC grant. UTOPES, no. 681652). The Marie-Curie Fellowship grantedto SK via the VINNMER program (Vinnova, grant no. 2013-04343) co-funded by Marie Curie Actions FP7-PEOPLE-2011-COFUND (GROWTH291795) is gratefully acknowledged. ME gratefully acknowledges thefinancial support from the Swedish Research Council (contract VR-NT2014-4667), and NMR equipment grants from the Knut and AliceWallenberg Foundation as well as the Swedish Research Council. Theauthors would further like to thank Karin Lundstedt from RISE Glass,RISE Research Institutes of Sweden for the glass preparation as well asdilatometer measurements, and Dietmar Güttler from the Otto SchottInstitute of Materials Research, Friedrich Schiller University of Jena, forperforming the thermal analysis.

References

[1] L. Wondraczek, J.C. Mauro, J. Eckert, U. Kühn, J. Horbach, J. Deubener,T. Rouxel, Towards ultrastrong glasses, Adv. Mater. 23 (39) (2011) 4578–4586.

[2] D.J. Green, R. Tandon, V.M. Sglavo, Crack arrest and multiple cracking in glassthrough the use of designed residual stress profiles, Science 283 (5406) (1999)1295–1297.

[3] S. Karlsson, B. Jonson, C. Stalhandske, The technology of chemical glassstrengthening - a review, Glass Technol.: Eur. J. Glass Sci. Technol. A 51 (2)(2010) 41–54.

[4] H. Morozumi, H. Nakano, S. Yoshida, J. Matsuoka, Crack initiation tendency ofchemically strengthened glasses, Int. J. Appl. Glas. Sci. 6 (1) (2015) 64–71.

[5] T. Rouxel, P. Sellappan, F. Celarie, P. Houizot, J.C. Sangleboeuf, Toward glasseswith better indentation cracking resistance, C. R. Mecanique 342 (1) (2014)46–51.

[6] E. Kilinc, R.J. Hand, Mechanical properties of soda-lime-silica glasses with varyingalkaline earth contents, J. Non-Cryst. Solids 429 (2015) 190–197.

[7] C. Hermansen, J. Matsuoka, S. Yoshida, H. Yamazaki, Y. Kato, Y.Z. Yue,Densification and plastic deformation under microindentation in silicate glassesand the relation to hardness and crack resistance, J. Non-Cryst. Solids 364 (2013)40–43.

[8] R.J. Hand, D.R. Tadjiev, Mechanical properties of silicate glasses as a function ofcomposition, J. Non-Cryst. Solids 356 (44-49) (2010) 2417–2423.

[9] S. Dériano, T. Rouxel, M. LeFloch, B. Beuneu, Structure and mechanical propertiesof alkali-alkaline earth-silicate glasses, Phys. Chem. Glasses 45 (1) (2004) 37–44.

[10] J. Sehgal, S. Ito, A new low-brittleness glass in the soda-lime-silica glass family, J.Am. Ceram. Soc. 81 (9) (1998) 2485–2488.

[11] P. Malchow, K.E. Johanns, D. Möncke, S. Korte-Kerzel, L. Wondraczek, K. Durst,Composition and cooling-rate dependence of plastic deformation, densification,and cracking in sodium borosilicate glasses during pyramidal indentation, J. Non-Cryst. Solids 419 (2015) 97–109.

[12] M. Barlet, J.M. Delaye, T. Charpentier, M. Gennisson, D. Bonamy, T. Rouxel,C.L. Rountree, Hardness and toughness of sodium borosilicate glasses via Vickers'sindentations, J. Non-Cryst. Solids 417 (2015) 66–79.

[13] R. Limbach, A. Winterstein-Beckmann, J. Dellith, D. Möncke, L. Wondraczek,Plasticity, crack initiation and defect resistance in alkali-borosilicate glasses: fromnormal to anomalous behavior, J. Non-Cryst. Solids 417-418 (2015) 15–27.

[14] A. Winterstein-Beckmann, D. Möncke, D. Palles, E.I. Kamitsos, L. Wondraczek, ARaman-spectroscopic study of indentation-induced structural changes in technicalalkali-borosilicate glasses with varying silicate network connectivity, J. Non-Cryst.Solids 405 (2014) 196–206.

[15] A. Winterstein-Beckmann, D. Möncke, D. Palles, E.I. Kamitsos, L. Wondraczek,Raman spectroscopic study of structural changes induced by micro-indentation inlow alkali borosilicate glasses, J. Non-Cryst. Solids 401 (2014) 110–114.

[16] Y. Kato, H. Yamazaki, Y. Kubo, S. Yoshida, J. Matsuoka, T. Akai, Effect of B2O3

content on crack initiation under Vickers indentation test, J. Ceram. Soc. Jpn. 118(1381) (2010) 792–798.

[17] A. Pönitzsch, M. Nofz, L. Wondraczek, J. Deubener, Bulk elastic properties,hardness and fatigue of calcium aluminosilicate glasses in the intermediate-silicarange, J. Non-Cryst. Solids 434 (2016) 1–12.

[18] S. Yoshida, A. Hidaka, J. Matsuoka, Crack initiation behavior of sodium alumi-nosilicate glasses, J. Non-Cryst. Solids 344 (1-2) (2004) 37–43.

[19] A. Winkelmann, O. Schott, Ueber die Elasticität und über die Zug- undDruckfestigkeit verschiedener neuer Gläser in ihrer Abhängigkeit von der

chemischen Zusammensetzung, Ann. Phys. 287 (4) (1894) 697–729.[20] C.J. Phillips, Calculation of Young's modulus of elasticity from composition of

simple complex silicate glasses, Glass Technol. 5 (6) (1964) 216–223.[21] M.L. Williams, G.E. Scott, Young's modulus of alkali-free glass, Glass Technol. 11

(3) (1970) 76–79.[22] A. Fluegel, Statistical regression modelling of glass properties - a tutorial, Glass

Technol. Eur. J. Glass Sci. Technol. Part A 50 (1) (2009) 25–46.[23] A. Makishima, J.D. Mackenzie, Direct calculation of Young's modulus of glass, J.

Non-Cryst. Solids 12 (1) (1973) 35–45.[24] S. Inaba, S. Fujino, K. Morinaga, Young's modulus and compositional parameters

of oxide glasses, J. Am. Ceram. Soc. 82 (12) (1999) 3501–3507.[25] A. Makishima, J.D. Mackenzie, Calculation of bulk modulus, shear modulus and

Poisson's ratio of glass, J. Non-Cryst. Solids 17 (2) (1975) 147–157.[26] R. Limbach, B.P. Rodrigues, D. Möncke, L. Wondraczek, Elasticity, deformation

and fracture of mixed fluoride-phosphate glasses, J. Non-Cryst. Solids 430 (2015)99–107.

[27] A.K. Swarnakar, A. Stamboulis, D. Holland, O. Van der Biest, Improved predictionof Young's modulus of fluorine-containing glasses using MAS-NMR structural data,J. Am. Ceram. Soc. 96 (4) (2013) 1271–1277.

[28] C.C. Lin, L.G. Liu, Composition dependence of elasticity in aluminosilicate glasses,Phys. Chem. Miner. 33 (5) (2006) 332–346.

[29] A. Mohajerani, V. Martin, D. Boyd, J.W. Zwanziger, On the mechanical propertiesof lead borate glass, J. Non-Cryst. Solids 381 (2013) 29–34.

[30] G.L. Paraschiv, S. Gomez, J.C. Mauro, L. Wondraczek, Y.Z. Yue, M.M. Smedskjaer,Hardness of oxynitride glasses: topological origin, J. Phys. Chem. B 119 (10)(2015) 4109–4115.

[31] J. Rocherulle, C. Ecolivet, M. Poulain, P. Verdier, Y. Laurent, Elastic moduli ofoxynitride glasses: extension of Makishima and Mackenzie theory, J. Non-Cryst.Solids 108 (2) (1989) 187–193.

[32] G. Scannell, L. Huang, T. Rouxel, Elastic properties and indentation cracking be-havior of Na2O-TiO2-SiO2 glasses, J. Non-Cryst. Solids 429 (2015) 129–142.

[33] A. Makishima, Y. Tamura, T. Sakaino, Elastic moduli and refractive indices ofaluminosilicate glasses containing Y2O3, La2O3, and TiO2, J. Am. Ceram. Soc. 61(5-6) (1978) 247–249.

[34] M.M. Morsi, A.W.A. El-Shennawi, Some physical properties of silicate glassescontaining TiO2 in relation to their structure, Phys. Chem. Glasses 25 (3) (1984)64–68.

[35] K.E. Hrdina, B.G. Ackerman, A.W. Fanning, C.E. Heckle, D.C. Jenne, W.D. Navan,Measuring and tailoring CTE within ULE glass, SPIE Proc. 5037 (2003) 227–235.

[36] S. Richter, D. Moncke, F. Zimmermann, E.I. Kamitsos, L. Wondraczek,A. Tunermann, S. Nolte, Ultrashort pulse induced modifications in ULE - fromnanograting formation to laser darkening, Opt. Mater. Express 5 (8) (2015)1834–1850.

[37] P.C. Schultz, Binary titania-silica glasses containing 10 to 20 wt% TiO2, J. Am.Ceram. Soc. 59 (5-6) (1976) 214–219.

[38] S. Karlsson, L. Grund Bäck, P. Kidkhunthod, K. Lundstedt, L. Wondraczek, Effect ofTiO2 on optical properties of glasses in the soda-lime-silicate system, Opt. Mater.Express 6 (4) (2016) 1198–1216.

[39] V. Dimitrov, T. Komatsu, Electronic polarizability and average single bondstrength of ternary oxide glasses with high TiO2 contents, Phys. Chem. Glasses:Eur. J. Glass Sci. Technol. B 52 (6) (2011) 225–230.

[40] M. Abdel-Baki, F.A.A. Wahab, F. El-Diasty, Optical characterization of xTiO2-(60-x)SiO2-40Na2O glasses: I. Linear and nonlinear dispersion properties, Mater.Chem. Phys. 96 (2-3) (2006) 201–210.

[41] M. Abdel-Baki, F. El-Diasty, F.A.A. Wahab, Optical characterization of xTiO2-(60-x)SiO2-40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizabilityand optical basicity, Opt. Commun. 261 (1) (2006) 65–70.

[42] M.A. Villegas, A. Depablos, J.M. Fernandeznavarro, Properties of CaO-TiO2-SiO2

glasses, Glass Technol. 35 (6) (1994) 276–280.[43] A.A. Higazy, A. Hussein, M.A. Ewaida, M. Elhofy, The effect of temperature on the

optical-absorption edge of the titanium oxide doped soda-lime silica glasses, J.Mater. Sci. Lett. 7 (5) (1988) 453–456.

[44] C.A. Hogarth, M.N. Khan, A study of optical absorption in some sodium titaniumsilicate glasses, J. Non-Cryst. Solids 24 (2) (1977) 277–281.

[45] R.C. Turnbull, W.G. Lawrence, The role of titania in silica glasses, J. Am. Ceram.Soc. 35 (2) (1952) 48–53.

[46] M.A. Villegas, A. de Pablos, J.M.F. Navarro, Caracterización de vidrios del sistemaNa2O-TiO2-SiO2, Bol. Soc. Esp. Ceram. Vidr. 33 (1) (1994) 23–28.

[47] K. Takahashi, N. Mochida, Y. Yoshida, Properties and structure of silicate glassescontaining tetravalent cations, J. Ceram. Soc. Jpn. 85 (1977) 330–340.

[48] R.A. Johnston, C.L. Babcock, Composition dependence of elastic moduli in Na2O-TiO2-SiO2 glasses, J. Am. Ceram. Soc. 58 (3-4) (1975) 85–87.

[49] M.H. Manghnani, Pressure and temperature dependence of elastic moduli of Na2O-TiO2-SiO2 glasses, J. Am. Ceram. Soc. 55 (7) (1972) 360–365.

[50] J.H. Strimple, E.A. Giess, Glass formation and properties of glasses in the systemNa2O-B2O3-SiO2-TiO2, J. Am. Ceram. Soc. 41 (7) (1958) 231–237.

[51] M. Hojamberdiev, H.J. Stevens, Indentation recovery of soda-lime silicate glassescontaining titania, zirconia and hafnia at low temperatures, Mat. Sci. Eng. A 532(2012) 456–461.

[52] A.A. Higazy, A.M. Hussein, M.A. Ewaida, M.I. Elhofy, Elastic constants of soda-lime-silica glasses doped with titanium oxide, Phys. Chem. Glasses 28 (4) (1987)164–167.

[53] M. Edén, The split network analysis for exploring composition-structure correla-tions in multi-component glasses: I. Rationalizing bioactivity-composition trendsof bioglasses, J. Non-Cryst. Solids 357 (6-7) (2011) 1595–1602.

[54] R.D. Shannon, Revised Effective Ionic Radii and Systematic Studies of Interatomic

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

17

Distances in Halides and Chalcogenides, Acta Crystallogr. A (1976) 751–767.[55] A.N. Cormack, J.C. Du, Molecular dynamics simulations of soda-lime-silicate

glasses, J. Non-Cryst. Solids 293 (2001) 283–289.[56] A. Tilocca, N.H. de Leeuw, Structural and electronic properties of modified sodium

and soda-lime silicate glasses by Car-Parrinello molecular dynamics, J. Mater.Chem. 16 (20) (2006) 1950–1955.

[57] G.N. Greaves, A. Fontaine, P. Lagarde, D. Raoux, S.J. Gurman, Local structure ofsilicate glasses, Nature 293 (5834) (1981) 611–616.

[58] L. Cormier, D.R. Neuville, Ca and Na environments in Na2O-CaO-Al2O3-SiO2

glasses: influence of cation mixing and cation-network interactions, Chem. Geol.213 (1-3) (2004) 103–113.

[59] T. Rouxel, Elastic properties and short-to medium-range order in glasses, J. Am.Ceram. Soc. 90 (10) (2007) 3019–3039.

[60] Lide, D.R., Handbook of Chemistry and Physics. Vol. 74. 1993-1994, Boca Raton:CRC Press.

[61] A. Thieme, D. Möncke, R. Limbach, S. Fuhrmann, E.I. Kamitsos, L. Wondraczek,Structure and properties of alkali and silver sulfophosphate glasses, J. Non-Cryst.Solids 410 (2015) 142–150.

[62] R. Limbach, B.P. Rodrigues, L. Wondraczek, Strain-rate sensitivity of glasses, J.Non-Cryst. Solids 404 (2014) 124–134.

[63] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness andelastic modulus using load and displacement sensing indentation experiments, J.Mater. Res. 7 (6) (1992) 1564–1583.

[64] V. Maier, B. Merle, M. Göken, K. Durst, An improved long-term nanoindentationcreep testing approach for studying the local deformation processes in nanocrys-talline metals at room and elevated temperatures, J. Mater. Res. 28 (9) (2013)1177–1188.

[65] L. Shen, W.C.D. Cheong, Y.L. Foo, Z. Chen, Nanoindentation creep of tin andaluminium: A comparative study between constant load and constant strain ratemethods, Mat. Sci. Eng. A (2012) 505–510.

[66] B.N. Lucas, W.C. Oliver, Indentation power-law creep of high-purity indium,Metall. Mater. Trans. A 30 (3) (1999) 601–610.

[67] G.R. Anstis, P. Chantikul, B.R. Lawn, D.B. Marshall, A critical evaluation of in-dentation techniques for measuring fracture toughness: I, direct crack measure-ments, J. Am. Ceram. Soc. 64 (9) (1981) 533–538.

[68] B.R. Lawn, D.B. Marshall, Hardness, toughness, and brittleness: an indentationanalysis, J. Am. Ceram. Soc. 62 (7-8) (1979) 347–350.

[69] Y. Kato, H. Yamazaki, S. Yoshida, J. Matsuoka, Effect of densification on crackinitiation under Vickers indentation test, J. Non-Cryst. Solids 356 (35-36) (2010)1768–1773.

[70] P.F. McMillan, B.T. Poe, P. Gillet, B. Reynard, A study of SiO2 glass and super-cooled liquid to 1950 K via high-temperature Raman spectroscopy, Geochim.Cosmochim. Acta 58 (17) (1994) 3653–3664.

[71] M. Wojdyr, Fityk: a general-purpose peak fitting program, J. Appl. Crystallogr. 43(2010) 1126–1128.

[72] M. Edén, NMR studies on oxide-based glasses, Annu. Rep. Prog. Chem., Sect. C:Phys. Chem. 108 (2012) 177–221.

[73] M.W.G. Lockyer, D. Holland, R. Dupree, NMR investigation of the structure ofsome bioactive and related glasses, J. Non-Cryst. Solids 188 (3) (1995) 207–219.

[74] A.R. Jones, R. Winter, G.N. Greaves, I.H. Smith, MAS NMR study of soda-lime-silicate glasses with variable degree of polymerisation, J. Non-Cryst. Solids 293(2001) 87–92.

[75] R. Mathew, B. Stevensson, A. Tilocca, M. Edén, Toward a rational design ofbioactive glasses with optimal structural features: composition-structure correla-tions unveiled by solid-state NMR and MD simulations, J. Phys. Chem. B 118 (3)(2014) 833–844.

[76] D.S. Knight, C.G. Pantano, W.B. White, Raman spectra of gel-prepared titania-silica glasses, Mater. Lett. 8 (5) (1989) 156–160.

[77] B. Mysen, D. Neuville, Effect of temperature and TiO2 content on the structure ofNa2Si2O5-Na2Ti2O5 melts and glasses, Geochim. Cosmochim. Acta 59 (2) (1995)325–342.

[78] K. Inoue, S. Sakida, T. Nanba, Y. Miura, Structure and optical properties of TiO2

containing oxide glasses, Mater. Sci. Technol.: Mater. Syst. 1 (2006) 583–593.[79] J.L. Li, Q.F. Shu, K.C. Chou, Structural study of glassy CaO-SiO2-CaF2-TiO2 slags by

raman spectroscopy and MAS-NMR, ISIJ Int. 54 (4) (2014) 721–727.[80] M.L. Balmer, B.C. Bunker, L.Q. Wang, C.H.F. Peden, Y.L. Su, Solid-state 29Si MAS

NMR study of titanosilicates, J. Phys. Chem. B 101 (45) (1997) 9170–9179.[81] S.W. Martin, A. Bhatnagar, C. Parameswar, S. Feller, J. MacKenzie, 29Si MAS-NMR

study of the short-range order in potassium borosilicate glasses, J. Am. Ceram. Soc.78 (4) (1995) 952–960.

[82] L. van Wüllen, W. Müller-Warmuth, D. Papageorgiou, H.J. Pentinghaus,Characterization and structural developments of gel-derived borosilicate glasses: amultinuclear MAS-NMR study, J. Non-Cryst. Solids 171 (1) (1994) 53–67.

[83] B.L. Sherriff, B. Zhou, 29Si and 23Na MAS NMR spectroscopic study of the poly-types of the titanosilicate penkvilksite, Can. Mineral. 42 (2004) 1027–1035.

[84] G.S. Henderson, The structure of silicate melts: a glass perspective, Can. Mineral.43 (2005) 1921–1958.

[85] G.S. Henderson, M.E. Fleet, The structure of Ti silicate-glasses by micro-Ramanspectroscopy, Can. Mineral. 33 (1995) 399–408.

[86] A.A. Osipov, G.G. Korinevskaya, L.M. Osipova, V.A. Muftakhov, Titanium co-ordination in TiO2-Na2O-SiO2 glasses of xTiO2 · (100 − x) [2Na2O · 3SiO2](0≤ x≤ 30) composition based on Raman spectroscopy, Glass Phys. Chem. 38(4) (2012) 357–360.

[87] C.W. Ponader, H. Boek, J.E. Dickinson, X-ray absorption study of the coordination

of titanium in sodium-titanium-silicate glasses, J. Non-Cryst. Solids 201 (1-2)(1996) 81–94.

[88] F.H. Larsen, S. Rossano, I. Farnan, Order and disorder in titanosilicate glass by 17OMAS, off-MAS, and 3Q-QCPMG-MAS solid-state NMR, J. Phys. Chem. B 111 (28)(2007) 8014–8019.

[89] S. Iftekhar, B. Pahari, K. Okhotnikov, A. Jaworski, B. Stevensson, J. Grins,M. Edén, Properties and structures of RE2O3-Al2O3-SiO2 (RE = Y, Lu) glassesprobed by molecular dynamics simulations and solid-state NMR: the roles ofaluminum and rare-earth ions for dictating the microhardness, J. Phys. Chem. C116 (34) (2012) 18394–18406.

[90] K. Okhotnikov, B. Stevensson, M. Edén, New interatomic potential parameters formolecular dynamics simulations of rare-earth (RE = La, Y, Lu, Sc) aluminosilicateglass structures: exploration of RE3+ field-strength effects, Phys. Chem. Chem.Phys. 15 (36) (2013) 15041–15055.

[91] B. Stevensson, M. Edén, Structural rationalization of the microhardness trends ofrare-earth aluminosilicate glasses: interplay between the RE3+ field-strength andthe aluminum coordinations, J. Non-Cryst. Solids 378 (2013) 163–167.

[92] G.S. Henderson, X. Liu, M.E. Fleet, A Ti L-edge X-ray absorption study of Ti-silicateglasses, Phys. Chem. Miner. 29 (1) (2002) 32–42.

[93] B. Reynard, S.L. Webb, High-temperature Raman spectroscopy of Na2TiSi2O7 glassand melt: coordination of Ti4+ and nature of the configurational changes in theliquid, Eur. J. Mineral. 10 (1) (1998) 49–58.

[94] F. Farges, G.E. Brown, J.J. Rehr, Coordination chemistry of Ti(IV) in silicateglasses and melts: I. XAFS study of titanium coordination in oxide model com-pounds, Geochim. Cosmochim. Acta 60 (16) (1996) 3023–3038.

[95] F. Farges, G.E. Brown, A. Navrotsky, H. Gan, J.R. Rehr, Coordination chemistry ofTi(IV) in silicate glasses and melts: III. Glasses and melts from ambient to hightemperaturesa, Geochim. Cosmochim. Acta 60 (16) (1996) 3055–3065.

[96] G. Scannell, A. Koike, L.P. Huang, Structure and thermo-mechanical response ofTiO2-SiO2 glasses to temperature, J. Non-Cryst. Solids 447 (2016) 238–247.

[97] G. Scannell, S. Barra, L.P. Huang, Structure and properties of Na2O-TiO2-SiO2

glasses: role of Na and Ti on modifying the silica network, J. Non-Cryst. Solids 448(2016) 52–61.

[98] A.G. Kalampounias, S.N. Yannopoulos, G.N. Papatheodorou, Temperature-inducedstructural changes in glassy, supercooled, and molten silica from 77 to 2150 K, J.Chem. Phys. 124 (1) (2006) 014504 (1-15).

[99] V.N. Bykov, A.A. Osipov, V.N. Anfilogov, Structure of high-alkali aluminosilicatemelts from the high-temperature Raman spectroscopic data, Glass Phys. Chem. 29(2) (2003) 105–107.

[100] K. Kusabiraki, Infrared and Raman spectra of vitreous silica and sodium silicatescontaining titanium, J. Non-Cryst. Solids 95-6 (1987) 411–418.

[101] P. Schultz, H. Smyth, Ultra-low-Expansion Glasses and their Structure in the SiO2-TiO2 System, in: R.W. Douglas, B. Ellis (Eds.), Amorphous Materials, WileyInterscience, New York, 1970, pp. 453–461.

[102] K. Kamiya, S. Sakka, Thermal expansion of TiO2-SiO2 and TiO2-GeO2 glasses, J.Non-Cryst. Solids 52 (1-3) (1982) 357–363.

[103] A. Dietzel, Die Kationenfeldstärken und ihre Beziehungen zuEntglasungsvorgängen, zur Verbindungsbildung und zu den Schmelzpunkten vonSilicaten, Z. Elektrochem. Angew. Phys. Chem. 48 (1) (1942) 9–23.

[104] Z.Y. Yao, D. Möncke, E.I. Kamitsos, P. Houizot, F. Célarié, T. Rouxel,L. Wondraczek, Structure and mechanical properties of copper-lead and copper-zinc borate glasses, J. Non-Cryst. Solids 435 (2016) 55–68.

[105] V. Le Houérou, J.C. Sangleboeuf, S. Dériano, T. Rouxel, G. Duisit, Surface damageof soda-lime-silica glasses: indentation scratch behavior, J. Non-Cryst. Solids 316(1) (2003) 54–63.

[106] S. Yoshida, J.C. Sangleboeuf, T. Rouxel, Quantitative evaluation of indentation-induced densification in glass, J. Mater. Res. 20 (12) (2005) 3404–3412.

[107] P. Sellappan, T. Rouxel, F. Celarie, E. Becker, P. Houizot, R. Conradt, Compositiondependence of indentation deformation and indentation cracking in glass, ActaMater. 61 (16) (2013) 5949–5965.

[108] W.C. Oliver, G.M. Pharr, Measurement of hardness and elastic modulus by in-strumented indentation: advances in understanding and refinements to metho-dology, J. Mater. Res. 19 (1) (2004) 3–20.

[109] K.W. Peter, Densification and flow phenomena of glass in indentation experiments,J. Non-Cryst. Solids 5 (2) (1970) 103–115.

[110] T. Rouxel, H. Ji, T. Hammouda, A. Moreac, Poisson's ratio and the densification ofglass under high pressure, Phys. Rev. Lett. 100 (22) (2008) 225501 (1-4).

[111] D.M. Marsh, Plastic flow and fracture of glass, Proc. R. Soc. Lon. Ser. A 282 (1388)(1964) 33–43.

[112] D. Möncke, E.I. Kamitsos, D. Palles, R. Limbach, A. Winterstein-Beckmann,T. Honma, Z. Yao, T. Rouxel, L. Wondraczek, Transition and post-transition metalions in borate glasses: borate ligand speciation, cluster formation, and their effecton glass transition and mechanical properties, J. Chem. Phys. (2016) 145(12).

[113] J.P. Guin, T. Rouxel, V. Keryvin, J.C. Sangleboeuf, I. Serre, J. Lucas, Indentationcreep of Ge-Se chalcogenide glasses below Tg: elastic recovery and non-Newtonianflow, J. Non-Cryst. Solids 298 (2-3) (2002) 260–269.

[114] R.F. Cook, G.M. Pharr, Direct observation and analysis of indentation cracking inglasses and ceramics, J. Am. Ceram. Soc. 73 (4) (1990) 787–817.

[115] T.M. Gross, M. Tomozawa, Crack-free high load Vickers indentation of silica glass,J. Non-Cryst. Solids 354 (52–54) (2008) 5567–5569.

[116] G.D. Quinn, R.C. Bradt, On the Vickers indentation fracture toughness test, J. Am.Ceram. Soc. 90 (3) (2007) 673–680.

[117] J. Sehgal, S. Ito, Brittleness of glass, J. Non-Cryst. Solids 253 (1-3) (1999)126–132.

R. Limbach et al. Journal of Non-Crystalline Solids 471 (2017) 6–18

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