Temperature-Driven Structural Transitions in Molten ...

Temperature-Driven Structural Transitions in Molten Sodium Borates Na2O-B2O3: X-ray Diffraction, Thermodynamic Modelling and Implications for Topological Constraint Theory O.L.G. Alderman1,2,*, M. Liška3, J. Macháček4, C.J. Benmore2, A. Lin1,5, A. Tamalonis1, J.K.R. Weber1,2 1. Materials Development, Inc., Arlington Heights, IL 60004, USA 2. X-Ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA 3. Vitrum Laugaricio, Joint Glass Center of Institute of Inorganic Chemistry of SAS, Alexander Dubček University of Trenčín and RONA, j.s.c., Študentská 2, Trenčín, 911 50, Slovak Republic 4. Department of Glass and Ceramics, Institute of Chemical Technology Prague, Technická 5, 166 28 Prague, Czech Republic 5. Department of Materials Science and Engineering, McCormick School of Engineering and Applied Science, 2220 Campus Drive, Northwestern University, Evanston, IL 60208, USA *Corresponding author [email protected]

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Abstract Temperature dependent measurements of the x-ray structure factor of molten Na2B4O7 reveal a continuous structural transition. We demonstrate that the thermodynamic model of ideal associated solutions is capable of predicting this evolution of melt structure, between a low density, depolymerized melt at ≳ 300 K above the liquidus, toward a dense, polymerized melt close to the glass transition. This temperature dependent nature of melt structure is predicted to be strongly composition dependent, with the B-O coordination number depending on temperature only in the range 20 – 50 mol% Na2O, which appears to be manifest in the broad maximum observed in the glass transition temperatures. We discuss the ramifications of these findings for the application of topological constraint theory, with relevance to industrial glass design and manufacture, crystal growth from melts of non-linear optical materials, geochemistry, and the understanding of melt fragility and the glass transition.

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Introduction Modern glass and metallurgical industries rely increasingly on models of melt properties as a cost effective means for identifying compositions with improved functionality or cost-saving benefits such as lower working temperatures.1 Such models include the theory of topological constraints1-2 and the thermodynamic model of ideal associated solutions.3-4 Whilst these models have been vindicated at ambient temperature by comparison to measurements on glasses, aspects including the temperature dependence often remain untested, despite offering computationally inexpensive results compared to e.g. molecular dynamics. Here we use the model of ideal associated solutions to predict a continuous structural transition in a network liquid, use highenergy x-ray diffraction to test the prediction, and discuss some consequences for temperature dependent constraint theory. Structural transitions in network liquids have retained an air of mystery owing to the experimental difficulties involved in their study.5-6

Much progress has been made in

understanding pressure dependence of structure by probing cold-compressed glasses in-situ7-9 and melts in-situ under high P-T conditions.7, 10-11 Temperature driven transitions have received relatively little attention, in part because ‘strong’ liquids (with close to Arrhenian viscosities), such as SiO2, show only subtle changes.12 In fragile liquids, structural rearrangements are expected to be greater,13 and have been measured e.g. in CaAl2O4,14-16 where the average Al coordination number, nAlO, in the glass is 4.04(3), and in the 1973(30) K melt is 4.20(4).14 Measurement of nAlO(T)16 indicates that most structural rearrangement occurs below about 1.25Tg. However, in CaAl2O4, there is ambiguity in nAlO(T) derived from diffraction, because Al-O and Ca-O peaks in the real-space correlation functions overlap.16 Here we have chosen to

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study Na2B4O7 liquid, where B-O and Na-O peaks are well separated, thus removing ambiguity in nBO(T). Borates represent a key class of glass-forming oxide liquids and are end members to widely used borosilicate systems such as Na2O-B2O3-SiO2 on which Pyrex® and Vycor® are based. Borate melts and glasses are also important in the growth of non-linear optical crystals such as βBaB4O7.17-19 Structural changes in borate liquids contribute to configurational heat capacity and provide mechanisms for viscous flow.20-22 Na2B4O7 liquid is glass-forming (Tg ≈ 738 K), with fragility index, m, between 61.423 and 84.5,24 cf. liquid B2O3, m = 35.25 The Na2B4O7 (x = 33.3 mol% Na2O) glass composition maximizes nBO(x), having about N4 = nBO – 3 = 43% of B atoms on tetrahedral sites, and the rest in trigonal-planar environments.26-29 This maximum in nBO(x) is related to observed extrema in physical properties – a phenomenon termed the ‘borate anomaly’ in comparison to silicates which do not display such behavior. Previous measurements of nBO in Na2B4O7 liquid are summarized in Fig. 1a. There is much greater spread in nBO for the liquid, than for the glass, with Raman30-31 and NMR27 spectroscopies yielding smaller values than neutron diffraction28,

32

and molecular dynamics.32

This motivates more detailed

measurements with an alternative technique – x-ray diffraction.33-34,35 Furthermore, no nBO are reported for the supercooled liquid (Fig. 1a).

4

Tg T Tmelt

a)

nBO = 3 + N4

3.5 3.4 3.3 3.2 3.1 3.0

nBO = 3 + N4

3.5

b)

3.4 3.3 3.2 3.1 3.0 400

800

1200

1600

T/K Figure 1: nBO in glassy (white region), supercooled liquid (blue region) and liquid (red region) Na2B4O7. The glass transition region is indicated by the grey region around 738 K. The dashdot (blue) curve indicates the values in crystalline Na2B4O7, showing the α reconstructive phase transition at T-α = 844 K.36 The solid (grey) curve with dashed extrapolation to room temperature and the star are existing TD models.4, 37-38 The solid (dark red) curve with dashed extrapolation to room temperature is the TD model of the present work with nBO = 3.5 of Na2B4O739-40 as input. The dash-dot-dot curve uses nBO = 3.375 of α-Na2B4O741 as input. Part a) shows existing literature data: diamonds,30 upward triangles 31 – Raman spectroscopy; downward triangles,27 circle26 – 11B NMR; leftward triangle,28 square32 – neutron diffraction; hexagon32 – molecular dynamics. A number of points overlay at 298 K, and Ref. 27, 30-32 refer to 30Na2O·70B2O3, rather than Na2B4O7. Part b) shows x-ray diffraction data of the present study: squares – direct determination (statistical error bars only); diamonds – bond length based determinations; blue points – 8 s measurements; black and grey points – 20 s measurements. In color online.

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We present high-energy x-ray diffraction measurements of nBO(T), for aerodynamically levitated Na2B4O7, as it supercools from equilibrium liquid through the glass transition.

We make

predictions for nBO(x,T) based on the thermodynamic (TD) model of ideal associated solutions,3 which describes an oxide liquid as an ideal solution of end member oxides and any stoichiometric compounds forming within the system.

The model has no free parameters,

requiring as input only the melt composition and free energies of formation, ΔfG(T), of each compound, and outputs their relative amounts (interpreted as locally stoichiometric groupings in the melt) based on the laws of mass action and mass balance.3 We include the compounds Na2O, Na3BO3, Na4B2O5, NaBO2, Na2B4O7, NaB3O5, Na2B8O13, NaB5O8, NaB9O14, B2O3, and use ΔfG(T) compiled in FactSage.42 Na3B7O1243 and Na12B26O4544 also exist, but their significance for the liquid structure has been deemed small based on their Prigogine-Defay thermodynamic stabilities and stressed-rigid nature.45 At the Na2B4O7 composition, a number of polymorphs have been reported,36, 46 although later work showed the β-phase had Na12B26O45 composition.44 Structures of low-T -Na2B4O739-40 (nBO = 3.5) and high-T α-Na2B4O741 (nBO = 3.375) are known, and related by reconstructive transition at Tα = 844 K (Fig. 1).36 A remarkable feature of the α transition is that it involves a drop in nBO, with the α-phase representing a highly unusual case of M+2B4O7 or M2+B4O7 structure with nBO < 3.5. Methods X-ray diffraction measurements were made at beamline 6-ID-D of the Advanced Photon Source (Argonne, IL, USA) using 100.24 keV x-rays and an aerodynamic levitation furnace.47-48 Levitation eliminates container scattering and chemical contamination, and increases the propensity for supercooling by elimination of heterogeneous nucleation at the melt-container interface. Diffraction patterns were collected during cooling of melts in two ways i) isothermal 6

20 s measurements during stepwise cooling from 996(13) K, ii) 8s measurements during linear PID controlled cooling at -2.57 K·s-1 from 1257(15) K.

These parameters allowed for a

compromise between signal-to-noise and minimization of sample volatilization. Measured mass losses imply compositional drifts of < 1 mol% Na2O. Temperature was measured using 5 μm wavelength optical pyrometry, the long wavelength being necessary to avoid near-infrared transparency of the borate melts at the lower temperatures investigated. Apparent temperature was corrected using a Wien’s displacement law approximation49 with a spectral emissivity value of 0.96 estimated from the Fresnel losses for a material with a refractive index of 1.5.50 The pyrometer temperature was also corrected for reflection losses from a CaF2 window and lens that were in the optical path.

Melt densities were estimated by interpolation of published

measurements.51 The diffraction data analysis follows that described in Ref. 47-48. Samples of Na2B4O7 were obtained by mixing H3BO3 (Aldrich, 99.999%) and Na2CO3 (Alfa Aesar 100.00 ± 0.05%) in the correct ratio and sintering the mixture in a Pt crucible at 923 K for 30 mins. The resultant material was then formed into roughly spherical beads suitable for levitation using a water-cooled copper hearth and a 100 W CO2 laser. Sample contamination has been shown to be negligible by this method.52 The beads were then levitated in Ar gas and heated to a temperature close to the liquidus and held until any visible bubbles disappeared. The melt was then quenched by switching off the laser to obtain nearly spherical glass beads. Samples were held in bottles purged with dry N2, inside a desiccator until required. The model of ideal associated solutions considers a melt as an ideal solution of chemical groupings each having the stoichiometry of crystalline phases existing within the equilibrium phase diagram, including the end-member components (single oxides). A binary oxide such as the soda-boria system considered here can be represented by xNa2O·(1 – x)B2O3, with x the 7

molar fraction of soda. The ith stoichiometric compound forming within the system can be written jiNa2O·kiB2O3, ji,ki ∈ ℕ.

If we let index i run first through the M single oxides

composing the system (M = 2 in our case), followed by the (N – M) compounds represented by pairs ji,ki observed in the equilibrium phase diagram, then the number of moles of each are ni with i = (1,2,…M < N) for the single oxides and i = (M + 1,M + 2,…N) for the compounds. The quantities that we seek from our model are the

Xi 

ni

(1)



N

n i 1 i

which are the mole fractions of each of the N components making up the melt. These are calculated using the laws of mass action and mass balance. The law of mass action yields the equilibrium constants

KiM 

X iM  exp   f GiM (T ) / RT  X 1ji X 2ki

(2)

for reactions jiNa2O + kiB2O3 ⇌ jiNa2O·kiB2O3. ΔfGi(T) are Gibbs energies of formation for the ith compound, which are required as inputs for the calculations, and R is the molar gas constant. Equation 2 represents N – M equations whilst the Xi of equation 1 represent N unknown quantities, hence the law of mass balance is required for closure of the system of equations:

x





N 1 n1  i M 1 ji ni , Z

1 x 

(3)





N 1 n2  i M 1 ki ni , Z

Z  n1  n2  i M 1  ji  ki ni . N

(4)

(5) 8

The only required inputs to the model are the (N – M) ΔfGi(T) and the melt composition, which in the binary oxide case is represented by a single parameter, x. To calculate structural parameters such as the B-O coordination number, nBO, one assumes local structural similarity between the melt components and the crystalline compounds of the same composition. Then a simple average is taken, making sure to weight by (1/2ki) where 2ki is the number of boron atoms in a given compound jiNa2O·kiB2O3. The calculated nBO is then

nBO  i 2 N

1 X i nBO,i 2k i

(6)

if nBO,i are the average coordination numbers of boron in B2O3 (i=2) or the ith compound (i > M = 2). 2.0 1257K 1.5 1099K 1.0 943K

S(Q)

0.5 708K 0.0 298K -0.5 -1.0 Short range fitted model (298K)

-1.5 -2.0

0

5

10

15

Q/Å

20

25

-1

Figure 2: Exemplary x-ray structure factors for Na2B4O7 at ambient pressure. Glass at 298 K (150 s measurement), supercooled liquid at 708 K and 943 K (20 s measurements) and equilibrium liquid at 1099 K and 1257 K (8 s measurements). The lowest (broken) curve is a fit 9

to the short range structure at 298 K (see Fig. 3 caption). Vertical offsets have been applied for clarity.

16 1257K

12

1099K

943K

T(r) / Å-2

8 708K

4 298K

0 Total

-4

B-O O-O Na-O B-B

-8 0

1

2

3

4

5

r/Å Figure 3: Exemplary x-ray correlation functions for Na2B4O7. Glass at 298 K (150 s measurement), supercooled liquid at 708 K and 943 K (20 s measurements) and equilibrium liquid at 1099 K and 1257 K (8 s measurements). Qmax = 24.47 Å-1 or 20 Å-1 (1099 K and 1257 K). The five lower curves show model peaks fitted to the 298 K data. The following parameters were always held fixed: rBB = 2.41 Å, 〈uBB2〉1/2 = 0.070 Å, nBB = 3.5, rOO = 2.41 Å, rNaO = 2.40 Å, whilst at room temperature it was necessary also to fix 〈uNaO2〉1/2 = 0.10 Å,

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nNaO = 5. The choice of fitting constraints had negligible effect on the rBO and 〈uBO2〉1/2 obtained, but introduces a systematic uncertainty in nBO of about 1%. In color online.

Results and Discussion Exemplary x-ray structure factors are shown in Fig. 2, and Fig. 3 shows their Fourier transforms (defined in Ref.

47-48

). In order to extract average B-O coordination number and bond length,

Gaussian distributions convolved with the appropriate peak function,47 were fitted to the first peak circa 1.42 Å. Although contributions from [BO3] and [BO4] units are expected, these are separated by only 0.1 Å, and are not resolved in our experiment. Nearest-neighbor O-O, Na-O and B-B peaks were also modelled as described in Fig. 3 caption. The nBO obtained are plotted in Fig. 1b and display a clear decline with increasing temperature, throughout supercooled and equilibrium liquid regions. rBO also declines with T increasing, from 1.427(2) Å at ambient, to 1.400(1) Å at 1257(15) K (Fig. 4).

11

1.43

Na2B4O7

rBO / Å

1.42 1.41 1.40

-

[BO4/2]-

[BO2/2Onb]-

1.39

B2O3

1.38 400

600

800 1000 1200 1400 1600

T/K Figure 4: Measured average B-O bond lengths as a function of temperature for liquid B2O347 and Na2B4O7. Open squares: 8s measurements, filled squares: 20s measurements. This bond-length contraction is indicative of coordination change due to [BO4/2]-  [BO2/2Onb-], where Onb- is a non-bridging oxygen (bonded to only one B cation), and therefore supports the trend observed in the directly obtained nBO. In liquid B2O3, the B-O bonds within [BO3] triangles expand with coefficient αBO = rBO-1 ∂rBO/∂T = 3.7(2) x 10-6 K-1 (Fig. 4).47 nBO and rBO can be related using the empirical bond-valence method,53 which yields   R (T )  rBO (T )   nBO (T )  VB  exp  BO   b   

1

(7)

where VB = 3 is the formal boron valence, b = 0.37 Å is an empirical constant, and we have introduced a temperature-dependent bond-valence parameter RBO(T) = RBO(298 K) [1 + αBO(T – 298)] which accounts for normal B-O bond thermal expansion, with αBO and RBO(298 K) = 12

1.377(1) Å taken from Ref. 47. The above procedure (equation 7) applied to the rBO(T) of molten B2O347 yields nBO = 3, independent of T, whilst the results for molten Na2B4O7 are plotted in Fig. 1b. There is a systematic offset to higher values for the nBO(T) derived from equation 7 as compared to those determined directly from fitting, and this appears larger at high T. Note that the correction for αBO in equation 1 is negative (≤ 0.04 in magnitude), and so brings the two sets of nBO(T) closer together. We believe that the main reasons for the difference are systematic uncertainties inherent in direct determination of nBO, which arise from absolute normalization of the diffraction data. In the case of B2O3 nBO of 2.87(3) (at 298 K) to 2.78(2) (at 1707(24) K), rather than 3 were found,47 and we therefore estimate the systematic uncertainty on nBO to be 5%. Bond-lengths measured by diffraction have smaller uncertainties, of order 0.1%, and the nBO derived from equation 7 are considered more reliable. Possible sources of uncertainty in bondvalence derived nBO are effects secondary to coordination change which nonetheless affect B-O bond lengths to a minor extent, such as changes in B-O-B bond angles and non-bridging oxygen content.54 We have therefore used error bars in Fig. 1b to illustrate the size of this correction and resulting uncertainty.

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Boron species %

Na2B4O7

Na2B8O13

60

40

20

NaBO2

NaB3O5

B2O3 0 800

1000

1200

1400

1600

T/K Figure 5: Temperature dependence of chemical species present in Na2B4O7 melt, according to the thermodynamic model of ideal associated solutions. Results are normalized to a single B atom per formula unit so that they are relevant to the fractions of B environments of each grouping in the melt (equation 6). The (super)structural units associated with the dominant groupings in the melt at low and high T are inset to left and right respectively. Note that the components with higher melting temperatures tend to dominate at higher T. Average nBO were calculated from the thermodynamic model of ideal associated solutions using crystallographic values for each compound,39-41,

46, 55-65,66

and are shown in Fig. 1. The only

important contributions to the Na2B4O7 melt structure are found to be from NaBO2, Na2B4O7, NaB3O5 and Na2B8O13 (Fig. 5). The nBO prediction for the glass is in good agreement with reported measurements26-29 and the result derived from rBO herein, whilst being slightly lower than a published TD model.37-38 Above Tg, our TD model diverges from the published result,37-38 and nBO initially drops off more rapidly with T. Following this the TD model predicts an asymptotic limit of nBO ≈ 3.16, approached for T ≳ 1400 K (boiling point ≈ 1850 K). Note that

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using nBO = 3.375 for α-Na2B4O741 leads to a result in disagreement with numerous measurements on Na2B4O7 glass (Fig. 1). Indeed Wright45 has argued that assumption of the diborate group (nBO = 3.5) as the borate anion in Na2B4O7 yields better agreement between TD model and experimental nBO, for glasses. This assumption is not necessary if one uses Na2B4O739-40 (nBO = 3.5), despite the fact that it contains different polyanions (equal numbers of dipentaborate and [BO4] groups). This raises an important issue regarding TD modelling where multiple polymorphs exist. Ideally free energies for all polymorphs should be input, whereas, thermodynamic data is often only available for a single (not always identified) polymorph. This leads to additional uncertainty in any TD model, along with measurement uncertainties of the thermodynamic data itself. Judged by x-ray diffraction data, our TD model is an improvement on those published.4,

37-38

Qualitatively, the experimental data do not hint at an asymptotic approach to a high-T limiting nBO, however, measurement to higher T would be required to determine if this difference is real. Quantitatively, the experimental nBO are offset to lower values compared to the TD model (Fig. 1b). Furthermore, there is a discrepancy between room-temperature measurement and those close to Tg, despite the fact that no structural rearrangement for T < Tg can occur. In addition to aforementioned sources of uncertainty in TD model and experimental nBO, there is uncertainty arising from temperature gradients, ΔT, across the levitated droplet. Such ΔT can lead to mismatch in T between volumes probed by pyrometry and the x-ray beam, despite the fact that these are close together within the upper hemisphere of the droplet.

From the

discrepancy between TD model and our two sets of nBO(T) derived from equation 7, we estimate ΔT of 130-260 K at Tg and 60-100 K at Tmelt. These values are large but not unreasonable given the single-sided laser-heating setup, while the fact that ΔT apparently decreases with increasing T 15

is expected based on the rapidly decreasing viscosity and increased mixing. On the other hand, the TD model should not be expected to give exact predictions given its inherent assumptions. Indeed, although the Na2O-B2O3 phase diagram shows many adjacent phases mix close to ideally, the presence of eutectics belies the underlying assumption of ideality. As such, the

3.5

3 + x/(100 - x)

Tg(x)

900

Kodama et al. Feller et al.

3.4

nBO = 3 + N4

Tg / K

observed similarity of measured and modelled nBO(T) is remarkable.

nBO(x) Bray & O'Keefe Kroeker et al.

3.3

673K 873K 1073K 1273K 1473K 1673K

3.2 3.1

800

700

600

3.0 0

20

40

60

80

x / mol% Na2O Figure 6: nBO(x,T) of the thermodynamic model compared to 11B NMR determinations for glasses26, 29 (open symbols). Glass transition temperatures67-68 (filled symbols, right ordinate axis) are overlaid to demonstrate the correlation between nBO and Tg for x ≲ 20 mol% Na2O. In color online. Compositional dependence of the TD model is illustrated in Fig. 6 which shows that temperature dependence of nBO is predicted only for 20 < x < 50 mol% Na2O, and that the models are in fair agreement with literature data26, 29 on glasses (comparison should be made for T ≈ Tg e.g. Ref. 6769

, Fig. 6). The observed broad maximum in Tg(x) (Fig. 6) has been related to the maximum in

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nBO(x) using temperature dependent topological constraint theory.69 This relationship is based on the Adam-Gibbs70 relation between viscosity and configurational entropy, SC, of the melt. Since Tg can be considered to occur at a fixed viscosity of 1012 Pa s, it can be shown that SC(Tg) is approximately inversely proportional to Tg.69 From this point, SC(Tg) is argued to be proportional to the number of floppy modes71 and therefore to the difference between the network dimensionality and the number of degrees of freedom per atom. It is this latter quantity which depends largely on nBO in the Na borate case and therefore nBO and Tg should be approximately proportional. In Fig. 6 it can be seen that indeed Tg and nBO are correlated for x ≲ 20 mol% Na2O, however, above this composition they diverge. This divergence has been explained69 by invoking a constraint onset temperature, which is a fitting parameter of the temperature dependent topological constraint theory. Remarkably however, the regions of distinct Tg(x) dependence line up with regions of the TD model with distinctly different T dependencies (Fig. 6), and may well be causally linked. Qualitatively, the rise in Tg with x < 20 mol% Na2O would be expected to continue above 20 mol% Na2O if the nBO of the melts followed the trend for the glasses, based on constraint counting arguments alone (without invoking any constraint onset temperature).69 However, for x > 20 mol% Na2O, the supercooled melts have lower nBO than the glasses, and therefore lower viscosities - there are isothermal viscosity maxima circa 20 mol% Na2O72 - with higher fragilities,23-24, 69 such that the melts can supercool to lower T, before glass transition ensues.

Our data and models indicate that temperature dependence of the

number of constraints is of great importance, and knowledge of nBO(x,T), such as is provided by the TD model, could eliminate the need for empirical fitting of constraint onset temperatures. On the other hand, the predictive ability of temperature dependent topological constraint theory appears to break down as soon as the number of constraints becomes T dependent. This is

17

because in order to predict Tg within the theory, one is required to know the number of degrees of freedom per atom at Tg – the calculation becomes intractable. The present results, along with the approximate inverse proportionality between SC(Tg) and Tg69 imply that temperature dependent structural changes in the intermediate composition region (20 < x < 50 mol% Na2O) increase the configurational entropy and thereby suppress Tg. This is a qualitatively reasonable result which also follows from the fact that configurational heat capacity is increased by temperature driven structural rearrangements20 and this in turn increases SC(Tg).70

Boron species %

a) 80

873K

B2O3

1:1

1:9

1:3

60

3:1

1:2

1:5

40 20

1:4 2:1

0

Boron species %

b) 80

B2O3

1273K 1:1

1:4

3:1

60 40 20 1:3 1:2

1:9

2:1

0 0

20

40

60

80

x / mol% Na2O Figure 7: TD model species distributions at a) 873K and b) 1273K. Normalized per B as in Fig. 5, equation 6. Labels ji:ki represent stoichiometries of jiNa2O.kiB2O3. Whilst our model shows considerable similarity to those published3,

37-38, 61, 73

(Fig. 7), a key

qualitative difference is that it predicts an extremely simple NaBO2 melt structure, based solely

18

on the NaBO2 grouping, Fig. 7, and therefore on B3O63- metaborate ring anions, as in crystalline sodium metaborate. This in part explains the observed gap in glass formation, from about 40 to 60 mol% Na2O.74 Although existing Raman evidence75 is not interpreted in this way, we note that Raman spectra for NaBO2 melt show very little variation with temperature,75 in contrast to lower Na2O compositions.30-31 We note that published measurements14-16 and a TD model76 for nAlO(T) in molten CaAl2O4 agree at least semi-quantitatively in this unusual case77 in which Al-O coordination in the melt exceeds that in the corresponding glass and crystal. Conclusions In conclusion, we have demonstrated the existence of a continuous structural transition in molten Na2B4O7 and that this can be reasonably well predicted by the thermodynamic model of ideal associated solutions. The thermodynamic model predicts temperature dependence of the B-O coordination only in the composition region 20 – 50 mol% Na2O, and we argue that this is manifest in the broad maximum observed in the glass transition temperatures, Tg(x). These results bear relevance to industrial glass design and manufacture, the theory of topological constraints, crystal growth from the melt of materials such as non-linear optical borates,17-19 geochemistry, and the understanding of melt rheology, fragility and the glass transition. Acknowledgements Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. OLGA, JKRW, AL, AT and CJB

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were supported by U.S. DOE grant No. DE-SC0007564. Thanks to Diane Holland, University of Warwick, for helpful discussions. References 1. Mauro, J. C.; Ellison, A. J.; Allan, D. C.; Smedskjaer, M. M., Topological model for the viscosity of multicomponent glass‐forming liquids. Int. J. Appl. Glass. Sci. 2013, 4, 408-413. 2. Mauro, J. C., Topological constraint theory of glass. Am. Ceram. Soc. Bull. 2011, 90, 31-37. 3. Shakhmatkin, B. A.; Vedishcheva, N. M.; Shultz, M. M.; Wright, A. C., The thermodynamic properties of oxide glasses and glass-forming liquids and their chemical-structure. J. Non-Cryst. Solids 1994, 177, 249-256. 4. Zhang, Z.; Reddy, R. G., Structure model and properties of alkali borate melts. Miner. Process. and Extr. Metall. 2005, 114, 192-199. 5. McMillan, P. F.; Wilson, M.; Wilding, M. C.; Daisenberger, D.; Mezouar, M.; Greaves, G. N., Polyamorphism and liquid–liquid phase transitions: challenges for experiment and theory. J. Phys.: Condens. Matter 2007, 19, 415101. 6. Meadley, S. L.; Angell, C. A., Water and its relatives: the stable, supercooled and particularly the stretched, regimes. arXiv preprint arXiv:1404.4031 2014. 7. Brazhkin, V. V.; Katayama, Y.; Trachenko, K.; Tsiok, O. B.; Lyapin, A. G.; Artacho, E.; Dove, M.; Ferlat, G.; Inamura, Y.; Saitoh, H., Nature of the structural transformations in B2O3 glass under high pressure. Phys. Rev. Lett. 2008, 101, 035702. 8. Zeidler, A.; Wezka, K.; Whittaker, D. A. J.; Salmon, P. S.; Baroni, A.; Klotz, S.; Fischer, H. E.; Wilding, M. C.; Bull, C. L.; Tucker, M. G.; Salanne, M.; Ferlat, G.; Micoulaut, M., Density-driven structural transformations in B2O3. Phys. Rev. B 2014, 90, 024206. 9. Zeidler, A.; Wezka, K.; Rowlands, R. F.; Whittaker, D. A. J.; Salmon, P. S.; Polidori, A.; Drewitt, J. W. E.; Klotz, S.; Fischer, H. E.; Wilding, M. C.; Bull, C. L.; Tucker, M. G.; Wilson, M., High-pressure transformation of SiO2 glass from a tetrahedral to an octahedral network: a joint approach using neutron diffraction and molecular dynamics. Phys. Rev. Lett. 2014, 113, 135501. 10. Brazhkin, V. V.; Katayama, Y.; Lyapin, A. G.; Saitoh, H., P-T phase diagram and structural transformations of molten P2O5 under pressure. Phys. Rev. B 2014, 89, 104203. 11. Brazhkin, V. V.; Farnan, I.; Funakoshi, K.-i.; Kanzaki, M.; Katayama, Y.; Lyapin, A. G.; Saitoh, H., Structural transformations and anomalous viscosity in the B2O3 melt under high pressure. Phys. Rev. Lett. 2010, 105, 115701. 12. Skinner, L. B.; Benmore, C. J.; Weber, J. K. R.; Wilding, M. C.; Tumber, S. K.; Parise, J. B., A time resolved high energy x-ray diffraction study of cooling liquid SiO2. Phys. Chem. Chem. Phys. 2013, 15, 8566-8572. 13. Wei, S.; Stolpe, M.; Gross, O.; Evenson, Z.; Gallino, I.; Hembree, W.; Bednarcik, J.; Kruzic, J. J.; Busch, R., Linking structure to fragility in bulk metallic glass-forming liquids. Appl. Phys. Lett. 2015, 106, 181901. 14. Drewitt, J. W. E.; Hennet, L.; Zeidler, A.; Jahn, S.; Salmon, P. S.; Neuville, D. R.; Fischer, H. E., Structural transformations on vitrification in the fragile glass-forming system CaAl2O4. Phys. Rev. Lett. 2012, 109. 15. Hennet, L.; Pozdnyakova, I.; Bytchkov, A.; Drewitt, J. W. E.; Kozaily, J.; Leydier, M.; Brassamin, S.; Zanghi, D.; Fischer, H. E.; Greaves, G. N.; Price, D. L., Application of time resolved x-ray diffraction to study the solidification of glass-forming melts. High Temp.-High Press. 2011, 40, 263-270.

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TOC graphic

3.4 3.3 3.2 3.1 3.0

Glass 400

800

Equilibrium melt 1200

T/K

1600

Temperature dependent local structure

3.5

1000

Tg / K

Na2B4O7

Boron-Oxygen coordination

3.5

Tmelt

Supercooled melt

Boron-Oxygen coordination

Tg

Tg(x)

900

3.4

nBO(x,T)

3.3

673K 873K 1073K 1273K 1473K 1673K

3.2 3.1

800 700 600

3.0 0

20

40

60

80

x / mol% Na2O

24