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Continuous Structural Transition in Glass-Forming Molten Titanate BaTiO Oliver L G Alderman, Chris J. Benmore, Anthony Tamalonis, Samuel Sendelbach, Steve M. Heald, and Richard Weber J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08248 • Publication Date (Web): 01 Nov 2016 Downloaded from http://pubs.acs.org on November 4, 2016

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The Journal of Physical Chemistry

Continuous Structural Transition in Glass-Forming Molten Titanate BaTi2O5 O.L.G. Aldermana,b,*, C.J. Benmoreb, A. Tamalonisa S. Sendelbacha, S. Healdb, R. Webera,b a. Materials Development, Inc., Arlington Heights, IL 60004, USA b. X-Ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA *Corresponding author [email protected]

Abstract The structure of the model titanate glass former BaTi2O5 has been studied over a wide temperature (T) range in the molten, supercooled and glassy states under conditions of aerodynamic levitation. Both high-energy x-ray diffraction and Ti K-edge x-ray absorption spectroscopy reveal a continuous structural transition involving reduction of the cation-oxygen (and oxygen-cation) average coordination numbers and bond lengths with increasing T. Ti-O coordination in the moderately supercooled and equilibrium melt follows a linear trend nTiO = 5.4(1) − [3.5(7) × 10−4]T [K] (1300 ≤ T ≤ 1830 K, Tg = 960 K, Tm = 1660 K). Comparison to the melt-quenched glass implies an increase in ∂nTiO/∂T at lower T, as Tg is approached from above. Both Ba-O coordination and bond length also decrease at higher T, and the role of Ba addition is to reduce nTiO below its value in pure molten TiO2, which is related to the presence of density maxima in molten BaO-TiO2. Density measurements made by imaging of the levitated melt yielded ρ(T) = 4.82(55) – 0.0004(3)T, in units of K and g cm-3. Whilst BaTi2O5 glass likely consists of a fully connected Ti-O network, free of non-bridging oxygen (NBO) [OTi1] and with at least 13(4)% [OTi3] triclusters, the 1835(40) K equilibrium melt contains at least 10(4)% NBO along with 90(4)% bridging oxygen [OTi2]. The results highlight the fact that glasses can be considered as structural analogues of melts only for those melts deeply supercooled into the glass transition region. The results imply possible fictive T dependence of titanate glass structure, suggesting applications as e.g. laser written waveguides with large refractive indices, and refractive index contrasts. The temperature dependent structure further implies a super-Arrhenian melt viscosity with consequences for glass manufacture, titanate rich slags produced in iron smelting, TiO2 bearing magmas and, by analogy, silicate melts at high pressures, as found in planetary interiors.

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1. Introduction The structure and properties of molten oxides are of critical importance across a diverse range of natural and industrial settings. Melt viscosity is a key structure-dependent parameter in glass batch melting, fining, forming and annealing1-2 as well as in metallurgical smelting3-9 where viscosity must be low enough to allow separation of the molten metal and oxide slag. The temperature (T) dependence of melt viscosity is described as increasingly ‘fragile’ the more it departs from Arrhenian behavior, and this departure is driven by changes in configurational entropy,10-12 and thereby the local and intermediate scale structure, of the melts with T.13-14 Studies of fragile glass-forming melts including aluminates14-16 and borates17-22 have revealed T dependence of the network forming cation-oxygen coordination numbers of B3+ and Al3+. Here we focus on Ti-O coordination of tetravalent titanium in a novel silica-free glass-forming titanate BaTi2O5.23-25 Titanate and TiO2 bearing glasses tend to have excellent optical properties, including refractive indices as high as 2.3 and Abbe numbers as low as 17.26 This allows for the replacement of heavy metal oxides27 by titania,28 leading to lightweight glasses with lower mass densities and lower potential toxicity hazards, whilst maintaining the desired optical properties. At low concentrations, titania is used as a nucleating agent in glass-ceramics29-30 and in ultra-low thermal expansion TiO2-SiO2 glass formulations.3133 TiO2 rich slags in ferrous metallurgy are becoming increasingly common due to increased usage of cheaper, lower-grade ores such as those rich in ilmenite (FeTiO3) and vanadium-titanium magnetite.3, 5-9 TiO2 rich melts have also been investigated34 as candidate systems for direct electrochemical reduction e.g., for metal production with low CO2 emissions or extraterrestrial resource generation.35 Crystalline titanates, including ferroelectric BaTiO336 and BaTi2O5,23, 37-39 are an important class of materials and the growth of high quality crystals from the melt depends on knowledge of its transport properties and thereby structure. TiO2 is a constituent of natural silicic rocks, melts and magmas,40-41 but also represents a useful analogue for SiO2 at much higher pressures,42 Ti4+ having a larger ionic radius and typically higher coordination numbers to oxygen than does Si4+. Hence the study of molten titanates can shed light on the behavior of natural silicate melts at depth within planetary interiors. Titanate materials exhibit considerable structural complexity, with ambient pressure phases containing Ti4+ on tetrahedral and octahedral sites, as well as in 5-fold coordination to oxygen. For example, even within the BaO-TiO2 pseudobinary system one finds [TiO4] tetrahedra in Ba2TiO4,43-44 [TiO5] polyhedra in metastable β-BaTi2O5,24 and the more common [TiO6] octahedra in BaTiO3 perovskite,36 among others. Amorphous TiO2 has an average Ti-O coordination number of nTiO ≈ 5.5,45-46 lower than the known crystalline polymorphs which are built from octahedra. A diffraction measurement of aerodynamically levitated molten TiO2 yielded yet lower nTiO = 5.0(2) at T = 2250(30) K.46 The physical properties of molten TiO2 make it rather unstable under aerodynamic levitation and therefore difficult to supercool or obtain structural information systematically as a function of T. Nonetheless, molecular dynamics models46 in agreement with available diffraction and density measurements predicted a continuous evolution of the Ti-O coordination in the melt given by nTiO = 5.85(2) − [3.0(1) × 10−4]T [K], and furthermore predicted nTiO of the hypothetical glass in agreement with measurements on amorphous films.45-46 In melt-quenched glasses nTiO has been measured to be close to five,24, 47-53 and has been suggested to exist mostly in different types of 5-fold polyhedra, including [TiO1+4] with a short titanyl 2 ACS Paragon Plus Environment

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bond in K2O.TiO2.2SiO2,49-50 or with [TiO4+1] in BaTi2O5 glass.24 Dingwell et al.48 and Farges et al.51-52 showed that nTiO in titanosilicate glasses depends on the type of alkali or alkaline earth modifier present, as well as on the silica content. Such composition dependence of nTiO is also inferred from the measured densities of titanosilicate melts.40, 42, 54 Furthermore, nTiO in a Rb2O.TiO2.4SiO2 glass-forming melt was inferred to be T dependent47 with an implied nTiO = 5.26 − [3.0 × 10−4]T [K]. Farges et al.53 on the other hand stated that “No clear evidence was found for a significant change in the average nearest-neighbor coordination environment of Ti” in the alkali titanosilicate melts studied, and anomalous heat capacity changes55-58 were therefore associated with structural rearrangements on longer length scales. Nonetheless, those authors53 reported that lower quench rates resulted in lower nTiO for a TiO2 doped K2O.2SiO2 glass, whilst the pre-Ti K-edge x-ray absorption feature in Na2O.TiO2.2SiO2 melt was clearly observed to increase in height with melt T, implying a reduction in nTiO. Measured alkali titanosilicate melt densities42 also imply nTiO decreasing with increasing T, with ∂nTiO/∂T varying from zero in melts bearing only tetrahedral Ti, up to around –15.0 × 10−4 K-1.42 The Ti-O coordination numbers discussed above have been derived from glasses using neutron diffraction,24 sometimes using Ti isotope substitution,49-50 x-ray diffraction24, 45-46 and Ti K-edge X-ray Absorption Near Edge Structure (XANES) spectroscopy.24, 47-48, 50-53 The nTiO measured for melts however are almost entirely derived from the pre-edge features of Ti K-edge XANES spectra,47, 53 which is a semiquantitative method. A neutron diffraction study59 (without the use of Ti isotopic substitution) of molten K2O.TiO2.2SiO2 reported insensitivity to any changes in nTiO. Here we use both Ti K-edge XANES spectroscopy and high-energy x-ray diffraction to study the novel glass-forming BaTi2O5 titanate glass, equilibrium melt and supercooled melt in-situ under conditions of aerodynamic levitation. The use of diffraction allows for direct quantification of nTiO due to the absence of silica and the limited overlap of Ti-O and Ba-O bond-length distributions. We thereby measure directly the function nTiO(T) in an effort to determine if changes can be detected, to quantify how large these might be, and discuss the findings in the context of molten and glassy titanates and oxides in general. 2. Experimental Details Materials. Polycrystalline beads suitable for levitation, and of diameter ≈ 2 mm, were obtained by CO2 laser melting of mixtures of BaTiO3 (Aldrich, 99.995%) or BaCO3 (Cerac, 99.999%) and TiO2 (Aldrich, 99.99%) in a water-cooled copper hearth.60 1g of precursor powder mixture was obtained by weighing appropriate amounts of reagents to yield a 1:2 Ba:Ti ratio into an HDPE bottle and tumble mixing with a single alumina mixing bead. Larger beads of ≈ 3 mm diameter were used for density measurements. Aerodynamic levitation and laser heating. The scattering, spectroscopic and physical property data presented herein all exploit the combination of aerodynamic levitation and laser heating to allow the study of high temperature molten and supercooled liquid materials. Levitation eliminates scattering and absorption of probe (e.g. x-ray) beams by a container, as well as chemical contamination by container material, and increases the propensity for supercooling and glass formation by elimination of heterogeneous nucleation of crystals at the melt-container interface. In a typical experiment a 2 to 3 mm diameter bead of sample material is levitated on a gas stream flowing through a converging-



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diverging conical nozzle. A 500 W, 10.6 μm, CO2 laser impinges onto the top of the sample from above, and sample temperature is measured by optical pyrometry in the infrared region.61-62 Melt Density Measurements. Volumes of the levitated molten droplets were estimated by ellipse fitting to their outline in photographs taken with suitable filters in place, and assuming rotational symmetry. Densities were then obtained using the measured sample masses which remained within 0.1 mg, or 0.14% during the course of measurement. A low profile Al levitation nozzle was used in order to maximize the amount of sample that was imaged using a Nikon D3200 camera which viewed the sample along the horizontal direction, in profile (Fig. 1). The camera was equipped with an 80 mm extension tube and a 70-210 mm zoom lens set to approximately 150 mm focal length. The front of the camera lens was fitted with a 5X close up lens, an 8X neutral density filter and a 670 ± 5 nm bandpass filter. This arrangement enabled self-illumination of the hot sample over a range of temperatures that could be selected by adjusting the camera shutter speed. A shutter speed of 1/800 s was used and typically 20 frames collected (at 4 fps, 200 ISO) at each temperature point. Temperature was measured with a single color pyrometer (Chino model IRCS) sighted onto the top of the sample where it was also being heated. The apparent temperature was corrected using a Wien’s displacement law approximation63 with a spectral emissivity value of 0.87 at the pyrometer wavelength of 0.9 μm. Pyrometer temperature was also corrected for reflection losses from a lens that was in the optical path. The length scale was calibrated using precision steel ball bearings of 2.78, 3.0 and 3.5 mm diameters (2.5 μm precision) placed in the levitation nozzle. These solid samples were imaged in silhouette using a bright halogen backlight and ellipse fitting yielded an average calibration factor of 2.40(2) μm/pixel. After calibration, the halogen lamp was switched off and measurements were made on hot samples without any changes to the set up. BaTi2O5 samples of approximately 3 mm diameter were levitated on pure O2 gas on a convergingdiverging conical nozzle, open to the air. The laser power was held fixed during each set of 20 frames which were analyzed using edge-detection and ellipse fitting to yield average volumes of rotation. Since the sample symmetry is not typically known, two volumes of revolution were derived by rotating about the minor and major axes of the fitted ellipse, and the mean was taken as the result. The low profile nozzle used allowed for the viewing of a large proportion of the sample profile (Fig. 1 inset), necessary for accurate ellipse fitting (it is essential that the equator be clearly above the nozzle rim). However, levitation was also much less stable than in a typical nozzle, often leading to movement and deformations of the sample. With clear outliers (sample shape obviously non-ellipsoidal, nonsymmetrical, or touching or wetting to the nozzle) removed, typical standard deviations in sample density between frames taken at a given temperature varied between about 0.5 and 9% and we estimate the typical accuracy of the method to be 5%, as indicated by the error bar in Fig. 1. As a check on the calibration, a molten Al2O3 sample was measured for comparison to literature values64 from electrostatic levitation, which are more accurate, in part due to the full profile of the sample being visible. Over the range 2373 ≤ T ≤ 2573 K our results agreed with those published64 within an average deviation of 2.5%. The apparent thermal expansion however was larger by a factor 7.4, which is an effect observed in other high temperature self-illumination measurements,65-66 compared to shadow casting.67-68 Top-to-bottom temperature gradients across the droplet are reduced to some extent by 4 ACS Paragon Plus Environment

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forced convection driven by the levitation gas jet, but nonetheless can lead to overestimation of the average temperature (measured at the top) and overestimation of the sample volume (cooler base at higher density occluded by nozzle). These two systematic effects cancel one another to some extent, with the primary uncertainty (overestimation) being in the temperature range of the measurements, as opposed to the linear ρ(T) relation (section 3, Fig. 1). Ti K-Edge X-ray Absorption Spectroscopy. XANES spectra were collected at the Ti K-edge on beamline 20-BM-B of the Advanced Photon Source (APS, Argonne, IL, USA) with an unfocussed beam cross-section of 2.5 mm wide by 1.0 mm high. Similar experiments on levitated melts, at the Fe K-edge, have been previously described.69-70 The choice was made to optimize measurements for the XANES region, and not the EXAFS region because: i) the latter is strongly damped at high temperatures; ii) shorter measurement times mitigate against compositional drift in the sample due to incongruent volatilization. The chamber enclosing the sample included a large x-ray outlet window with its normal perpendicular to the incident x-ray beam and facing a 13-element Ge detector (Canberra Lege with XIA Xmap electronics) for measuring the fluorescence signal from the sample. Inserts were used on both x-ray inlet and outlet ports to reduce the x-ray path length through the chamber gas to circa 1 cm prior to absorption by the sample and circa 1 cm for the fluorescence (see Supporting Information Fig. S1). This was done to reduce absorption by Ar bearing gas mixtures (Helium is not suitable for aerodynamic levitation), with the remaining paths outside of the thin (9 μm) Kapton windows purged continuously with He. The two thin Kapton windows located only about 10 mm from the hot melts throughout the measurements were periodically checked for damage. They were found to withstand the measurement conditions well, and only to incur damage (and therefore leak) in the unusual event of a macroscopic portion of hot sample impinging upon them, necessitating their replacement. Ionization chambers, one upstream and two downstream of the sample position were used to measure transmission through a Ti metal foil for energy calibration (first inflection point of the edge set to 4966.0 eV), as well as for measurements on finely powdered recovered samples mounted on tape. A Si(111) double-crystal monochromator was used, with energy resolution ΔE/E = 1.4 x 10-4 or 0.70 eV at the Ti K-edge. This is to be compared to the intrinsic width due to the core-hole lifetime of 0.94 eV,71 which yields a total expected width after convolution of about 1.3 eV. XANES spectra were collected from 150 eV below to 380 eV above the Ti K-edge. Fine, 0.2 eV, steps in the range 15 eV below to 50 eV above the edge were used. Total measurement time was about 10.33 minutes per spectrum. The absorption length, μ(E), in molten BaTi2O5 is about 16 μm at 4900 eV and decreases to about 7.5 μm above the edge, at 5000 eV. The thickness of the samples relative to μ(E) required the fluorescence intensities to be corrected due to the effects of self-absorption. This effect arises due to modulation of μ(E), and thereby the probed volume of the sample, as the x-ray energy is stepped through the edge of interest, and results in a suppression of the spectral features above the edge and an enhancement of the pre-edge region. The larger the contribution of the element of interest to the total absorption coefficient, the larger the effect. Here we have used the Fluo algorithm72 available within Athena.73 This correction is applicable to flat-plate sample geometry, and therefore not necessarily suited to the liquid and solid beads of the present study (approx. 1.0 mm radii of curvature). However, we tested the algorithm on Fe K-edge measurements of a pure iron sphere placed within the levitator nozzle and 5 ACS Paragon Plus Environment


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compared the results to that obtained by transmission measurement through a reference Fe foil. It was found empirically that the choice of 45o incident and 20o ± 10o take-off angles gave a suitable correction at least up to about 100 eV above the edge, beyond which the intensities are overcorrected slightly, presumably due to the curved sample geometry.70 Levitation gas flow was turned off when measuring the fluorescence signal from room-temperature beads quenched from the melts. This was to reduce noise due to motion of the more irregularly shaped (compared to melts) polycrystalline beads. Temperature was measured as described above for the density measurements, with an additional correction for reflection losses from a silica window that was in the optical path. XANES spectra were corrected and normalized using the IFEFFIT software74 via the Athena interface73 as described in detail elsewhere.69-70 In order to isolate the pre-edge peaks (Fig. 2), two Lorentzian peaks were fitted to the main edge, with the energy range containing the pre-edge peaks excluded. The isolated pre-edge peaks were then characterized by integrating over the interval 4965.0 ≤ E ≤ 4972.0 eV to obtain their total areas, and deriving the first moment of the distribution to yield the centroid position. This was found to give similar results to those obtained by fitting a series of Gaussian lineshapes and excluding those centered at E > 4972.0 eV. High-Energy X-ray Diffraction. X-ray diffraction measurements were made at beamline 6-ID-D of the APS using 100.23 keV x-rays and an aerodynamic levitation furnace.46, 75 Diffraction patterns were collected during cooling of melts in two ways i) isothermal 60 s measurements during stepwise cooling from 1835(40) K, ii) 300 ms measurements during free cooling from 1930(40) K after switching off the heating laser, which yields the highest cooling rate (Fig. 3, inset) and is the only way glass was obtained from the BaTi2O5 melt, as long as a sample diameter ≲ 2mm was used.23-24 The maximum cooling rate of -450 Ks-1 was reached shortly after cutting the laser power, and this reduced to about -110 Ks-1 at Tg. The reported temperatures were averaged over each 300 ms measurement window. Measured mass losses imply negligible compositional drift for the rapidly quenched sample, and loss of < 0.33 mol% BaO from the step cooled sample. The glass obtained by rapid cooling was measured for 300 s duration. An area x-ray detector (Perkin Elmer XRD1621, 2048 x 2048 pixels of 200 μm x 200 μm Tl doped CsI) was used with sample-to-detector distance of 332.0 mm. Temperature was measured using 5 μm wavelength optical pyrometry, the long wavelength being chosen to avoid near-infrared transparency of the melts at the lower temperatures investigated. Apparent temperature was corrected using a Wien’s displacement law approximation63 with a spectral emissivity value of 0.88 estimated from the Fresnel losses for a material with a refractive index of 2.05.25 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 from the ambient BaTi2O5 glass density of 4.56 g cm-3,25 an estimated glass volume thermal expansion coefficient of α = 4.0 × 10−5 K-1,42 a BaTi2O5 melt volume expansion coefficient interpolated from those of molten TiO254 and molten BaTiO3,67-68 and using the estimated glass density at Tg = 960 K23 as a fixed point, see Fig. 1. This estimate was found to be consistent with the measurements described above (see section 3), as well as the literature data used in its derivation, and was used in preference to extrapolation of fits to the experimental density data, which cover a limited temperature range. The diffraction data reduction and definitions of the scattering functions used are given elsewhere.46, 75 The measured structure factors, S(Q), represented as functions of Q = (4πsinϑ)/λ, with 2ϑ the scattering 6 ACS Paragon Plus Environment

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angle, and λ = 0.12370 Å the x-ray wavelength, were Fourier transformed with Qmax = 20 Å-1 for the ≥ 60 s measurements. The 300 ms data were noisier due to the factor 1/200 in measurement time, which necessitated a reduced Qmax = 15 Å-1, and resultant lower real-space resolution, Δr. In all cases, no modification (window) function was used, in order to avoid further reduction of Δr. Quantification of the local cation-oxygen coordination environments was achieved by sequential peak fitting46, 75 to the leading edge of the main Ti-O peak in T(r), followed by the leading edge of the main BaO peak in the residual, and finally by fitting of a 2nd Ti-O peak, at longer interatomic distance, to the remaining residual. 3. Results Melt Density. The measured melt densities (Fig. 1) are least-squares fitted by a linear trend ρ(T) = 4.82(55) – 0.0004(3)T, with T in Kelvin. This is in reasonable agreement with the estimated ρ(T) = 4.7496 – 0.00032T (Fig. 1), and slightly in excess of the values reported by Ikemiya et al.76 for a 35 mol% BaO titanate melt, which can be represented by ρ(T) = 4.69 – 0.0004T. We note that backlighting and silhouetting for hot molten samples is a preferable technique to the selfillumination method employed here, because it allows measurements over a wider temperature range for a given setup.77 However, no suitable backlight was available at the time of measurement, the halogen lamp giving insufficient contrast with hot samples in the 670 ± 5 nm region, whilst laser sources at other wavelengths (with suitable filters) tended to produce either speckle patterns (HeNe laser) which interfere with the edge detection, or had azimuthally varying divergence (405 nm diode laser) which distorted the silhouette. UV backlighting of the sample has been used with evacuated electrostatic levitation,64, 67-68, 78 but this has the undesirable effect of producing toxic ozone via photolysis of O2 in air. Ti K-Edge XANES. In the high temperature melt, the post absorption edge XANES and EXAFS features are strongly damped compared to those of the room temperature glass, Fig. 2, due to Debye-Waller type thermal disordering. On the other hand the pre-edge peak is strongly enhanced by more than 30% in integrated area, Table 1. Although thermal motion likely contributes to symmetry lowering and hence to the pre-edge peak enhancement,79 such effects are typically less than that observed,80 and the larger peak for the melt phase is indicative of a lower average Ti-O coordination number.81-82 Hence a structural transition is implied between the equilibrium melt, with average nTiO between 4 and 5, and the glass obtained via supercooling, with average nTiO reported to be close to 5.24, 83 Note that no difference was observed in the melt spectrum between measurements in oxidizing and highly reducing atmospheres (Table 1). This implies that very little reduction of Ti4+ to lower valence states occurred, either due to structural stabilization of tetravalent Ti, or due to slow redox kinetics compared to the experimental timescale (despite forced convective mixing due to the levitation gas jet). Nonetheless, quenching the reduced melt resulted in crystallization rather than glass formation, with the resulting material being black in appearance, presumably due to a very small fraction of Ti3+ cations. The small fraction of Ti3+ therefore appear to act as nucleation sites, suppressing glass formation, and in the present case allowing the formation of γ-BaTi2O5, as identified from the XANES spectrum, Fig. 2.24 7 ACS Paragon Plus Environment


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High-Energy X-ray Diffraction. Diffraction patterns for glassy and molten BaTi2O5 are shown in Fig. 3. Whilst the most obvious changes in low Q ≲ 7 Å-1 structure, associated with intermediate range ordering, are broadening with increasing T, the changes in high Q structure include a clear change in periodicity, indicative of a change in short range structure, as expected in light of the Ti K-Edge XANES results above. Exemplary Fourier transforms of the diffraction patterns are shown in Fig. 4, and yield the total correlation, or pair distribution functions, which are weighted distributions of interatomic distances. The most striking difference between glass and melt, other than the large increase in thermal broadening at high T, is the fact that the nearest-neighbor peaks arising from bonded Ti-O and Ba-O pairs appear at shorter distances in the melt. This is the opposite effect to that expected for simple isotropic thermal expansion of the bonds, and is associated with reduced cation-oxygen coordination numbers in the melt, as indicated qualitatively by Ti K-Edge XANES. The average Ti-O bond lengths and coordination numbers extracted from peak fitting are displayed in Fig. 5. The results for the glass are in good agreement with those published.24, 83 4.

Discussion

Temperature Driven Coordination Changes. It is evident in Fig. 5 that both nTiO and rTiO are smaller in the melt and both increase continuously as T decreases toward Tg. Concentrating on the higher realspace resolution (Δr) data (solid squares, Fig. 5), linear extrapolations of the melt data to T = Tg yield nTiO and rTiO that are smaller than those for the room temperature glass (Fig. 5). This implies that the rate of change of both nTiO(T) and rTiO(T), ∂nTiO/∂T and ∂rTiO/∂T, increase as the glass transition is approached from above. In order to obviate the need for extrapolation to Tg, diffraction measurements were taken during rapid cooling (Fig. 3, inset) and glass formation, Fig. 5 (open circles). These data show the same qualitative trend as the higher Δr data, but cover the full range of supercooling, down through Tg and into the hot glass. Unfortunately the increased noise which accompanies the 200-fold reduction in acquisition time does not permit the determination of a change in ∂nTiO/∂T or ∂rTiO/∂T, as Tg is approached from above. The value of ∂nTiO/∂T obtained from a linear fit to the higher Δr data (Fig. 5) is 3.5(7) ×10-4 K-1, very similar to that found in classical molecular dynamics models of molten TiO2 (-3.0(1) ×10-4 K-1),46 and to that implied for Rb2O.TiO2.4SiO2 glass-forming melt47 from Ti K-edge XANES spectra (-3.0 × 10−4 K-1). Note however that the total average ∂nTiO/∂T obtained by assuming that nTiO(298K) = nTiO(Tg = 960K) is larger, at -6.7(1) ×10-4 K-1. All of these values are within the range inferred from comparison of Ti K-edge XANES pre-edge spectra to changes in the partial molar volume of TiO2 in alkali titanosilicate melts.42 Changes of similar magnitude have been observed around trivalent networkformer cations Al3+ and B3+, e.g. ∂nAlO/∂T = +2.0 ×10-4 K-1 in CaAl2O415 and ∂nBO/∂T ≈ -5.0 ×10-4 K-1 in Na2B4O7.17 Similarly to Ti-O, the Ba-O distance and coordination appear to decrease with T in the melt, Fig. 6. The nBaO are somewhat less quantitative than the nTiO due to the fact that intensity from the O-O partial likely contributes to the fitted Ba-O peak areas, and any longer Ba-O bonds in an asymmetric distribution with high r tail are not considered. See the MD models of Inoue et al.83 for example. Nonetheless, the peak position clearly shifts to lower r in the melt, indicative of a coordination decrease. The fractional change in bond length is about -4.4%, larger than that for Ti-O of about -1.5 to -2.0%. Similarly the change in Ba8 ACS Paragon Plus Environment

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O coordination between glass and melt is about -27%, whilst the change in nTiO is -7 to -11% over the T range of the high Δr dataset. Again, the linear extrapolation of the melt data in Fig. 6 down to Tg yields much smaller values than found for the glass, suggesting that the local structure must begin to change much more rapidly as Tg is approached from above. Again the rapid cooling data (not shown) do not clarify the situation due to a large scatter in the fit parameters owing to the increased noise in the data, as well as the lower real-space resolution (Qmax = 15 Å-1) chosen to partially mitigate against the effects of high Q noise. This lower Δr leads to increased overlap of the Ti-O and Ba-O peaks and an increased covariance between fit parameters. Hennet et al.14, 84 studied the x-ray structure factor of CaAl2O4 as the equilibrium melt was supercooled to form a glass. Those authors reported nAlO(T), rAlO(T), and the width, ΔQ1(T), and height, S(Q1,T), of the first sharp diffraction peak (FSDP). All four parameters showed changes in slope at a temperature T = 1.25Tg which they associate with the dynamical crossover temperature at which viscosity becomes clearly super-Arrhenius in fragile liquids. We do not observe any such obvious discontinuities in our equivalent data for BaTi2O5 (Fig. 5, 6 and 7), despite better statistics and much less overlap between Ti-O and Ba-O real-space peaks, cf. Al-O and Ca-O. The structural parameters derived from the higher resolution data in Fig. 5, 6 and 7 do imply an increase in the rates of change, as Tg is approached from above, but this is not directly observed due to crystallization (at the relatively low cooling rate). The data taken during rapid cooling are too noisy to reveal any discontinuity in the real-space peak parameters. However, the FSDP parameters are obtained from the least noisy, low Q, part of the diffraction pattern, and the rapid cooling data in Fig. 7 reveal a) changes in the slope of Q1(T) at Tg and at 0.85Tg, b) that the width ΔQ1(T) decreases linearly with decreasing T, even through Tg. Hence there is no direct evidence for a sudden structural change in the supercooled liquid that can be associated with a dynamical crossover.

The parameters of the two individual Ti-O peaks fitted to the T(r,T), Fig. 5a, shed light on the mechanism of Ti-O coordination change. As T increases, the average short Ti-O bond (of which there are about nTiO(1) = 3.8) has a constant length of 1.849(2) Å, while the longer bonds increase in length from 2.111(5) Å to 2.131(5) Å over the 1308(21)-1835(40) K temperature interval. The overall mean bond length decreases over this T interval (Fig. 5a), facilitated by the number of short bonds growing from 3.8(1) to 3.9(1), and the number of longer Ti-O bonds diminishing from 1.2(1) to 0.9(1) at higher T. This situation is highly reminiscent of phenomena observed in the crystalline state, for example, in rutile TiO2 the two longer axial bonds of the [TiO6] octahedra have thermal expansion coefficients 1.4 to 7.4 times larger than those of the four, shorter, equatorial bonds.85-86 Average Ti-O coordination in the glass is 5.33(9), and therefore at least 33(9)% of the Ti4+ likely occupy 6fold [TiO6] sites. In the melt nTiO ≲ 5 (4.97(9) at 1308(21) K to 4.74(11) at 1835(40) K, high resolution data), such that there are few or even zero [TiO6], whilst the number of tetrahedral [TiO4] likely increases at high T, up to about 26(11)%, assuming the remaining 74(11)% are 5-fold [TiO5]. Alternatively, one can consider the average O-Ti coordination, nOTi = (cTi/cO)nTiO, the ci being atomic fractions. In the glass nOTi = 2.13(4), such that at least 13(4)% of the O2- are likely bound in [OTi3] 9 ACS Paragon Plus Environment


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triclusters. In the melt, nOTi ≲ 2 (1.99(4) at 1308(21) K to 1.90(4) at 1835(40) K, high resolution data), such that there are few or even zero triclusters, whilst the number of non-bridging oxygen [OTi1] atoms likely increases at high T, up to about 10(4)%, assuming the remaining 90(4)% are bridging oxygen [OTi2]. The effect of oxygen triclusters and non-bridging oxygen have been discussed extensively in the context of aluminate and aluminosilicate melts and glasses,87-91 and their interconversion with increasing temperature in the titanate melt can be expected to increase the melt fragility. Melt Density and the Role of Barium. It is noteworthy that, as a function of BaO-TiO2 melt composition, a density maximum exists76 such that e.g. the molten BaTi2O5 is more dense than both of the bracketing TiO2 and BaTiO3 compositions, as can be seen in Fig. 1. This is reminiscent of the density maxima, and extrema observed in various physical properties, of binary germanate and borate glasses.92-96 These so called germanate and borate anomalies have been related to composition dependent changes in Ge-O and B-O coordination numbers.92, 96-100 As such, one might expect the Ti-O coordination to vary, or even pass through a maximum with varying BaO-TiO2 melt composition. Comparison to the structure of molten TiO2, which, in the T range of this study, contains Ti with close to 5.4 O neighbors46 (Fig. 5b), implies that Ba2+ modifier cations tend to lead to a reduction in the Ti-O coordination. This may be driven by the need to accommodate the large Ba2+ cations, necessitating a more open network structure, facilitated by Ti-O units with fewer bonds and larger Ti-O-Ti bond angles. If the trend were to continue up to the BaTiO3 melt composition one would expect yet lower nTiO (linear extrapolation of nTiO(T = 0 K) and ∂nTiO/∂T yields a predicted nTiO = 5.18 − [3.75 × 10−4]T [K]). Note that whilst the bond lengths are observed to contract with increasing temperature, overall bulk thermal expansion is supported by the decreasing FSDP position, Q1, from 1.97(1) Å-1 in the glass to 1.90(1) Å-1 in the 1930(40) K melt, Fig. 7. This peak in the x-ray structure factor of metal oxides and silicates is typically dominated by metal-metal pair terms,101 and in this case by the dominant Ba-Ti (and Ba-Ba) pair terms. The metal-metal periodicities, 2π/Q1, in the melts increase from 3.19(2) Å in the glass to 3.30(2) Å in the 1930(40) K melt, with concomitant decrease in the correlation lengths, 2π/ΔQ1, from 12.5(4) Å to 8.2(2) Å respectively, where ΔQ1 is the FSDP Lorentzian full-width at half maximum. The number of ordered metal cation shells, Q1/ΔQ1, therefore decreases from about 3.9 to 2.5. Implications for the Viscous Behavior of Titanate Melts and Slags. Viscosity is a key parameter for industrial processes involving molten oxides, including glass production1-2 and metallurgical smelting.3-9 Replacing SiO2 with TiO2 in a melt reduces the viscosity dramatically.3-8 The temperature dependence of the titanate melt structure observed herein furthermore implies fragile behavior – super-Arrhenius temperature dependence of the viscosity and other transport properties – and therefore an increased propensity of the supercooled titanate melts to crystallize. At superliquidus temperatures titanate melts are therefore very fluid, reducing their ability to stabilize foams3 and increasing both metal/slag separability and gas permeability.7 Analogy to High-Pressure Silicate and Germanate Liquids and Glasses. Titanate melts are analogues for germanates and silicates since all are based on tetravalent (network former) cations, M4+. M-O coordination numbers typically increase with increasing cation radius, Ti4+ > Ge4+ > Si4+, and so the titanate materials are structural analogues for high pressure germanates and silicates, because M-O 10 ACS Paragon Plus Environment

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coordination numbers typically also increase with increasing pressure.102-105 This has been observed in both the crystalline and amorphous states, for example, rutile (6-fold M) is the stable ambient pressure TiO2 polymorph, whilst rutile SiO2 (stishovite) is stable only above pressures of about 8.7 GPa. In the amorphous state, Si is almost exclusively found in tetrahedral environments at ambient pressure,103, 106107 whilst germanate glasses can contain Ge on tetrahedral as well as 5- and 6-fold sites,92, 97, 99-100, 108-109 and titanate melts and glasses have yet higher average nMO.24, 46, 49-50, 83 High pressure molten silicates bear particular relevance to the Earth’s and planetary interiors,102-103 but experimental study is challenging under such extreme conditions. The study of titanate melts as analogues of high pressure silicate melts and glasses obviates the need for pressure cells and allows for collection of high quality scattering and spectroscopic information. The results of this study suggest that, whilst M-O coordination tends to increase with pressure, increasing the temperature of a molten silicate will tend to counteract that change, bringing the density and nMO back down. This further implies that the viscosity of molten silicates at pressure should become increasingly fragile (super-Arrhenius), and the glass-forming tendency will therefore decrease. The structure-composition-pressure relationship in JaO-SiO2 (J a mono- or divalent metal, a = 1, 2) systems is therefore expected to be complex. At ambient pressure only [SiO4] tetrahedra are present, but at intermediate pressures one would expect germanate-type Si-O coordination maxima as a function of JaO, modifier oxide, content. At yet higher pressures, the limited data available for molten titanates suggest that these coordination maxima may disappear, since the BaTi2O5 melt has lower nTiO than molten TiO2 (Fig. 5b),46 cf. e.g. CaGe2O5 glass which is close to the Ge-O coordination maximum.92 This latter point may however be particular to the barium titanates, and indeed both nTiO and nGeO depend not only on T and P, but also on the type of modifier cation(s) present.92, 97, 99-100, 108-111 Quantitative estimates of the ‘silicate equivalent pressure’ of germanate or titanate melts or glasses, at which Si-O coordination matches Ge-O or Ti-O coordination of the ambient pressure analogue, is therefore difficult, because values obtained from comparisons to in-situ measurements or modelling studies on high pressure silicates will not transfer to different compositions. Of course, analogies can only go so far. One key difference is that the Ti-O bond is 10.7 to 11.7% longer than the Si-O bond for a given coordination number (between 4 and 6), as estimated from bond-valence parameters.112 If one were to scale down the titanate structure accordingly, the Ba-O bonds would approach those expected for Ca-O, since Ba-O bonds are 13 to 14% longer than Ca-O bonds.112 Therefore BaTi2O5 is a reasonable analogue for CaSi2O5 at high P, within a scaling factor of ~12%, and measuring e.g. the viscosity of molten BaTi2O5 could provide useful insight into the dynamics of the geologically relevant calcium silicate melt at depth. CaSi2O5 glass at 10 GPa113 has a similar nSiO to nGeO in ambient CaGe2O5 glass,92 the titanate analogue, with higher nMO is therefore representative of yet higher P > 10 GPa. Finally, one would expect solubilities of metal cations in silicate melts to increase with pressure, and the immiscibility gaps found at ambient pressure114 to close at sufficiently high pressures. This is by analogy to titanate systems which do not show two-liquid regions in the equilibrium phase diagrams at ambient pressure.



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Applied Titanate Glasses and Ceramics. The structural changes occurring in supercooled molten BaTi2O5 imply that the structure (as well as density) of the glass may vary with its fictive temperature. Titanate glasses may therefore represent suitable target materials for e.g. laser written waveguides115-116 with large refractive indices, and refractive index contrasts. Furthermore, the phase-selection during devitrification of titanate glasses to obtain ferroelectric glass-ceramics23-24 is likely sensitive to the thermal history of the glass. 5. Conclusions Temperature-driven changes in the local structure of molten titanate BaTi2O5 have been observed by high-energy x-ray diffraction and Ti K-edge XANES spectroscopy of the aerodynamically levitated liquid. The measurements represent the first direct, quantitative assessment by diffraction of the temperature dependence of the titanium-oxygen coordination and bond lengths in a molten oxide. In fact both nMO and rMO are observed to decrease with increasing T for M = Ti and Ba, with the fractional changes being larger for the Ba cations. The linear trend nTiO = 5.4(1) − [3.5(7) × 10−4]T [K] observed for the equilibrium melt down to moderate supercooling (1300 ≤ T ≤ 1830 K, Tg = 960 K, Tm = 1660 K) must deviate to larger negative values of ∂nTiO/∂T at lower T, as Tg is approached from above, by comparison to measurements on the melt-quenched glass. This deviation was not resolved in rapid 300 ms diffraction measurements during quenching owing to increased noise. Longer (lower noise) measurements at deeper supercooling were precluded by crystallization of the melt. The role of barium is to reduce nTiO below its value in pure molten TiO2, which is related to the existence of density maxima with composition in the molten BaO-TiO2 system. Whilst both BaTi2O5 glass and the high temperature melt contain predominantly bridging oxygen species [OTi2], at 1835(40) K the melt contains at least 10(4)% non-bridging oxygen (NBO) [OTi1], whilst the glass contains at least 13(4)% [OTi3] triclusters and may be NBO free. The results highlight the fact that glasses cannot be considered as structural analogues of melts in general except in the deeply supercooled, narrow glass transition region. The observed structural transition implies possible fictive T dependence of titanate glass structure, suggesting applications as e.g. laser written waveguides with large refractive indices, and refractive index contrasts. Furthermore a super-Arrhenian melt viscosity is implied, with consequences for glass manufacture, handling of titanate rich slags found in ferrous metal smelting, TiO2 bearing magmas and, by analogy, silicate melts at high pressures as found in planetary interiors. Supporting Information Drawings of environmental chamber used for synchrotron x-ray measurements. Acknowledgements Work was supported by U.S. Department of Energy (DOE) under grant number DE-SC0007564 (OLGA, AT, SS, RW). Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. DOE Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.


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79. Yamamoto, T., Assignment of Pre-Edge Peaks in K-Edge X-ray Absorption Spectra of 3d Transition Metal Compounds: Electric Dipole or Quadrupole? X-Ray Spectrom. 2008, 37, 572-584. 80. Hiratoko, T.; Yoshiasa, A.; Nakatani, T.; Okube, M.; Nakatsuka, A.; Sugiyama, K., Temperature Dependence of Pre-Edge Features in Ti K-Edge XANES Spectra for ATiO3 (A= Ca and Sr), A2TiO4 (A= Mg and Fe), TiO2 Rutile and TiO2 Anatase. J. Synchrotron Radiat. 2013, 20, 641-643. 81. Farges, F.; Brown Jr, G. E.; Rehr, J. J., Coordination Chemistry of Ti(IV) in Silicate Glasses and Melts: I. XAFS Study of Titanium Coordination in Oxide Model Compounds. Geochim. Cosmochim. Ac. 1996, 60, 3023-3038. 82. Farges, F.; Brown, G. E.; Rehr, J. J., Ti K-Edge XANES Studies of Ti Coordination and Disorder in Oxide Compounds: Comparison Between Theory and Experiment. Phys. Rev. B 1997, 56, 1809. 83. Inoue, H.; Masuno, A.; Kohara, S.; Watanabe, Y., The Local Structure and Vibrational Properties of BaTi2O5 Glass Revealed by Molecular Dynamics Simulation. J. Phys. Chem. B 2013, 117, 6823-6829. 84. Hennet, L.; Pozdnyakova, I.; Bytchkov, A.; Drewitt, J. W. E.; Kozaily, J.; Leydier, M.; Brassamin, S.; Zanghi, D.; Fischer, H. E.; Greaves, G. N., et al., Application of Time Resolved X-ray Diffraction to Study the Solidification of Glass-Forming Melts. High Temp.-High Press. 2011, 40, 263-270. 85. Sugiyama, K.; Takeuchi, Y., The Crystal Structure of Rutile as a Function of Temperature up to o 1600 C. Z. Kristallogr.-Cryst. Mater. 1991, 194, 305-314. 86. Henderson, C.; Knight, K.; Lennie, A., Temperature Dependence of Rutile (TiO2) and Geikielite (MgTiO3) Structures Determined Using Neutron Powder Diffraction. Open Mineralogy Journal 2009, 3, 111. 87. Toplis, M. J.; Dingwell, D. B.; Lenci, T., Peraluminous Viscosity Maxima in Na2OAl2O3SiO2 Liquids: The Role of Triclusters in Tectosilicate Melts. Geochim. Cosmochim. Ac. 1997, 61, 2605-2612. 88. Stebbins, J. F.; Oglesby, J. V.; Kroeker, S., Oxygen Triclusters in Crystalline CaAl4O7 (grossite) and in Calcium Aluminosilicate Glasses: O-17 NMR. Am. Mineral. 2001, 86, 1307-1311. 89. Lee, S. K.; Lin, J.-F.; Cai, Y. Q.; Hiraoka, N.; Eng, P. J.; Okuchi, T.; Mao, H.-k.; Meng, Y.; Hu, M. Y.; Chow, P., X-ray Raman Scattering Study of MgSiO3 Glass at High Pressure: Implication for Triclustered MgSiO3 Melt in Earth's Mantle. Proc. Natl. Acad. Sci. USA 2008, 105, 7925-7929. 90. Jakse, N.; Bouhadja, M.; Kozaily, J.; Drewitt, J. W. E.; Hennet, L.; Neuville, D. R.; Fischer, H. E.; Cristiglio, V.; Pasturel, A., Interplay Between Non-Bridging Oxygen, Triclusters, and Fivefold Al Coordination in Low Silica Content Calcium Aluminosilicate Melts. Appl. Phys. Lett. 2012, 101. 91. Skinner, L. B.; Barnes, A. C.; Salmon, P. S.; Fischer, H. E.; Drewitt, J. W. E.; Honkimaki, V., Structure and Triclustering in Ba-Al-O Glass. Phys. Rev. B 2012, 85, 064201. 92. Alderman, O. L. G. The Structure of Vitreous Binary Oxides: Silicate, Germanate and Plumbite Networks. University of Warwick, 2013. 93. Ivanov, A. O.; Evstropiev, K. S., Structure of Simple Germanate Glasses. Dokl. Akad. Nauk SSSR 1962, 145, 797. 94. Murthy, M. K.; Ip, J., Some Physical Properties of Alkali Germanate Glasses. Nature 1964, 201, 285-286. 95. Lower, N. P.; McRae, J. L.; Feller, H. A.; Betzen, A. R.; Kapoor, S.; Affatigato, M.; Feller, S. A., Physical Properties of Alkaline-Earth and Alkali Borate Glasses Prepared Over an Extended Range of Compositions. J. Non-Cryst. Solids 2001, 293, 669-675. 96. Wright, A. C., Borate Structures: Crystalline and Vitreous. Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 2010, 51, 1-39. 97. Hannon, A. C.; Di Martino, D.; Santos, L. F.; Almeida, R. M., Ge-O Coordination in Cesium Germanate Glasses. J. Phys. Chem. B 2007, 111, 3342-3354. 98. Hoppe, U.; Kranold, R.; Weber, H. J.; Neuefeind, J.; Hannon, A. C., The Structure of Potassium Germanate Glasses - a Combined X-ray and Neutron Scattering Study. J. Non-Cryst. Solids 2000, 278, 99114. 17 ACS Paragon Plus Environment


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99. Ueno, M.; Misawa, M.; Suzuki, K., On the Change in Coordination of Ge Atoms in Na2O-GeO2 Glasses. Physica B & C 1983, 120, 347-351. 100. Alderman, O. L. G.; Hannon, A. C.; Holland, D.; Umesaki, N., On the Germanium–Oxygen Coordination Number in Lead Germanate Glasses. J. Non-Cryst. Solids 2014, 386, 56-60. 101. Alderman, O. L. G.; Hannon, A. C.; Holland, D.; Feller, S.; Lehr, G.; Vitale, A. J.; Hoppe, U.; Von Zimmermann, M.; Watenphul, A., Lone-Pair Distribution and Plumbite Network Formation in High Lead Silicate Glass, 80PbO.20SiO2. Phys. Chem. Chem. Phys. 2013, 15, 8506-8519. 102. Lee, S. K.; Cody, G. D.; Fei, Y.; Mysen, B. O., Nature of Polymerization and Properties of Silicate melts and Glasses at High Pressure. Geochim. Cosmochim. Ac. 2004, 68, 4189-4200. 103. Stolper, E. M.; Ahrens, T. J., On the Nature of Pressure-Induced Coordination Changes in Silicate Melts and Glasses. Geophys. Res. Lett. 1987, 14, 1231-1233. 104. Benmore, C. J.; Soignard, E.; Amin, S. A.; Guthrie, M.; Shastri, S. D.; Lee, P. L.; Yarger, J. L., Structural and Topological Changes in Silica Glass at Pressure. Phys. Rev. B 2010, 81, 054105. 105. Sato, T.; Funamori, N., High-Pressure Structural Transformation of SiO2 Glass up to 100 GPa. Phys. Rev. B 2010, 82, 184102. 106. Schlenz, H.; Kirfel, A.; Schulmeister, K.; Wartner, N.; Mader, W.; Raberg, W.; Wandelt, K.; Oligschleger, C.; Bender, S.; Franke, R., et al., Structure Analyses of Ba-Silicate Glasses. J. Non-Cryst. Solids 2002, 297, 37-54. 107. Mysen, B. O.; Richet, P., Silicate Glasses and Melts: Properties and Structure. Elsevier: 2005; Vol. 10. 108. Schlenz, H.; Rings, S.; Schmucker, M.; Schulmeister, K.; Mader, W.; Kirfel, A.; Neuefeind, J., Short-Range and Medium-Range Order in Amorphous Barium Germanate. J. Non-Cryst. Solids 2003, 320, 133-142. 109. Hoppe, U.; Kranold, R.; Weber, H. J.; Hannon, A. C., The Change of the Ge-O Coordination Number in Potassium Germanate Glasses Probed by Neutron Diffraction with High Real-Space Resolution. J. Non-Cryst. Solids 1999, 248, 1-10. 110. Sakka, S.; Miyaji, F.; Fukumi, K., Structure of Binary K2O.2TiO2 and Cs2O-TiO2 Glasses. J. NonCryst. Solids 1989, 112, 64-68. 111. Miyaji, F.; Yoko, T.; Kozuka, H.; Sakka, S., Structure of Na2O·2TiO2 Glass. J. Mater. Sci. 1991, 26, 248-252. 112. Brese, N. E.; O'Keeffe, M., Bond-Valence Parameters for Solids. Acta Crystallogr. B 1991, 47, 192197. 113. Mead, R. N.; Mountjoy, G., A Molecular Dynamics Study of Densification Mechanisms in Calcium Silicate Glasses CaSi2O5 and CaSiO3 at Pressures of 5 and 10 GPa. J. Chem. Phys. 2006, 125, 154501. 114. Hudon, P.; Baker, D. R., The Nature of Phase Separation in Binary Oxide Melts and Glasses. I. Silicate Systems. J. Non-Cryst. Solids 2002, 303, 299-345. 115. Davis, K. M.; Miura, K.; Sugimoto, N.; Hirao, K., Writing Waveguides in Glass with a Femtosecond Laser. Opt. Lett. 1996, 21, 1729-1731. 116. Gattass, R. R.; Mazur, E., Femtosecond Laser Micromachining in Transparent Materials. Nat. Photonics 2008, 2, 219-225.


Page 19 of 27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1: Ti K-edge XANES measurement conditions and extracted pre-edge peak parameters for various forms of BaTi2O5. Gas mix

T (K)

O2 Ar:5%(99CO:1CO2) O2 Ar:5%(99CO:1CO2) a O2

1990(30) 2032(32) 298 298 298

log p(O2) 0 -10.8

Phase Melt Melt Glass γ-BaTi2O5 Glass

Centroid (eV) ± 0.1 4969.71 4969.69 4969.84 4970.25 4969.84

Intensity (eV) 1.34(20) 1.36(20) 0.98(15) 0.69(10) 0.93(9)

a. Powder transmission measurement.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 27

Figure 1: Mass densities for various titanate materials. Those measured herein for molten BaTi2O5 are represented by grey diamonds and have estimated uncertainties Δρ/ρ = 5%, as illustrated by the error bar on the highest T point. Inset shows an exemplary photograph of the levitated BaTi2O5 melt at 2073 K used to estimate the density by ellipse fitting (white curve) to the limb. Open diamonds represent measurements by Ikemiya et al.76 for a 35 mol% BaO titanate melt. Ambient BaTi2O5 glass density is 4.56 g cm-3.25 The glass density at higher temperatures (black points and line) was estimated using a volume thermal expansion coefficient of α = 4.0 × 10−5 K-1.42 The BaTi2O5 melt density was also estimated (open points, blue line) by interpolating between the measured volume expansion coefficients of molten TiO254 (thick black line) and molten BaTiO3,67-68 (thick red line) and using the glass density at Tg = 960 K23 as a fixed point. The ambient temperature densities of two crystalline polymorphs of BaTi2O5 are shown for comparison.24-25


Page 21 of 27

BaTi2O5

1.2

Normalized XANES

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8

0.6

1990 K melt Glass powder γ-BaTi2O5

0.4

0.4 0.2

0.0 0.0 4970

5000

4975

5050

5100

E / eV Figure 2: Ti K-edge XANES spectra for molten (1990 K), glassy and crystalline BaTi2O5. The glass and crystalline γ-BaTi2O5 were obtained by quenching the levitated melt droplet in oxidizing (pure O2) and reducing (Ar:5%(99CO:1CO2)) atmospheres respectively. Inset: close-up of the pre-edge features. The melt spectrum measured in the reducing gas mixture (not shown) was indistinguishable from that measured in oxygen atmosphere.



-10

0

10

20

30

4 Tm

T/K

1600

3

Q.(S(Q) - 1) / Å-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 27

*

1200

2

Tg 800

1

-2

0

2

t/s

4

6

0 -1

Glass at 298K 300s

-2 5

Melt at 1516K 300ms 60s

10

15

20

-1

Q/Å

Figure 3: Exemplary Q-multiplied x-ray structure factors for supercooled molten and glassy BaTi2O5. The glass was measured for a total of 5 minutes, whilst the melt measurements correspond to a 1 minute measurement taken during stepwise cooling (resulting in crystallization, see inset; recalescence peak marked by asterisk, onset at 1180 K) and a 300 ms measurement taken during rapid cooling (cooling curve inset, resulting in glass formation). Very small Bragg diffraction peaks at Q = 3.08 and 4.36 Å-1 in the glass pattern are due to a small crystalline fraction.


Page 23 of 27

0

D(r) / Å-2

2

2

4

r/Å

6

8

10

Glass at 298K Melt at 1835K

a)

1 0 -1 -2

Ba-Ba

Ba-O

0

Glass at 298K Ba-Ti

2

Ti-O(2)

Ti-O

4

Ti-Ti

b)

T(r) / Å-2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Melt at 1835K

-2

1

2

r/Å

3

4

Figure 4: Real-space x-ray pair distribution functions obtained by Fourier transform of the measured BaTi2O5 diffraction patterns (Fig. 3). a) Comparison of D(r) for the glass and equilibrium melt, 5 minute and 1 minute measurements respectively. b) Corresponding T(r) = D(r) + 4πrρ0 (ρ0 the atomic number density) and 3 peak fits used to obtain local structural information on the Ti-O and Ba-O environments. The data for the melt are offset vertically by -3 Å-2 for clarity. Vertical dashed lines are at the positions of the main Ti-O and Ba-O peaks in the glass and help to clearly show a reduction in peak bond-lengths in the melt.



2.15

a)

rTiO / Å

2.10 1.95

1.90 rTiO mean rTiO(1)

1.85

rTiO(2)

6.0

b) TiO m elt 2

5.5

nTiO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 27

5.0

4.5

4.0 400

800

1200

1600

2000

T/K Figure 5: Local Ti environment structural parameters obtained from peak fitting to T(r) (Fig. 4) as a function of temperature in molten, supercooled and glassy BaTi2O5. Black squares and red open circles are from high and low real-space resolution data respectively. a) Mean Ti-O bond lengths, as well as those for the two individual Ti-O peaks fitted to the high resolution data (open triangles and squares). b) Mean Ti-O coordination numbers nTiO, including those for molten TiO2 from molecular dynamics46 (dash-dot grey line). The vertical lines indicate the glass transition at Tg = 960 K23 and melting point at Tm = 1661 K. Published values for the glass are also shown, from molecular dynamics83 (magenta triangle), neutron diffraction (blue square)24 and x-ray diffraction (green diamonds).24 Linear fits to the highresolution data are shown along with their extrapolations (thin black lines). Extrapolations of the ambient data up to Tg, assuming constant values, are shown (thin dashed lines). This gives a minimum rTiO at Tg, since the bonds in the solid are expected to expand with increasing T, on average.


Page 25 of 27

2.75

rBaO / Å

8

nBaO 2.70

7

nBaO

rBaO / Å

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.65

6 2.60

5

2.55 400

800

1200

1600

2000

T/K Figure 6: Local Ba environment, bond length and coordination number to oxygen obtained from peak fitting to T(r) (Fig. 4) as a function of temperature in molten, supercooled and glassy BaTi2O5. The vertical lines indicate the glass transition at Tg = 960 K23 and melting point at Tm = 1661 K.



3.32

a) 2π/Q1 / Å

3.28

3.24

3.20 S (Q ) - 1

1

3.16

c)

0

-1

-2

2π/∆Q1 / Å

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 27

12

0

2

Q / Å-1

4

10

8

b) 400

800

1200

1600

2000

T/K Figure 7: First sharp diffraction peak parameters obtained from peak fitting to S(Q) – 1 (Fig. 3) as a function of temperature in molten, supercooled and glassy BaTi2O5. a) Periodicities 2π/Q1. b) Correlation lengths 2π/ΔQ1. The vertical lines indicate the glass transition at Tg = 960 K23 and melting point at Tm = 1661 K. c) Exemplary Lorentzian fit to S(Q) – 1 for the 60s measurement of supercooled molten BaTi2O5 at T = 1308(21) K. Shaded regions indicate 1σ uncertainties. Black squares and red open circles are from 60 s and 300 ms measurements respectively.


Page 27 of 27

Ba-Ba

Ba-O

0

Glass at 298K Ba-Ti

2

Ti-O(2)

Ti-O

4

Ti-Ti

TOC Graphic

T(r) / Å-2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Melt at 1835K

-2 1

2

r/Å

3

4


Continuous Structural Transition in Glass-Forming ... - ACS Publications

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