Microgravity effects on nonequilibrium melt processing of neodymium titanate: thermophysical properties, atomic structure, glass formation and crystallization

The relationships between materials processing and structure can vary between terrestrial and reduced gravity environments. As one case study, we compare the nonequilibrium melt processing of a rare-earth titanate, nominally 83TiO2-17Nd2O3, and the structure of its glassy and crystalline products. Density and thermal expansion for the liquid, supercooled liquid, and glass are measured over 300–1850 °C using the Electrostatic Levitation Furnace (ELF) in microgravity, and two replicate density measurements were reproducible to within 0.4%. Cooling rates in ELF are 40–110 °C s−1 lower than those in a terrestrial aerodynamic levitator due to the absence of forced convection. X-ray/neutron total scattering and Raman spectroscopy indicate that glasses processed on Earth and in microgravity exhibit similar atomic structures, with only subtle differences that are consistent with compositional variations of ~2 mol. % Nd2O3. The glass atomic network contains a mixture of corner- and edge-sharing Ti-O polyhedra, and the fraction of edge-sharing arrangements decreases with increasing Nd2O3 content. X-ray tomography and electron microscopy of crystalline products reveal substantial differences in microstructure, grain size, and crystalline phases, which arise from differences in the melt processes.


Pyrometry and temperature corrections
Temperature measurements in ELF used an optical pyrometer sensitive to 1.45-1.8μm radiation, or nominally λ = 1.55 μm.The apparent temperature measured by the pyrometer, Tapp, must be corrected to obtain the absolute temperature, Tabs, according to Wien's law: In Supplementary Equation 1, λ is the pyrometer wavelength, C2 = 1.4388 cm K is the second radiation constant, and   is the effective emissivity, which contains contributions from the sample and any windows (reflective surfaces) between the sample and pyrometer.In ELF, two sapphire windows separate the pyrometer's detector from the sample 1 .The index of refraction, n, and the reflection per window surface, R0, are related by the Fresnel equation: where n1 = 1.77 for sapphire and n2 = 1.0 for air, so R0 = 0.0773.The sample emissivity is estimated as 0.86, based on the previously measured refractive index of 2.2 for lanthanum titanate glass 2 .This yields an effective emissivity of   = 0.86 × (1 -0.0773) 4 = 0.63.The effective emissivity was also estimated via a second approach, using the recalescence temperatures of materials with known melting points.During crystallization from a supercooled melt, the sample is expected to self-heat back up to its equilibrium melting point (Tm) as the latent heat of fusion is released.Using this assumption, the peak temperature of recalescence would correspond to Tm, from which   could be calculated using Supplementary Equation 1 and the measured Tapp.However, this assumption can often fail for at least two reasons: (i) if the liquid has supercooled sufficiently, its latent heat is not sufficient to heat back to Tm (also called hypercooling); (ii) the solid's emissivity is often lower than that of the melt, due to loss of a specular, spherical surface.In both of these scenarios,   would be underestimated by this method based on the recalescence temperature.With that acknowledgement, several recalescence events were analyzed for materials other than the NT samples reported in this paper: Al2O3, Gd2O3, Tm2O3, lanthanum titanate, and barium titanates.Of this set, the   estimates typically ranged 0.6 to 0.7.
Based on these two approaches to estimating   , a value of 0.63 was used for all analyses in this study.The temperature uncertainty arising from   = 0.63 ± 0.05 is ± 30 °C at 1800 °C and is smaller at lower temperatures.
When liquids were held isothermally in ELF, pyrometer noise was typically ± 15 °C (standard deviation).Thus, the overall temperature uncertainty for the ELF measurements in this study is estimated as ± 30 °C.
In the terrestrial aerodynamic levitator, the temperature of liquid samples varies spatially by ~40 °C from top to bottom, since the single heating laser only heats the top of the sample. 3Using the sample emissivity of 0.86 and appropriate window corrections,   = 0.79.The temperature measurement uncertainty arising from   = 0.79 ± 0.05 is ± 27 °C at 1800 °C and is smaller at lower temperatures.

Density analysis and possible measurement artifacts Glass density at room temperature
A literature estimate for NT glass density is available from pycnometry measurements by Arai et al. 4 on lanthanum titanate (LT) glasses.In their study, LT with 18.2 mol.% La2O3 had a density of 4.89 g cm -3 , which is 98.6% of the density for the compositionally identical crystal phase La4Ti9O24 (4.96 g cm -3 ).Assuming the same ratio of glass-to-crystal density, NT glass with 18.2 mol.% Nd2O3 is expected to have a density of 5.10 g cm -3 (using ρ = 5.18 g cm -3 for crystalline Nd4Ti9O24 5 ).Arai et al. also observed a density increase of 2.3% in LT glasses as La2O3 content increased from 15.4 to 18.2 mol.%.Based on our atomic structural characterizations, the NT microgravity glasses likely contained ~19 mol.% Nd2O3, so a linear extrapolation of Arai's compositional trend would yield a final estimate of 5.13 g cm -3 for the MG1 and MG2 glasses here.Thus, the room temperature glass density according to the ELF measurements, 5.28 g cm -3 , is 2.9% larger than the literature-based estimate.
For comparison, the MG1 and MG2 glass densities at room temperature have been assessed using two other techniques in this study, X-ray tomography and light microscopy.The results are summarized in Supplementary Table 2 alongside the ELF measurement and literature-based estimate.The volume calculations from tomography and microscopy are assumed to have uncertainties of ca.5%.In X-ray tomography, uncertainty arises from the image calibration factor and the thresholding algorithm used for image segmentation.For light microscopy, uncertainty arises from focal depth and assuming the sample is a perfect spherical shape.For ELF, an uncertainty of 2.5% is listed in Supplementary Table 2 based on prior reports 6 .For the estimate based on Arai et al. 4 , no uncertainty is given in Supplementary Table 2 since no information on replicate measurements were reported.All four values for glass density in Supplementary Table 2 are almost within their collective uncertainties.

Anomalous thermal expansion near Tg
As discussed in the main text, the density-temperature relationship in Fig. 2 exhibits a steeper slope between 720-930 °C than either the glass or liquid regions.To explain this unexpected observation, several possible scenarios involving measurement artifacts were explored, including: (i) sample transparency to the silhouette backlight, (ii) changes in bubble volume inside the sample, and (iii) sample transparency at the pyrometer wavelength.These are discussed in detail below.
ELF measurements of liquid densities have been shown to be in good agreement with prior (terrestrial) studies, for example with Al2O3 1 , Y2O3 7 , lanthanoid sesquioxides 8 , Ga2O3 9 , Zr 10 , and Au 11 .These examples provide validation of the ELF instrument for measuring liquid density.However, the measurements here for NT are the first to be reported from ELF for glass density upon cooling, so we explored whether transparency of the glassy state may be leading to an underestimation of the sample volume.Specifically, if the sample becomes partially transparent near the wavelength of the ultraviolet backlight, some of the backlight may pass through the edges of the sample, making its silhouette appear smaller in the camera image than the true size.Sample volume is calculated based on edge detection of this silhouette image (see Methods section).The typical ELF sample has a radius of ~120 pixels in the camera image, so if sample transparency introduces an error of ~1 pixel to the edge detection algorithm, a volume error of ~2.5% would result.This error may onset suddenly during cooling if the sample transparency changes at a particular temperature, which matches what is observed in the anomalous density increase (i.e., volume decrease) ca.720-930 °C near Tg = 786 °C.For illustrative purposes, Supplementary Fig. 6a compares the measured data against the hypothetical "true" density suggested by this explanation (green lines).To test this hypothesis, precision spheres of optically-transparent ruby, sapphire, and BK7 glass were levitated at room temperature under vacuum in a ground-based electrostatic levitator that uses the same silhouette imaging technique.The measured volumes of all three standards matched the expected values within 0.5%.This provides strong evidence against the hypothesis of edge transparency causing an underestimation of sample volume.
A second hypothesis for explaining the anomalous 720-930 °C region is that gas bubbles inside the samples shrank suddenly near 930 °C and then became fixed in size as the sample became viscous near Tg.The shrinking bubbles would result in the apparent sample volume decreasing, and the calculated density would increase.Supplementary Fig. 6b provides a comparison of the measured data and the hypothetical density suggested by this explanation.Since the internal voids of the glass samples were measured to be ≤ 0.25% of the total volume, the gas bubbles would have to be 10× larger in the melt to account for the magnitude of the density discrepancy.This seems unlikely.Furthermore, the two replicate samples exhibited reproducible density-temperature relationships (Fig. 2), and it is unlikely that such a bubble process would occur identically in both samples.
A third hypothesis involves the sample becoming partially transparent at the pyrometer wavelength during cooling.If the transition to partial transparency began near 930 °C, then the pyrometer would start seeing some of the radiation emitted by the sample's hotter interior.This would result in a higher reading than the surface temperature, until the sample interior had also cooled enough to become partially transparent.Supplementary Fig. 6c shows a comparison of the measured data and the hypothetical density suggested by this explanation.This scenario seems the most convincing of the considered measurement artifacts, so it was presented in the main text.