Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “thermal diffusion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Property Measurements of LiF-NaF-KF Molten Salts Doped with Surrogate Fission Products

Measurements of molten salt properties including transition temperatures, phase behavior, heat capacity, density, volumetric thermal expansion, surface tension, viscosity thermal diffusivity, thermal conductivity, and vapor pressure are performed at Argonne. The properties of several fuel and coolant salts including eutectic LiF-NaF-KF (FLiNaK) have been measured. These properties are suitable for use in evaluating reactor performance during startup and early operating conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Property Measurements of LiF-NaF-KF Molten Salts Doped with Corrosion Products and Oxygen

Measurements of thermophysical properties of molten salts are needed for modeling and simulation activities that support the development of molten salt reactor (MSR) technologies. Properties of interest including transition temperatures, phase behavior, heat capacity, density, volumetric thermal expansion, surface tension, viscosity, thermal diffusivity, thermal conductivity, and vapor pressure are being performed at Argonne. Results of these property measurements are suitable for use in evaluating reactor performance during startup and the early operating life of the reactor. Ingressions of oxygen and moisture into the fuel salt are expected to occur at different times during the operating life of the reactor due to system leaks, maintenance, and refueling activities. The presence of these environmental contaminants induces corrosion of structural materials. The introduction of corrosion-derived species, oxygen and moisture is expected to affect the physical and chemical properties of the salt and operation of the reactor. Previous work performed at Argonne evaluated the effects of fission product dopants on the thermal properties of eutectic LiF-NaF-KF (FLiNaK). Properties of FLiNaK are commonly used to represent those of fluoride-bearing fuel salts. Metallic corrosion products such as chromium and nickel ions together with dissolved oxygen are expected to affect system redox differently than the accumulation of fission products. Work summarized in this report was performed to measure the effects of corrosion products and dissolved oxygen on the phase transitions, and specific heat capacity of FLiNaK. Thermophysical property measurements were made using four salts that were prepared by doping aliquots of a eutectic mixture of FLiNaK with surrogate corrosion products. Controlled additions of CrF 3 and NiF 2 were used as surrogates for corrosion product contamination anticipated during extended reactor operations in which fuel salt is in contact with steel reactor components. Controlled additions of UF 4 from two sources containing known amounts of UO 2 at different concentrations were used to represent oxygen contamination. The phase transitions and specific heat capacities of the four salts were measured by using differential scanning calorimetry. Measurements were made at temperatures spanning the range of 500−900 °C, which is the expected operating range of MSRs. Measured property values were compared to values measured previously with eutectic FLiNaK without dopants. Differences between property values measured for the doped and non-doped salts were compared with the uncertainties of the measurements to determine the significance of the effect of corrosion products and oxygen on salt properties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermophysical Properties of Ti3SiC2 MAX Phase Composites with SiC Reinforcement

In the present work, dense (∼100%) Ti 3 SiC 2 composites (TSC) are processed along with 20 vol% of SiC reinforcement (TSC20) via spark plasma sintering at 1400°C, 40 MPa, 15 min, and dynamic vacuum environment. Thermal expansion of both the composites increases from RT to 1273 K and linear fitting of data yields coefficient of thermal expansion (CTE) of 9.4 × 10 −6 K −1 for TSC which decreases to 8.3 × 10 −6 K −1 for TSC20. With increase in temperature from RT to 773 K, specific heat for both TSC and TSC20 composites is observed to increase from 598-850 J.kg −1 .K −1 , whereas thermal diffusivity and thermal conductivity values decrease with testing temperature. SiC reinforcement in Ti 3 SiC 2 resulted in improved thermal diffusivity from 12.7 to 18.7 mm 2 .s −1 and thermal conductivity from ∼57 to ∼79 W.m −1 .K −1 at RT. However, with increase in temperature (773 K), thermal diffusivity and conductivity decrease, and values get closer for both TSC and TSC20 composites. Further extrapolation of thermal conductivity data showed cross-over at ∼973 K due to domination of phonon-phonon scattering and thus lower values of thermal conductivity for TSC20 than TSC. Therefore, reduced CTE and higher thermal conductivity of TSC20 make it a viable choice for applications in high temperatures.

36 MATERIALS SCIENCE↗

Hydrogen transport in yttrium hydride under asymmetric heat

Metal hydrides are a promising moderator material for high temperature fission reactors. Yttrium hydride can be loaded to a high hydrogen density with relatively high hydrogen stability at temperatures up to 800°C. This makes yttrium hydride a potential moderator material for microreactors as foreseen in the fission surface power program. However, during the operation of such advanced reactors temperature gradients are expected which can change the local hydrogen density in the moderator. Hydrogen diffusion in metals is driven by a concentration gradient (Fick’s law) and thermal diffusion (Soret diffusion). Thermal diffusion is the transport of hydrogen, or other species, due to a temperature gradient. For example, hydrogen might migrate from the hot side of a sample to the cold side of a sample. Measuring Fickian diffusion is achieved through various permeation or absorption experiments, however measuring thermal diffusion is challenging and has rarely been performed. The Hydrogen Experimental Apparatus for Thermal Diffusion (HEATD) experiment is designed to induce thermal diffusion in samples and quench those samples so that the hydrogen distribution can be analyzed using hot vacuum extraction (HVE). One side of the sample was heated to a high temperature e.g., 800°C, while the other side of the sample is at a lower temperature. The sample was held under the applied temperature gradient for a given time until the anticipated hydrogen diffusion has occurred. The actual time depends depend on the sample composition and hydrogen concentration. The results from HVE showed that thermal diffusion took place in the specimen and the Soret coefficient was calculated.

36 MATERIALS SCIENCE↗

Impact of neutron irradiation on the thermophysical properties of additively manufactured stainless steel and inconel

The deployment of additive manufacturing (AM) technologies to support the nuclear energy industry is limited by the current lack of data related to the irradiation performance of AM parts. The Colorado School of Mines is conducting a multi-year irradiation and post irradiation examination project to study the impacts of neutron irradiation on stainless steel 316L and Inconel 718 and 625 specimens produced by several commercially available AM techniques and irradiated in the Advanced Test Reactor (ATR) at the Idaho National Laboratory (INL). This paper presents initial results on the impact of neutron irradiation on the heat capacity, the thermal diffusivity, and the thermal conductivity of the specimens at temperatures between 100 oC and 400 oC. The unirradiated AM specimens have heat capacity values similar to, or lower than, the reference values, regardless of manufacturing method or material. The irradiated AM specimens have average heat capacities greater than the unirradiated specimens and reference values in every case. Additionally, the thermal diffusivities of the unirradiated AM specimens are either larger or statistically similar to the reference values. The irradiated AM specimens exhibit lower thermal diffusivities compared to the reference thermal diffusivity values. One of the stainless steel 316L laser powder bed fusion samples exhibited thermal diffusivity values with statistically significant anisotropy prior to and after irradiation. The thermal conductivities of the unirradiated AM stainless steel 316L specimens and the unirradiated Inconel 718 specimens are lower or statistically similar to the reference values. The unirradiated Inconel 625 specimens exhibit slightly higher thermal conductivity values than the reference values. The irradiated specimens show a significant increase in thermal conductivity compared to the unirradiated specimens and the reference values for all materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal transport measurements through the charge density wave transition in CsV 3 Sb 5

We study thermal transport and thermalization in single crystals of CsV 3 Sb 5 through the CDW transition by directly measuring thermal diffusivity (D), thermal conductivity (κ), specific heat (c), and resistivity (ρ). Commensurate with previous reports, we observe a sharp, narrow anomaly in specific heat associated with a first-order transition that results in a CDW state below ~94 K. While a corresponding sharp anomaly in thermal diffusivity is also observed, resistivity and thermal conductivity only exhibit small steps at the transition, where the feature is sharp for resistivity and broader for thermal conductivity. Scrutinizing the thermal Einstein relation κ = cD, we find that this relation is generally satisfied, except in the narrow two-phase regime of the putative first-order transition. Here, the Wiedemann-Franz law as well seems to work outside the two-phase regime, where strong resemblance between the specific heat and the resistivity derivative below the transition may point to a concurrent emergence of a secondary electronic order parameter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermophysical properties of the Ghareb formation relevant for nuclear waste disposal

The Ghareb formation, a shallowly buried porous chalk in Israel, is currently a candidate for nuclear waste disposal. The potential repository is somewhat unique for its host rock and emplacement in shallow (500 m) engineered large diameter boreholes. Herein, the thermal properties of the Ghareb are determined to support design and performance assessment; the relevant properties measured are thermal conductivity, specific heat capacity, thermal diffusivity, and thermal expansion coefficient along with their relationship with varying temperature. For the temperature range of 40 to 275 °C, the thermal conductivity ranges from 0.30 to 1.10 W/m·K, the thermal diffusivity ranges from 0.20 to 0.72 mm 2 /s, and volumetric heat capacity ranges from 0.86 to 2.00 MJ/m 3 ·K. Thermal strain measurements were used to estimate the linear thermal expansion coefficient to be 6·10 –4 –9·10 –2 °C -1 from 40 to 300 °C. These measured properties were used in a thermomechanical model to estimate near-field stresses an hour and 10 years after waste emplacement; the borehole was found to be stable. Thermal loading after 10 years was predicted to elevate local pore pressures by 1–1.5 MPa. The laboratory measurements coupled with analyses are the first attempts at performance assessment characterization for this first of its kind potential repository setting with this chosen host rock.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Technical Guidance on Use of the Netzsch LFA 447 Nanoflash for Measurement of Ceramic-Metallic (Cermet) Pellet Specimen

The Netzsch LFA 447 Nanoflash Instrument uses the laser flash method to measure thermal diffusivity of a material. Thermal conductivity can be determined if specific heat and density are known for that material. The 238 Pu Supply Program is interested in re-establishing the capability to determine thermal diffusivity and thermal conductivity of various 237Np Al/cermet samples during heating. The bottom side of a plane parallel sample is heated by an energy pulse from a light source (in this case a xenon lamp). An infrared (IR) detector is on the top side of the sample which detects the time dependent temperature rise of the sample due to the energy input from the xenon lamp. The LFA 447 Nanoflash is user-friendly, simple to operate, and has minor sample preparation which will allow technicians to be trained easily on its use. When using the multi-property measurement option, the LFA 447 Nanoflash can determine both thermal diffusivity and specific heat which means only density is needed to identify the thermal conductivity of a sample. This equipment is recognized for being highly accurate and having fast test times, replacing steady-state methods which have proven to be difficult and much slower.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Thermal Conductivity Degradation in High Burnup U-Pu-Zr Fuel

Recent advancements in the characterization of irradiated U-Pu-Zr fuels have revealed complexities that challenge existing understanding of constituent redistribution. Traditionally, models have proposed three concentric regions within the fuel, each characterized by distinctive phases and porosity. However, through detailed analysis of high burnup U-Pu-Zr, we discovered the presence of four distinct constituent redistribution regions. Particularly novel is the observation of significant Pu redistribution, a previously unreported phenomenon that necessitates a reevaluation of current models. This work aims to delve deeper into these findings, seeking to correlate mesoscale measurements of thermal diffusivity and respective thermal conductivity with the phases present in each redistribution region. To achieve this objective, we employed mesoscale thermoreflectance methods using the unique, Idaho National Laboratory (INL) developed, Thermal Conductivity Microscope (TCM) at INL’s Irradiated Materials Characterization Laboratory. The TCM employs two tightly focused lasers: one for heating to generate periodic thermal waves in the substrate, and another spatially separated probe laser to detect changes in the optical reflectivity of the gold-coated substrate resulting from thermal wave diffusion. We conducted several thermal diffusivity measurements within each region of constituent redistribution of a U-19Pu-10Zr fuel pin cross section irradiated to 11 at. % burnup. The TCM measurement positions strategically aligned with transmission electron microscopy (TEM) lift-out locations previously collected from the fuel sample. Complementary microstructural analysis techniques such as optical and scanning electron microscopy (OM/SEM), electron probe microanalysis for chemical compositions, and TEM-based selective area electron diffraction (SAED) analysis for crystallographic insights into each phase were also utilized. This comprehensive approach allowed us to correlate local thermal diffusivity data with microstructural characteristics, enabling the computation of local thermal conductivity at each position. The significance of this contribution lies in its pioneering use of the TCM for ternary fuel mesoscale examination, shedding light on the previously overlooked effects of Pu redistribution on local thermal conductivity. By informing current models capturing constituent redistribution and heat transfer, our findings pave the way for more accurate predictions of metallic fuel performance. Moreover, this work sets the stage for future comparisons with similar TCM examinations on U-19Pu-10Zr fuels at ultra-low burnup, facilitating a comprehensive understanding of thermal property changes across different burnup levels. Ultimately, our study not only enriches our understanding of the thermophysical properties of individual redistribution regions within U-Pu-Zr fuel but also offers valuable insights for the design and operational parameters of proposed next-generation fast reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Prediction of divertor heat flux width for ITER pre-fusion power operation using BOUT++ transport code

Prediction of divertor heat flux width is performed for the first and the second pre-fusion power operation (PFPO) phases specified in the new ITER research plan using BOUT++ transport code (Li et al 2018 Comput. Phys. Commun.228 69–82). Here the initial plasma profiles inside the separatrix are taken from CORSICA scenario studies. Transport coefficients in transport code are calculated by inverting the plasma profiles inside the separatrix and are assumed to be constants in the scrape-off-layer. An anomalous thermal diffusivity scan is performed with E × B and magnetic drifts. The results in two scenarios identifying two distinct regimes: a drift-dominant regime when diffusivity is smaller than the respective critical thermal diffusivity χ c and a turbulence-dominant regime when diffusivity is larger than it. The Goldston heuristic drift model and the ITPA multi-machine experimental scaling yield a lower limit of the width λ q . From transport simulations, we obtain the critical thermal diffusivity χ c = 0.5 m 2 s –1 for the PFPO-1 scenario with toroidal magnetic field B = 1.77 T and plasma current I p = 5 MA, and χ c = 0.3 m 2 s –1 for the PFPO-2 scenario with toroidal magnetic field B = 2.65 T and plasma current I p = 7.5 MA. Separatrix temperature and collisionality also have a significant impact on the heat flux width in the drift-dominant regime. The investigation clearly yields a scaling for critical thermal diffusivity ${\chi }_{\text{c}}\propto {A}^{1/2}/(Z{\left(1+Z\right)}^{\frac{1}{2}}{B}_{\text{p}}^{2})$ using ITER scenarios with fixed safety factor q 95 , major radius R, aspect ratio R/a, and the separatrix temperature T sep , and establishes the connection with CFETR and C-Mod discharges. This scaling implies that for a given tokamak device with q 95 , R, R/a, and T sep fixed, a reduction of poloidal magnetic field by a factor of 3 leads to a 9 times higher critical value of thermal diffusivity χ c , possibly yielding a transition from turbulence- to drift-dominant regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermal properties of HfN-MoW surrogate cermet fuel for nuclear thermal propulsion

Here, the thermal properties of MoW-HfN, a surrogate cermet for MoW-UN nuclear thermal propulsion fuel, were characterized over a wide range of elevated temperatures. Thermal diffusivity, coefficient of thermal expansion (CTE), and heat capacity were measured. Optical and scanning electron microscopy were performed to characterize the microstructure and draw structure–property correlations. The thermal diffusivity was obtained using the laser flash method. Diffusivity values ranged from about 0.18 cm 2 /s at 200°C to 0.15 cm 2 /s at 1800°C. The CTE was measured using push-rod dilatometry up to 1600°C, giving values between 6.0 and 9.0 μm/m. A scientific rationalization of the effective material properties is made using the rule-of-mixtures and other effective properties models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Report summarizing demonstration of thermal conductivity measurement methods for coated zirconium cladding

Thermal diffusivity measurements on Zirconium-based cladding materials have historically been a challenge due to the difficulty to measure on specimens with curved geometries, including nuclear grade Zircaloy cladding materials. In this work, we first used Laser Flash Analysis methods to measure the thermal diffusivity of Zircaloy tubes, which show good agreement with Zircaloy plates in this work, as well as previously published data. The consistent results proved the applicability of the Laser Flash Analysis setup for investigating thermal diffusivity of Zircaloy tubes. We further investigate the hydrogen effect on thermal diffusivity of Zircaloy tubes. Hydrogen plays significant roles in temperature dependent thermal diffusivity trends of Zircaloy tube. For low hydrogen concentration, where hydride dissolved into single phase α-Zr at higher temperature, thermal diffusivity is relatively unchanged at low temperature at two phase regions (α-Zr and δ-hydride), and it increases as a function of temperature at single phase α-Zr region. For high hydrogen concentration, where phase transformation (α-Zr + δ-hydride → α-Zr + β-Zr) occurs at 567 °C, thermal diffusivity decreases as a function of temperature below 567 °C before the transformation (α-Zr and δ-hydride), while increase at higher temperature after the transformation (α-Zr and β-Zr).

36 MATERIALS SCIENCE↗

Electron temperature gradient driven transport model for tokamak plasmas

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β'), collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. Furthermore, the electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electron Temperature Gradient Driven Transport Model for Tokamak Plasmas

A new model for electron temperature gradient (ETG) modes is developed as a component of the Multi-Mode anomalous transport module [T. Rafiq \textit{et al.,} Phys Plasmas \textbf{20}, 032506 (2013)] to predict a time dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, $\beta$ and gradient of $\beta$ $(\betap)$, collisionality, safety factor, and toroidicity, where $\beta$ is the ratio of plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

ETG↗

First in operando transient grating spectroscopy measurements on tungsten during high flux plasma operation in PISCES-RF

This work details the construction and first in operando transient grating spectroscopy measurements conducted on PISCES-RF during plasma operation. A preliminary study on a tungsten sample with varied plasma species (Ar and D 2 ), ion flux (4 × 10 21 to 6 × 10 22 ion/m 2 /s), ion energy (5 to 80 eV), and surface temperature (20 to 200 °C) is presented. Prior to plasma exposure, the thermal diffusivity and surface acoustic wave (SAW) speed, (6.9 ± 0.2) × 10 −5 m 2 /s and (2.66 ± 0.02) km/s, were measured in situ with a thermal grating period of 12.5 μm. During Ar plasma exposure, these two quantities vary according to the sample surface temperature. At low flux and varied ion energy, D 2 plasma exposure also results in thermal diffusivity and SAW speed varying with surface temperature alone. At high flux, D 2 plasma exposure results in no convincing change to the thermal diffusivity, but the SAW speed is reduced. After returning to 20 °C, post plasma exposures, the thermal diffusivity and SAW speed almost recover to the initial value prior to exposure.

Surface acoustic wave SAW↗

A Square Pulse Thermoreflectance Technique for the Measurement of Thermal Properties

We report on a laser-based square pulse thermoreflectance (SPTR) technique for the measurement of thermal properties for a wide range of materials. SPTR adopts the pump-probe thermoreflectance principle to monitor the evolution of local temperature after square pulse excitation. The technique features a compact setup, high spatial resolution, and fast data collection. By comparing the acquired SPTR signals with a continuum heat transfer model, material thermal properties can be obtained. Taking advantage of various spot sizes and modulation frequencies, SPTR can measure both the thermal diffusivity and thermal conductivity of poorly to moderately conductive materials and the thermal conductivity of conductive materials with satisfactory accuracy, with potential to be applied to more conductive materials. The technique was validated on three materials: fused silica, single crystal CaF2 and single crystal nickel (with conductivities ranging from 1 W·m -1 ·K -1 to 100 W·m -1 ·K -1 ) with typical measurement errors of 5 % to 20 %. The leading sources of error have been identified by Monte Carlo simulations, and the primary limitations of SPTR are discussed. The compact, fiberized platform we describe here will allow instruments based on this methodology to be deployed in complex, multi-analytical environments for the type of high-throughput correlative analyses that are key to materials design and discovery.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Analysis of radially resolved thermal conductivity in high burnup mixed oxide fuel and comparison to thermal conductivity correlations implemented in fuel performance codes

The thermal diffusivity and thermal conductivity of high burnup (19 % FIMA) mixed oxide (U, Pu)O 2 nuclear fuel has been measured along the radial direction using a thermoreflectance-based method. Measured thermal conductivity exhibits a notable radial variation consistent with the expectations that a large temperature gradient across the annular fuel pellet leads to a heterogeneous microstructure. A common fuel performance model of thermal conductivity, the Lucuta-Inoue model, is used to analyze the measured thermal conductivity profile. Further, this model adequately captures the radial dependence of thermal conductivity except in the periphery. The analysis suggests that the characteristic radial shape of the thermal conductivity profile follows the burnup profile within the fuel pin. In the periphery, the high burnup structure is formed and the conductivity model, not capturing this effect, likely overestimates the thermal conductivity.

36 MATERIALS SCIENCE↗

Thermal properties of field-assisted-sintered SiCN–Y 2 O 3 composites

Polymer-derived amorphous SiCN has excellent high-temperature stability and properties. To reduce the shrinkage during pyrolysis and to improve the high-temperature oxidation resistance, Y 2 O 3 was added as a filler. In this study, polymer-derived SiCN–Y 2 O 3 composites were fabricated by mixing a polymeric precursor of SiCN with Y 2 O 3 submicron powders in different ratios. The mixtures were cross-linked and pyrolyzed in argon. SiCN–Y 2 O 3 composites were processed using field-assisted sintering technology at 1350°C for 5 min under vacuum. Dense SiCN–Y 2 O 3 composite pellets were successfully made with relative density higher than 98% and homogeneous microstructure. Due to low temperature and short time of the heat-treatment, the grain growth of Y 2 O 3 was substantially inhibited. The Y 2 O 3 grain size was ~1 μm after sintering. The composites’ heat capacity, thermal diffusivity, and thermal expansion coefficients were characterized as a function of temperature. The thermal conductivity of the composites ceramics decreased as the amount of amorphous SiCN increased and the coefficient of thermal expansion (CTE) of the composites increased with Y 2 O 3 content. However, the thermal conductivity and CTE did not follow the rule of mixture. This is likely due to the partial oxidation of SiCN and the resultant impurity phases such as Y 2 SiO 5 , Y 2 Si 2 O 7 , and Y 4.67 (SiO 4 ) 3 O.

36 MATERIALS SCIENCE↗