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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Emergence of Intermediate Range Order in Jammed Packings

We perform a structural analysis of large scale jammed packings of monodisperse, frictionless and frictional spheres to elucidate structural signatures of the static structure factor in the low-to-intermediate wave number region. We employ discrete element method simulations containing up to 8×10^{7} particles, in which the particle friction coefficient(s), including sliding, rolling, and twisting interactions, are varied. At intermediate wave number values, corresponding to length scales that lie between that of the nearest neighbor primary peak and the system size, we find the emergence of a prepeak-a signature of intermediate range order-that grows with increasing friction. We correlate the emergence of this peak to real space fluctuations in the local particle coordination number, which exhibits a grainy fluctuating field throughout the packing process that is retained in the final, mechanically stable state. While the formation of the prepeak shows varying degrees of robustness to packing protocol changes, our results suggest that preparation history may be used to construct packings with variable large length scale structural properties.

Monti, Joseph M↗
DOE OSTI2026

Reverse segregation and self-organization in inclined chute flows of bidisperse granular mixtures

In the usual segregation scenario for stable inclined chute flows of bidisperse mixtures of fine and coarse spherical particles, coarse particles rise toward the free surface, forming a coarse-rich region atop the flowing pile. Beyond a threshold coarse-to-fine diameter ratio of approximately 4, conversely, the weight of the coarse particles exceeds the segregation driving forces, causing individual coarse particles to sink within the pile and producing a reversed segregation state. However, an understanding of the collective evolution of the pile structure is still lacking when the particle diameter ratio exceeds 4 and the coarse-particle mass fraction is appreciable. To explore this broadly bidisperse limit, we perform discrete element method simulations considering mean particle diameter ratios of up to 8 and coarse-particle mass fractions spanning 0.1 to 0.9. The steady-state flow profiles reveal several intriguing behaviors that depend on the diameter ratio and mass fraction. These include a previously identified transition from usual to reverse segregation and a newfound tendency to self-organize into alternating coarse- and fine-rich particle layers stacked along the shear gradient direction, with layer thickness dictated by the coarse-particle diameter. A fuller understanding of segregation at this scale could pave the way for enhanced mixing or demixing techniques at the commercial scale.

granular flow↗
DOE OSTI2018

More are better, but the details matter: combinations of multiple Fresnel zone plates for improved resolution and efficiency in X-ray microscopy

Fresnel zone plates used for X-ray nanofocusing face high-aspect-ratio nanofabrication challenges in combining narrow transverse features (for high spatial resolution) along with extended optical modulation along the X-ray beam direction (to improve efficiency). The stacking of multiple Fresnel zone plates along the beam direction has already been shown to offer improved characteristics of resolution and efficiency when compared with thin single zone plates. Using multislice wave propagation simulation methods, here a number of new schemes for the stacking of multiple Fresnel zone plates are considered. These include consideration of optimal thickness and spacing in the axial direction, and methods to capture a fraction of the light otherwise diffracted into unwanted orders, and instead bring it into the desired first-order focus. In conclusion, the alignment tolerances for stacking multiple Fresnel zone plates are also considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Additively Manufactured Copper Windings with Hilbert Structure

In this paper, finite element method simulations and frequency analysis of additively manufactured windings with a Hilbert–cross section pattern were performed over a wide frequency range. The current density distributions for the proposed winding conductor and for a square-wire winding conductor at selected frequencies were compared. An approximately 25% winding loss reduction at higher frequencies and an approximately 5% increase at low frequencies were observed for the analyzed Hilbert structure.

Wojda, Rafal↗
DOE OSTI2020

Thermal Overloading Risk Mitigation With a Semi-Analytical Probabilistic Model on Branch Current

A semi-analytical formulation is presented in this paper for the probability computation of branch current in multiphase systems. The developed formula is derived based on the linear power flow model in rectangular coordinates. The system uncertainty injections can be renewable energy resources or loads and are modeled using a Gaussian mixture model (GMM). The developed formula can be used to compute the line current violation probability as well as integrate into optimal power flow problem as chance-constraint relaxation. Here, the proposed formula is first compared with the Matlab embedded numerical integration function to show its performance. Besides, the semi-analytical formula is validated and compared with the Monte Carlo simulation method using the IEEE 123-bus system, EPRI Ckt5, and Ckt7 systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

How Much Chemistry Does a Deep Neural Network Need to Know to Make Accurate Predictions?

In the last few years, we have seen the rise of deep learning applications in a broad range of computational chemistry research problems. Using human-engineered chemical features, such as molecular descriptors and fingerprints, deep learning models have shown similar, if not better performance that most traditional machine learning algorithms. Recently, we reported on the development of Chemception, a deep convolutional neural network (CNN) architecture for general-purpose small molecule property prediction. On average, Chemception matched the performance of expert-developed QSAR/QSPR models trained on chemical features (molecular fingerprints), despite that it was trained on just 2D images of molecular drawings with minimal chemical information. Here, we investigate the effects of systematically removing and adding basic chemical information to the image channels of the 2D images used to train Chemception. By augmenting our images with only 3 additional basic chemical information, we demonstrate the improvement of Chemception performance – that it is now more accurate than contemporary deep learning models trained on ECFP fingerprints for the prediction of toxicity, activity and solvation free energy, as well as physics-based free energy simulation methods for computing solvation properties. By altering the chemical information content in the image channels, and examining the resulting performance of Chemception, we also identify to two different “learning patterns” in toxicity/activity as compared to solvation free energy, and it parallels the fundamental differences in contemporary chemistry research for predicting toxicity/activity and solvation free energy.

Artificial Intelligence, Cheminformatics, Computat↗
DOE OSTI2019

Calculation of Friction Factors and Nusselt Numbers for Twisted Elliptical Tube Heat Exchangers Using Nek5000

Twisted elliptical tube geometries for heat exchanger design are expected to offer significant enhancement in heat transfer with a marginal increase in frictional losses. The presented work focuses on computational fluid dynamics (CFD) simulations of heated molten salt flows through twisted elliptical tube geometries at low modified Froude numbers. In this work, the objectives are to evaluate the available correlations at low Froude numbers and to determine the impact of using a small gap to resolve contact points. The spectral element CFD code Nek5000 was used for all simulations, which were performed in periodic domains of triangular and square unit cells surrounding a single tube through a complete twist using an explicit filtering large eddy simulation (LES) method. The simulation methodology was validated by comparing to the experimental data of Tan et al. Excellent agreement was observed for this comparison. The Dzyubenko correlation for transitional flow was evaluated for a range of Froude numbers. This correlation demonstrated good agreement with LES results at high modified Froude number. As Froude number was decreased toward the bounds of the correlation, the agreement worsened. Cases were then simulated at low Froude number, testing the effects of tube spacing. It was determined that the laminar case for the square unit cell is the most affected by increasing gap size, which should be minimized to mitigate the effect. In the triangular unit cell, the laminar flow regime is also more significantly impacted by increasing gap size compared to the turbulent flow regime which was only marginally impacted.

42 ENGINEERING↗
DOE OSTI2022

Exploring the Effects of Guide Vane on Dimpled Cooling Channel of Gas Turbine Blade

Abstract The purpose of the current study is to find out the heat transfer and pressure drop phenomena of the cooling channel with dimples and guide vane and compare the results with the no guide vane dimpled cooling channel. The first leg of the cooling channel is 490 mm, and the second leg is 460 mm. The two legs relate to the 180 deg turn region. The guide vane was inserted at the bend region of the dimpled cooling channel. The study was conducted with two different guide vanes geometry at two different orientations, i.e., U-guide vane with protrusion and depression orientation and curve-guide vane with protrusion and depression orientations both experimentally and numerically. The numerical study was performed with the large eddy simulation method. The result shows that for both stationary and rotational motion, the U-guide vane with depression experiences the highest thermal performance. The friction factor is comparatively higher for curve-guide vane with protrusion under stationary motion. However, under rotation, the curve-protrusion guide encounters the highest friction factor, which is higher compared to the no guide vane cooling channel.

Energy & Fuels↗
DOE OSTI2013

Measurement of breast tissue composition with dual energy cone-beam computed tomography: A postmortem study

Purpose: To investigate the feasibility of a three-material compositional measurement of water, lipid, and protein content of breast tissue with dual kVp cone-beam computed tomography (CT) for diagnostic purposes. Methods: Simulations were performed on a flat panel-based computed tomography system with a dual kVp technique in order to guide the selection of experimental acquisition parameters. The expected errors induced by using the proposed calibration materials were also estimated by simulation. Twenty pairs of postmortem breast samples were imaged with a flat-panel based dual kVp cone-beam CT system, followed by image-based material decomposition using calibration data obtained from a three-material phantom consisting of water, vegetable oil, and polyoxymethylene plastic. The tissue samples were then chemically decomposed into their respective water, lipid, and protein contents after imaging to allow direct comparison with data from dual energy decomposition. Results: Guided by results from simulation, the beam energies for the dual kVp cone-beam CT system were selected to be 50 and 120 kVp with the mean glandular dose divided equally between each exposure. The simulation also suggested that the use of polyoxymethylene as the calibration material for the measurement of pure protein may introduce an error of -11.0%. However, the tissue decomposition experiments, which employed a calibration phantom made out of water, oil, and polyoxymethylene, exhibited strong correlation with data from the chemical analysis. The average root-mean-square percentage error for water, lipid, and protein contents was 3.58% as compared with chemical analysis. Conclusions: The results of this study suggest that the water, lipid, and protein contents can be accurately measured using dual kVp cone-beam CT. The tissue compositional information may improve the sensitivity and specificity for breast cancer diagnosis.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

SU-D-18A-01: Tumor Motion Tracking with a Regional Deformable Registration Model for Four Dimensional Radiation Treatment of Lung Cancer

Purpose: To develop a tumor motion model from four-dimensional computed tomography (4DCT) of thoracic patients and demonstrate its impact on 4D radiation therapy simulation. Methods: A regional deformable image registration algorithm was introduced to extract tumor motion out of patient's breathing cycle. The gross target volume (GTV) was manually delineated on a selected phase of 4DCT and a subregion with 10mm margin supplemented to the GTV was created on the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA). Together with 4DCT the structures were exported into an inhouse research platform. A free form B-Spline deformable registration was carried out to map the subregion to other respiratory phases. The displacement vector fields were employed to propagate GTV contours with which the center of mass (CoM) of the GTV was computed for each breathing phase of 4DCT. The resultant GTV motion and its volumetric shape are utilized to facilitate 4D treatment planning. Five lung cancer patients undergoing stereotactic body radiation therapy were enrolled and their 4DCT sets were included in the study. Results: Application of the algorithm to five thoracic patients indicates that clinically satisfactory outcomes were achievable with a spatial accuracy better than 2mm for GTV contour propagation between adjacent phases, and 3mm between opposite phases. The GTV CoM was found to be in the range of 2.0mm through 2.5cm, depending upon the tumor location. Compared to the traditional whole image based registration, the computation of the regional model was found to be an order of magnitude more efficient. Conclusion: A regional deformable registration model was implemented to extract tumor motion. It will have widespread application in 4D radiation treatment planning in the future to maximally utilize the available spatial-tempo information.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-J-137: Incorporating Tumor Regression Into Robust Plan Optimization for Head and Neck Radiotherapy

Purpose: To develop a robust planning paradigm which incorporates a tumor regression model into the optimization process to ensure tumor coverage in head and neck radiotherapy. Methods: Simulation and weekly MR images were acquired for a group of head and neck patients to characterize tumor regression during radiotherapy. For each patient, the tumor and parotid glands were segmented on the MR images and the weekly changes were formulated with an affine transformation, where morphological shrinkage and positional changes are modeled by a scaling factor, and centroid shifts, respectively. The tumor and parotid contours were also transferred to the planning CT via rigid registration. To perform the robust planning, weekly predicted PTV and parotid structures were created by transforming the corresponding simulation structures according to the weekly affine transformation matrix averaged over patients other than him/herself. Next, robust PTV and parotid structures were generated as the union of the simulation and weekly prediction contours. In the subsequent robust optimization process, attainment of the clinical dose objectives was required for the robust PTV and parotids, as well as other organs at risk (OAR). The resulting robust plans were evaluated by looking at the weekly and total accumulated dose to the actual weekly PTV and parotid structures. The robust plan was compared with the original plan based on the planning CT to determine its potential clinical benefit. Results: For four patients, the average weekly change to tumor volume and position was −4% and 1.2 mm laterally-posteriorly. Due to these temporal changes, the robust plans resulted in an accumulated PTV D95 that was, on average, 2.7 Gy higher than the plan created from the planning CT. OAR doses were similar. Conclusion: Integration of a tumor regression model into target delineation and plan robust optimization is feasible and may yield improved tumor coverage. Part of this research is supported by Varian Medical System.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TU-A-9A-11: Gold Nanoparticles Enhanced Diffuse Optical Tomography: A Proof of Concept Study

Purpose: To investigate the feasibility and potential of gold nanoparticles (GNP) enhanced diffuse optical tomography (DOT) as a novel imaging strategy for tumor detection. Methods: Simulation was performed on a digital homogeneous cylindrical phantom of 30mm×30mm. Gold nanorods (GNR) with aspect ratio 3.9 and effective radius 21.86nm were used as contrast agent. The peak light absorption for these GNR occurs at 842nm within the near-infrared region, with the absorption cross-section of 1.97×10{sup -14}m{sup -2} and scatter cross-section of 1.07×10{sup -14}m{sup -2}. A 6mmdiameter sphere of GNR solution was positioned inside the tissue-simulating phantom. Simulations were performed at the GNR concentration level of 1nM, 100pM and 10pM, respectively. The points representing laser sources and light detectors were around the phantom with 30o apart tangentially and 1mm apart axially for 9 rows. As one point being source, all the other points within the current row and nearby four rows become detectors. Hence there are 108 source points in total and 55 detector points corresponding to each source. Forward light transport at 842nm wavelength was run on a three-dimensional mesh of 33186 nodes (∼0.5mm resolution) to acquire the light emission data. Reconstruction was performed on a coarse mesh of 19408 nodes (∼1mm resolution) with ∼20minutes on a 2.4GHz CPU and 8GB RAM computer. Results: The position of the GNR solution at 1nM, 100pM and 10pM concentration was reconstructed, respectively, with <1mm error. The GNR concentration was interpreted from the reconstructed absorption coefficient within the enhanced volume. The reconstructed maximum concentrations were 0.3nM, 120.0pM, and 5.3pM, respectively. Conclusion: To the best of our knowledge, this is the first time to apply GNP to enhance DOT. The simulation results showed the high sensitivity of GNP enhanced DOT, which is in pM concentration level, compared to the μM level for MRI agents and nM level for PET agents.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-A-18C-08: Design of a Small Animal Contrast Enhanced Dual Energy CT

Purpose: Dual energy CT has a variety of uses in a small animal setting including quantification and enhanced visualization of contrast agent. This study aims to determine the best energy combinations for contrast enhanced DECT on the XRAD 225Cx (Precision x-ray), a small animal IGRT system with a nominal energy range of 20 – 225 kVp. Focus was placed on material density accuracy and low contrast detectability. Methods: Simulations of single energy scans of an object containing concentrations of iodine varying from 0.5 to 50 mg/ml were performed using the simulation package ImaSim. Energy spectra from 50 – 220 kVp were calculated using the same software. For approximate Poisson noise modeling, mAs were chosen such that 30% of the total 10cGy dose was assigned to the low energy scan. A calibration involving projections of objects containing different thicknesses of iodine (0–0.5 mm) and water (0–50 mm) was performed for each energy and fit to a cubic equation as the calibration curve for each energy pair. Results: Contrast to noise ratios of the iodine material images and accuracies in iodine density measurements were measured. Gradual improvements in each metric were seen with increasing high energy. Larger improvements in CNR were observed for decreasing the low energy. Errors in iodine density were generally close to 5% for concentrations of iodine above 3 mg/ml but increased to around 15% for 50 kVp, likely due to its proximity to the discontinuity caused by the k-edge of iodine. Conclusion: Based on these simulations, the best energy combination for detecting low concentrations of iodine using a projection space calibration procedure is 50/200 kVp. However, if accuracy is most important 80/220 kVp is ideal, with 60/220 kVp being a good compromise to achieve both goals. Future work is necessary to verify these conclusions with physical data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

SU-E-J-188: Theoretical Estimation of Margin Necessary for Markerless Motion Tracking

Purpose: To estimate the margin necessary to adequately cover the target using markerless motion tracking (MMT) of lung lesions given the uncertainty in tracking and the size of the target. Methods: Simulations were developed in Matlab to determine the effect of tumor size and tracking uncertainty on the margin necessary to achieve adequate coverage of the target. For simplicity, the lung tumor was approximated by a circle on a 2D radiograph. The tumor was varied in size from a diameter of 0.1 − 30 mm in increments of 0.1 mm. From our previous studies using dual energy markerless motion tracking, we estimated tracking uncertainties in x and y to have a standard deviation of 2 mm. A Gaussian was used to simulate the deviation between the tracked location and true target location. For each size tumor, 100,000 deviations were randomly generated, the margin necessary to achieve at least 95% coverage 95% of the time was recorded. Additional simulations were run for varying uncertainties to demonstrate the effect of the tracking accuracy on the margin size. Results: The simulations showed an inverse relationship between tumor size and margin necessary to achieve 95% coverage 95% of the time using the MMT technique. The margin decreased exponentially with target size. An increase in tracking accuracy expectedly showed a decrease in margin size as well. Conclusion: In our clinic a 5 mm expansion of the internal target volume (ITV) is used to define the planning target volume (PTV). These simulations show that for tracking accuracies in x and y better than 2 mm, the margin required is less than 5 mm. This simple simulation can provide physicians with a guideline estimation for the margin necessary for use of MMT clinically based on the accuracy of their tracking and the size of the tumor.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

MO-FG-303-06: Evaluation of the Performance of Very High-Energy Electron (VHEE) Beams in Radiotherapy: Five Clinical Cases

Purpose: To evaluate the performance of 100–120 MeV very-high energy electron (VHEE) scanning pencil beams to radiotherapy by means of Monte Carlo (MC) simulations. Methods: We selected five clinical cases with target sizes of 1.2 cm{sup 3} to 990.4 cm{sup 3}. We calculated VHEE treatment plans using the MC EGSnrc code implemented in a MATLAB-based graphical user interface developed by our group. We generated phase space data for beam energies: 100 and 120 MeV and pencil beam spot sizes of 1, 3, and 5 mm at FWHM. The number of equidistant beams considered in this work was 16 or 32. Dose was calculated and then imported into a research version of RayStation where treatment plan optimization was performed. We compared the VHEE plans with the clinically delivered volumetric modulated arc therapy (VMAT) plan to evaluate VHEE plans performance. Results: VHEE plans provided the same PTV coverage and dose homogeneity than VMAT plans for all the cases. In average, the mean dose to organs at risk (OARs) was 24% lower for the VHEE plans. The structures that benefited the most from using VHEE were: large bowel for the esophagus case, chest wall for the liver case, brainstem for the acoustic case, carina for the lung case, and genitalia for the anal case, with 23.7–34.6% lower dose. VHEE dose distributions were more conformal than VMAT solution as confirmed by conformity indices CI100 and CI50. Integral dose to the body was in average 19.6% (9.2%–36.5%) lower for the VHEE plans. Conclusion: We have shown that VHEE plans resulted in similar or superior dose distributions compared to clinical VMAT plans for five different cases and a wide range of target volumes, including a case with a small target (1.2 cm{sup 3}), which represents a challenge for VMAT planning and might require the use of more complex non-coplanar VMAT plans. B Palma: None. M Bazalova: None. B Hardemark: Employee, RaySearch Laboratories AB. E Hynning: Employee, RaySearch Laboratories AB. B Qu: None. B Loo Jr.: Research support, RaySearch, Varian. P Maxim: Research support, RaySearch, Varian.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-G-IeP4-14: Prostate Brachytherapy Activity Measurement and Source Localization by Using a Dual Photon Emission Computed Tomography System: A Feasibility Study

Purpose: To monitor the activity distribution and needle position during and after implantation in operating rooms. Methods: Simulation studies were conducted to assess the feasibility of measurement activity distribution and seed localization using the DuPECT system. The system consists of a LaBr3-based probe and planar detection heads, a collimation system, and a coincidence circuit. The two heads can be manipulated independently. Simplified Yb-169 brachytherapy seeds were used. A water-filled cylindrical phantom with a 40-mm diameter and 40-mm length was used to model a simplified prostate of the Asian man. Two simplified seeds were placed at a radial distance of 10 mm and tangential distance of 10 mm from the center of the phantom. The probe head was arranged perpendicular to the planar head. Results of various imaging durations were analyzed and the accuracy of the seed localization was assessed by calculating the centroid of the seed. Results: The reconstructed images indicate that the DuPECT can measure the activity distribution and locate the seeds dwelt in different positions intraoperatively. The calculated centroid on average turned out to be accurate within the pixel size of 0.5 mm. The two sources were identified when the duration is longer than 15 s. The sensitivity measured in water was merely 0.07 cps/MBq. Conclusion: Preliminary results show that the measurement of the activity distribution and seed localization are feasible using the DuPECT system intraoperatively. It indicates the DuPECT system has potential to be an approach for dose-distribution-validation. The efficacy of acvtivity distribution measurement and source localization using the DuPECT system will evaluated in more realistic phantom studies (e.g., various attenuation materials and greater number of seeds) in the future investigation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Sci-Thur AM: YIS – 07: Optimizing dual-energy x-ray parameters using a single filter for both high and low-energy images to enhance soft-tissue imaging

Objective: To optimize dual-energy parameters of ExacTrac stereoscopic x-ray imaging system for lung SBRT patients Methods: Simulated spectra and a lung phantom were used to optimize filter material, thickness, kVps, and weighting factors to obtain bone subtracted dual-energy images. Spektr simulations were used to identify material in the atomic number (Z) range [3–83] based on a metric defined to separate spectrums of high and low energies. Both energies used the same filter due to time constraints of image acquisition in lung SBRT imaging. A lung phantom containing bone, soft tissue, and a tumor mimicking material was imaged with filter thicknesses range [0–1] mm and kVp range [60–140]. A cost function based on contrast-to-noise-ratio of bone, soft tissue, and tumor, as well as image noise content, was defined to optimize filter thickness and kVp. Using the optimized parameters, dual-energy images of anthropomorphic Rando phantom were acquired and evaluated for bone subtraction. Imaging dose was measured with dual-energy technique using tin filtering. Results: Tin was the material of choice providing the best energy separation, non-toxicity, and non-reactiveness. The best soft-tissue-only image in the lung phantom was obtained using 0.3 mm tin and [140, 80] kVp pair. Dual-energy images of the Rando phantom had noticeable bone elimination when compared to no filtration. Dose was lower with tin filtering compared to no filtration. Conclusions: Dual-energy soft-tissue imaging is feasible using ExacTrac stereoscopic imaging system utilizing a single tin filter for both high and low energies and optimized acquisition parameters.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Atomistic and Ab initio modeling of CaAl{sub 2}O{sub 4} high-pressure polymorphs under Earth’s mantle conditions

Semi-empirical and ab initio theoretical investigation of crystal structure geometry, interatomic distances, phase densities and elastic properties for some CaAl{sub 2}O{sub 4} phases under pressures up to 200 GPa was performed. Two independent simulation methods predicted the appearance of a still unknown super-dense CaAl{sub 2}O{sub 4} modification. In this structure, the Al coordination polyhedron might be described as distorted one with seven vertices. Ca atoms were situated inside polyhedra with ten vertices and Ca–O distances from 1.96 to 2.49 Å. It became the densest modification under pressures of 170 GPa (density functional theory prediction) or 150 GPa (semi-empirical prediction). Both approaches indicated that this super-dense CaAl{sub 2}O{sub 4} modification with a “stuffed α-PbO{sub 2}” type structure could be a probable candidate for mutual accumulation of Ca and Al in the lower mantle. The existence of this phase can be verified experimentally using high pressure techniques.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗