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DOE OSTI2022

Ion temperature anisotropy model with cross‐field drifts in the scrape‐off layer

Abstract An ion temperature anisotropy model including cross‐field drifts has been implemented in the 2D transport code UEDGE. Two ion temperature equations are solved in the model to give separate ion temperatures perpendicular and parallel to the magnetic field, which results in an additional mirror force for ion parallel transport and also leads to an additional curvature drift in the perpendicular direction. In our previous work, an ion temperature anisotropy model was implemented and applied to the full 2D version of UEDGE including recycled neutrals. The simulation results showed that the mirror force due to anisotropy reduces ion parallel flow velocity, however, the simulations were presented without cross‐field electric and magnetic drifts. Nevertheless, in present medium‐size tokamaks or future compact fusion devices, cross‐fields are important. In this work, the anisotropy model is extended to be compatible with the inclusion of cross‐field drifts. Preliminary results on comparison between the model solutions with and without cross‐field drifts are presented.

Zhao, Menglong↗

DOE OSTI2024

Demonstration of a multi-channel fluidized bed particle–supercritical carbon dioxide heat exchanger for concentrating solar applications

High-temperature thermal energy storage in oxide particles at temperatures above 600°C can couple concentrated solar energy with high-efficiency thermal power cycles to provide dispatchable solar-driven electricity. Challenges remain in developing cost-effective primary heat exchangers, which require expensive alloys, to extract the high-temperature thermal energy from the particles to power cycle fluids, such as supercritical CO 2 (sCO 2 ) in recuperated Brayton cycles. To explore one pathway for cost-effective, high-temperature particle heat exchangers, the current study demonstrates a shell-and-plate, particle–sCO 2 heat exchanger with narrow- channel fluidized beds coupled with micro-channel sCO 2 flows in the heat exchanger walls. This study evaluates the feasibility of multiple parallel, narrow-channel fluidized beds in shell-and-plate particle–sCO 2 HXs, to achieve high bed-wall heat fluxes at elevated temperatures. A reduced-order model simulates the narrow- channel, fluidized-bed particle–sCO 2 heat exchanger to design the fluidized bed geometry, in terms of depth, height, and number of channels,for a nominal 40-kWth heat exchanger at particle and sCO 2 inlet temperatures up to 600 °C and 400 °C respectively. The resulting shell-and-plate heat exchanger design operates with bubbling fluidization of the downward-flowing oxide particles to enhance bed-wall heat transfer. The heat exchanger core is fabricated with etched sCO 2 micro-channels in thin wall plates that are diffusion bonded to spacer frames to form the shell-and-plate structure with 12 parallel, fluidized bed channels, 10.4 mm deep. The heat exchanger is tested at the National Solar Thermal Test Facility at Sandia National Laboratories with CARBOBEAD HSP particles at design particle flow rates of 0.20 kg s –1 and inlet temperatures up to 525 °C. Results show that fluidization across multiple parallel channel beds can maintain uniform particle inventory with a common freeboard zone above the heat exchanger core. Bubbling fluidization improves particle–wall heat transfer coefficients but also increases axial dispersion of particle thermal energy, which lowers the log- mean temperature difference such that total heat transfer remains relatively constant to within ±10% over a broad range of fluidization gas velocities. The axial dispersion required particle and sCO 2 flow rates to be increased by 25% over model-designed conditions to achieve the targeted 40 kWth, which indicates the importance of incorporating axial dispersion into heat exchanger design models and of deploying bed structures to suppress it. Furthermore, this study demonstrates the feasibility and preferred fluidizing gas conditions for particle heat exchangers for releasing high-temperature thermal energy storage systems.

14 SOLAR ENERGY↗

DOE OSTI2025

Impact of Different Thermal Gradients on the Dynamics of Cylindrical Lithium-ion Cells Subject to Accelerated Aging and on Module Performance

This study investigates the impacts of applying different thermal gradient patterns to cylindrical lithium-ion cells in a module on cell dynamics (temperatures, current flows, state of charge), module performance (evolution of resistance, capacity, and energy versus cycle number), and module lifetime. The thermal gradients were generated using cooling plates (CPs) with three different flow-field designs, namely, straight, perpendicular, and U-turn. The study uses computational fluid dynamics (CFD), the pseudo-two-dimensional (P2D) battery model, capacity loss and increased impedance due to the growth of a solid-electrolyte-interphase, and the electric current distribution from module terminals to cells that depends on the series-parallel electrical connections among the cells. The impact of the thermal gradient (resulting from the CP designs) on the variability in resistance, current, state of charge, and voltage among the cells was analyzed and linked to differences in the module's performance. Applying a thermal gradient to parallel-connected strings of series-connected cells led to variation in the current through each parallel string and an imbalance in the voltage of series-connected cells. Module performance is poorer when the thermal gradient causes a voltage imbalance than when it causes a current imbalance. Module performance becomes the worst when both current variation and voltage imbalance happen together. For instance, the module's lifetime (estimated as reaching 80% of its initial capacity) varied by 5% to 17.5%, depending on the magnitude and pattern of the imposed thermal gradient. As the relative orientation between thermal gradients and cells' electrical connectivity influences the module's performance, appropriate consideration should be given to the choice of the CP, especially if large thermal gradients are allowed.

Battery thermal management↗

DOE OSTI2020

GPU acceleration of all-electron electronic structure theory using localized numeric atom-centered basis functions

We present an implementation of all-electron density-functional theory for massively parallel GPU-based platforms, using localized atom-centered basis functions and real-space integration grids. Special attention is paid to domain decomposition of the problem on non-uniform grids, which enables compute- and memory-parallel execution across thousands of nodes for real-space operations, e.g. the update of the electron density, the integration of the real-space Hamiltonian matrix, and calculation of Pulay forces. To assess the performance of our GPU implementation, we performed benchmarks on three different architectures using a 103-material test set. We find that operations which rely on dense serial linear algebra show dramatic speedups from GPU acceleration: in particular, SCF iterations including force and stress calculations exhibit speedups ranging from 4.5 to 6.6. For the architectures and problem types investigated here, this translates to an expected overall speedup between 3–4 for the entire calculation (including non-GPU accelerated parts), for problems featuring several tens to hundreds of atoms. Additional calculations for a 375-atom Bi2Se3 bilayer show that the present GPU strategy scales for large-scale distributed-parallel simulations.

42 ENGINEERING↗

DOE OSTI2021

Simulation of lithium transport using the BOUT++ framework

A numerical model that calculates the collisional interactions between the lithium atoms from a lithium pellet and the background plasmas has been upgraded. The ion density ($N_t$), electron temperature ($T_e$), ion temperature ($T_i$) and parallel ion velocity ($V_{∥, i}$) are used to characterize the background plasmas. The lithium atom density ($N^{a}_{Li}$) and parallel velocity ($V_{∥,a}$) of lithium atoms evolve with time. For each lithium ion, the density ($N_{Li^{n+}}$), temperature ($T_{Li^{n+}}$) and parallel velocity ($V_{∥, Li^{n+}}$) are self-consistently calculated. A C-mod lower single null equilibrium is used to generate the grid for the BOUT++ simulation. The lithium atoms can be fully ionized to $Li^{3+}$ in ~2 μs. The rapid radial and poloidal expansion of the lithium ions are found in the simulation. After the collision interaction process, the electron temperature rapidly decreases at the pellet location; then, it rapidly poloidally expands, and the temperature at the pellet location starts to recover. The electron pressure increases at the pellet location despite the decrease in electron temperature because of the extra electrons from the lithium ionization. The ion pressure profile decreases in the pellet location due to the decrease in ion temperature.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Coupling Surface Flow with High-performance Subsurface Reactive Flow and Transport Code PFLOTRAN

Water exchange between the surface and subsurface is important for both water resource management and environmental protection. In this paper, we develop coupled surface and subsurface flow simulation capability in a parallel subsurface flow and reactive transport code PFLOTRAN. We sequentially couple the diffusion wave-based surface flow with the subsurface flow governedby the Richards equation in PFLOTRAN. These two flow domains are linked with a boundary condition switching method that ensures continuity of pressure and flux at the surface-subsurface interface. We verify the coupled code against other existing hydrologic models and observation data using a number of numerical experiments. The coupled hydrological model exhibits good performance in strong parallel scaling tests. The new coupled surface and subsurface simulator significantly advance community simulation capability towards improving integrated hydrologic and biogeochemical understanding of complex systems such as watersheds and river corridors. Keywords: Surface flow, Integrated hydrological modeling, Boundary condition switching, Parallel computing

Wu, Runjian↗

DOE OSTI2024

CG-Kit: Code Generation Toolkit for performant and maintainable variants of source code applied to Flash-X hydrodynamics simulations

CG-Kit is a new Code Generation tool-Kit that we have developed as a part of the solution for portability and maintainability for multiphysics computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. To efficiently use computing resources on a heterogeneous node, an application must have a map of computation to resources and a mechanism to move the data and computation to the resources according to the map. Most existing performance portability solutions are focussed on abstracting the expression of computations so that a unified source code can be specialized to run on different resources. However, such an approach is insufficient for a code like Flash-X, which has a multitude of code components that can be assembled in various permutations and combinations to form different instances of applications. Similar challenges apply to any code that has composability, where a single specified way of apportioning work among devices may not be optimal. Additionally, use cases arise where the optimal control flow of computation may differ for different devices while the underlying numerics remain identical. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed and shared memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. All of these challenges demand that scientific software developers apply existing knowledge about domain applications, algorithms, and computing platforms to determine custom abstractions and granularity for code generation. There is a critical lack of tools to tackle those problems. CG-Kit is designed to fill this gap by providing a user with the ability to express their desired control flow and computation-to-resource map in the form a pseudocode-like recipe. It consists of standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability toolchains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. They are agnostic to the programming language of the source code targeted for code generation. In conclusion, we demonstrate the capabilities of the toolkit with two examples, first, multithreaded variants of the basic AXPY operation, and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes.

Algorithmic portability↗

DOE OSTI2023

Quantitative proton radiography and shadowgraphy for arbitrary intensities

Charged-particle radiography and shadowgraphy data can be directly inverted to obtain a line-integrated transverse Lorentz force or a line-integrated transverse refractive index gradient if intensity modulations due to scattering and absorption are negligible, and angular deflections are small. We develop a new direct-inversion algorithm based on plasma physics and compare it to a new Monge–Ampère code and an existing power diagram code. The measured or source intensity is represented by electrons subject to drag, and the other intensity by fixed ions. The decrease in kinetic plus electrostatic energy determines convergence. The displacement of the electrons from their initial to their equilibrium positions determines the line-integrated force or refractive index gradient. We have implemented two approaches: PIC (particle in cell) and Lagrangian fluid, in 1-D and 2-D. The PIC code works for arbitrary intensities, can work efficiently in parallel, and can make use of existing codes. The Lagrangian code requires less memory and is faster than the PIC code without massively parallel processing, but fails in 2-D for large intensity modulations. The Monge–Ampère code is by far the fastest in 2-D, without massively parallel processing, but fails for intensities with large voids, high contrast ratios and large deflections across the boundaries, and could not obtain the degree of convergence possible with the PIC code. As a result, the power diagram code was by far the slowest and most memory intensive, and failed for large peaks in the measured intensity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

In this work, we present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates

Here, this paper presents a novel formulation and its robust numerical implementation of strain-gradient (SG) crystal plasticity within a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. The resulting non-local SG-LS-EVPFFT formulation is used to model and understand the process of kink band formation during layer-parallel compression of nano-metallic laminates (NMLs). NMLs are layered composites with nanoscale thicknesses, thus requiring consideration of the interaction between dislocations and interfaces within the micromechanical model. The length-scale parameter of the SG model is calibrated by simulating a double pile-up and comparing predictions to analytical solution. This required new expressions for the defect energy, resulting in more accurate double pile-up predictions. The calibrated SG-LS-EVPFFT model is then used to simulate layer-parallel compression of copper-niobium NML. Formation of kink bands is predicted, and the model is used to rationalize the microscopic mechanisms enabling the formation process. It is found that accumulation of dislocations at interfaces leads to activation of layer-parallel slip, which in turn leads to kink band formation.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Analysis of several high-resolution infrared bands of perdeutero-spiropentane, C5D8

Perdeutero-spiropentane (C5D8) has been synthesized and infrared spectra were taken from 400 to 4000 cm-1 at low sample pressures in a 22 meter multipass cell. The spectral resolution (0.0015 cm-1) reveals thousands of individual rovibrational transitions for several fundamental bands occurring in the spectral region of 500 to 1100 cm-1. C5D8 ground state constants reported in a previous study of a ?15 parallel band at 1054 cm-1 [1] were improved significantly in the present work by adding combination-differences derived from ?16 parallel and ?24 perpendicular band analyses. The larger data set at higher J values also allowed determination of the ground state K? = 2 splitting constant (?2? = 0.76(2) ×10-9 cm-1). For ?16, the band origin is 847.16933(5) cm-1 and changes in upper state rotational constants are ?A = –0.0013411(5) and ?B = –0.0002021(1) (in units of cm-1). Overlapping, and in Fermi resonance with ?16, is a second parallel band which, from Gaussian calculations at the anharmonic level, is assigned as the b2 combination ?8+?12, with band origin of 840.5434(1) and ?A = –0.0003500(7) and ?B = –0.0003502(1) cm-1. For ?24 analogous values are 556.41453(2) and ?A = –0.00032295(9) and ?B = –0.00016782(4) cm-1. The analyses also yields accurate values for the changes in both quartic and sextic centrifugal distortion constants and, for ?24, values for the l-doubling constants q+ and q-. Theoretical calculations of the rovibrational parameters aided in the analysis and the numerical values are in good agreement with experimental results.

Nibler, Joseph W.↗

DOE OSTI2022

Mass transport limitations in polymer electrolyte water electrolyzers using spatially-resolved current measurement

Here this work utilizes spatially-resolved current measurements to provide insight into mass transport limitations in electrolyzers that are not observable from traditional polarization measurement. In this study, two types of flow-fields (parallel and triple-serpentine) and two types of diffusion media (patterned porous thin titanium foil LGDLs and Ir-coated titanium felt PTLs) were examined. A non-uniform current distribution dominated by mass transport limitations was observed to be instigated by the restriction of liquid water transport to catalyst sites. Additionally, conditions are revealed which yield similar polarization performance but dissimilar current distributions. In such cases, the transport limitations for different architectures and porous media affect polarization in different regions of the active area. Furthermore, the triple-serpentine flow-field used in this study performs better than the parallel flow-field under mass transport limited operating conditions. This indicates that the parallel flow-field used in this study is more susceptible to starvation than the triple-serpentine flow-field for the electrolyzer studied.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Immortal rays: Rethinking random ray neutron transport on GPU architectures

The Random Ray Method (TRRM) is a recently developed adaptation of the Method of Characteristics for neutral particle transport simulations. TRRM has demonstrated excellent performance on 3D nuclear reactor benchmark problems using CPU-based compute systems. When porting to GPU-based systems, however, new performance challenges arise that are unique to processors targeting massive fine-grained parallelism. For smaller problems, or for large problems that are domain decomposed across many computational nodes, the problem size per node has insufficient parallelism to saturate GPU node resources, thus greatly limiting speedup. In this study, we report on a newly developed “immortal ray” variant of TRRM. Here, the immortal ray technique exposes significantly more fine-grained parallelism by fundamentally reformulating the numerical details of ray discretization, resulting in performance tradeoffs with significant overall benefit on GPUs. For very small 2D simulation problems we found the new immortal ray variant allowed for up to a 4.4x speedup when run on a single GPU. For larger 3D simulation problems we found the new variant improved strong scaling by 3x when run on the Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗

DOE OSTI2020

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. Finally, in all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Crystal structure of aminopentamide hydrogen sulfate, (C 19 H 25 N 2 O)(HSO 4 )

The crystal structure of aminopentamide hydrogen sulfate has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. Aminopentamide hydrogen sulfate crystallizes in space group P2 1 /c (#14) with a = 17.62255(14), b = 6.35534(4), c = 17.82499(10) Å, β = 96.4005(6)°, V = 1983.906(14) Å 3 , and Z = 4. The structure consists of layers parallel to the bc-plane with hydrogen sulfate anions at the core and aminopentamide cations on the outside. There is a strong charge-assisted O49–H53∙∙∙O52 hydrogen bond between the hydrogen sulfate anions. This hydrogen bond links the anions in a chain parallel to the b-axis. The cation forms a discrete N–H∙∙∙O hydrogen bond to the anion. The amide group also forms two weaker discrete hydrogen bonds to the anion. The three N–H∙∙∙O hydrogen bonds link the cations and anions into columns parallel to the b-axis. This commercial material from USP contained an unidentified impurity, the powder pattern of which could be indexed on a monoclinic unit cell. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).

36 MATERIALS SCIENCE↗