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At least 145 records · Page 8

Implementation of the Windowed Multipole Method in Shift

The windowed multipole (WMP) method has been implemented in the Shift Monte Carlo (MC) radiation transport code with support for both CPU and GPU execution. With this method, small WMP data libraries (~100 MB) can be used to accurately Doppler broaden cross sections to arbitrary temperatures “on the fly” during an MC simulation. This approach yields significant memory savings relative to traditional methods, making it ideal for high-fidelity analysis such as coupled multiphysics simulations. This document provides the exact forms of the WMP equations used by Shift, as well as a detailed description of the structure of WMP HDF5 data files provided by the Massachusetts Institute of Technology (MIT). The Shift implementation has been validated against the OpenMC radiation transport code, with excellent agreement demonstrated for 70 nuclides across an operative range of temperatures. CPU and GPU performance testing using a small module reactor (SMR) problem demonstrated that this method decreases the neutron tracking rate by a factor of ~2 on the Summitdev machine. A new set of WMP data being developed in-house will employ novel methods to improve tracking rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Nanoconfined Interfaces for Highly Selective Separation of Critical Rare Earth Elements

Industrial demand for rare earth elements (REEs) has surged over the past three decades due to their unique properties that support sustainable energy and new technologies. Separating individual REEs is challenging and hazardous, typically done through liquid-liquid extraction. There is an urgent need for environmentally friendly and efficient separation technologies for REEs. Porous materials offer promising advances for sustainable REE separation via ion-selective capture. We hypothesize that REE separation can be efficiently achieved in reactive nanopores, such as Zr(IV) and Cr(III) metal-organic frameworks (MOFs), through surface functionalization. By integrating material synthesis, interfacial chemistry experiments, theory, computation, and machine learning, we gained insights into the chemical factors controlling REE speciation and their competitive adsorption on MOFs. Our findings show that these materials’ selectivity can be tuned by surface functionalization. The machine learning component addressed ion-specific diffusion based on MOF topology and chemistry.

36 MATERIALS SCIENCE↗

Global 1 km land surface parameters for kilometer-scale Earth system modeling

Earth system models (ESMs) are progressively advancing towards the kilometer scale (“k-scale”). However, the surface parameters for land surface models (LSMs) within ESMs running at the k-scale are typically derived from coarse-resolution and outdated datasets. This study aims to develop a new set of global land surface parameters with a resolution of 1 km for multiple years from 2001 to 2020, utilizing the latest and most accurate available datasets. Specifically, the datasets consist of parameters related to land use and land cover, vegetation, soil, and topography. Differences between the newly developed 1 km land surface parameters and conventional parameters emphasize their potential for higher accuracy due to the incorporation of the most advanced and latest data sources. To demonstrate the capability of these new parameters, we conducted 1 km resolution simulations using the E3SM Land Model version 2 (ELM2) over the contiguous United States. Our results demonstrate that land surface parameters contribute to significant spatial heterogeneity in ELM2 simulations of soil moisture, latent heat, emitted longwave radiation, and absorbed shortwave radiation. On average, about 31 % to 54 % of spatial information is lost by upscaling the 1 km ELM2 simulations to a 12 km resolution. Using eXplainable Machine Learning (XML) methods, the influential factors driving the spatial variability and spatial information loss of ELM2 simulations were identified, highlighting the substantial impact of the spatial variability and information loss of various land surface parameters, as well as the mean climate conditions. The comparison against four benchmark datasets indicates that ELM generally performs well in simulating soil moisture and surface energy fluxes. The new land surface parameters are tailored to meet the emerging needs of k-scale LSM and ESM modeling with significant implications for advancing our understanding of water, carbon, and energy cycles under global change. The 1 km land surface parameters are publicly available at https://doi.org/10.5281/zenodo.10815170 (Li et al., 2024).

54 ENVIRONMENTAL SCIENCES↗

Application of HFE to the design and V and V of a computerized procedure system: benefits and challenges - 234

The application of Human Factors Engineering (HFE) practices to the Human Machine Interface design and subsequent Verification and Validation (V and V) is a widely applied practice when talking about the design of complete control rooms or important control room modernizations, but not so often applied to the design of computerized operator support systems. In order to overcome the challenges faced on designing a Computerized Operation Support System (COSS) that meets the process efficiency requirements and integrates seemingly with hybrid plant operation concept, the involvement of a HFE team early in the COSS design and implementation process along with operation, Instrumentation and Control (I and C) and cybersecurity experts will guarantee the project success. This paper documents the HFE process applied during the design and evaluation of a Computerized Procedure System (CPS) and how final product was shaped to ensure that the transition from paper to computerized procedures will help in meeting Delivering the Nuclear Promise (DNP) goals, improving plant efficiency. The HFE program included the following activities: 1. A review of existing operating experience 2. An analysis of functions and tasks associated to the use and maintenance of CPS 3. A design verification of the system to meet guidelines prescribed in the NUREG-0700 (Rev.2), requirements of the ISG-05 and cybersecurity criteria (NEI 08-09, IEC-62646, EPRI 1015313, these among others). 4. An integrated system validation in a full scope simulator The application of HFE practices in the design and implementation of COSS helps not only to ensure that efficiency and safety improvement requirements are met, but also to evaluate the potential return of the investment, that such tools should bring. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improving Automation Transparency: Addressing Some of Machine Learning’s Unique Challenges

Abstract. A variety of factors can affect one’s reliance on an automated aid. Some of these factors include one’s per-ception of the system’s trustworthiness, such as perceived reliability of the system or one’s ability to understand the system’s underlying reasoning. A mismatch between the operator’s perception and the true capabilities and charac-teristics of the system can lead to inappropriate reliance on the tool. This improper use of the system can manifest as either underutilization of the technology or complacency resulting from over-trusting the system. Increasing an au-tomated tool’s transparency is one approach that enables the operator to more appropriately rely on the technology. Transparent automated systems provide additional infor-mation that allows the user to see the system’s intent and understand its underlying processes and capabilities. Sev-eral researchers have developed frameworks to support the design of more transparent automation. However, these frameworks may not fully consider the particular challeng-es to transparency design introduced by automation that leverages machine learning. Like all automation, these systems can benefit from transparency. However, artificial intelligence poses new challenges that must be considered when designing for transparency. Unique considerations must be made in terms of the type, and amount or level of transparency information conveyed to the user.

Transparency, Machine Learning, Automation↗

A Multi-Step Adaptive Interpolation Approach to Mitigating the Impact of Nonlinearity on Dynamic State Estimation

Accurate estimation of dynamic states (such as synchronous machine rotor angle and speed) is critical for monitoring and controlling transient stability. Extended Kalman filter (EKF)--based approaches have been developed for estimating dynamic states. In order to improve the EKF's performance in estimating dynamic states of a synchronous machine, this paper proposes a multi-step adaptive interpolation (MSAI) approach to achieve balance between estimation accuracy and computational time. This approach consists of three major steps. First, two indexes are calculated to quantify the nonlinearity of the state transition function and measurement function, respectively. Second, based on the nonlinearity indexes, the interpolation factor is determined using a finite state machine model. And finally, to mitigate the negative impact of nonlinearity on the estimation accuracy, pseudo-measurements are added between consecutive measurements through linear interpolation. A simple example is used to validate the proposed nonlinear indexes. The two-area four-machine system and 16-machine 68-bus system are used to evaluate the effectiveness of the proposed MSAI approach. It is shown through the Monte-Carlo method that the estimation accuracy can be improved through interpolation. In addition, a good trade-off between estimation accuracy and computational time can be achieved effectively through the proposed MSAI approach.

Dynamic State Estimation, extended Kalman filter (↗

Computerized operator support system and human performance in the control room - 262

An operator aid technology to assist nuclear plant operators maintain situation awareness and detect faults earlier than would be possible using conventional control room technologies is described. Coined the Computerized Operator Support System (COSS), this technology is aimed at the human-machine interface. The COSS has been implemented as a prototype system operating in the control room environment of a full-scale simulator for a commercial nuclear power plant. A human factors assessment that involved two licensed reactor crews was performed to evaluate crew performance. This paper describes the development of the COSS, the underlying fault-detection architecture, and feedback received based on operator-in-the-loop studies. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Assessment of Multi-Step CADIS Parameter Sensitivity to Neutron Flux Spectrum in Shutdown Dose Rate Calculations

Shutdown dose rate (SDDR) analysis requires (a) a neutron transport calculation to estimate neutron flux fields, (b) an activation calculation to compute radionuclide inventories and associated photon sources, and (c) a photon transport calculation to estimate final dose rate. In some applications, accurate full-scale Monte Carlo (MC) SDDR simulations are needed for very large systems with massive amounts of shielding materials. For example, SDDR assessments are required throughout the biological shield (bio-shield) of the ITER experimental facility to evaluate the required waiting period after the shutdown of ITER and to identify the locations where human accessibility should be prohibited. The bio-shield is a large cylindrical concrete structure (30 m tall and 34 m in diameter) surrounding the very complex tokamak machine. Determining the effects on SDDR of important factors, such as the cross talk (interactions) between the different ports of ITER, is possible only through full-scale simulations that involve all the complex inner details of the ITER tokamak machine. These simulations are impractical because calculation of space- and energy-dependent neutron fluxes throughout the structural materials is needed to estimate the distribution of radioisotopes causing the SDDR. Determining a good importance function that can be used in biasing a neutron MC calculation for SDDR is complicated because it is difficult to explicitly express the SDDR response function, which depends on subsequent computational steps. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid MC/deterministic method was developed to speed up the SDDR MC neutron transport calculation using an importance function that represents the neutron importance to the final SDDR. The MS-CADIS method uses the CADIS method, which has been Notice: This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). successfully used for more than a decade in radiation shielding applications to generate consistent source biasing and weight window (WW) variance reduction parameters to accelerate continuous-energy MC simulations. However, because MS-CADIS focuses on multi-step shielding calculations such as SDDR calculations, it develops an importance function for the initial radiation transport calculation (e.g., the neutron calculations in SDDR simulations) that represents the importance of particles to the final response of the overall simulation. To develop this importance function, the MS-CADIS method uses an adjoint calculation with a specific neutron adjoint source that represents the neutron's contribution to the final SDDR. Brute force calculation of the MS-CADIS neutron adjoint source requires a deterministic neutron transport calculation coupled with activation calculations in each element of the deterministic mesh. These calculations are needed to determine the MS-CADIS parameter for the neutron interactions that produce radioisotopes contributing to the SDDR. The MS-CADIS parameter is the microscopic cross section of the radioisotope-producing interaction, multiplied by the mass of this radioisotope existing at the end of the irradiation and decay scenario, and divided by the steady-state rate of the interaction. Because the activation calculations are performed for each radionuclide in each mesh element, implementation of the MS-CADIS method can be computationally expensive. However, these neutron transport and activation calculations are not needed if we assume that the radioisotopes are created due to single neutron interactions and their concentrations do not change as a result of burnup by neutron irradiation. The use of this approximation, which renders the MS-CADIS parameter independent of the neutron flux, seems reasonable in calculating the MS-CADIS importance function because this function is needed only to speed up the MC calculation, not to calculate the final SDDR. In this work, we investigate the validity of this approximation by investigating the behavior of the MS-CADIS parameter as a function of the neutron flux spectra in the Fusion Evaluated Nuclear Data Library (FENDL) Neutronics and Shielding Benchmark problem that contains representative isotopes and flux environments of fusion energy systems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Unraveling Hydrogen Induced Geochemical Reaction Mechanisms through Coupled Geochemical Modeling and Machine Learning

Underground hydrogen storage (UHS) provides a promising large-scale, long-term energy storage solution. A reasonable recovery of stored hydrogen is critical for a successful storage scheme. However, in subsurface reservoirs hydrogen is subject to active geochemical reactions that might result in hydrogen loss. In this study, we implemented a geochemical modeling approach coupled with an unsupervised machine learning technique called non-negative matrix factorization (NMF) to unravel the complex brine-rock-H 2 geochemical processes responsible for hydrogen losses, with particular focus on sulfate reduction reactions. NMF is applied to modeled mineral evolution and fluid component profiles to retrieve profiles that can be interpreted to more easily assess competing processes. NMF decouples simulated competing equilibrium reactions. This facilitates separation of overlapping reaction profiles from redox processes, dissolution fronts, and secondary precipitation while considering the effects of simulation parameters such as salinity, temperature, and total H 2 pressure. NMF successfully discriminates these competing effects in nonlinear ways, allowing robust interpretation. In addition, NMF reveals subtle coupled mineral associations and reaction fronts that are invisible to conventional model analysis. This integrated approach strengthens the conceptual understanding of complex nonlinear hydrogen-brine-rock interactions and advances geochemical research on UHS systems to resolve complexities in modeled geochemical systems without the need for direct experiments or prior knowledge. Furthermore, this study highlights the efficacy of combining geochemical modeling with machine learning techniques to enhance the interpretability of the intricate geochemical simulation output through deciphering the overlapping reaction path that cannot be achieved only using conventional analysis of geochemical models alone.

08 HYDROGEN↗

Human-Machine Shared Control for Path Following Considering Driver Fatigue Characteristics

Fatigue driving has been regarded as one of the most important factors that cause traffic accidents. This paper proposes a robust human-machine shared control strategy to improve the vehicle performance for different driver fatigue states. Firstly, the time-varying driver steering model is proposed to address the model mismatch caused by fatigue driving. And the driver fatigue evaluation system is established based on facial features to quantify driver fatigue levels. Based on the quantified fatigue levels, a novel strategy for allocating authorities of the driver and controller is developed for building the driver-vehicle interaction system. Then, to weaken the influence of parameter perturbations caused by the time-varying driver states, we design a fatigue-based shared controller through state feedback. The actuator saturation and system constraints are considered in the controller design through the robust set-invariance property to improve vehicle safety and driving comfort. The driver-in-the-loop platform is conducted to validate the effectiveness of the proposed shared steering controller. In conclusion, the experimental results show that the proposed strategy can adaptively optimize the human-machine authorities according to fatigue states and comprehensively improve vehicle performance.

97 MATHEMATICS AND COMPUTING↗

Agreement Between Institutional Measurements and Treatment Planning System Calculations for Basic Dosimetric Parameters as Measured by the Imaging and Radiation Oncology Core-Houston

Purpose: To compare radiation machine measurement data collected by the Imaging and Radiation Oncology Core at Houston (IROC-H) with institutional treatment planning system (TPS) values, to identify parameters with large differences in agreement; the findings will help institutions focus their efforts to improve the accuracy of their TPS models. Methods and Materials: Between 2000 and 2014, IROC-H visited more than 250 institutions and conducted independent measurements of machine dosimetric data points, including percentage depth dose, output factors, off-axis factors, multileaf collimator small fields, and wedge data. We compared these data with the institutional TPS values for the same points by energy, class, and parameter to identify differences and similarities using criteria involving both the medians and standard deviations for Varian linear accelerators. Distributions of differences between machine measurements and institutional TPS values were generated for basic dosimetric parameters. Results: On average, intensity modulated radiation therapy–style and stereotactic body radiation therapy–style output factors and upper physical wedge output factors were the most problematic. Percentage depth dose, jaw output factors, and enhanced dynamic wedge output factors agreed best between the IROC-H measurements and the TPS values. Although small differences were shown between 2 common TPS systems, neither was superior to the other. Parameter agreement was constant over time from 2000 to 2014. Conclusions: Differences in basic dosimetric parameters between machine measurements and TPS values vary widely depending on the parameter, although agreement does not seem to vary by TPS and has not changed over time. Intensity modulated radiation therapy–style output factors, stereotactic body radiation therapy–style output factors, and upper physical wedge output factors had the largest disagreement and should be carefully modeled to ensure accuracy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

TU-C-BRE-03: Aggregation of Linac Measurement Data

Purpose: Accurate data of linear accelerator radiation characteristics is important for treatment planning system commissioning as well as regular quality assurance of the machine. The RPC has performed site visits of numerous machines . Data gathered from Varian machines from the past 15 years are presented. The data collected can be used as a secondary check or when commissioning a new machine to verify that values are reasonable. Methods: Data from the past 15 years of RPC site visits was compiled and analyzed. Data was composed from measurements from approximately 400 Varian machines. Each dataset consists of several point measurements at various locations in a water phantom to measure percentage depth dose, output factors, including small MLC fields, off-axis factors, and wedge factors if applicable. Common statistical values are presented for each machine type. Where applicable, data was compared to other reference data given by the vendor or a select number of previous researchers. Results: Data is separated by energy and parameter and then analyzed by machine class. Data distributions of the parameter data were normal except occasionally at the tails. Distributions of the data for each class and parameter are tabulated to give not simply a singular reference value, but metrics about the distribution: 5th and 95th percentile values and the standard deviation as well as the median. Conclusion: The RPC has collected numerous data on Varian linacs and presented the finding of the past 15 years. The data can be used as a reference data set for physicists to compare against. A linac that deviates from the values does not necessarily indicate there is a problem as long as the treatment planning system correlates to the machine. Comparison of linac and treatment planning system data to external reference data can prevent serious treatment errors.

07 ISOTOPE AND RADIATION SOURCES↗

SU-E-T-225: Correction Matrix for PinPoint Ionization Chamber for Dosimetric Measurements in the Newly Released Incise™ Multileaf Collimator Shaped Small Field for CyberKnife M6™ Machine

Purpose: For small field dosimetry, such as measurements of output factors for cones or MLC-shaped irregular small fields, ion chambers often Result in an underestimation of the dose, due to both the volume averaging effect and the lack of lateral charged particle equilibrium. This work presents a mathematical model for correction matrix for a PTW PinPoint ionization chamber for dosimetric measurements made in the newly released Incise™ Multileaf collimator fields of the CyberKnife M6™ machine. Methods: A correction matrix for a PTW 0.015cc PinPoint ionization chamber was developed by modeling its 3D dose response in twelve cone-shaped circular fields created using the 5mm, 7.5mm, 10mm, 12.5mm, 15mm, 20mm, 25mm, 30mm, 35mm, 40mm, 50mm, 60mm cones in a CyberKnife M6™ machine. For each field size, hundreds of readings were recorded for every 2mm chamber shift in the horizontal plane. The contribution of each dose pixel to a measurement point depended on the radial distance and the angle to the chamber axis. These readings were then compared with the theoretical dose as obtained with Monte Carlo calculation. A penalized least-square optimization algorithm was developed to generate the correction matrix. After the parameter fitting, the mathematical model was validated for MLC-shaped irregular fields. Results: The optimization algorithm used for parameter fitting was stable and the resulted response factors were smooth in spatial domain. After correction with the mathematical model, the chamber reading matched with the calculation for all the tested fields to within 2%. Conclusion: A novel mathematical model has been developed for PinPoint chamber for dosimetric measurements in small MLC-shaped irregular fields. The correction matrix is dependent on detector, treatment unit and the geometry of setup. The model can be applied to non-standard composite fields and provides an access to IMRT point dose validation.

60 APPLIED LIFE SCIENCES↗

Multimodal X-ray nano-spectromicroscopy analysis of chemically heterogeneous systems

Abstract Understanding the nanoscale chemical speciation of heterogeneous systems in their native environment is critical for several disciplines such as life and environmental sciences, biogeochemistry, and materials science. Synchrotron-based X-ray spectromicroscopy tools are widely used to understand the chemistry and morphology of complex material systems owing to their high penetration depth and sensitivity. The multidimensional (4D+) structure of spectromicroscopy data poses visualization and data-reduction challenges. This paper reports the strategies for the visualization and analysis of spectromicroscopy data. We created a new graphical user interface and data analysis platform named XMIDAS (X-ray multimodal image data analysis software) to visualize spectromicroscopy data from both image and spectrum representations. The interactive data analysis toolkit combined conventional analysis methods with well-established machine learning classification algorithms (e.g. nonnegative matrix factorization) for data reduction. The data visualization and analysis methodologies were then defined and optimized using a model particle aggregate with known chemical composition. Nanoprobe-based X-ray fluorescence (nano-XRF) and X-ray absorption near edge structure (nano-XANES) spectromicroscopy techniques were used to probe elemental and chemical state information of the aggregate sample. We illustrated the complete chemical speciation methodology of the model particle by using XMIDAS. Next, we demonstrated the application of this approach in detecting and characterizing nanoparticles associated with alveolar macrophages. Our multimodal approach combining nano-XRF, nano-XANES, and differential phase-contrast imaging efficiently visualizes the chemistry of localized nanostructure with the morphology. We believe that the optimized data-reduction strategies and tool development will facilitate the analysis of complex biological and environmental samples using X-ray spectromicroscopy techniques.

36 MATERIALS SCIENCE↗

Local structure elucidation of tungsten-substituted vanadium dioxide (V$$_{1-x}$$W$$_x$$O$$_2$$)

Abstract Initially, vanadium dioxide seems to be an ideal first-order phase transition case study due to its deceptively simple structure and composition, but upon closer inspection there are nuances to the driving mechanism of the metal-insulator transition (MIT) that are still unexplained. In this study, a local structure analysis across a bulk powder tungsten-substitution series is utilized to tease out the nuances of this first-order phase transition. A comparison of the average structure to the local structure using synchrotron x-ray diffraction and total scattering pair-distribution function methods, respectively, is discussed as well as comparison to bright field transmission electron microscopy imaging through a similar temperature-series as the local structure characterization. Extended x-ray absorption fine structure fitting of thin film data across the substitution-series is also presented and compared to bulk. Machine learning technique, non-negative matrix factorization, is applied to analyze the total scattering data. The bulk MIT is probed through magnetic susceptibility as well as differential scanning calorimetry. The findings indicate the local transition temperature ( $$T_c$$ T c ) is less than the average $$T_c$$ T c supporting the Peierls-Mott MIT mechanism, and demonstrate that in bulk powder and thin-films, increasing tungsten-substitution instigates local V-oxidation through the phase pathway VO $$_2\, \rightarrow$$ 2 → V $$_6$$ 6 O $$_{13} \, \rightarrow$$ 13 → V $$_2$$ 2 O $$_5$$ 5 .

Wilson, Catrina E. (ORCID:0000000173397318)↗

Multiphysics Analysis of Frequency Detuning in Superconducting RF Cavities for Proton Particle Accelerators

Multiphysics analyses for superconducting cavities are essential in the course of cavity design to meet stringent requirements on cavity frequency detuning. Superconducting RF cavities are the core accelerating elements in modern particle accelerators whether it is proton or electron machine, as they offer extremely high quality factors thus reducing the RF losses per cavity. However, the superior quality factor comes with the challenge of controlling the resonance frequency of the cavity within few tens of hertz bandwidth. In this paper, we investigate how the multiphysics analysis plays a major role in proactively minimizing sources of frequency detuning, specifically; microphonics and Lorentz Force Detuning (LFD) in the stage of RF design of the cavity and mechanical design of the niobium shell and the helium vessel.

43 PARTICLE ACCELERATORS↗

Machine Learning assisted optimization and parameter space exploration dataset of spin ice Hamiltonian

This repository contains both simulated and experimental structure factor data for the data challenge involving the inverse scattering problem. The simulated data were generated during a machine-learning-assisted optimization routine described in ref[1]. The experimental structure factor was measured on a rare-earth oxide, Dy2Ti2O7 using diffuse neutron scattering from time-of-flight techniques on the CORELLI instrument at the Spallation Neutron Source, Oak Ridge National Laboratory. A Metropolis Monte Carlo code implemented to run in a High-performance computing setting was used to calculated simulated structure factors for the spin-ice Hamiltonian at 680 mK, which is the same temperature as for the experimental data. The total size of all the files in this repository is 5.12 GB. A detailed description of the files is given below. ExperimentalData_630mK.dat – A linearized version of 3-dimensional experimental data of size 61×81×21. This data was processed to remove an estimation of non-magnetic background, including nuclear scattering signal and instrumentation background. Parameters.dat – 6700 samples were evaluated over the 4-dimensional parameter space (J_1, J_2, J_3 and J_(3^' )). There is an additional parameter, D in the spin Hamiltonian to mimic the dipolar interaction between magnetic ions. However, this parameter, D was fixed to a value determined by prior work. This file contains five columns for the parameters J_1, J_2, J_3, J_(3^' ) and D respectively. 3D_Simulation_Data.dat – The simulated structure factor, S(Q) data are included in this file. Each raw contains a linearized array of 3D volumes of S(Q) calculated for the parameter set given in the corresponding row of the file Parameters.dat. The size of the volume data was matched to the experimental data. Qx(h,-h,0).dat, Qy(k,k,-2k).dat, Qz(l,l,l).dat – These files contain the h, k, and l values along with the reciprocal vectors [h,-h,0], [k,k,-2k] and [l,l,l] respectively.

36 MATERIALS SCIENCE↗