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Shocked Transport: Experiments to Study Dynamic Particle Behavior under Varying Volume Fraction Conditions

Shocks interacting with densely-packed porous media is common in volcanic eruptions or in engineering applications such as ordinance. Large-scale, exploratory experiments have been performed by Frost and collaborators examining the behavior of a bed of particles subjected to a detonation wave. The detonation replaces the central explosive with a high-density, high-temperature gas that propagates outward. A shock wave travels through the particle bed, followed by a contact discontinuity between the shocked air and the explosive products. In the early times, the detonation wave causes many of the particles to collide and compact with each other. As the particles disperse, the experiments demonstrate a series of large-scale jets or fingers that form in the advancing particle front.

42 ENGINEERING↗

Mechanistic Source Term Considerations for Advanced Non-LWRs (Revision 1)

This report is a functional review of the radionuclide containment strategies of fluoride-salt-cooled high temperature reactor (FHR), molten salt reactor (MSR) and high temperature gas reactor (HTGR) systems. This analysis serves as a starting point for further, more in-depth analyses geared towards identifying phenomenological gaps that still exist, hindering the creation of a mechanistic source term for these reactor types. As background information to this review, an overview of how a mechanistic source term is created and used for consequence assessment necessary for licensing is provided. How a mechanistic source term is used within the Licensing Modernization Project (LMP) is also provided. Lastly, the characteristics of non-LWR mechanistic source terms are examined. This report does not assess the viability of any software system for use with advanced reactor designs, but instead covers system function requirements. Future work within the Nuclear Energy Advanced Modeling and Simulations (NEAMS) program will address such gaps. This document is an update of SAND 2020-6730. An additional chapter is included as well as edits to original content.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Gen 3 Particle Pilot Plant (G3P3) -- High-Temperature Particle System for Concentrating Solar Power (Phases 1 and 2)

The U.S. Department of Energy Solar Energy Technologies Office initiated the Generation 3 Concentrating Solar Power (CSP) program to achieve higher operating temperatures (>700 °C) to enable next-generation CSP high-temperature power cycles such as the supercritical CO 2 (sCO2) Brayton Cycle. Three teams were selected to pursue high-temperature gas, liquid, and solid pathways for the heat-transfer media. Phases 1 and 2, which lasted from 2018 – 2020, consisted of design, modeling, and testing activities to further de-risk each of the technologies and develop a design for construction, commissioning, and operation of a pilot-scale facility in Phase 3 (2021 – 2024). This report summarizes the activities in Phases 1 and 2 for the solid-particle pathway led by Sandia National Laboratories. In Phases 1 and 2, Sandia successfully de-risked key elements of the proposed Gen 3 Particle Pilot Plant (G3P3) by improving the design, operation, and performance of key particle component technologies including the receiver, storage bins, particle-to-sCO2 heat exchanger, particle lift, and data acquisition and controls. Modeling and testing of critical components have led to optimized designs that meet desired performance metrics. Detailed drawings, piping and instrumentation diagrams, and process flow diagrams were generated for the integrated system, and structural analyses of the assembled tower structure were performed to demonstrate compliance with relevant codes and standards. Instrumentation and control systems of key subsystems were also demonstrated. Together with Bridgers & Paxton, Bohannan Huston, and Sandia Facilities, we have completed a 100% G3P3 tower design package with stamped engineering drawings suitable for construction bid in Phase 3.

14 SOLAR ENERGY↗

U.S. Domestic Pebble Bed Reactor: Security-by-Design

U.S. nuclear power facilities face increasing challenges in meeting dynamic security requirements caused by evolving and expanding threats while keeping cost reasonable to make nuclear energy competitive. The past approach has often included implementing security features after a facility has been designed and without attention to optimization, which can lead to cost overruns. Incorporating security in the design process can provide robust, cost effective, and sufficient physical protection systems. The purpose of this work is both to develop a framework for the integration of security into the design phase of High Temperature Gas Reactors (HTGRs) that utilize pebble-based fuels and increase the use of modeling and simulation tools to optimize the design of physical protection systems. Specifically, this effort focuses on integrating security into the design phase of a model HTGR that meets current Nuclear Regulatory Commission (NRC) physical protection requirements and providing advanced solutions to improve physical protection and decrease costs. A suite of tools, including SCRIBE3D©, PATHTRACE© and Blender© were used to model a hypothetical, generic domestic HTGR facility. Physical protection elements such as sensors, cameras, barriers, and guard forces were added to the model based on best practices for physical protection systems. Multiple outsider sabotage scenarios were examined with four-to eight adversaries to determine security metrics. The results of this work will influence physical protection system designs and facility designs for U.S. domestic HTGRs. This work will also demonstrate how a series of experimental and modeling capabilities across the Department of Energy (DOE) Complex can impact the design of and complete Safeguards and Security by Design (SSBD) for SMRs. The conclusions and recommendations in this document may be applicable to all SMR designs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Material Control & Accountancy for Molten Salt Reactors (FY2021 Report)

There is significant domestic and international interest, investment, and research and development momentum to pursue advanced nuclear reactor technologies. Molten salt reactor (MSR) concepts display the largest variability in fuel type and design features among the current advanced concepts. MSRs have been proposed with various core designs, sizes (power), and fuel cycles. Salt-fueled molten salt systems represent the only advanced reactor type with fuel that is not in a solid form during operation. These “liquid-fueled” MSRs are unique from perspectives of fuel fabrication, spent irradiated fuel and waste components, licensing, and material control and accountability (MC&A) including the potential of fissile material holdup. The liquid fuel salt is the defining distinction in comparison to other advanced reactors that propose TRI-structural ISOtropic particle fuel pebbles, various coolant options (e.g., molten salts or metals, high temperature gas), or small modular alternatives using solid fuel variants including both light water reactors and non-light water reactors. MSRs are appealing to the nuclear energy industry because of the diverse reactor characteristics they can support including various neutron energy spectra, fueling requirements, fuel cycles, and/or fuel utilization. However, because of the significant deviation and diversity of a salt-fueled system compared to traditional solid fuel light water-cooled reactors (LWRs), the history, regulatory licensing framework, modeling capabilities, and supporting engineering technology are either lacking or, in some cases, nonexistent. Therefore, the research community is actively supporting advanced MSR development on many of these fronts in particular to assist MSR vendors with licensing requirements. ORNL is leading the research and development of respective MC&A approaches for salt-fueled MSRs. This report summarizes the research performed at Oak Ridge National Laboratory (ORNL) under the US Department of Energy, Office of Nuclear Energy, Advanced Reactor Safeguards (ARS) program to investigate safeguards and security by design concepts, licensing and regulatory considerations, and dynamic system-level modeling to understand radioisotope concentrations for salt-fueled MSRs. The report builds upon the previous research and literature, identifies the MC&A challenges inherent to a salt-fueled MSR, reviews current regulatory frameworks for LWRs and their applicability towards salt-fueled MSRs, summarizes the status and progress of an MSR dynamic modeling tool, and discusses a prospective MC&A approach based on the Molten Salt Demonstration Reactor (MSDR) model.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

MELCOR Accident Progression and Source Term Demonstration Calculations for a HTGR

MELCOR is an integrated thermal hydraulics, accident progression, and source term code for reactor safety analysis that has been developed at Sandia National Laboratories for the United States Nuclear Regulatory Commission (NRC) since the early 1980s. Though MELCOR originated as a light water reactor (LWR) code, development and modernization efforts over the past decades have expanded its application scope to include non-LWR reactor concepts. Current MELCOR development efforts include providing the NRC with the analytical capabilities to support regulatory readiness for licensing non-LWR technologies under Strategy 2 of the NRC's near-term Implementation Action Plans. Beginning with the Next Generation Nuclear Project (NGNP), MELCOR ha s undergone a range of enhancements to provide analytical capabilities for modeling the spectrum of advanced non-LWR concepts. This report describes the generic plant model developed to demonstrate MELCOR capabilities to perform high-temperature gas reactor (HTGR) safety evaluations. The generic plant model is based on publicly available PMBR-400 design information. For plant aspects (e.g., reactor building size and leak rate) that are not described in the PBMR-400 references, the analysts made assumptions needed to construct a MELCOR full-plant model. The HTGR model uses a TRi-structural ISOtropic (TRISO)-particle fuel pebble-bed reactor with a primary system rejecting heat to a recuperative heat exchange r. Surrounding the reactor vessel is a reactor cavity contained within a confinement room cooled by the Reactor Cavity Cooling System (RCCS). Example calculations are performed to show the plant response and MELCOR capabilities to characterize a range of accident conditions. The accidents selected for evaluation consider a range of degraded and failed modes of operation for key safety functions providing reactivity control, primary system heat removal and reactor vessel decay heat removal, and confinement cooling.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Preliminary Primary System Thermal Fluids Analysis of a Horizontal Compact HTGR

The Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers, under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe, low-cost HTGR. Argonne National Laboratory (Argonne) is collaborating on the thermal hydraulic design and analysis of the HC-HTGR reactor pressure vessel internals. The scope of this work includes ensuring the reactor is able to maintain maximum core temperatures below designated safety thresholds during normal operation, shutdown, and accident conditions. This report documents the preliminary thermal hydraulic analysis of the HC-HTGR core design performed with a 1D fluid-3D solid coupled model built using the System Analysis Module (SAM). This assembly level model was utilized to inform the core assembly design, predict the temperature distribution in the peak power assembly including the peak fuel temperature, coolant channel outlet temperatures, and graphite temperature gradients. A key result of this analysis was the determination that the peak fuel temperature remains below the safety threshold of 1250°C. Additionally, this model was used to assess the assembly coolant channel and bypass flow mass flow rate distribution. Following the assembly level analysis, attention turned to the development of a full core reduced order model to be used to predict the core wide coolant flow distribution and to model certain operational and accidental transients.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

ORNL Progress Report on Microreactor Functional Containment Economics

A summary of Oak Ridge National Laboratory’s (ORNL’s) initial contributions to the economic and functional containment evaluation approach for microreactors is presented. A final report will be completed at the end of 2022. This initial progress report does not represent a final product or an expression of a complete technical analysis. Initial contributions from ORNL can be categorized into two parts: (1) description of functional containment as a design optimization tool, and (2) summary of high level technology concepts for an evaluation of economic and functional containment analysis. Additionally, the initial portion of a functional containment evaluation is presented for a generic high temperature gas reactor technology. Remaining tasks include completing the functional containment evaluation by connecting economic and consequence metrics, as well as performing the same effort for other select reactor technologies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Validation of Robustness in TCR Design Strategies

Advanced Manufacturing (AM) has been identified as one of key pathways in accelerating deployment of next generation of nuclear power plants. The nuclear industry continues to predominately rely on fabrication techniques and materials that their codes and standards were approved decades ago. This legacy approach in the highly regulated nuclear sector has brought uncertainty to commercial viability of nuclear energy in the U.S. The Transformational Challenge Reactor (TCR), sought to utilize AM methods for fabrication of a High Temperature Gas Reactor (HTGR). The program sought to leverage AM to construct a non-conventional geometry made up of TRISO fuel and hydride moderator in SiC matrix. This project objective was to provide independent analysis of the core configuration with separate set of tools and approaches than utilized by the TCR team in a 2-year time frame. This NEUP project also tackled a question: Can AM be a cost-effective tool in changing the commercial paradigm of nuclear. We investigated this question in-context of a micro HTGR. While respecting the inherit uncertainty in our input parameters, overall we saw that AM has potential in improving economic competitiveness of nuclear energy when employed on multiple fronts (i.e. few percentage cost improvement per component). Given realizing AM requires mass orders and large R&D investment for commercial utilization, Department of Energy should focus its support on few key enabling technologies and support their codes and standards development and qualification cost (including irradiation as applicable) rather than taking a diluted approach.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal Extraction Modeling within HYBRID: Nominal and Extraction Conditions in Advanced Reactor Systems

This document details continuing development of thermal extraction modeling within the HYBRID repository, the modeling repository of the Integrated Energy Systems program at Idaho National Laboratory. The focus of the thermal extraction work is setting up template energy conversion systems for advanced reactor systems. Based on these nominal conditions, the IES team is developing extraction capability maps that present the system thermal-to-electric efficiency of the remaining system and the mass extraction fraction capability of these systems when extracting steam at various pressures to send steam to applications at a lower given pressure. These curves are mapped on what has become termed “whale chart” due to the appearance of the results. Multiple advanced reactor systems are complete, and it is anticipated that all four of the main advanced reactor types: advanced light-water reactors, high temperature gas reactors, liquid metal fast reactors, and molten salt reactors, will be complete by the end of the fiscal year.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Molten Salt Reactor Experiment Simulation using Shift/Griffin

The Department of Energy (DOE)’s NEAMS focuses its efforts on the development of advanced modeling and simulation (M&S) tools for light-water reactors (LWRs) and non–LWRs (i.e., molten salt reactors, high-temperature gas reactors, microreactors, and fast reactors). In the previous fiscal year, the Multiphysics Applications Driver Technical Area funded molten salt reactor (MSR) M&S at Oak Ridge National Laboratory (ORNL) to generate multigroup macroscopic cross sections with Shift for a MSRE 2D lattice model in Griffin. In addition, Shift’s capability to calculate gamma dose rates from activated components in the primary exchangers in a molten salt breeder reactor was also demonstrated. In fiscal year 2023, ORNL generated multigroup macroscopic cross sections using Shift for a 3D MSRE core model. MSRE depletion calculations using Griffin were also demonstrated in this fiscal year. For the depletion calculation, one-group microscopic cross sections for the 3D MSRE core were generated using Shift, and the decay transmutation library from ORIGEN was converted to an ISOXML file, which is required as input in Griffin. Several Monte Carlo codes, such as OpenMC and Serpent, were also used to benchmark and supplement multigroup cross sections generated by Shift. Multigroup libraries were generated with 8 and 20 group structures, and the study found the 8-group structure to be more accurate when comparing Griffin results to continuous energy (CE) Monte Carlo results. The average flux from CE Shift calculations is up to ~6% higher than the CE Serpent calculations because of different values applied for the energy released per fission (κ values). The average flux in the fuel salt calculated by Griffin using cross sections generated with Shift agrees well with the reference CE Shift solution; the same is valid for the corresponding Serpent results. The maximum relative error is ~6% and ~2% compared to the CE Shift and Serpent reference solutions, respectively. Meanwhile, the average flux calculated by Griffin in the graphite moderator shows a higher difference in the thermal range when compared to both reference Monte Carlo solutions; this result suggests a need for improvement in cross section generation for the graphite moderator in the thermal range in both Monte Carlo codes. Griffin depletion calculations using cross sections from Shift and Serpent were performed and compared against ORIGEN calculations, and the nuclide densities calculated by Griffin were found to be generally in agreement with those of ORIGEN. Because a different approach was taken to calculate the energy released per fission ( κ values) in Shift and Serpent, a difference in nuclide densities from differences in the average flux was observed between Griffin using Serpent and Shift cross sections. Griffin calculations with Shift cross sections produced higher average flux in the salt than with Serpent cross sections, leading to higher consumption of 235 U and higher production of 135 Xe. For time-dependent depletion calculations, cross sections were generated with Serpent, and Griffin’s results using these cross sections were compared to CE Serpent depletion results, demonstrating good agreement. The average difference in keff between Serpent and Griffin as a function of burnup is about 155 pcm. Similarly, good agreement with small differences up to ~0.5% was also noticed in the nuclide density of 235 U and 135 Xe. More details regarding the methodologies invoked to generate the cross section to make code-to-code comparisons are discussed further in this report. User feedback on Griffin and Shift capabilities that will enhance these calculations is provided in this report for future consideration. The work performed this fiscal year can be extended further for multiphysics coupling of Griffin-Pronghorn/SAM with Mole to study precursor flow and salt chemistry.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Concept of Operations for Microreactor Transportation

Microreactors are very small nuclear reactors with a power output of 20 MWe or less and are designed to be factory-built, modular in nature, and highly portable. The Idaho National Laboratory (INL) has been identified as a potential location to demonstrate microreactors and two microreactor concepts currently under consideration for demonstration at the INL include a tristructural isotropic (TRISO) fueled high-temperature gas reactor and a sodium cooled reactor using a SNAP-10A style fuel pin design. The objective of this report is to identify a concept of operations (CONOPS) for shipping these microreactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

U.S. Domestic Security-by-Design: On Site Response Force Strategies

U.S. nuclear power facilities face increasing challenges in meeting dynamic security requirements caused by evolving and expanding threats while keeping cost reasonable to make nuclear energy competitive. The past approach has often included implementing security features after a facility has been designed and without attention to optimization, which can lead to cost overruns. Incorporating security in the design process can provide robust, cost- effective, and sufficient physical protection systems. The purpose of this work is both to develop a framework for the integration of security into the design phase of High Temperature Gas Reactors (HTGRs) that utilize pebble-based fuels and microreactors. Specifically, this effort focuses on integrating security into the design phase of a model HTGR and microreactor that meets current Nuclear Regulatory Commission (NRC) physical protection requirements and providing advanced solutions to improve physical protection and decrease costs. A suite of tools, including SCRIBE3D©, PATHTRACE© and Blender© were used to model a hypothetical, generic domestic HTGR facility and microreactor facility. Physical protection elements such as sensors, cameras, barriers, and onsite response forces were added to the model based on best practices for physical protection systems. Multiple outsider sabotage scenarios were examined with four-to-eight adversaries to determine security metrics. The results of this work will influence physical protection system designs and facility designs for U.S. domestic HTGRs and microreactors. This work will also demonstrate how a series of experimental and modeling capabilities across the Department of Energy (DOE) Complex can lead to efficient security systems that utilize an onsite response force. The conclusions and recommendations in this document may be applicable to all SMR designs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Automated Segmentation of Twin Boundaries in TRISO Silicon Carbide Using Deep Neural Networks

Coated particle fuels, such as the tristructural isotropic (TRISO) fuel particle, are essential for high-temperature gas reactor (HTGR) applications due to their efficiency and stability under normal and off-normal conditions. However, widespread commercialization and deployment of this technology for next-generation nuclear applications require robust quality assurance and quality control (QA/QC) methods linking fabrication, properties, and performance. Of the many important metrics for TRISO QA/QC, quantification of the silicon carbide (SiC) microstructure is critical because it correlates with fission product retention during irradiation. Previous work has shown extensive twinning of the SiC microstructure, which strongly affects microstructural metrics; however, twin grain boundaries are not expected play a significant role in fission product diffusion. This report summarizes the initial development, training, and testing of a machine learning image processing algorithm to detect twin grain boundaries in a backscattered electron image, which can be removed so that microstructural metrics can be recalculated for legacy data. Further development and deployment of this model will provide automated, scalable improvement of potential QA/QC methods for the SiC layer of TRISO particles.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Advanced Reactor Designs Security Analysis, Risk, and Recommendations: Risks, Consequences, and Possible by-Design Mitigation Approaches Associated with Select Advanced Reactors

Next-generation advanced reactors (ARs) incorporate enhanced safety systems, have smaller source terms, and feature compact modular designs, which should lessen their collective risk profiles. However, to fully evaluate risk, security needs to be a part of the equation. Without taking security into consideration, safety systems and components in the new ARs may be vulnerable to sabotage. These base attributes, coupled with enhanced security features specific to AR design through sound engineering and security-by-design (SeBD), should provide developers and operators with lower inherent security risk profiles. Building security early into the AR design may remove or passively secure potential critical targets from an adversary’s reach , thereby increasing overall safety and security. An integrated approach and diverse design team that includes engineering, operations, and security experts are fundamental to building security into the design without sacrificing fundamental operational efficiencies and principles. The objective of this project was to evaluate the security and safety interfaces for five classes of reactors, identify potential security vulnerabilities of structures, systems, and components (SSC), and underscore the need to consider security alongside safety in the design o f these concepts. The five reactor classes evaluated in this project and presented in this report are molten-salt reactors (MSR), high temperature gas reactors (HTGR), sodium-fast reactors (SFR), advanced light-water reactors (ALWR), and microreactors. These designs were selected because they reflect the concepts that are closest to market deployment and have received significant resource investments from the public and private sector. This project assesses the inherent security risks posed by common classes of ARs, provides a methodology and framework to assess security along with safety, and offers an analysis of potential mitigation strategies that could be incorporated. For each AR technology, the SSCs that relate to radionuclide source safety functions are discussed to understand the SSC contribution to safety and relative importance in the protective strategy for the design. The assumptions that went into evaluating each reactor concept originated from generic publicly available nonproprietary information and should not directly be used to qualify an absolute risk profile nor to rank specific AR designs. Instead, the purpose of the analysis is to understand and compare the generic inherent security risks of different AR technologies.

98 - NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL↗

Development of an Advanced Multiphysics Simulation Capability for Radiant's Microreactor Design

Argonne National Laboratory and Idaho National Laboratory, through a Department of Energy Gateway for Accelerated Innovation in Nuclear Voucher, supported key analysis needs of Radiant related to (i) air jacket thermal fluid performance, (ii) evaluation of decay heat source terms defining air jacket technical requirements, and (iii) assessment of modeling methodologies employed for core analysis. All of these activities center on numerical simulation of various aspects of Kaleidos using the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, the Cardinal multiphysics application, the OpenMC Monte Carlo code, and the Nek5000 computational fluid dynamics (CFD) code. This project builds upon an earlier Nuclear Energy Advanced Modeling and Simulation (NEAMS) Thermal-Hydraulic (T/H) Center of Excellence (CoE) project focused on initial demonstration of Cardinal multiphysics simulation of High Temperature Gas Reactors (HTGRs) and now focuses on Radiant’s Kaleidos concept.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

First-Principles Cost Analysis of Advanced High-Temperature Nuclear Plants

Due to the vast number of recent nuclear reactor innovations, particularly those pertaining to generation IV reactor types like high-temperature gas cooled reactors (HTGRs) and sodium-cooled fast reactors (SFRs), and the newer deployment strategies envisioned, such as use of small modular reactors (SMRs) or even microreactors, reliable, detailed, and complete costs of these nuclear innovations are needed in wide availability. The types of models that generally achieve these objectives are those incorporating the fundamental nature of the real-world systems they aspire to predict, such as first-principles models. Furthermore, first principles models typically offer predictiveness that is not attained by most other types of individual-models. However, detailed, first-principles cost modeling of nuclear reactors and entire nuclear plants is relatively limited. To address this limitation in the availability of detailed, predictive models based on fundamentals, we recently developed a range of cost models, mostly based on first-principles methodologies, to project full lifecycle costs (LCCs) of nuclear power plants (NPPs) based on multiple parallel SM-HTG-pebble bed reactors (PBRs) and SM-SFRs.

Prosser, Jacob H. [Strategic Analysis, Inc., Arlin↗

Structural Principles in Liquids and Glasses: Bottom-Up or Top-Down

The conventional approach to elucidate the atomic structure of liquid and glass is to start with local structural units made of several atoms, and to use them as building blocks to form a global structure, the bottom-up approach. We propose to add an alternative top-down approach in which we start with a global high-temperature gas state and then apply interatomic potentials to all atoms at once. This causes collective density wave instability in all directions with the same wavelength. These two driving forces, local and global, are in competition and are mutually frustrated. The final structure is determined through the compromise of frustration between these two, which creates the medium-range-order. This even-handed approach on global and local potential energy landscapes explains the distinct natures of short-range order and medium-range order, and strong temperature dependence of various properties of liquid.

36 MATERIALS SCIENCE↗