Search NASASearch

SEARCH · Search NASA

Results for “Potential Theory”

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

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

436 records · Page 9

Pinning ångström-size solid ionic channels for rare-earth element separation

High-purity rare-earth elements are essential for modern technologies, yet current solvent extraction processes are energy-intensive and environmentally harmful because of inadequate selectivity and ligand toxicity. Although combining size exclusion and binding affinity can improve lanthanide separation, the role of long-range confinement remains underexplored. Here we report lanthanide separation in aqueous systems using extremely confined manganese oxide solid ionic channels with optimized layer spacing. Different lanthanides induce distinct solid-state phase transformations in manganese oxide, creating a strong driving force for separation. Two lanthanide groups, differing by ~1.4 Å in spacing, were identified and confirmed to be stable by density functional theory. The narrower confinement of heavier Group II lanthanides improves cross-group separation by increasing the dehydration barrier for lighter Group I lanthanides without inducing strong binding. Here, we further developed a strategy to pin the confinement dimensions and enhance same-group separation, increasing enrichment factors for La–Nd and La–Pr pairs from 1.6 ± 0.1 and 1.5 ± 0.1 to 5.4 ± 0.1 and 4.2 ± 0.1, respectively.

Chemical engineering

Unravelling ultralow thermal conductivity in perovskite Cs2AgBiBr6: dominant wave-like phonon tunnelling and strong anharmonicity

Abstract Understanding the lattice dynamics and heat transport physics in the lead-free halide double perovskites remains an outstanding challenge due to their lattice dynamical instability and strong anharmonicity. In this work, we investigate the microscopic mechanisms of anharmonic lattice dynamics and thermal transport in lead-free halide double perovskite Cs 2 AgBiBr 6 from first principles. We combine self-consistent phonon calculations with bubble diagram correction and a unified theory of lattice thermal transport that considers both the particle-like phonon propagation and wave-like tunnelling of phonons. An ultra-low thermal conductivity at room temperature (~0.21 Wm −1 K −1 ) is predicted with weak temperature dependence( ~ T −0.34 ), in sharp contrast to the conventional ~T −1 dependence. Particularly, the vibrational properties of Cs 2 AgBiBr 6 are featured by strong anharmonicity and wave-like tunnelling of phonons. Anharmonic phonon renormalization from both the cubic and quartic anharmonicities are found essential in precisely predicting the phase transition temperature in Cs 2 AgBiBr 6 while the negative phonon energy shifts induced by cubic anharmonicity has a significant influence on particle-like phonon propagation. Further, the contribution of the wave-like tunnelling to the total thermal conductivity surpasses that of the particle-like propagation above around 310 K, indicating the breakdown of the phonon gas picture conventionally used in the Peierls-Boltzmann Transport Equation. Importantly, further including four-phonon scatterings is required in achieving the dominance of wave-like tunnelling, as compared to the dominant particle-like propagation channel when considering only three-phonon scatterings. Our work highlights the importance of lattice anharmonicity and wave-like tunnelling of phonons in the thermal transport in lead-free halide double perovskites.

Chemistry

Hydrogen Production and Li-Ion Battery Performance with MoS2-SiNWs-SWNTs@ZnONPs Nanocomposites

This study explores the hydrogen generation potential via water-splitting reactions under UV-vis radiation by using a synergistic assembly of ZnO nanoparticles integrated with MoS2, single-walled carbon nanotubes (SWNTs), and crystalline silicon nanowires (SiNWs) to create the MoS2-SiNWs-SWNTs@ZnONPs nanocomposites. A comparative analysis of MoS2 synthesized through chemical and physical exfoliation methods revealed that the chemically exfoliated MoS2 exhibited superior performance, thereby being selected for all subsequent measurements. The nanostructured materials demonstrated exceptional surface characteristics, with specific surface areas exceeding 300 m2 g−1. Notably, the hydrogen production rate achieved by a composite comprising 5% MoS2, 1.7% SiNWs, and 13.3% SWNTs at an 80% ZnONPs base was approximately 3909 µmol h−1g−1 under 500 nm wavelength radiation, marking a significant improvement of over 40-fold relative to pristine ZnONPs. This enhancement underscores the remarkable photocatalytic efficiency of the composites, maintaining high hydrogen production rates above 1500 µmol h−1g−1 even under radiation wavelengths exceeding 600 nm. Furthermore, the potential of these composites for energy storage and conversion applications, specifically within rechargeable lithium-ion batteries, was investigated. Composites, similar to those utilized for hydrogen production but excluding ZnONPs to address its limited theoretical capacity and electrical conductivity, were developed. The focus was on utilizing MoS2, SiNWs, and SWNTs as anode materials for Li-ion batteries. This strategic combination significantly improved the electronic conductivity and mechanical stability of the composite. Specifically, the composite with 56% MoS2, 24% SiNWs, and 20% SWNTs offered remarkable cyclic performance with high specific capacity values, achieving a complete stability of 1000 mA h g−1 after 100 cycles at 1 A g−1. These results illuminate the dual utility of the composites, not only as innovative catalysts for hydrogen production but also as advanced materials for energy storage technologies, showcasing their potential in contributing to sustainable energy solutions.

Chemistry

High-Throughput Uniformity and Defect Monitoring in Low-Temperature Electrolysis Porous Transport Layers Using X-Ray Radiography

Effective quality control (QC) for manufacturing proton exchange membrane water electrolysis (PEMWE) components is critical to enabling widespread adoption of the technology for hydrogen generation. This study investigates X-ray radiography as a novel, high-throughput, potentially in-line QC technique for detecting defects and assessing material property distributions in titanium-based porous transport layers (PTLs) which constitute a crucial component of low temperature PEMWE stacks. We obtain radiographs of a set of fifteen PTLs and model their absorbance of the broadband radiation as a second-order polynomial to account for the non-monoenergetic radiation source used in this study. The resulting model serves as a basis for predicting the areal density and porosity distributions of the PTLs. We find radiography successful in detecting multiple instances of defects, including holes/depressions, cracks, and excess material on the surface or in the pores of the material, demonstrating its potential as a robust in-line QC tool for PTL manufacturing.

08 HYDROGEN

Patchy nanoparticles by atomic stencilling

Stencilling, in which patterns are created by painting over masks, has ubiquitous applications in art, architecture and manufacturing. Modern, top-down microfabrication methods have succeeded in reducing mask sizes to under 10 nm, enabling ever smaller microdevices as today’s fastest computer chips. Meanwhile, bottom-up masking using chemical bonds or physical interactions has remained largely unexplored, despite its advantages of low cost, solution-processability, scalability and high compatibility with complex, curved and three-dimensional (3D) surfaces. Here we report atomic stencilling to make patchy nanoparticles (NPs), using surface-adsorbed iodide submonolayers to create the mask and ligand-mediated grafted polymers onto unmasked regions as ‘paint’. We use this approach to synthesize more than 20 different types of NP coated with polymer patches in high yield. Polymer scaling theory and molecular dynamics (MD) simulation show that stencilling, along with the interplay of enthalpic and entropic effects of polymers, generates patchy particle morphologies not reported previously. These polymer-patched NPs self-assemble into extended crystals owing to highly uniform patches, including different non-closely packed superlattices. We propose that atomic stencilling opens new avenues in patterning NPs and other substrates at the nanometre length scale, leading to precise control of their chemistry, reactivity and interactions for a wide range of applications, such as targeted delivery, catalysis, microelectronics, integrated metamaterials and tissue engineering.

36 MATERIALS SCIENCE

Advancing technologies for lignin-based jet fuel production in aqueous phase

Integrating lignin into a cellulosic ethanol plant for the co-production of lignin-based jet fuel (LJF) in aqueous phase offers a significant opportunity to boost operational efficiency, economic viability, carbon conversion, and the overall sustainability of biofuel and chemical production. LJF is lignin-structure-based jet fuel blendstocks primarily composed of alkyl-substituted mono-, bi-, and tri-cyclohexanes. It exhibits high energy density, potential for low emissions, and favourable blend characteristics that comply with drop-in specifications. An overview of lignin feedstock, catalytic processes, LJF chemical compositions, fuel properties tests, and techno-economic analysis (TEA) and life cycle assessment (LCA) indicate that (1) the reactivity of lignin plays a crucial role in its structure transformation to LJF molecules; (2) catalytic processing of lignin to LJF can occur through a simultaneous depolymerization and hydrodeoxygenation process, bypassing the intermediate step of producing and upgrading lignin-derived oil; (3) LJF's uniqueness molecules making it more promising for high energy content and low emission jet fuel properties for next generation sustainable aviation fuel (SAF); and (4) TEA and LCA demonstrate that LJF is not only potentially cost-effective but also offers favourable carbon footprint compared to other SAFs. In conclusion, this review highlights the most recent advancements in LJF technology, along with the challenges and opportunities that lie ahead in fulfilling its potential.

09 BIOMASS FUELS

Electrochemical Deconstruction of Ortho-Phthalate Plasticizers and Recovery of Plasticizing Moieties

Electrochemical methods for the direct reduction of alkyl esters have been understudied but provide a potential advantage for addressing specific waste streams given that such strategies often require only a minimal chemical profile. One such waste stream that could benefit from electrochemical remediation is poly(vinyl chloride) (PVC) plastics. PVC recycling often faces challenges due to the complexity of such waste. Solvent-based recycling methods pose several advantages for addressing post-use PVC; however, such methods are complicated by the high amounts of toxic legacy plasticizers (ortho-phthalates) present in PVC. A potential solution to addressing such phthalates is to address them electrochemically, coupled with recovery of the resulting valuable products. Presented herein is an optimized electrochemical method for ester activation that is leveraged to separate and recover the aromatic and alkyl components of ortho-phthalate plasticizers. The resulting aliphatic alcohols may be reused to prepare other non-toxic plasticizers. This electro-degradation method is demonstrated on six phthalates that have been identified to pose health concerns in addition to plasticizers recovered from commercial samples of PVC.

di-(2-ethylhexyl) phthalate

Integrated optical frequency division for microwave and mmWave generation

Abstract The generation of ultra-low-noise microwave and mmWave in miniaturized, chip-based platforms can transform communication, radar and sensing systems 1–3 . Optical frequency division that leverages optical references and optical frequency combs has emerged as a powerful technique to generate microwaves with superior spectral purity than any other approaches 4–7 . Here we demonstrate a miniaturized optical frequency division system that can potentially transfer the approach to a complementary metal-oxide-semiconductor-compatible integrated photonic platform. Phase stability is provided by a large mode volume, planar-waveguide-based optical reference coil cavity 8,9 and is divided down from optical to mmWave frequency by using soliton microcombs generated in a waveguide-coupled microresonator 10–12 . Besides achieving record-low phase noise for integrated photonic mmWave oscillators, these devices can be heterogeneously integrated with semiconductor lasers, amplifiers and photodiodes, holding the potential of large-volume, low-cost manufacturing for fundamental and mass-market applications 13 .

Science & Technology - Other Topics

Physical Modeling and Design of a Nonvolatile Optically Gated High‐Power Diamond Transistor

In this work, we present the theory and modeling framework of a diamond optically gated junction field‐effect transistor (DOGFET). The device utilizes nitrogen substitutional centers in type‐1b diamond to optically modulate a p‐ boron doped diamond channel. Using sub‐gap lasers with intensities as low as 100 W/cm 2 , electrons are optically excited from substitutional nitrogen sites to the conduction band of the diamond substrate, thus enabling the optical gate to exercise control on modulating the space‐charge region at the junction and therefore the channel conductivity. We show that the device can deliver a current of 7 μA/μm, or equivalently 1750 A/cm 2 , while switching at a frequency greater than 100 kHz, in a form factor of 5 μm 2 . The breakdown voltage is found to be greater than 1850 V, with a breakdown field strength of ~13 MV/cm. Moreover, the device supports nonvolatile operation with a “memory effect” enabling single transistor state retention. The presented simulation framework provides a physically grounded insight into the limits and opportunities of optoelectronic diamond systems.

Engineering - Electronic and electrical engineerin

Purcell enhancement of directional edge photocurrent in a van der Waals self-cavity

Cavities provide a means to manipulate the optical and electronic responses of quantum materials by selectively enhancing light-matter interaction at specific frequencies and momenta. While cavities typically involve external structures, exfoliated flakes of van der Waals (vdW) materials can form intrinsic self-cavities due to their small finite dimensions, confining electromagnetic fields into plasmonic cavity modes, characterized by standing-wave current distributions. While cavity-enhanced phenomena are well-studied at optical frequencies, the impact of self-cavities on nonlinear electronic responses—such as directional photocurrent—remains largely unexplored, particularly in the terahertz regime, critical for emerging ultrafast optoelectronic technologies. Here, we report a self-cavity-induced Purcell enhancement of directional photocurrents in the vdW semimetal WTe 2 . Using ultrafast optoelectronic circuitry, we measured coherent near-field THz emission resulting from nonlinear photocurrents excited at the sample edges. We observed enhanced emission at finite frequencies, tunable via excitation fluence and sample geometry, which we attribute to plasmonic interference effects controlled by the cavity boundaries. We developed an analytical theory that captures the cavity resonance conditions and spectral response across multiple devices. Our findings establish WTe 2 as a bias-free, geometry-tunable THz emitter and demonstrate the potential of self-cavity engineering for controlling nonlinear, nonequilibrium dynamics in quantum materials.

condensed-matter physics

Fluidized Bed Gasification For Conversion of Biomass and Waste Materials to Renewable Hydrogen

This project was undertaken in order to study the potential for hydrogen production, at low cost, from mixtures of biomass and municipal solid waste (MSW). This approach allows for the production of hydrogen with a very low fossil carbon burden, while taking advantage of tipping fees (associated with MSW) to improved process economics. The team sourced three primary feedstocks (wood, MSW, and waste plastics) and characterized them comprehensively using established techniques with a long track record in the field of gasification. All three primary feedstocks were highly reactive and lost most of their mass during initial devolatilization. The production of tars, including heavy tars, was quite high, and was most problematic in the case of the MSW and Waste Plastics feedstocks. Little practical difference was identified between the MSW and Waste Plastics materials, and the addition of bed-forming materials (dolomite and brown alumina) to the feedstocks was found to reduce production of tars during devolatilization under thermogravimetric analysis and/or Fischer Assay conditions. A series of four tests in a lab-scale bubbling-fluidized-bed gasifier, at 50 psig of pressure and about 825 C, confirmed these findings. Pellet feedstocks, broken into fragments, were used for these tests, and pellets comprised of 50% MSW and 50% biomass were found to be the best option in terms of fossil carbon burden, economic potential, and gasification characteristics. Tests were then undertaken in a pilot-scale gasifier facility based on the GTI U-Gas fluidized-bed gasification technology. The feedstock handling train of the 20 TPD U-Gas pilot-scale gasifier located in Des Plaines, IL, was operated under simulated gasification conditions, and the 50/50 pellets were found to be very robust and unproblematic. An improved design for the forward end of the feedstock injection screw of the gasifier was developed and installed. The design approach was based on improved passive cooling of the front-most shroud at the end of the screw, since this approach was found in comprehensive modeling studies to be more than sufficient to accomplish the project objectives associated with this phase of the work, while also avoiding thermal gradients that could have caused heat-stress-induced damage to the refractory around the feedstock inlet if an active cooling approach had been applied. Careful technoeconomic analysis (TEA) of two possible 1000 TPD facilities was carried out. The TEA of conversion of MSW with corn stover in one case, and MSW with woody feedstock in the other case, showed that both had the potential to provide hydrogen at about $1/kg (minimum selling price, 2018 dollar basis). Of the two TEA cases, the one that was based on the conversion of wood in the southeastern USA was found to have slightly better economic potential. The other TEA case was based on a real location in Nebraska and called for corn stover feedstock conversion along with MSW. An underserved communities outreach program plan was developed in cooperation with personnel from the Nebraska Public Power District.

08 HYDROGEN

Reversible Ferroelectric Polarization Modulation of Chiral Molecular Ferroelectrics by Circularly Polarized Light

Abstract The optical modulation of ferroelectric polarization constitutes a transformative, non‐contact strategy for the precise manipulation of ferroelectric properties, heralding advancements in optically stimulated ferroelectric devices. Despite its potential, progress in this domain is constrained by material limitations and the intricate nature of the underlying mechanisms. Recent studies have achieved efficient regulation of ferroelectric polarization and thermal conductivity in chiral ferroelectric thin films through the application of left‐ and right‐handed circularly polarized light (LCP and RCP). Differential absorption of circularly polarized light (CPL) induces nonequilibrium carrier dynamics, generating distinctive interfacial electrostatic fields that enable precise control of ultrathin ferroelectric films. For (R)‐BINOL−DIPASi and (S)‐BINOL−DIPASi (C 26 H 26 O 2 Si), polarization changes surpass 23%, exhibiting opposite response under LCP and RCP excitation. In R chiral films, remnant polarization decreases from 1.05 µC cm − 2 under LCP to 0.85 µC cm − 2 under RCP, whereas in S chiral films, polarization increases from 0.85 µC cm − 2 under LCP to 0.98 µC cm − 2 under RCP. This reversible modulation facilitates reliable switching between ON and OFF states, presenting the potential of chiral ferroelectric materials for flexible, high‐speed integrated photonic sensor technologies.

Chemistry

Dual atom catalysts for rapid electrochemical reduction of CO to ethylene

Strong CO adsorption and facile CO dimerization are the key challenges in electrochemical CO2 reduction towards multi-carbon (C2+) products. We recently showed that CoPc immobilized on a single-walled carbon nanotube can selectively reduce CO2 to methanol. This is enabled through molecular strain, which dramatically improves the CO adsorption energy to CoPc, which in turn facilitates methanol formation. We now examine the extended Phthalocyanine (PcEx) dual atom catalyst (DAC), which is intrinsically strained and contains two catalyst centers, making it a candidate for reducing CO to C2+ products. Using Quantum Mechanics (QM), we screened 20 elements embedded in the PcEx, seeking catalysts with weak hydrogen binding, strong CO binding, and facile CO dimerization. We identi>ied Fe, Ru, Co, and Ir as the best performers and subsequently evaluated the entire CO to C2H4 mechanism (9 steps) using each of these elements as catalysts. In terms of limiting potential and overall exergonicity, we identi>ied CoPcEx as the best catalyst, followed by IrPcEx. We then examined the full CO to C2H4 mechanism on the bimetallic IrCoPcEx catalyst using grand canonical QM to obtain the reaction energetics as a function of applied potential. We conclude that the bimetallic IrCoPcEx is most promising for ef>iciently converting CO to ethylene.

Musgrave, Charles B.

Pressure induced modification of electronic and magnetic properties of MnCrNbAl and MnCrTaAl

Spin-gapless semiconductor (SGS) is a new class of material that has been studied recently for potential applications in spintronics. This material behaves as an insulator for one spin channel, and as a gapless semiconductor for the opposite spin. In this work, we present results of a computational study of two quaternary Heusler alloys, MnCrNbAl and MnCrTaAl that have been recently reported to exhibit spin-gapless semiconducting electronic structure. In particular, using density functional calculations we analyze the effect of external pressure on electronic and magnetic properties of these compounds. It is shown that while these two alloys exhibit nearly SGS behavior at optimal lattice constants and at negative pressure (expansion), they are half-metals at equilibrium, and magnetic semiconductors at larger lattice constant. At the same time, reduction of the unit cell volume has a detrimental effect on electronic properties of these materials, by modifying the exchange splitting of their electronic structure and ultimately destroying their half-metallic/semiconducting behavior. Thus, our results indicate that both MnCrNbAl and MnCrTaAl may be attractive for practical device applications in spin-based electronics, but a potential compression of the unit cell volume (e.g. in thin-film applications) should be avoided.

Materials Science

Polaron catastrophe within quantum acoustics

The quantum acoustic framework has recently emerged as a nonperturbative, coherent approach to electron–lattice interactions, uncovering rich physics often obscured by perturbative methods with incoherent scattering events. Here, we model the strongly coupled dynamics of electrons and acoustic lattice vibrations within this framework, representing lattice vibrations as coherent states and electrons as quantum wave packets, in a manner distinctively different from tight-binding or discrete hopping-based approaches. We derive and numerically implement electron backaction on the lattice, providing both visual and quantitative insights into electron wave packet evolution and the formation of acoustic polarons. We investigate polaron binding energies across varying material parameters and compute key observables—including mean square displacement, kinetic energy, potential energy, and vibrational energy—over time. Our findings reveal the conditions that favor polaron formation, which is enhanced by low temperatures, high deformation potential constants, slow sound velocities, and high effective masses. Additionally, we explore the impact of external electric and magnetic fields, showing that while polaron formation remains robust under moderate fields, it is weakly suppressed at higher field strengths. These results deepen our understanding of polaron dynamics and pave the way for future studies into nontrivial transport behavior in quantum materials.

Science & Technology - Other Topics

Interface Evolutionand Long-Term Performance of NegativeCarbon Fiber Structural Electrodes

Abstract Laminated structural batteries present a transformative solution to reducing weight constraints in electric vehicles. These structural batteries are based on a multifunctional material that incorporates an energy storage function within a carbon fiber-reinforced polymer. Despite the potential of this technology, the intricate morphology of fiber–matrix or electrode–electrolyte interfaces and the impact of long-term cycling at low current rates (C-rates) on these interfaces remain insufficiently understood. This study addresses these critical knowledge gaps by examining the influence of matrix composition on the long-term electrochemical performance of structural battery electrodes and exploring advanced techniques to investigate carbon fiber–matrix interfaces. Localized imaging and X-ray scattering techniques were used to characterize morphological changes at the electrode–electrolyte interfaces by analyzing negative structural electrodes. The findings revealed that the matrix composition influences long-term electrochemical behavior and fiber–matrix interface formation. While the intrinsic properties of carbon fibers largely remain unaffected by long-term cycling, cycling promotes debonding at fiber–matrix interfaces. Nonetheless, residual regions of adhesion persist, underscoring the potential for preserving multifunctionality even under prolonged cycling conditions. These insights advance the understanding of interface dynamics, which is critical for optimizing structural battery technologies.

Chemistry

Innovations Driven by Advanced Characterization to Strategize Critical Mineral Production and Beneficial Reuse from Fossil Energy Waste

Critical minerals (CM), such as rare earth elements (REE), cobalt, nickel, and lithium, have important uses in modern electronics and advanced manufacturing, yet are vulnerable to potential supply chain disruptions. Relatively abundant and readily available fossil energy (FE) wastes, such as coal combustion ash, acid mine drainage (AMD) and treatment solids (AMD solids), and Oil and Gas (O&G) drilling wastes (drill cuttings and produced waters) are under consideration as CM feedstocks. The National Energy Technology Laboratory (NETL) has studied CM resources for various FE wastes as part of the U.S. Department of Energy’s mission of bolstering the domestic CM supply, and makes the data available to the public on EDX at sites such as the NEWTS group. Advanced characterization utilizing synchrotron x-ray techniques coupled with laboratory extractions has been performed to identify CM hosting phases in these FE wastes to inform CM recoverability mechanisms. Novel methods to selectively recover CMs while co-producing other valuable byproducts have been developed. Successful examples discussed here include: (1) The identification of REE/Co/Ni/Sc binding and hosting phases in select FE waste (coal combustion ash and AMD solids), resulting in the development of a patented CM step-extraction process, (2) coupled production of functional sorbents from these extraction wastes and for CM recovery. A pilot-scale testing to evaluate the patent’s technical feasibility for extracting REE from coal ash on a barrel scale has been successfully performed. Additionally, (3) evaluation and measurements of brine geochemistry from U.S. O&G produced waters has informed a high Li recovery potential from Marcellus Shale produced water. NETL researchers have been developing tailored pre-treatment processes, an innovative and highly durable lithium sorbent, and geochemical model guided precipitation to accelerate Li production from the Marcellus Shale produced waters. These innovations driven by characterization are integral for maximizing and advancing the potential for CM recovery while offsetting the cost and environmental footprint for FE waste management.

critical mineral processing

CASM Monte Carlo: Calculations of the thermodynamic and kinetic properties of complex multicomponent crystals

Monte Carlo techniques play a central role in statistical mechanics approaches that connect macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo techniques for the study of multicomponent crystalline materials within the Clusters Approach to Statistical Mechanics (CASM) software suite, and demonstrates their use in model systems to calculate free energies and kinetic coefficients, study phase transitions, and construct phase diagrams from first principles. Many crystal structures are complex, with multiple sublattices occupied by differing sets of chemical species, along with the presence of vacancies or interstitial species. This imposes constraints on concentration variables, the form of thermodynamic potentials, and the values of kinetic transport coefficients. The framework used by CASM to formulate thermodynamic potentials and kinetic transport coefficients accounting for arbitrarily complex crystal structures is presented and demonstrated with examples of increasing complexity. Additionally, an overview of the capabilities of the CASM software specific to Monte Carlo methods is given, and a new CASM software package is introduced, casm-flow, which helps automate the setup, submission, management, and analysis of Monte Carlo simulations.

Cluster expansion