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At least 541 records · Page 30

Microstructure & Mechanical Properties of Scaled Thermally Aged LPBF 316H SS Builds

As part of the US Department of Energy’s Advanced Materials and Manufacturing Technologies program’s mission to accelerate qualification of advanced manufacturing pathways for nuclear applications, laser powder bed fusion (LPBF) 316H stainless steel (SS) has been selected as a model system to develop a rapid code case framework. This effort directly addresses the grand challenges of (1)expanding the limited portfolio of materials currently codified for elevated-temperature nuclear structural service under Section III, Division 5of the American Society of Mechanical Engineers’ Boiler and Pressure Vessel Code; and (2) significantly reducing qualification timelines that traditionally exceed a decade. The strategic importance of LPBF 316H lies in its immediate industrial relevance, existing data foundation from wrought 316H, and alignment with ongoing code case development for LPBF 316L.Prior work revealed accelerated precipitation of deleterious secondary phases and reduced creep ductility in as-printed LPBF 316H. Building on that prior research, FY2025activities focused on establishing an understanding of the key failure mechanisms of crept 316H specimens to aid in code case development and on evaluating stress relief (SR) parameters on the high-temperature performance and thermal aging-induced degradation of tensile and fracture behavior in LPBF316H.

36 MATERIALS SCIENCE↗

Microstructure and Mechanical Properties of Scaled Thermally Aged LPBF 316H SS Builds

As part of the US Department of Energy’s Advanced Materials and Manufacturing Technologies program’s mission to accelerate qualification of advanced manufacturing pathways for nuclear applications, laser powder bed fusion (LPBF) 316H stainless steel (SS) has been selected as a model system to develop a rapid code case framework. This effort directly addresses the grand challenges of (1) expanding the limited portfolio of materials currently codified for elevated-temperature nuclear structural service under Section III, Division 5 of the American Society of Mechanical Engineers’ Boiler and Pressure Vessel Code; and (2) significantly reducing qualification timelines that traditionally exceed a decade. The strategic importance of LPBF 316H lies in its immediate industrial relevance, existing data foundation from wrought 316H, and alignment with ongoing code case development for LPBF 316L. Prior work revealed accelerated precipitation of deleterious secondary phases and reduced creep ductility in as-printed LPBF 316H. Building on that prior research, FY 2025 activities focused on establishing an understanding of the key failure mechanisms of crept 316H specimens to aid in code case development and on evaluating stress relief (SR) parameters on the high-temperature performance and thermal aging induced degradation of tensile and fracture behavior in LPBF 316H.

36 MATERIALS SCIENCE↗

Bio-inspired alula-based winglet design for enhanced heat transfer in high temperature fin-and-tube heat exchangers

Fin-and-tube heat exchangers (FTHEs) are widely used for high-temperature flue-gas heat recovery, but their performance is often limited by wake regions and non-uniform fin-surface temperatures. This study proposes and numerically evaluates four bio-inspired longitudinal vortex generator (VG) configurations in a high-temperature FTHE with flue-gas inlet temperature ∼1230 K: double-delta, curved double-delta, alula, and a new curved-alula geometry. The reference fin is not hydraulically plain; it already incorporates leading-edge separation columns and convex protrusions, so the alula-type winglets are assessed as downstream add-ons acting on a strongly disturbed flow. In a second step, perforations (one, two and three circular holes) are introduced into the curved-alula VGs to further tailor the flow field. Three-dimensional simulations with the Shear Stress Transpor (SST) $k - ω$ model, temperature-dependent flue-gas properties and conjugate conduction are carried out for gas-side Reynolds numbers $Re_g ≈ 8.0$ x $10^2 - 3.6$ x $10^3$ (mass flow rates 0.5 – 2.5 g/s), and the designs are compared in terms of surface heat flux, Nusselt number, friction factor and hydrothermal performance factor (HTPF). For this already-promoted fin, the additional downstream winglets provide moderate, incremental hydrothermal gains. At the highest Reynolds number, the best non-perforated design (curved-alula) increases surface heat flux from 1630.9 to 1794.7 kW/m² (∼ 10 % gain) and the Nusselt number from 227.6 to 242.6 (∼ 7 % gain), while the friction factor rises from 0.26 to about 0.30, yielding HTPF values close to unity (∼ 0.9 – 1.0). Introducing circular perforations into the curved-alula winglets acts mainly as a wake-bleeding refinement: the three-hole configuration provides a heat flux of 1824.7 kW/m² and a pressure drop of 127.9 Pa, with HTPF in the range ∼ 1.03 – 1.14 and a small (∼ 1 – 3 %) improvement over the solid curved-alula design. Flow-field analysis shows that the perforated curved-alula VGs shrink tube-wake regions, thin the thermal boundary layer and homogenize the fin-surface temperature (outlet-gas temperature ∼ 510 – 520 K and fin-surface temperature ∼ 420 – 421 K for the three-hole case). An optimal flue-gas mass flow rate of ∼ 1 g/s ($Re_g ≈ 1.5$ x $10^3$) is identified, beyond which additional heat-transfer gains are offset by rapidly increasing pressure losses. Overall, the results highlight that initial fin geometry and VG placement are as important as VG shape: alula-based winglets are expected to yield larger relative gains on simpler flat-fin layouts or when positioned closer to the fin leading edge and tube

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

In–Depth Analysis of the Degradation Mechanisms of High–Nickel, Low/No–Cobalt Layered Oxide Cathodes for Lithium–Ion Batteries

A rational compositional design of high-nickel, cobalt-free layered oxide materials for high-energy and low-cost lithium-ion batteries would be expected to further propel the widespread adoption of electric vehicles (EVs), yet a composition with satisfactory electrochemical properties has yet to emerge. The previous work has demonstrated a promising LiNi 0.883 Mn 0.056 Al 0.061 O 2 (NMA-89) composition that outperformed high-nickel, cobalt-containing analogs in cycling stability and maintained a comparable rate performance and thermal stability. Herein, the capacity fading mechanism of NMA-89 in a pouch full cell with a 4.2 V cutoff is compared to that of its cobalt-containing analogs. The results reveal that particle cracking in LiNi 0.89 Mn 0.055 Co 0.055 O 2 (NMC-89) and LiNi 0.883 Co 0.053 Al 0.064 O 2 (NCA-89) leads to a loss of active material and an increase in surface area, thereby exacerbating structural and surface instabilities, accelerating impedance and polarization growth, and ultimately reducing their capacity retentions. LiNi 0.89 Mn 0.044 Co 0.042 Al 0.013 Mg 0.011 O 2 (NMCAM-89) and NMA-89 experience subdued surface reactions and maintain spherical particle structures, both of which are conducive to their capacity retentions during long-term cycling. Furthermore, this investigation offers insights into how specific transition-metal ions dictate the electrochemical stability of high-Ni layered oxide cathode materials, highlights the benefit of Mn-Al combination in NMA-89, and presents potential strategies to further enhance the performance of this novel class of cathode materials.

degradation mechanisms↗

High Flux Microchannel Receiver Development (Final Report)

The opportunity addressed in this project was using microscale heat exchanger technology for improving solar thermal central receiver efficiency. This will result in smaller, less expensive components and reduce the levelized cost of electricity from concentrated solar thermal power. This micro-pin solar receiver (MSR) directly heats high pressure (25 MPa) supercritical carbon dioxide (sCO 2 ) from 550°C to 720°C with an incident flux of at least 120 W/cm 2 at a receiver efficiency of >90% (assuming availability of 95% absorptivity coating), and receiver cost target of less than $\$$150/kWt. Realization of the MSR required an understanding of thermal hydraulic performance of sCO 2 in micro-pin passages, mechanical behavior of high nickel alloys at high temperatures including joints, advanced fabrication methods of high nickel alloys (etching, machining, brazing, welding, diffusion bonding), and the cost implications of these when the concept is scaled to production volumes. The technology can be used with gases (sCO 2 , helium, etc.) or with liquids such as molten salt or liquid metal. Given the high pressure associated with sCO 2 , its use demonstrates a “worst case” scenario, and the successful development of the MSR for this application will result in the development of a technology also applicable to a range of other heat transfer fluids that will enable next generation CSP plants, including support of the Gen3CSP program.

14 SOLAR ENERGY↗

A Novel Framework for Performance Evaluation and Design Optimization of PCM Embedded Heat Exchangers for the Built Environment

This research sheds light on the performance evaluation and design optimization of PCM-HXs for the built environment, addressing several barriers to practical issues to PCM-HX commercialization such as modeling aspects (i.e., modeling expertise and computational / time investment, etc.), manufacturing aspects (i.e., at-scale manufacturing, cost assessments, etc.) and experimental performance assessment (i.e., reliable experimental data, assessment of multiple PCM-working fluid combinations, etc.). We present a novel, comprehensive, and experimentally-validated design optimization framework for PCM-HXs capable of simulating any PCM-HX geometry with reasonable accuracy and significant computational time savings when compared to traditional CFD-based design practices. The framework was validated for a wide range of PCM-HX configurations, including a design optimization for a domestic hot water heater application where TES partially replaces electrical heating input. The resulting PCM-HXs were found to deliver 34-68% of the total daily hot water supply with only 5-10% package volume increase from the water heater, thus within U.S. DOE targets for TES systems. To identify the most promising HXs for PCM applications, first-order geometry and cost analyses were conducted based on off-the-shelf HX products. As part of this work, 9 PCM-HX prototypes were manufactured using additive and conventional manufacturing methods. Detailed economy-of-scale assessments were conducted for the most promising PCM-HXs and were found to have a good outlook for the next 5-10 years. The PCM-HX design optimization framework was validated through comprehensive in-house experimental testing using newly-developed PCM-to-fluid test facilities. In total,10 total in-house component-level experiments were conducted using these prototypes, including 9 with water and 1 with refrigerant (R410A) as the working fluid. It was found that the framework can successfully predict experimental thermal-hydraulic performance within ±10-20% the first time without manual design changes, eliminating the need for time-consuming and expensive prototyping efforts as part of the design process. As part of this work, a publicly-available PCM web tool was released which includes a PCM property database (531 PCMs) and PCM-HX modeling tool to assist the design community on common PCM-HX use-cases, e.g., single/multiple flow path(s) fluid-to-PCM and air-to-fluid-to-PCM configurations (https://ceeeweb.umd.edu/pcmapp/). This work will accelerate the design and time to market for next generation PCM-HXs.

25 ENERGY STORAGE↗

Toward integrating high-fidelity CFD approaches in the thermal-hydraulic analysis of turbulent dry cask systems

Nuclear power plants have been supplying resilient and reliable electricity for decades, contributing to energy independence of the U.S.. However, nuclear waste management remains one of the most significant challenges in the industry. The safety of dry cask storage systems relies heavily on their thermal-hydraulic performance. Computational Fluid Dynamics (CFD) simulations are often used to demonstrate this performance and ensure that the system design meets safety standards. This study presents reduced numerical models for various types of dry cask systems. These numerical models can produce efficient and fast results based on the employed modeling strategies. Additionally, the study uses a novel approach to high-fidelity simulations to evaluate modeling assumptions in dry cask modeling. Large Eddy Simulations (LES) are used for this purpose, particularly in regions where fluid velocity is relatively high and the turbulence characteristics become important. Furthermore, the results of these high-fidelity simulations will enhance the interpretation of outcomes produced from a lower-fidelity CFD model.

CFD↗

Trap‐Engineering the Persistent Luminescence of Ca 3 Ga 4 O 9 :Tb 3+ via Al 3+ Substitution for Optical Data Storage

Abstract Optically stimulated luminescence (OSL) materials hold great potential for optical data storage (ODS) and anticounterfeiting applications. Nevertheless, the scarcity of suitable luminescent materials with deep‐level traps remains a significant obstacle. Herein, a host substation strategy have been employed to tune the persistent luminescence (PersL) and OSL properties of Ca 3 Ga 4 O 9 :Tb 3+ by Al 3+ substitution through trap engineering and demonstrated their potential. Specifically, the photoluminescence of the Ca 2.985 (Ga 1‐y% Al y% ) 4 O 9 :0.5%Tb 3+ of Tb 3+ is first investigated due to its different occupancies of Ca 2+ . The influence of host substitution on the crystal structure, trap depth, trap density, PersL, and OSL properties have further investigated. A series of strong PersL and OSL peaks from the Ca 2.985 (Ga 1‐y% Al y% ) 4 O 9 :0.5%Tb 3+ with bluish‐green emissions have been observed. The Ca 2.985 (Ga 1‐y% Al y% ) 4 O 9 :0.5%Tb 3+ have shown controllable photon release upon thermal and optical stimuli, enhancing their performance for ODS. Thermally stimulated luminescence suggests that vacancy and defect concentrations inside the Ca 3‐x% (Ga 1‐y% Al y% ) 4 O 9 :x%Tb 3+ can be manipulated by Tb 3+ doping and Al 3+ substitution, which ultimately leads to the formation of deep traps and a broad distribution of traps with increased deep trap concentration. The work demonstrates that trap engineering through Al 3 ⁺ substitution is an effective method for tuning PersL and OSL properties of Ca 2.985 (Ga 1‐y% Al y% ) 4 O 9 :0.5%Tb 3+ for ODS.

Abeywickrama, Thulitha M. [Department of Chemistry↗

Correlation of SWIR imaging with LPBF 304L stainless steel part properties

In the Laser Powder Bed Fusion (LPBF) process, the local thermal history can vary significantly over a part as the heat transfer characteristics and the laser scan path are geometry dependent. The variations introduce the potential for defects that lead to part failure, some of which are difficult to identify non-destructively with common ex-situ evaluation techniques. These defects include significant microstructural and mechanical property differences in the part interiors. In this paper, thermal features are extracted from in-situ Short-Wave Infrared (SWIR) imaging measurements to compile voxel based part representations and understand how the complexities in the thermal history affect part performance. The deviations in thermal features due to different laser processing parameters and complex scan pathing are explored. Empirical correlations are developed to map thermal features with the engineering properties (bulk yield strength, area percentage porosity, and local state) of 304L stainless steel parts manufactured by LPBF. Processing modes (insufficient melting and keyholing) are determined by mapping part property measurements with multiple thermal features. Generating the relationships between thermographic measurements and resulting SLM part properties lays the foundation for in-situ part qualification.

36 MATERIALS SCIENCE↗

Numerical and experimental analysis of precooled desiccant system

This paper presents a numerical and experimental study of four novel, desiccant air-conditioning systems based on pre-cooling of the ambient air. The purpose of the study is to: 1) establish which configuration is most profitable for the future studies through numerical and experimental methods; 2) verify the concept of precooled system and confirm that it is working in experimental conditions (for this purpose two prototypes of evaporative cooling units were developed and compared for different operation arrangements with desiccant wheel); 3) Analyze practical aspects of the systems, which includes water consumption analysis, economic analysis and establishing operational modes during a cooling season in temperate climate conditions (the proposed solution has a significant advantage during operation in a temperate climate, since it can utilize its first evaporative cooler the only source of cooling energy when the humidity of outdoor air allows to to meet the latent cooling load). Four arrangements of the system with different dew point evaporative air cooler prototypes were selected and developed for comparative analysis. The system was simulated as a whole, also, each component was individually tested on measurement station. develop the optimal arrangement of the system through numerical and experimental analysis. Four different performance indicators were considered: thermal COP (Coefficient Of Performance), the ERR (Energy Efficiency Ratio), coefficient a describing the potential in compensating indoor cooling loads, water consumption ratio. Also costs of the systems were compared through economic analysis. It was established that arrangement which is characterized by best-averaged performance in terms of all considered factors is a unit combined with two different types of evaporative coolers (marked as System B)- this is caused by the favorable arrangement of two units, where one is better suited to the pre-cooler role, while the other is better suited as the post-cooler.

42 ENGINEERING↗

Wettability and CHF limits of Accident-Tolerant nuclear fuel cladding materials in light water reactor conditions

Here, we present the results of experimental investigations aimed at evaluating the thermal–hydraulic performance of chromium-coated zircaloy, i.e., one of the most promising accident tolerant fuel (ATF) cladding material for light water nuclear reactors. Precisely, we investigate the wettability and critical heat flux (CHF) limits of chromium-coated and conventional zircaloy surfaces in prototypical reactor conditions. For both surface types, we measure the contact angle in a vapor-saturated atmosphere from ambient pressure to the operating pressure of pressurized water reactors (PWRs), i.e., ~15 MPa. We measure the ambient-pressure steady-state flow boiling CHF with a spatially uniform heat flux. We measure the high-pressure steady-state flow boiling CHF with a cosine shape heat flux (up to 20 MPa) and with a uniform heat flux (up to 15 MPa), also exploring the effect of CRUD deposits on the chromium-coated surface. Our results reveal that the chromium surface and the bare zircaloy surface have similar wettability and both become super-hydrophilic in PWR conditions, and that there is practically no difference in the steady-state CHF limits, both at low-pressure and high-pressure conditions, also when the chromium-coated surface is covered by a CRUD deposit. However, while the chromium-coating does not improve the CHF compared to the bare zircaloy surface, it improves the post-CHF behavior. The chromium coating prevents the reaction between zircaloy and steam, which results in the formation of a brittle zirconium oxide through the surface of the cladding. We also measure the transient CHF under exponentially escalating heat flux inputs of a nano-smooth and a rough surface mimicking a chromium-coated zircaloy cladding. Interestingly, the results of the transient heat flux tests suggest that the CHF limit for very short periods (i.e., fast transients) is independent of the surface finish, being the same for a rough chromium surface or a nano-smooth surface.

36 MATERIALS SCIENCE↗

Enhanced internal condensation of R1233zd(E) on micro- and nanostructured copper and aluminum surfaces

In-tube condensation of refrigerants is an important process which affects thermal efficiency in many applications, ranging from refrigeration and air conditioning to electronics thermal management. In-tube heat transfer and pressure drop are important to heat exchanger sizing and design. Here, in this work, micro- and nanostructured surfaces are applied to the internal wetted areas of copper and aluminum mini-channels to enhance the condensation heat transfer coefficient of hydrofluorocarbon R1233zd(E) refrigerant. To achieve scalable nanomanufacturing, surfaces were uniformly structured by relying on hydrochloric acid etching of aluminum and chemical oxidation of copper. The etched aluminum surfaces exhibited a 150% increase in heat transfer coefficient compared to smooth aluminum channels at specific qualities, with a 66% heat transfer coefficient improvement for complete phase change from saturated vapor to saturated liquid. Copper oxide structures showed no discernable difference in thermal-hydraulic performance when compared to smooth copper channels. Critical dimensionless parameters governing the heat transfer enhancement were identified by varying the tube internal diameter (2.3 mm to 4.7 mm), refrigerant mass flux (50 to 300 kg/(m 2 ·s)), and refrigerant quality (0 to 1). The dimensionless parameters include the Bond number normalized to the condensate film thickness, and the Weber number modified by the vapor friction factor. The relatively small increase in pressure drop (< 10%) associated with these surface enhancements further supports the promise of this method. The scalable and cost-effective techniques used to create these aluminum microstructures may reduce manufacturing cost when compared with current enhancement approaches such as extrusion, drawing, and welding.

42 ENGINEERING↗

Design, optimization, and validation of a triply periodic minimal surface based heat exchanger for extreme temperature applications

Heat exchanger (HX) innovation offers potential for significant improvements in energy efficiency for a host of applications including but not limited to aviation and power generation cycles. Triply Periodic Minimal Surfaces (TPMS) have received significant attention in recent years due to their incredibly high surface area density, which makes them very attractive from a heat transfer point of view. Recent efforts have largely focused on thermal-hydraulic characterization of the many available TPMS and the testing of small-scale HX prototypes. However, practical implementation remains largely unexplored, partially due to the extreme computational cost associated with accurately simulating these complex structures. In this work, we present the design, simulation, and optimization of a TPMS-HX for high temperature (900 °C) and pressure (25 MPa) applications. Detailed analysis of HX sub-sections is conducted to define the smallest repeatable section which may be used to characterize the thermal-hydraulic performance of the entire HX, enabling rapid design and iteration with significantly reduced computational cost. Compared to preliminary results for a water-to-water experiment, calibrated heat transfer and pressure drop predictions were within ±5 % and ±10 %, respectively. Optimization results show a 10x increase in volumetric power density over the initial design, which is verified against a parametric exhaustive search of the HX design space. Furthermore, it was found that reducing the unit cell hydraulic diameter cell plays the largest role in increasing heat transfer, increasing the surface area density and enabling a more compact and efficient HX.

42 ENGINEERING↗

Evolution of Microstructure and Surface Characteristics of FeCrAl alloys when Subjected to Flow Boiling Testing

FeCrAl alloys are candidate materials for manufacturing accident-tolerant fuel (ATF) cladding intended for light water reactors to increase fuel reliability and safety during design-basis and beyond-design-basis accident scenarios. The evolution of the materials' surface characteristics, microstructure, and mechanical properties when exposed to the Critical Heat Flux (CHF) in flow boiling testing is crucial for safety analysis while providing insights into their thermal-hydraulic performance in nuclear reactors. After CHF, the surface chemistry of two FeCrAl alloys, APMT and C26M, was studied to understand their evolution at the early stage of high-temperature excursions in short time periods. The results indicated a thin layer composed of oxides and hydroxides of Al, Cr, and Fe with varying proportions at different depths in the layer, as indicated by X-ray photoelectron spectroscopy (XPS) and depth profiling. The cross-sections prepared by focused ion beam (FIB) revealed the growth of an oxide layer, in the range of 90-180 nm thick, on the alloys' surfaces. The evolution of the materials' surface chemistry also led to a noticeable post CHF excursion increase in their wettability, with a slight increase in roughness. Further, the investigation of the materials' mechanical properties indicated a modest increase in hardness by 10-15% as well as an increase in their yield strength, as evidenced by the microindentation and ring compression tests conducted before and after CHF testing. Scanning electron Microscopy (SEM) and X-ray diffraction (XRD) were used to investigate microstructural features of the materials and their changes after CHF treatment.

36 MATERIALS SCIENCE↗

A study on texture stability and the biaxial creep behavior of as-hydrided CWSR Zircaloy-4 cladding at the effective stresses from 55 MPa to 65 MPa and temperatures from 300°C to 400°C

The creep rupture of high burnup used nuclear fuel (> 45 GWD/MTU) cladding is regarded as one of the failure mechanisms during long-term dry storage. A high amount of zirconium hydride in the cladding matrix would degrade the mechanical properties of the cladding especially leading to delayed hydride cracking. To better understand the influence of zirconium hydride on the biaxial thermal creep performance and the crystalline texture stability of Zircaloy-4 cladding, the pressurized tube technique is applied to test the durability of the as-hydrided material. Tests were performed on as-received Zircaloy-4 tubular specimens as well as-hydrided ones with targeted 300 wt parts per million (wppm) or 750 wppm hydrogen. The biaxial creep experiments were conducted at temperatures from 300 degrees C to 400 degrees C and at equivalent stresses at mid-wall from 55 MPa to 65 MPa. The hydridation process prior to creep tests induces the formation of FCC delta-hydride platelets along the circumferential direction of the tube. This alignment and phase structure of hydride show no significant change after biaxial creep tests. The creep strain-rate negatively depends on the hydrogen content. The synchrotron wide-angle X-ray diffraction (WAXD) technique and electron backscatter diffraction (EBSD) analysis were applied for the study of the crystallographic orientation relationship. zirconium-to-hydride grain orientation follows Shoji-Nishiyama crystallographic relationship. This relationship is stable before and after creep deformation. These results of creep performance and texture stability of Zircaloy-4 claddings can help support the design basis of interim and long-term dry storage facilities.

creep↗

Sub-critical assembly die-away analysis with organic scintillators

Determining the reactivity of systems containing fissile material is essential for verifying safety, and possession and enrichment levels. The goal of this experiment was to characterize a subcritical nuclear fuel assembly irradiated by a pulsed neutron generator through differential die-away analysis. Similar characterizations are commonly performed with thermal neutron detectors, but these detectors are bulky and cumbersome, the materials are not widely available, and timing can be clouded by the required thermalization time. In this work, an organic scintillator capable of detecting both neutrons and photons was used to measure the die-away profiles of both particles. These time profiles were then used to estimate the reactivity of the assembly. Here, the calculated reactivity estimates compare favorably to simulated estimates, and therefore provide a useful tool for fissile material characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Thermofield Theory for Finite-Temperature Electronic Structure

Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. Furthermore, they also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗