Ultra-low Temperature Research Articles

Energy, exergy and economical analysis of N2O based cascade refrigeration system for ultralow temperature cooling applications using different eco-friendly refrigerants in high temperature cycle

Implementing the Montreal Protocol has limited the use of conventional refrigerants and has led industries to find optimal or economical eco-friendly refrigerants to reduce environmental hazards. The present study analyzes an N2O-based cascade refrigeration system for achieving ultralow cooling temperatures using different eco-friendly refrigerants with low GWP and ODP in a high-temperature cycle. 3E (Energy, Exergy, and Economy) analysis of a cascade refrigeration system using eco-friendly refrigerants such as R290, R1270, RE170, R600, R600a, HFE7100, and HFE7000 in the upper cycle and N2O in the lower cycle was conducted. The R744A/R600 pair performed best among the other refrigerant pairs due to its lower discharge pressure and compression ratio. The refrigerant pair R744A/R600 results in a higher cascade cycle COP of approximately 0.87, with 48 % exergetic efficiency, while the refrigerant pair R41/HFE7100 has the lowest COP (0.68) and lowest exergetic efficiency (42 %). The minimal operational cost varies from 73006 to 76907 USD per annum for refrigerant pair R744A/R600, while for the other pairs, the cost varies from 98625 USD to 114674 USD. The R744A/R600 refrigerant pair provides COP values that are 1.38–5.38 % greater than the others, with a 1.01–3.45 % variation in exergy efficiency.

A cryogenic magnetic refrigerant: Magnetocaloric study of EuB2O4 compound

Adiabatic demagnetization refrigeration (ADR) technology has the advantage of not relying on helium-3 resources and gravity compared to traditional ultra-low temperature refrigeration technology. The key to the development of ADR technology is finding magnetic refrigeration materials with brilliant magnetocaloric properties. In this study, polycrystalline EuB2O4 was successfully prepared by solid-phase reaction method. The analysis of magnetic susceptibility curves and first-principles calculations reveals a magnetic phase transition from antiferromagnetic (AFM) to paramagnetic (PM) of EuB2O4, with TN = 0.72 K. The magnetic entropy change (-ΔSM) is evaluated up to 5 T, with the maximum value of 19.4 J·kg−1K−1 (88.7 mJ·cm−3K−1), 35.0 J·kg−1K−1 (160.0 mJ·cm−3K−1) and 50.8 J·kg−1K−1 (232.2 mJ·cm−3K−1) at around T = 1.3 K and under μ0ΔH = 1 T, 2 T and 5 T, respectively, which were significantly higher than those of the commercial magnetic refrigerant Gd3Ga5O12. The large -ΔSM suggest that EuB2O4 is a potentially great magnetic refrigerant for obtaining ultra-low temperature.

Thermodynamic performance analysis and environmental impact assessment of cascade refrigeration cycles using eco-friendly nano-refrigerants

There is a lack of research in the literature on the application of nanoparticles to different cascade cycle configurations with environmental refrigerants in ultra-low temperature refrigeration applications. This study is the first on the use of nano-refrigerants in cascade refrigeration cycles. In this study, the effect of 2 wt.% of CuO to RE170 and R170-pure refrigerant utilization in cascade vapor compression refrigeration cycle (CVCRC), cascade ejector refrigeration cycle (CERC) and cascade ejector intercooler refrigeration cycle (CEIRC) are investigated to achieve higher performance values in ultra-low temperature applications. For CVCRC, CERC and CEIRC, the increases in terms of coefficient of performance (COP) with the use of nano-refrigerant were found to be 12.77 %, 8.20 %, and 6.37 %, respectively, and 18.55 %, 14.05 %, and 6.07 %, for exergy efficiency. Upon scrutinizing the results with nano-refrigerant in relation to the COP, the analysis revealed that the CEIRC cycle exhibited an improvement ranging from 13.43 % to 20.49 % in comparison to CERC. Additionally, with nano-refrigerant, the CEIRC cycle demonstrated an increase ranging from 42.39 % to 75.41 % when compared to CVCRC in COP. It was observed that the utilization of CEIRC led to a 13.03 % decrease in kg CO2 emissions in compared to CERC and a reduction of 32.53 % compared to CVCRC with using nano-refrigerant.

A new cold cooling system using krypton for the future upgrade of the LHC after the long shutdown 4 (LS4)

Future silicon detectors for High Energy Physics Experiments will require operation at lower temperatures to cope with radiation damage of the sensors and consequent increase of the dark current, beyond the limit of the current CO2 evaporative cooling system. This, together with many other requirements such as mass minimization and high radiation hardness, pushes the need of a new advanced cooling technology. The new coolant shall be able to approach ultra-low temperatures below −60 °C, withstand high radiation levels while having cooling lines diameters comparable to the currently achieved with the CO2 technology. Among different natural working fluids, krypton appears as a promising coolant for the thermal management of future detectors in high-irradiated environments. The thermodynamic properties of krypton do not allow the use of a pumped loop cycle but rather impose a need of a novel cooling technology. A new ejector-supported krypton cycle is presented, highlighting the cycle dynamics involved due to the different temperature levels normally encountered during the detector lifetime.

Regulation strategy and analysis of the ultra-low temperature heat and mass transfer capacity of 3He-4He mixture in the mixing chamber of dilution refrigerator

As an important method for achieving millikelvin temperatures, dilution refrigerators (DRs) have been widely utilized in the fields of low-temperature superconductivity, low-temperature measurement, and space exploration. The mixing chamber (MC) uses a 3He-4He mixture as the refrigerant and serves as the cold end of the DR. However, the current research lacks a detailed study of the effect of the structure of porous media on the MC cooling capacity. In this study, the heat and mass transfer model in the MC is established using the finite element method. The model is based on the improved two-fluid model to evaluate its cooling capacity and propose regulation strategies. The reliability of the model is verified through experiments. When the load power stabilizes at 10 μW, the steady-state temperature is 59.6 mK, and the Kapitza thermal resistance significantly affects the cooling process of the MC. Three strategies for regulating Kapitza thermal resistance are provided. First, the optimal porosity of the sintering cylinder for the porous medium is ε = 0.5. Second, the extreme point of the sintering cylinder is at a height of h = 1.75 cm, and the cooling capacity is at its minimum at this location. Third, the steady-state temperature initially increases and then decreases with an increase in the cylinder radius. This study is of great significance as it reveals the influence of a porous medium heat exchanger on the heat and mass transfer process of mixtures at ultra-low temperatures, guiding the design of DR.

Analysis of the explosion risk of low-concentration oxygen-bearing coal bed methane in the low-temperature environment

In the process of deep cooling and liquefaction of low-concentration (concentration <30 %) oxygen-bearing coal bed methan, there is a risk of explosion because the methane concentration in the ultra-low temperature environment is within the explosion limit. It is of great guiding significance to study the occurrence mechanism and accident-causing process of such accidents. Firstly, the experimental system of low-temperature methane explosion characteristics is constructed, and it is found that when ignition energy exceeds a certain range, the process of deep cooling and liquefaction of low-concentration oxygen-bearing coal bed methane will cause explosion. Then, the occurrence of the gas explosion accident in low-temperature environment is briefly described, and the causes of the accident are analyzed preliminarily, and the dynamic characteristics of methane explosion propagation under ultra-low temperature conditions are studied by Fluent numerical simulation, and it is obtained that ultra-low temperature conditions have a promotion effect on the explosion pressure. Finally, based on the analysis of catastrophe theory, the traditional accident causation cusp catastrophe model is improved, and the “experimental safety state" and the “internal causes of explosion-external cause of explosion" are taken as the state variables and control variables respectively, and the explosion risk analysis model for deep cooling and liquefaction of low-concentration oxygen-bearing coal bed methane based on the cusp catastrophe theory is constructed. Based on the accident case, the process of accidents caused by risk factors is described, and the evolution mechanism of such disasters and accidents is clarified. Finally, the hazard state evaluation method for liquefaction explosion of low-concentration oxygen-bearing coal bed methane is proposed based on the catastrophe theory, and this evaluation model is applied to evaluate and analyze the hazard state of accident case. The evaluation results are consistent with the actual hazard state, confirming the rationality and feasibility of this evaluation method. In this paper, the key hazards of such accidents are found out in detail and provides support for safety decision-making in the deep cooling and liquefaction process of low-concentration oxygen-bearing coal bed methane.

Quantification of neurofilament light and glial fibrillary acidic protein in finger-prick blood.

An accurate diagnosis of neurodegenerative disease and traumatic brain injury is important for prognostication and treatment. Neurofilament light and glial fibrillary acidic protein (GFAP) are leading biomarkers for neurodegeneration and glial activation that are detectable in blood. Yet, current recommendations require rapid centrifugation and ultra-low temperature storage post-venepuncture. Here, we investigated if these markers can be accurately measured in finger-prick blood using dried plasma spot cards. Fifty patients (46 with dementia; 4 with traumatic brain injury) and 19 healthy volunteers underwent finger-prick and venous sampling using dried plasma spot cards and aligned plasma sampling. Neurofilament light and GFAP were quantified using a Single molecule array assay and correlations between plasma and dried plasma spot cards assessed. Biomarker concentrations in plasma and finger-prick dried plasma spot samples were significantly positively correlated (neurofilament light ρ = 0.57; GFAP ρ = 0.58, P < 0.001). Finger-prick neurofilament light and GFAP were significantly elevated after acute traumatic brain injury with non-significant group-level increases in dementia (91% having Alzheimer's disease dementia). In conclusion, we present preliminary evidence that quantifying GFAP and neurofilament light using finger-prick blood collection is viable, with samples stored at room temperature using dried plasma spot cards. This has potential to expand and promote equitable testing access, including in settings where trained personnel are unavailable to perform venepuncture.

Crystal orientation-dependent superconductivity in titanium nitride films

High-quality titanium nitride (TiN) films with different crystal orientations (001, 110, and 111) obtained under the same growth conditions are systematically investigated by both ultra-low temperature scanning tunneling microscope/spectroscopy and transport experiments. Our results reveal that all of them are conventional type-II superconductors, which exhibit spatially homogeneous superconducting properties. The superconductivity is uniform between surface and bulk. Intriguingly, the TiN (111) film has the highest transition temperature (Tc) but the lowest upper critical field (Hc2). This crystal orientation-dependent superconductivity could be explained by the fact that TiN (001) and TiN (110) films are dirtier than TiN (111). Our results suggest that (111)-oriented TiN is superior to design certain superconducting devices, including Josephson junction devices. The crystallographic orientation could offer an effective controlling parameter for designing TiN-based superconducting devices.

Cryogenic properties of PEG/nano-SiO2 co-toughened winding resin and its carbon fiber-reinforced composites

The epoxy/acid anhydride system was toughened with a homogeneous solution of surface-treated nano-SiO2 and polyethylene glycol (PEG), which satisfies the specific requirements of wet winding processes and effectively enhances the performance of resin and carbon fiber composites at ultra-low temperatures (108K). The results show that when the uniform solution formed by 1 phr SiO2 and 10 phr PEG is added, the tensile strength and elongation at break of the modified resin were increased by 21.4% and 16.1%, respectively, at room temperature. At 108K, the strength and modulus of the modified resin were increased, and the elongation at break was 2.8%. The fracture morphology was analyzed and compared at both room temperature and ultra-low temperature, verifying the relationship between material structure and properties across different temperatures. These findings offer both theoretical and empirical backing for the development of ultra-low temperature carbon fiber composite gas storage tanks.

Exceptional fatigue-resistant austenitic stainless steel for cryogenic applications

Most alloys change from ductile to brittle at cryogenic temperatures, whereas high-entropy alloys show better strength, ductility, and toughness. However, they suffer from cost and mass-production challenges. We discerned the fatigue behaviour of a cost-effective austenitic stainless steel, SS316L, at an ultra-low temperature (ULT) of 15 K. For the cryogenic applications, our work demonstrates that compared to room-temperature (RT), ULT exhibits eight times higher fatigue life, despite even higher applied stress [ σmax=1.3×σysRT/ULT (280 MPaRT; 517 MPa15 K)]. At 15 K, the fatigue mechanisms involve stacking faults, a two-step martensitic phase transformation (γ→ϵ→α′) and α′-martensite twinning, utilizing the applied fatigue strain efficiently. The remarkable improvement in the mechanical strength and fatigue life at ULT is the key to revolutionizing sustainable advancements in space exploration and energy storage.

Energy, exergy, environmental and exergoeconomic (4E) analysis of an ultra-low temperature cascade refrigeration system with environmental-friendly refrigerants

To ensure the efficacy of some special vaccines, the ultra-low temperature storage below −80 °C is strictly required and the classical cascade refrigeration system has a good application prospect in the production, storage, transportation and distribution of COVID-19 vaccines. Previous investigations are mainly focused on the thermodynamic performance of cascade refrigeration cycles (CRSs) to generate low temperature, and the impact of cascade refrigeration cycles on environmental and exergoeconomic aspects is few involved. In this paper, an energy-exergy-environmental-exergoeconomic (4E) analysis model was built to investigate the comprehensive performance of an ultra-low temperature cascade refrigeration system. Eight environmental-friendly refrigerant pairs, including R290-R170, R290-R1150, R717-R170, R717-R1150, R1270-R170, R1234yf-R170 and R1234yf-R1150, were chosen and the associated refrigeration performance was compared. The results show that the optimal refrigerant pair is propane-ethane (R290-R170). Compared with HFC refrigerant pair R404A-R508B CRS, R290-R170 CRS could improve the COP by 5.94%, save 5.68% power consumption, reduce 29.67% carbon dioxide emission and decrease 5% exergy economic cost. This work is significant to select environmental-friendly nature refrigerants, enrich understanding of comprehensive performance of cascade refrigeration system and enhance depth research on ultra-low temperature refrigeration.

Моделирование транспортной инфраструктуры в условиях Крайнего Севера

The article discusses the key problems of transport communication of the Far North regions. There are two difficulties in the construction of highways and railroads in the Far North: ultra-low temperatures and permafrost. The presence of centuries-old frozen rocks, or permafrost, containing ice in its composition, also greatly complicates the work of the transport infrastructure of the Far North. Air communication with these territories of the rest of the country is characterized by insufficient frequency and volume of material flows. Water routes that connect the territory of the Far North, in turn, are limited in terms of time of use, as well as the volume of goods transported. The wide variability of transport and logistics directions determines the possibility of their representation in the form of graphs. The aim of the work was to investigate the prospects of using modeling tools for designing transport infrastructure in the Far North. In the course of the study the hypothesis about the feasibility of using graph-analytical models to address complex integrated tasks was confirmed. In practice, they allow to combine mathematical and graphical models in various software products. Using graph theory, which is one of the key research methods, graph-analytical models have been constructed and analyzed, which allow solving applied problems of an unlimited number of industries.

Improved tribological behaviour of super duplex stainless steel through plasma nitriding at ultra-low temperature without prior polishing

Super duplex stainless steels (SDSS), widely used in industries such as offshore oil and gas, offer a unique combination of high strength and corrosion resistance. However, surface hardening treatments are crucial to enhance their performance and extend service life. This work investigates the effect of plasma nitriding on the tribological behaviour of SDSS SAF 2507. Samples are treated without prior polishing (as received, AR) at ultra-low temperatures (250 and 300 °C) aiming to avoid detrimental CrN precipitation. Comprehensive microstructural characterization, corrosion studies, and tribological tests (scratch and ball-on-disc) are conducted on samples that do not present CrN (PN). Results indicate that the hardness of PN samples nearly doubles that of AR samples due to the presence of expanded austenite. Corrosion tests show improvements in passivity for PN samples. In scratch tests, while the AR material undergoes progressive plastic deformation, in PN material the nitrided layer breaks down only after reaching a critical load. In ball-on-disc test, wear rates are remarkably lower for PN condition compared to AR condition. Wear mechanism is tribo-oxidative and abrasive for the AR condition. Wear of PN samples is characterized by asperity break-off and ratcheting. The nitrided layer in PN samples exhibits an enhanced load-bearing capacity that improves wear resistance in both tests.

Three-dimensional deformation measurement techniques in space multi-physical fields based on digital image correlation

Aiming at the three-dimensional deformation measurement requirement of the high-stability structure of spacecraft in space multi-physical fields, a comprehensive instrument protection device in a vacuum high-low temperature environment is developed using ultra-low temperature anti-condensation and vacuum heat insulation technology. This ensures that the digital image correlation (DIC) measurement camera always remains in a constant temperature and pressure environment and can stably exert its original efficiency in space multi-physical field environments. Subsequently, a path-dependent DIC method based on a graphics processing unit computing parallel acceleration is proposed by combining a pre-interpolation strategy and integrated image technology, which realizes high-precision matching of digital images before and after deformation in a spatial multi-physical field environment and improves the computing efficiency. To address the problem that a common reference point may deform significantly in a space environment with a large temperature change, which leads to inaccurate system accuracy, combined with a random sampling consistency algorithm and singular value decomposition method, the optimal registration of the coordinate system and the solution of deformation were realized by setting the threshold of the reference point margin screening. Finally, a three-dimensional deformation measurement system in high- and low-temperature vacuum environments was built, and the three-dimensional deformation measurement of the satellite antenna in high- and low-temperature vacuum environments was verified, which proves the effectiveness and accuracy of the above method.

Optimization and performance improvement of ultra-low temperature cascade refrigeration system based on the isentropic efficiency curve of single-screw compressor

In this paper, a cascade refrigeration system equipped with a single-screw compressor (SSC-CRS) is proposed and built in order to achieve the goal of high load cooling capacity under ultra-low temperature conditions. Firstly, the isentropic efficiency curve of the single-screw compressor (SSC) is fitted through experimental method in response to the characteristics of low suction temperature and large pressure ratio of the compressor. In addition, the analysis of SSC-CRS with 28 refrigerant pairs are made to compare the coefficient of refrigeration (COP) and power consumption. On the basis of the cascade system, the paper compares the improvement of performance between two circuits with SSC: vapor injection cascade refrigeration system (SSC-ICRS) and ejector vapor injection cascade refrigeration system (SSC-EICRS). The results indicate the COP improvement rate of SSC-ICRS system is 17.39 %–41.98 % and the COP improvement rate of SSC-EICRS system is 49.46 %–68.37 % compared with SSC-CRS.

Investigation of an efficient high cooling-capacity Stirling-type pulse tube refrigerator with passive rod displacer operating at 173 K

Pulse tube refrigerator (PTR) with passive rod displacer is of great potential to realize high-efficiency refrigeration and can be a feasible substitute for the vapor compression system in ultra-low temperature cold storage. However, PTRs with passive rod displacer in that application require high efficiency and substantial cooling capacity, which still need to be developed in previous research. In this paper, a high cooling-capacity PTR with passive rod displacer operating at 173 K was designed, fabricated, and investigated. The special property of acoustic power recovery was exhibited based on an electrical circuit analogy model and energy flow analysis. The structural parameters of PTR with passive rod displacer were optimized by one-dimensional numerical software. The experimental results showed that a cooling capacity of 157.5 W at 173 K was obtained with an input electric power of 500 W. The corresponding relative Carnot efficiency reached 21.8 %. The phase difference between the displacer and piston decreased slightly from 58.1° with the increase of cooling temperature when charging pressure and operating frequency were 2.8 MPa and 65 Hz, respectively. The phase difference was determined by the operating frequency and was slightly affected by charging pressure, cooling temperature, and input electric power. Based on the validated numerical models, PTR with passive rod displacer and inertance-tube-type PTR were compared. The numerical results showed that both enthalpy and PV power enlarged at the T-junction in the PTR with passive rod displacer due to acoustic power recovery. According to the acoustic-mechanical–electrical coupling phasor diagram, the phase difference between pressure and piston displacement decreased because of the mass flow superposition at the T-junction, affecting the output capability of the linear compressor. The efficient high cooling-capacity prototype verifies that PTR with passive rod displacer has a bright future in ultra-low temperature engineering applications.

Antifreezing, Antidrying, and Conductive Hydrogels for Electronic Skin Applications at Ultralow Temperatures.

Although conductive hydrogel-based flexible electronic devices have superb flexibility and high conductivities, they tend to malfunction in dry or frigid areas. Herein, an ultralow-temperature tolerant, antidrying, and conductive composite hydrogel is designed for electronic skin applications on the basis of the synergy of double-cross-linked polymer networks, Hofmeister effect, and electrostatic interaction and fabricated by in situ free radical polymerization of 2-acrylamido-2-methyl-1-propanesulfonic acid and acrylic acid in the presence of poly(vinyl alcohol) and conductive MXene sheets, followed by impregnation with LiCl. Thanks to the synergy of LiCl and the charged polar terminal groups of the synthesized polymers, the composite hydrogel can not only bear an ultralow temperature of -80 °C without freezing but also maintain its original mass. Meanwhile, the resultant hydrogel possesses satisfactory self-regeneration ability benefiting from the moisturizing effect of LiCl. The conductive network of MXene sheets greatly improves the ionic conductivity of the hydrogel at low temperatures, exhibiting an ionic conductivity of 1.4 S m-1 at -80 °C. Furthermore, the electronic skin assembled by the multifunctional hydrogel is efficient in monitoring human motions at -80 °C. The antifreezing and antidrying features along with favorable ionic conductivity, high tensile strength, and outstanding flexibility make the composite hydrogel promising for applications in frigid and dry regions.

Study on Cage Stability of Solid-Lubricated Angular Contact Ball Bearings in an Ultra-Low Temperature Environment

In the ultra-low temperature environment, the material properties of the bearing change, which puts forward higher requirements for the dynamic performance of the bearing cage. The bearings operating in ultra-low temperature environments commonly use solid lubricants. This study first focused on measuring the traction coefficients of molybdenum disulfide (MoS2) solid lubricant in a nitrogen atmosphere, and the Gupta fitting model is constructed to derive the traction equation. Subsequently, the dynamic differential equation of angular contact ball bearings was established, and the stability of the bearing cage in a nitrogen environment was simulated and analyzed based on the dynamic model. The accuracy of the simulation model was verified through comparison. The results show that less than 10% of errors exist between the experimental data and the traction curve fitted by the Gupta model, and the stability of the cage is closely related to operating parameters and bearing structure parameters. Cage stability increases with axial load but decreases with radial load. The cage stability is optimal when the radial internal clearance of the bearing is approximately 0.06 mm. When other conditions remain unchanged and the ratio of the cage pocket hole gap to the cage guide surface gap is 0.2, the cage stability is the best. The research results will provide a foundation for the design and application of solid-lubricated angular contact ball bearings in ultra-low temperature environments.

Tailoring tunnel-type potassium-free manganese oxide catalyst via cerium substitution for catalytic NO reduction with NH3 at ultra-low temperatures

Manganese oxide (KMn8O16, K-MO) was widely used for selective catalytic reduction (SCR) denitration due to its superior ability for activating and converting NO to N2 with NH3. However, the harmful K+ in its tunnel structure tends to consume NH3, leading to limited low-temperature activity and stability. Herein, a Ce substitution strategy was developed for the preparation of K-free Ce-MO for NH3-SCR. As-prepared Ce-MO exhibits a high NOx conversion (95%) at an ultra-low temperature of 75°C, with negligible activity decay within 60 h. Systematic characterizations elucidate the important role of Ce substitution in improvement of catalytic efficiency and stability for NO removal. The introduction of Ce not only eliminates harmful K+ and improves the stability of the catalyst, but also enhances the removal efficiency of NOx by the generation of oxygen vacancies. In addition, the formation of intermediate NH4NO3 is critical to improving the catalytic efficiency and stability over Ce-MO base on in-situ DRIFTS. This work provides a favorable strategy for the preparation of free-K tunnel-type manganese oxide catalyst for denitration with high activity and superior stability at ultra-low temperature.

Efficient recovery of Al foil and regeneration of cathode materials from spent lithium-ion batteries with methanol-citric acid

Efficient separation of cathode materials from current collectors is an important step to simplify the recycling process of spent lithium-ion batteries (LIBs). However, traditional methods have the shortcomings of incomplete separation, release of toxic substances and high cost. Here, the methanol-citric acid solvent (MeOH-CA), prepared from green and low-cost reagents methanol (MeOH) and citric acid (CA), can separate above 99.5 wt% of spent nickel-manganese-cobalt (NCM) cathode materials in 15 min with negligible metal loss at an ultralow temperature of 45 °C. The separated NCM has high purity and no structure changes, and the recovered Al foil is intact and non-corrosive. The mechanism analysis indicates that the reaction between MeOH-CA and Al foil and the inactivation of PVDF by the abundant hydrogen bonds in the MeOH-CA solvent cause the separation. Meanwhile, the formation of AlF3 passivation layer and the ester film on the surface of Al foil prevent further corrosion of Al foil. Through hydrothermal treatment combined with a short thermal annealing, the regenerated NCM delivers a reversible capacity of 151 mAh g−1 at 1C and 117 mAh g−1 after 100 cycles. The facile separation strategy provides a sustainable and economic solution for the recovery of spent LIBs.