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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.

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At least 181 records · Page 10

A robust high sensitivity scanning thermal probe for simultaneous microscale thermal and thermoelectric property mapping

Scanning Thermal Microscopy (SThM) provides efficient thermal property measurement with micro- or nanoscale spatial resolution. However, the sensitivity and accuracy of state-of-the-art thermal probes have been limited by excessive thermal contact resistance between the probe and sample. Introduced herein is a robust thermal microprobe that can increase the probe-sample contact force by more than two orders of magnitude, thereby reducing the probe-sample thermal contact resistance by as much as 96% and increasing measurement sensitivity by more than 240% compared to a commercial thermal probe with the same dimensions and measurement principle. The relationship between the probe-sample thermal contact resistance, thermal exchange radius, and sample thermal conductivity is determined experimentally. Simultaneous measurement of thermal conductivity and Seebeck coefficient with unprecedented sensitivity is demonstrated using the enhanced scanning thermal microprobe on samples of an extended range of thermal conductivity up to 18 W/m K, increasing the range of samples applicable to SThM when compared to the conventional commercial probe with diminished measurement sensitivity above ~10 W/m K. The probe is further demonstrated by simultaneously mapping thermal conductivity and Seebeck coefficient as a function of depth from the irradiated surface of an ion-irradiated bulk nanostructured thermoelectric material. In addition to enabling microscale thermal conductivity and Seebeck coefficient measurement of materials previously not applicable to SThM, the probe can also facilitate high-throughput characterization of combinatorial materials to aid the rapid discovery of compositions and processing conditions that yield highly desired thermal and thermoelectric properties.

36 MATERIALS SCIENCE↗

Finding the order in complexity: The electronic structure of 14-1-11 zintl compounds

Yb 14 MnSb 11 and Yb 14 MgSb 11 have rapidly risen to prominence as high-performing p-type thermoelectric materials. However, the fairly complex crystal structure of A 14 MX 11 Zintl compounds renders the interpretation of the electronic band structure obscure, making it difficult to chemically guide band engineering and optimization efforts. In this work, we delineate the valence-balanced Zintl chemistry of A 14 MX 11 compounds using the molecular orbital theory. By analyzing the electronic band structures of Yb 14 MgSb 11 and Yb 14 AlSb 11 , we show that the conduction band minimum is composed of either an antibonding molecular orbital originating from the (Sb 3 ) 7– trimer or a mix of atomic orbitals of A, M, and X. The singly degenerate valence band is comprised of non-bonding Sb pz orbitals primarily from the Sb atoms in the (MSb 4 ) m– tetrahedra and of isolated Sb atoms distributed throughout the unit cell. Such a chemical understanding of the electronic structure enables strategies to engineer electronic properties (e.g., the bandgap) of A 14 MX 11 compounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolution of structure and transport properties of the Ba 8 Cu 16 P 30 clathrate-I framework with the introduction of Ga

Two type-I clathrates were synthesized by introducing Ga into the framework of the Ba 8 Cu 16 P 30 type-I clathrate. The introduction of minute amounts of Ga, 1.9% Ga/M total (where M total = Cu + Ga), resulted in the disturbance of the completely ordered Pbcn superstructure of Ba 8 Cu 16 P 30 . Ba 8 Cu 15.43(2) Ga 0.3 P 30.26(3) crystallizes in a partially ordered orthorhombic Pmna clathrate-I superstructure with five out of 15 framework sites being jointly occupied by metal+phosphorus. Increasing the Ga content resulted in all framework sites being occupied by metal + phosphorus in the archetype cubic Pm n clathrate-I crystal structure of Ba 8 Cu 14.5(3) Ga 1.3 P 30.2(4) with 8.2% Ga/M total . A combination of energy dispersive x-ray spectroscopy, inductively coupled plasma mass spectroscopy, and single crystal x-ray diffraction was used to determine the structures alongside the compositions. The positional disorder was verified by 31 P solid state NMR spectroscopy. Characterization of the transport properties indicated that the Ga-substituted samples exhibit higher Seebeck coefficients and electrical resistivities compared to its pristine counterpart, in line with the expected reduction of the hole concentration due to Ga/Cu substitution. Moderate improvements in the thermoelectric power factor and overall figure-of-merit were observed for samples with 6.9% and 3.8% Ga/M total as compared to those for the pristine Ba 8 Cu 16 P 30 clathrate. Finally, band structure calculations shed light on how Ga substitution affects the electronic structure and thermoelectric properties of studied clathrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anomalous thermoelectricity at the two-dimensional structural transition of SnSe monolayers

The thermoelectric figure of merit ZT comprises electronic and vibrational contributions that drastically change across phase transitions, and the most common theoretical ab initio approach to thermoelectricity fails to describe the evolution of ZT across finite-temperature structural transitions in its entirety. Furthermore, while the thermoelectric behavior of bulk SnSe has been extensively studied, SnSe monolayers have been experimentally realized only recently, and the existent prediction of thermoelectricity on this two-dimensional material is unreliable because it misses its structural transition altogether. SnSe monolayers (and similar GeS, GeSe, GeTe, SnS, and SnTe monolayers) experience a temperature-induced two-dimensional Pnm2 1 → P4/nmm structural transition precipitated by the softening of vibrational modes, and we describe their thermoelectric properties across the phase transition, using molecular dynamics data to inform both electronic and vibrational coefficients directly and within the same footing. Similar to recent experimental observations pointing to an overestimated ZT past the transition temperature in bulk SnSe, we find a smaller ZT on SnSe monolayers when compared to its value predicted by the standard paradigm, due to the dramatic changes in the electrical conductivity and lattice thermal conductivity as the structural transition ensues. Here, the process described here lends a strong focus to both the vibrational and electronic evolutions throughout the structural transition, and it applies to thermoelectric materials undergoing thermally driven solid-to-solid structural phase transitions in one, two, and three dimensions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Hybridization-driven strong anharmonicity in Yb-filled skutterudites

A high-pressure study of the structural and thermal transport properties is carried out on one of the most efficient filled skutterudites, $\mathrm{Yb_{0.3}Co_4Sb_{12}}$, to understand the relatively low thermal conductivity behavior in this family. By combining x-ray diffraction and Raman scattering measurements, we detect a phase transition at around 12.4 GPa. The mode Grüneisen parameters of the observed phonon modes are obtained from the determined bulk modulus and the phonon frequency shifts with pressure. The strong anharmonicity in this material is demonstrated by the obtained large average Grüneisen parameter. We also find the depressed group velocity within the low-frequency range, the flat guest mode avoided crossing with the acoustic-phonon mode, and the significant contribution of optical phonons. The hybridization of the guest atom and host lattice and the related enhanced anharmonicity are suggested to account for the low lattice thermal conductivity in the studied system. So, these findings provide new insight into how phonon-phonon interactions lower lattice thermal conductivity in this important thermoelectric family.

36 MATERIALS SCIENCE↗

Thermal and thermoelectric properties of an antiferromagnetic topological insulator MnBi 2 Te 4

The discovery of an intrinsic antiferromagnetic topological insulator (AFMTI) in MnBi 2 Te 4 has attracted intense attention, most of which lies in its electrical properties. Here in this paper, we report electronic, thermal, and thermoelectric transport studies of this newly found AFMTI. The temperature and magnetic field dependence of its resistivity, thermal conductivity, and Seebeck coefficient indicate strong coupling between charge, lattice, and spin degrees of freedom in this system. Furthermore, MnBi 2 Te 4 exhibits a large anomalous Nernst signal, which is associated with nonzero Berry curvature of the field-induced canted antiferromagnetic state.

36 MATERIALS SCIENCE↗

Enhanced superconductivity and electron correlations in intercalated ZrTe 3

We report charge density waves (CDWs) with superconductivity, competing Fermi surface instabilities, and collective orders have captured much interest in two-dimensional van der Waals (vdW) materials. Understanding the CDW suppression mechanism, its connection to the emerging superconducting state, and electronic correlations provides opportunities for engineering the electronic properties of vdW heterostructures and thin-film devices. Using a combination of the thermal transport, x-ray photoemission spectroscopy, Raman measurements, and first-principles calculations, we observe an increase in electronic correlations of the conducting states as the CDW is suppressed in ZrT e3 with 5% Cu and Ni intercalation in the vdW gap. As superconductivity emerges, intercalation brings not only decoupling of quasi-one-dimensional conduction electrons with phonons as a consequence of intercalation-induced lattice expansion but also a drastic increase in Zr 2+ at the expense of Zr 4+ metal atoms. These observations not only demonstrate the potential of atomic intercalates in the vdW gap for ground-state tuning but also illustrate the crucial role of the Zr metal valence in the formation of collective electronic orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Thermal transport properties of IrSbSe

Here we report a thermal transport study of IrSbSe, which crystallizes in a noncentrosymmetric cubic structure with the P2 1 3 space group and shows a narrow-gap semiconducting behavior. The large discrepancy between the activation energy for conductivity [E ρ = 128(2) meV] and for thermopower [E S = 17.7 (9) meV] from 200 to 300 K indicates a polaronic transport mechanism. The electrical resistivity varies as exp (T 0 /T) 1/4 and thermopower varies as T 1/2 at low temperatures, indicating that it evolves into Mott variable-range hopping dominant conduction with decreasing temperature. IrSbSe shows a relatively low value of thermal conductivity (~1.65 W/Km) and thermopower of about 0.24 mV/K around 100 K, yet poor electrical conductivity. On the other hand, a high vacancy defect concentration on both Ir and Sb atomic sites of up to 15% suggests a high defect tolerance and points to the possibility of a future improvement of carrier density by chemical substitution or defect optimization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Contribution of the Hydroxyl Group on Interfacial Heat Conduction of Monohydric Alcohols: A Molecular Dynamics Study

Monohydric alcohols have been used as promising phase change materials (PCMs) for low-temperature latent heat storage. However, the heat storage/retrieval rates are limited due to the low thermal conductivity of such alcohols. In this work, nonequilibrium molecular dynamics (NEMD) simulations were performed to study the microscopic heat conduction in example monohydric alcohols, i.e., 1-dodecanol (C12H26O), 1-tetradecanol (C14H30O), and 1-hexadecanol (C16H34O). A simplified ideal crystal model was proposed to exploit the potential for improving the thermal conductivity of monohydric alcohols. The effect of ideal crystalline structures, especially the contribution of the hydroxyl group, on the microscopic heat conduction process was analyzed. The thermal conductivity of the ideal crystals of the various monohydric alcohols was predicted to be more than twice as compared to that of their respective solids. The major thermal resistance in the ideal crystals was found around the molecular interfaces, as a result of the excellent heat conduction performance along the linear molecular chains. The calculated vibrational density of states (VDOS) and interfacial heat transfer were then investigated. When the interfaces are surrounded by hydroxyl groups as walls, strong hydrogen bond (HB) interactions were observed. The interfacial heat transfer coefficient of the ideal crystalline structures of 1-tetradecanol was found to reach up to ~735.6 MW/m2 W. It was elucidated that the high interfacial heat transfer rate is clearly related to the stronger intermolecular interactions.

Engineering↗

High-Temperature Particle Heat Exchanger for sCO2 Power Cycles [Award 30342]

This report describes the design, development, and testing of a prototype 100 kWt particle-to-supercritical CO 2 (sCO2) heat exchanger. An analytic hierarchy process was implemented to compare and evaluate alternative heat-exchanger designs (fluidized bed, shell-and-plate moving packed bed, and shell-and-tube moving packed bed) that could meet the high pressure (≥ 20 MPa) and high temperature (≥ 700 °C) operational requirements associated with sCO2 power cycles. Cost, heat-transfer coefficient, structural reliability, manufacturability, parasitics and heat losses, scalability, compatibility, erosion and corrosion, transient operation, and inspection ease were considered in the evaluation. A 100 kWt shell-and-plate design was selected for construction and integration with Sandia’s falling particle receiver system that heats the particles using concentrated sunlight. Sandia worked with industry to design and construct the moving packed-bed shell-and-plate heat exchanger. Tests were performed to evaluate its performance using both electrical heating and concentrated sunlight to heat the particles. Overall heat transfer coefficients at off-design conditions (reduced operating temperatures and only three stainless steel banks in the counter-crossflow heat exchanger) were measured to be approximately ~25 - 70 W/m 2 -K, significantly lower than simulated values of >100 W/m 2 -K. Tests using the falling particle receiver to heat the particles with concentrated sunlight yielded overall heat transfer coefficients of ~35 – 80 W/m 2 -K with four banks (including a nickel-alloy bank above the three stainless steel banks). The overall heat transfer coefficient was observed to decrease with increasing particle inlet temperatures, which contrasted the results of simulations that showed an increase in heat transfer coefficient with temperature due to increased effective particle-bed thermal conductivity from radiation. The likely cause of the discrepancy was particle-flow maldistributions and funnel flow within the heat exchanger caused by internal ledges and cross-bracing, which could have been exacerbated by increased particle-wall friction at higher temperatures. Additional heat loss at higher temperatures may also contribute to a lower overall heat-transfer coefficient. Design challenges including pressure drop, particle and sCO2 flow maldistribution, and reduced heat transfer coefficient are discussed with approaches for mitigation in future designs. Lessons learned regarding instrumentation, performance characterization, and operation of particle components and sCO2 flow loops are also discussed. Finally, a 200 MWt commercial-scale shell-and-plate heat-exchanger design based on the concepts investigated in this report is proposed.

14 SOLAR ENERGY↗

Radiation Damage Mitigation in FeCrAl Alloy at Sub-Recrystallization Temperatures

Traditional defect recovery methods rely on high-temperature annealing, often exceeding 750 °C for FeCrAl. In this study, we introduce electron wind force (EWF)-assisted annealing as an alternative approach to mitigate irradiation-induced defects at significantly lower temperatures. FeCrAl samples irradiated with 5 MeV Zr 2+ ions at a dose of 10 14 cm −2 were annealed using EWF at 250 °C for 60 s. We demonstrate a remarkable transformation in the irradiated microstructure, where significant increases in kernel average misorientation (KAM) and low-angle grain boundaries (LAGBs) typically indicate heightened defect density; the use of EWF annealing reversed these effects. X-ray diffraction (XRD) confirmed these findings, showing substantial reductions in full width at half maximum (FWHM) values and a realignment of peak positions toward their original states, indicative of stress and defect recovery. To compare the effectiveness of EWF, we also conducted traditional thermal annealing at 250 °C for 7 h, which proved less effective in defect recovery as evidenced by less pronounced improvements in XRD FWHM values.

FeCrAl alloys↗

Dynamics of Laterally Propagating Flames in X-Ray Bursts. II. Realistic Burning and Rotation

In this work, we continue to investigate two-dimensional laterally propagating flames in type I X-ray bursts using fully compressible hydrodynamics simulations. In the current study we relax previous approximations where we artificially boosted the flames. We now use more physically realistic reaction rates, thermal conductivities, and rotation rates, exploring the effects of neutron star rotation rate and thermal structure on the flame. We find that at lower rotation rates the flame becomes harder to ignite, whereas at higher rotation rates the nuclear burning is enhanced by increased confinement from the Coriolis force and the flame propagates steadily. At higher crustal temperatures, the flame moves more quickly and accelerates as it propagates through the atmosphere. If the temperature is too high, instead of a flame propagating across the surface the entire atmosphere burns uniformly. Our findings could have implications for the relationship between observed burst rise times and neutron star rotation and accretion rates. All of the software used for these simulations is freely available.

79 ASTRONOMY AND ASTROPHYSICS↗

Prototype Modeling for a Light-Trapping Planar-Cavity Enclosed Particle Solar Receiver

Concentrating solar thermal (CST) systems present a promising avenue for affordable and reliable energy production. Solar receivers are key components that determine the efficiency and longevity of these systems. Particle-based solar receivers have emerged as a compelling alternative to traditional technologies, offering several advantages that address limitations in current CST systems. This is especially true as next-generation CST technologies target applications including electricity generation, thermochemical processes, and industrial process heat, many of which necessitate higher operating temperatures than current commercial molten salt systems. Molten-salt thermal energy storage (TES) systems, commonly used in CSP, face challenges related to freezing and corrosion. Particle-based TES systems, in contrast, do not experience these issues, as particles are stable at high temperatures, exceeding 1000 degrees Celsius. This capability allows for a wider range of applications, including those requiring higher temperatures for industrial processes and efficient electricity generation. A novel innovation in particle-based solar receiver technology is the light-trapping planar cavity receiver (LTPCR) configuration developed by NREL. The LTPCR design consists of small cavity-like structures using opaque planar surfaces, enabling efficient capture and absorption of solar energy. A high incident flux concentration at the cavity aperture is absorbed on the receiver walls, and subsequently transferred to particles on the inside of cavities. The particles flow through the system, forming a fluidized bed inside of the receiver panels, effectively capturing the absorbed solar heat. Air is used as a fluidizing medium in this process to enhance particle heat transfer and mixing. The effectiveness of this design lies in its ability to manage solar flux conditions and ensure high solar-to-thermal receiver efficiency. A 100-kW prototype is currently being tested at the King Saud University in Saudi Arabia to assess the receiver performance. A range of modeling analyses for the optical, thermal, and mechanical effects were conducted to assess the performance of the receiver under on-sun conditions. The solar flux resulting from the KSU heliostat field was modeled using NREL SolTrace software and produced up to 600 kW/m2 at the receiver aperture. The solar flux absorbed on the receiver walls was then used within a computational fluid dynamics (CFD) model to predict wall temperature distributions along with radiation and convection loss. A two-phase CFD model was developed for the fluidized bed of silica sand inside the receiver panels to predict local wall-to-particle heat transfer coefficients, particle temperature distributions, and outlet temperature of the particles. We have also conducted analyses to understand the thermomechanical behavior of these innovative enclosed light-trapping solar receivers optimized for particle heating. We used finite element analysis (FEA) to predict the receiver's performance using temperature distributions obtained from CFD and based on the resulting stress profiles, evaluated creep-fatigue damage with a goal of achieving a 30-year service life. Analysis showed a significant impact of the particle-to-wall heat transfer coefficients (HTCs) on receiver performance, with higher HTCs resulting in reduced stress and increased lifespan. For instance, when using Inconel 740H, increasing the HTC from 800 W/m2 K to 1400 W/m2 K increased the creep life from 4,000 hours to over 100,000 hours. This highlights the importance of understanding and optimizing heat transfer in the design of high-efficiency receivers.

14 SOLAR ENERGY↗

Effect of time and spatial domains on monolayer 2D material interface thermal conductance measurement using ns ET-Raman

Raman-based approaches to characterizing thermal properties of nanoscale and microscale materials have proven to be powerful experimental methods. Here, this work explores the potential of energy-transport state-resolved Raman (ET-Raman) for the precise determination of interfacial thermal conductance (G) between monolayer 2D materials and their substrates. ET-Raman employs a continuous wave laser and nanosecond (ns) pulsed laser to induce both steady state and transient heating while simultaneously collecting 2D material temperature information from the Raman signal. A 3D numerical model built using the finite volume method simulates the two differentiated thermal transport processes. The simulated temperature rises are compared with experimental Raman temperature information to extract G. In this study, we investigate the temporal effects of the pulse frequency and pulse width of the ns laser on precise characterization of G. By running multiple simulations for a range of pulsed laser frequencies and pulse widths, we determine that ET-Raman is most sensitive to precise interfacial thermal conductance measurements with short pulse widths (~below 20 ns) and with pulsing frequencies that ensure sufficient cooling time between consecutive pulses (~below 500 kHz). We also conclude that substrate thickness and laser spot size play critical roles in heat distribution and subsequent sensitivity to meaningful G measurements. As both laser spot size and SiO 2 substrate thickness decrease, detection of interfacial thermal transport becomes more difficult. These results offer essential guidance in the design of future Raman-based approaches to thermal measurements using pulsed lasers.

2D materials↗

An Instrumented Capsule Design to Measure Thermal Conductivity in Miniature UO2 Specimens

Numerous separate effects irradiations of miniature nuclear fuel specimens have been conducted in the High Flux Isotope Reactor (HFIR) under the experimental platform designated as MiniFuel. MiniFuel is a static irradiation capability in which microstructural evolution and fuel performance phenomena are observed during postirradiation examination thereby offering a snapshot of the terminal fuel characteristics. This approach inherently requires fielding an irradiation where the experimental conditions are determined using predictive models and the pertinent outcomes are measured at the end of the test. Static irradiations can provide useful insights to the relationships between fuel performance and the pivotal irradiation conditions, namely temperature and burnup, but the ability to monitor fuel performance in situ would further support fuel development and qualification. To this end, an instrumented experiment design is being developed at Oak Ridge National Laboratory to capture thermal conductivity degradation and fission gas release during HFIR irradiation. These phenomena will be monitored using unique capsule designs that each target a different phenomenon. This paper details the thermal conductivity capsule (TCC) design and its expected performance envelope as determined using computer models. Each TCC will contain a miniature UO2 disc specimen (~0.5 mm thick × 5 mm diameter) sandwiched between metallic slugs with embedded thermocouples. The coupling of in situ temperature measurements, known thermal conductivity of the metallic components, and heat generation rates computed using high-fidelity neutronics models make the thermal conductivity measurement possible. This paper describes the reactor physics and heat transfer models used to predict the capsule’s performance and the methodology for calculating the fuel specimen’s thermal conductivity from the thermocouple measurements.

Gorton, Jacob [ORNL] (ORCID:0000000269806083)↗

Accelerated Discovery and Design of Ultralow Lattice Thermal Conductivity Materials Using Chemical Bonding Principles

Semiconductors with very low lattice thermal conductivities are highly desired for applications relevant to thermal energy conversion and management, such as thermoelectrics and thermal barrier coatings. Although the crystal structure and chemical bonding are known to play vital roles in shaping heat transfer behavior, material design approaches of lowering lattice thermal conductivity using chemical bonding principles are uncommon. In this work, an effective strategy of weakening interatomic interactions and therefore suppressing lattice thermal conductivity based on chemical bonding principles is presented and a high-efficiency approach of discovering low κ L materials by screening the local coordination environments of crystalline compounds is developed. The resulting first-principles calculations uncover 30 hitherto unexplored compounds with (ultra)low lattice thermal conductivities from 13 prototype crystal structures contained in the Inorganic Crystal Structure Database. Furthermore, an approach of rationally designing high-performance thermoelectrics is demonstrated by additionally incorporating cations with stereochemically active lone-pair electrons. Here these results not only provide atomic-level insights into the physical origin of the low lattice thermal conductivity in a large family of copper/silver-based compounds but also offer an efficient approach to discover and design materials with targeted thermal transport properties.

36 MATERIALS SCIENCE↗

Experimental Investigation of Low Cost, Low Thermal Conductivity Thermal Barrier Coating on HCCI Combustion, Efficiency, and Emissions

In-cylinder surface temperature is of heightened importance for Homogeneous Charge Compression Ignition (HCCI) combustion since the combustion mechanism is thermo-kinetically driven. Thermal Barrier Coatings (TBCs) selectively manipulate the in-cylinder surface temperature, providing an avenue for improving thermal and combustion efficiency. A surface temperature swing during combustion/expansion reduces heat transfer losses, leading to more complete combustion and reduced emissions. At the same time, achieving a highly dynamic response sidesteps preheating of charge during intake and eliminates the volumetric efficiency penalty. The magnitude and temporal profile of the dynamic surface temperature swing is affected by the TBC material properties, thickness, morphology, engine speed, and heat flux from the combustion process. This study follows prior work of authors with Yttria Stabilized Zirconia, which systematically engineered coatings for HCCI combustion. Herein, a modeling study was used to assess the impacts of various TBC material properties, e.g. density, thickness, and thermal conductivity on the temperature swing effect. Reducing conductivity emerged as a most promising avenue, rather than reducing both the density and effective conductivity by increasing porosity, the current work emphasizes a material with natively low conductivity. A novel TBC formulation was developed, leverages a class of materials that, to the author’s best knowledge, have not been used as a thermal barrier coating previously. Here, a systematic experimental investigation was carried out using single-cylinder research engine. Experimental engine studies utilizing the novel ‘glassy’ low-K coating exhibit advanced ignition phasing and reduced combustion duration relative to the baseline engine. Heat transfer measurements indicate a net reduction in heat flux over the entire cycle, although main effect is felt during expansion, and the reduced heat transfer losses manifest in higher gross indicated thermal efficiency by approximately 5-6% on a relative basis.

42 ENGINEERING↗