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At least 1,459 records · Page 81
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Influence of turbulence intensity on vortex pattern for a rigid cylinder with turbulence stimulation in flow induced oscillations

The effect of ambient turbulence intensity on the flow induced oscillations of rigid circular cylinders with symmetric and asymmetric local turbulence stimulation is studied. Cylinders oscillate in one degree of freedom transversely to a steady uniform flow. Two-dimensional unsteady Reynolds-Average Navier-Stokes equations with the Spalart-Allmaras turbulence model are used to solve the problem numerically. Three freestream turbulence intensity values (0.2%, 1%, 5%) are used to study the influence of turbulence intensity on vortex pattern. Simulation results are compared with experimental data measured in the Marine Renewable Energy Laboratory of the University of Michigan in the range of 30,000 ≤ Re ≤ 110,000. The amplitude ratio, lift coefficient, vortex modes, and the interactions between vortices and cylinders are observed and discussed. In conclusion, major conclusions are: (a) Vortex patterns strongly depend on the freestream ambient turbulence intensity. (b) Low turbulence intensity can generate multi-vortex patterns at high Re. (c) High turbulence intensity results in fewer separations of a shed vortex into multiple vortices inducing emergence of elongated vortex patterns.

42 ENGINEERING↗
DOE OSTI2023

The spectroscopic quadrupole moment of the 2 1 + state of 12 C: A benchmark of theoretical models

The spectroscopic quadrupole moment of the first 2 + state of 12 C has been measured employing the Coulomb-excitation re-orientation technique. Our result of $Q_{s} (2^{+}_{1}) = +9.3^{+3.5}_{-3.8}$ efm 2 suggests a larger oblate deformation than previously reported. Combining this with the consistently re-analyzed adopted value, we present the most precise value to date of $Q_{s} (2^{+}_{1})$ = +9.5(18) efm 2 , which is consistent with a geometrical rotor description. This simple outcome is compared to state-of-the-art shell-model, mean-field, ab initio calculations, cluster-based and geometrical-like theories, which show varying degrees of emergent quadrupole collectivity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Process development for recovering critical elements from acid mine drainage

The rapid development of advanced technologies has increased the demand for critical elements, such as Mn, Co, and Ni. For this work, a systematic study was conducted to develop a process for producing high-purity Mn, Co, and Ni products from an acid mine drainage (AMD). As major contaminants, Fe and Al in the solution were sequentially precipitated and eliminated by elevating the pH to around 4.00 and 6.50, respectively. After that, a pre-concentrated slurry containing 3,794 mg/L Mn, 59 mg/L Co, 127 mg/L Ni, and 300 mg/L Zn was obtained by collecting the precipitates formed in the pH range of 6.50 to 10.00. The pH of the pre-concentrated slurry was decreased to around 5.00 by adding HCl to re-dissolve Co, Ni, and Zn for further purification. At this pH, greater than 50% of Mn remained undissolved, and filtration of the undissolved material resulted in a product with around 30 wt.% Mn. Sodium sulfide was added into the re-dissolved solution to selectively precipitate Co, Ni, and Zn while remaining Mn in the solution. Almost 100% of Co, Ni, and Zn but only around 15% of Mn were precipitated using a sulfur to metal molar ratio of 1 at pH 4.00. The sulfide precipitate was calcined at 200 °C for 2 h and then completely dissolved in 1.2 M HCl. The critical elements existing in the dissolved solution were efficiently separated using a two-stage solvent extraction process. Ultimately, Co and Ni products with almost 94% and 100% purity were obtained by sulfide and alkaline precipitation, respectively.

42 ENGINEERING↗
DOE OSTI2026

Structural dynamics of the renewable energy economy: A longitudinal input-output insights for a resilient transition

As countries accelerate their energy transitions, understanding how renewable energy (RE) systems structurally integrate into national economies is essential. This study presents a longitudinal economic input-output (EIO) analysis of the renewable energy sector in South Korea from 2016 to 2022. We develop a novel EIO-based framework that disaggregates the RE sector both by energy source (thermal, hydro, nuclear and renewable) and by industrial function (manufacturing, generation, and services), allowing for a detailed assessment of production dynamics, value-added creation, and import dependency. By quantifying backward and forward linkages and induced economic effects, the analysis reveals persistent structural vulnerabilities in renewable manufacturing and increasing sectoral interdependencies. Results reveal that while the renewable energy sector's production and value-added shares have increased, critical segments remain highly import-dependent, particularly in equipment manufacturing. The analysis highlights systemic gaps in domestic supply chain resilience and offers sector-specific insights for reducing vulnerability and enhancing energy security. Although applied to South Korea as a case study, the proposed framework is designed to be transferable to other national contexts where renewable energy planning requires economic structural insights. The findings offer policy-relevant guidance for enhancing domestic energy resilience and aligning industrial strategy with long-term decarbonization goals.

Economic linkage↗
DOE OSTI2020

Reactions during conversion of simplified low-activity waste glass feeds

The mechanisms that affect the incorporation of 99Tc, a volatile radioactive component of concern, into glass melt during vitrification of low-activity waste (LAW) are being investigated to develop the method to increase the retention of 99Tc in glass waste form. Previous studies with simulated LAW glass feeds (slurry mixture of liquid waste and chemical/mineral additives) demonstrated that the early stage feed-to-glass conversion reactions below 800°C are critical for the Re (used as a nonradioactive surrogate of 99Tc) retention in glass. To examine the effect of feed composition on the feed-to-glass conversion reactions, simplified systems containing major LAW components (NaNO3 and NaOH) and representative additive components (SiO2 and H3BO3) were designed and tested. The ratio of H3BO3 to NaNO3 was varied in three-component system without NaOH and that of NaOH to NaNO3 was varied in the four-component system at a fixed H3BO3 to NaNO3 ratio. As a first step of testing with simplified feeds, this study applied thermal analyses and phase characterization of the reacting feeds, which were performed without the addition of Re, to investigate the evolution of salt phases during slurry drying process and upon heating of dried feeds.

Jin, Tongan↗
DOE OSTI2024

Adaptive laboratory evolution and genetic engineering improved terephthalate utilization in Pseudomonas putida KT2440

Poly(ethylene terephthalate) (PET) is one of the most ubiquitous plastics and can be depolymerized through biological and chemo-catalytic routes to its constituent monomers, terephthalic acid (TPA) and ethylene glycol (EG). TPA and EG can be re-synthesized into PET for closed-loop recycling or microbially converted into higher-value products for open-loop recycling. Here, in this study, we expand on our previous efforts engineering and applying Pseudomonas putida KT2440 for PET conversion by employing adaptive laboratory evolution (ALE) to improve TPA catabolism. Three P. putida strains with varying degrees of metabolic engineering for EG catabolism underwent an automation-enabled ALE campaign on TPA, a TPA and EG mixture, and glucose as a control. ALE increased the growth rate on TPA and TPA-EG mixtures by 4.1- and 3.5-fold, respectively, in approximately 350 generations. Evolved isolates were collected at the midpoints and endpoints of 39 independent ALE experiments, and growth rates were increased by 0.15 and 0.20 h -1 on TPA and a TPA-EG, respectively, in the best performing isolates. Whole-genome re-sequencing identified multiple converged mutations, including loss-of-function mutations to global regulators gacS, gacA, and turA along with large duplication and intergenic deletion events that impacted the heterologously-expressed tphAB II catabolic genes. Reverse engineering of these targets confirmed causality, and a strain with all three regulators deleted and second copies of tphAB II and tpaK displayed improved TPA utilization compared to the base strain. Taken together, an iterative strain engineering process involving heterologous pathway engineering, ALE, whole genome sequencing, and genome editing identified five genetic interventions that improve P. putida growth on TPA, aimed at developing enhanced whole-cell biocatalysts for PET upcycling.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Flow in additively manufactured super-rough channels

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 $\mathrm {\mu }$ m). These super-rough channels pose previously unseen challenges for experimental measurements, data interpretation and roughness modelling. First, it is not clear if measurements at a particular streamwise and spanwise location still provide accurate representation of the mean (time- and plane-averaged) flow. Second, we do not know if the logarithmic layer survives. Third, it is unknown how well previously developed rough-wall models work for these large-scale roughnesses. To answer the above practical questions, we conduct direct numerical simulations of flow in additively manufactured super-rough channels. Three rough surfaces are considered, all of which are obtained from computed tomography scans of additively manufactured surfaces. The roughness’ trough to peak sizes are 0.1 $h$ , 0.3 $h$ and 0.8 $h$ , respectively, where $h$ is the intended half-channel height. Each rough surface is placed opposite a smooth wall and the other two rough surfaces, leading to six rough-wall channel configurations. Two Reynolds numbers are considered, namely $Re_\tau =180$ and $Re_\tau =395$ . We show first that measurements at one streamwise and spanwise location are insufficient due to strong mean flow inhomogeneity across the entire channel, second that the logarithmic law of the wall survives despite the mean flow inhomogeneity and third that the established roughness sheltering model remains accurate.

Altland, Samuel↗
DOE OSTI2022

Implications of inertial subrange scaling for stably stratified mixing

In this work, we investigate the effects of the turbulent dynamic range on active scalar mixing in stably stratified turbulence by adapting the theoretical passive scalar modelling and demonstrating their usefulness through consideration of the results of direct numerical simulations of statistically stationary homogeneous stratified and sheared turbulence. By analysis of inertial and inertial–convective subrange scalings, we show that the relationship between the active scalar and turbulence time scales is predicted by the ratio of the Kolmogorov and Obukhov–Corrsin constants, provided mean flow parameters permit the two subrange scalings to be appropriate approximations. We use the resulting relationship between time scales to parameterise an appropriate turbulent mixing coefficient $\varGamma \equiv \chi /\epsilon$, defined here as the ratio of available potential energy ($E_p$) and turbulent kinetic energy ($E_k$) dissipation rates. With the analysis presented here, we show that $\varGamma$ can be estimated by $E_p,E_k$ and a universal constant provided an appropriate Reynolds number is sufficiently high. This large Reynolds number regime appears here to occur at $ {{Re_b}} \equiv \epsilon / \nu N^{2} \gtrapprox 300$ where $\nu$ is the kinematic viscosity and $N$ is the characteristic buoyancy frequency. We propose a model framework for irreversible diapycnal mixing with robust theoretical parametrisation and asymptotic behaviour in this high-$ {{Re_b}}$ limit.

42 ENGINEERING↗
DOE OSTI2022

Dynamics of an inertially collapsing gas bubble between two parallel, rigid walls

The collapse of cavitation bubbles in channel flows can give rise to structural damage along neighbouring walls. Although the collapse of a bubble near a single wall has been studied extensively, less is known about bubble collapse between two walls, e.g. as in a channel. We conduct highly resolved, direct simulations of the Navier–Stokes equations to investigate the bubble dynamics and pressures produced by the collapse of a bubble between two parallel rigid walls. We examine the dependence of the dynamics and pressures on the initial bubble location, confinement and driving pressure. For a fixed initial stand-off distance, as the channel width increases the bubble volume, migration distance and re-entrant jet speed approach their single-wall counterparts. We obtain an expression for the minimum channel width at which the confinement does not affect the bubble dynamics depending on the driving pressure difference and initial stand-off distance. For a fixed channel width, varying stand-off distance reduced the maximum wall pressures in the channel relative to the single wall; the trend was consistent for three different driving pressures. Two different jetting behaviours are seen when the bubble is centred in the channel, depending on the channel width. Under significant confinement, wall-parallel re-entrant jets impinge upon each other and further intensify the collapse of the vortex ring.

Rodriguez, Jr, Mauro (ORCID:0000000305450265)↗
DOE OSTI2022

Self-similarity of scalar isosurface area density in a temporal mixing layer

Understanding the behaviour of scalar isosurfaces in a turbulent flow is of particular interest for many problems in turbulent mixing that contain sharp interfaces between regions of the flow. Common examples include combustion, where the chemical reactions occur in thin regions within the flow, and the turbulent/non-turbulent interface in shear flows, where a thin region separates the rotational, turbulent motions from the irrotational, non-turbulent background. Recent advances in computing technology allow for in-depth analysis of these interface problems that are difficult to quantify in a laboratory setting. In this paper, the results of a direct numerical simulation of a passive scalar $\varPhi$ evolving on a turbulent, temporally developing mixing layer are described. A novel approach has been taken to calculate the surface area of individual scalar isosurfaces, $A_{iso}$ , throughout the simulation, as well as the mean isosurface area density, $\varSigma$ , as a function of the cross-stream direction and time. A notable finding is that the profiles of $\varSigma$ develop in a self-similar manner when scaled by the Taylor scale of the scalar field, $\lambda _\phi$ . Remarkably, the scaling appears to hold for a wide range of isovalues. A rough scaling argument based on the formal definition of $\varSigma$ and properties of a temporal mixing layer is presented which also exposes a dependence on $\lambda _\phi$ . Based on these results, a possible scaling for the isosurface area is presented as $A_{iso}/A_0 \sim (Re \, Sc)^{1/2}$ , where $Re$ and $Sc$ are local Reynolds and Schmidt numbers, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers Re≈1–1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case specific. Here, in this work, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate Re. In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier–Stokes equations in the small-amplitude limit to obtain a system of linear partial differential equations. Using a combination of numerical (finite element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere–sphere interactions, between one sphere's motion and (1) the oscillating background flow induced by the other's motion, and (2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counterintuitive and rich motility is in the parameter space of finite inertia of particles and fluid.

42 ENGINEERING↗
DOE OSTI2023

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

In the present study an optimisation problem is formulated to determine the forcing of an eddy-viscosity-based linearised Navier–Stokes model in channel flow at $Re_\tau \approx 5200$ ( $Re_\tau$ is the friction Reynolds number), where the forcing is white-in-time and spatially decorrelated. The objective functional is prescribed such that the forcing drives a response to best match a set of velocity spectra from direct numerical simulation (DNS), as well as remaining sufficiently smooth. Strong quantitative agreement is obtained between the velocity spectra from the linear model with optimal forcing and from DNS, but only qualitative agreement between the Reynolds shear stress co-spectra from the model and DNS. The forcing spectra exhibit a level of self-similarity, associated with the primary peak in the velocity spectra, but they also reveal a non-negligible amount of energy spent in phenomenologically mimicking the non-self-similar part of the velocity spectra associated with energy cascade. By exploiting linearity, the effect of the individual forcing components is assessed and the contributions from the Orr mechanism and the lift-up effect are also identified. Finally, the effect of the strength of the eddy viscosity on the optimisation performance is investigated. The inclusion of the eddy viscosity diffusion operator is shown to be essential in modelling of the near-wall features, while still allowing the forcing of the self-similar primary peak. In particular, reducing the strength of the eddy viscosity results in a considerable increase in the near-wall forcing of wall-parallel components.

Mechanics↗
DOE OSTI2023

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, Re K = 2.56 , 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). Here, the mean flow and shear penetration depths increase with Re K and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

turbulence simulation↗
DOE OSTI2025

Inertial collapse of a gas bubble in a shear flow near a rigid wall

Despite the extensive research on bubble collapse near rigid walls, the bubble collapse dynamics in the presence of shear flow near a rigid wall is poorly understood. We conduct direct simulations of the Navier–Stokes equations to explore the bubble dynamics and pressures during bubble collapse near a rigid, flat wall under linear shear flow conditions. We examine the dependence of the bubble collapse morphology and wall pressures on the initial bubble location and shear rate. We find that shear distorts the bubble, generating two re-entrant jets – one developing from the side opposite to the mean flow and the other from the far end toward the wall. Upon impact of the jet on the opposite side of the bubble, water-hammer shocks are produced, which propagate outward and interact with the convoluted bubble shape. The shock stretches the bubble towards the wall, resulting in a closer impact location for the jet originating from the far end compared with the case with no shear flow. The water-hammer pressure location can be approximated as the theoretical distance travelled by a particle initialised at the bubble centre with the corresponding constant shear flow velocity. The maximum wall pressures can thus be predicted by considering the distance between the far jet impingement location and the wall along the wall-normal direction. As the shear rate is increased, the maximum wall pressure increases, although only marginally. We determine the critical initial stand-off distance from the wall at which the bubble morphology is shear dominated, i.e. characterised by converging re-entrant jets.

Bhola, Sahil (ORCID:0000000236766302)↗
DOE OSTI2024

Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range$Re_\tau \approx 550\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of$\lambda _x/y \approx 14$(and$\lambda _x/y \approx 8$for the wall-normal velocity). When extending the analysis to both homogeneous directions in$x$and$y$, the peak coherence is centred at$\lambda _x/\lambda _z \approx 2$and$\lambda _x/\lambda _z \approx 1$for$p_w$and$u$, and$p_w$and$v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of$Re_\tau \approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of$\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.

Mechanics↗
DOE OSTI2021

Structural Evolution of Layered Manganese Oxysulfides during Reversible Electrochemical Lithium Insertion and Copper Extrusion

The electrochemical lithiation and delithiation of the layered oxysulfide Sr 2 MnO 2 Cu 4-δ S 3 has been investigated by using a combination of in situ powder X-ray diffraction and ex situ neutron powder diffraction, X-ray absorption and 7 Li NMR spectroscopy, together with a range of electrochemical experiments. Sr 2 MnO 2 Cu 4-δ S 3 consists of [Sr 2 MnO 2 ] perovskite-type cationic layers alternating with highly defective antifluorite-type [Cu 4-δ S 3 ] (δ ≈ 0.5) anionic layers. It undergoes a combined displacement/intercalation (CDI) mechanism on reaction with Li, where the inserted Li replaces Cu, forming Li 4 S 3 slabs and Cu + is reduced and extruded as metallic particles. For the initial 2-3% of the first discharge process, the vacant sites in the sulfide layer are filled by Li; Cu extrusion then accompanies further insertion of Li. Mn 2.5+ is reduced to Mn 2+ during the first half of the discharge. The overall charging process involves the removal of Li and re-insertion of Cu into the sulfide layers with re-oxidation of Mn 2+ to Mn 2.5+ . However, due to the different diffusivities of Li and Cu, the processes operating on charge are quite different from those operating during the first discharge: charging to 2.75 V results in the removal of most of the Li, little reinsertion of Cu, and good capacity retention. A charge to 3.75 V is required to fully reinsert Cu, which results in significant changes to the sulfide sublattice during the following discharge and poor capacity retention. This detailed structure-property investigation will promote the design of new functional electrodes with improved device performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Role of Eu-Doping in the Electron Transport Behavior in the Zintl Thermoelectric Ca 5-x-y Yb x Eu y Al 2 Sb 6 System

A series of Eu-doped Zintl compounds belonging to theCa 5-x-y Yb x Eu y Al 2 Sb 6 (x = 0, 1.12; 0 ≤ y ≤ 0.63(2)) system have been successfully synthesized by both the arc-melting and the molten Pb-flux methods. All of the five title compounds initially crystallized in the Ca 5 Ga 2 As 6 -type phase (space group Pbam, Z = 2, Pearson code oP26) and maintained their original structure even after the post-heat treatment, unlike the recently reported n-type Zintl analogues in the Ca 5-x-y Yb x RE y Al 2 Sb 6 (RE = Pr, Nd, Sm) systems, which underwent a phase transition from the Ca 5 Ga 2 As 6 -type to the Ca 5 Al 2 Bi 6 -type phase after annealing. This research aimed to understand the origin of the structural preference of the title Ca 5-x-y Yb x Eu y Al 2 Sb 6 system, whether it was affected by the valence electron count or the cationic size. Electrical transport property measurements showed an increase in electrical conductivities and a decrease of Seebeck coefficients for Ca 4.89(1) Eu 0.11 Al 2 Sb 6 , Ca 4.82(1) Eu 0.18 Al 2 Sb 6 , and Ca 4.62(1) Eu 0.38 Al 2 Sb 6 , compared to the parental compound Ca 5 Al 2 Sb 6 . Hole effect measurements proved that these changes should be attributed to the reduced carrier concentration and enhanced carrier mobility. The comprehensive density functional theory calculations including electron density map analysis for the hypothetical model Ca 4.5 Eu 0.5 Al 2 Sb 6 revealed that the polarity between Al and Sb forming the anionic frameworks decreased as the Eu-dopants were introduced, which eventually affected the carrier mobility in the anionic frameworks. Thermal conductivity measurements proved that the Eu-doping successfully lowered the lattice thermal conductivity because of the enhanced atomic disordering. In conclusion, the magnetization measurements for Ca 4.37(2) Eu 0.63 Al 2 Sb 6 showed a typical Curie–Weiss behavior with weak antiferromagnetic nearest-neighbor interactions with θ p = -5.07 K.

36 MATERIALS SCIENCE↗