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DOE OSTI2022

Proton stopping measurements at low velocity in warm dense carbon

Abstract Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Dynamics of a single polyampholyte chain

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples—random charge densities and periodic charge densities—with different scaling properties. Additionally, under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

STELLAR DIAMETERS AND TEMPERATURES. III. MAIN-SEQUENCE A, F, G, AND K STARS: ADDITIONAL HIGH-PRECISION MEASUREMENTS AND EMPIRICAL RELATIONS

Based on CHARA Array measurements, we present the angular diameters of 23 nearby, main-sequence stars, ranging from spectral types A7 to K0, 5 of which are exoplanet host stars. We derive linear radii, effective temperatures, and absolute luminosities of the stars using Hipparcos parallaxes and measured bolometric fluxes. The new data are combined with previously published values to create an Angular Diameter Anthology of measured angular diameters to main-sequence stars (luminosity classes V and IV). This compilation consists of 125 stars with diameter uncertainties of less than 5%, ranging in spectral types from A to M. The large quantity of empirical data is used to derive color-temperature relations to an assortment of color indices in the Johnson (BVR{sub J} I{sub J} JHK), Cousins (R{sub C} I{sub C}), Kron (R{sub K} I{sub K}), Sloan (griz), and WISE (W{sub 3} W{sub 4}) photometric systems. These relations have an average standard deviation of {approx}3% and are valid for stars with spectral types A0-M4. To derive even more accurate relations for Sun-like stars, we also determined these temperature relations omitting early-type stars (T{sub eff} > 6750 K) that may have biased luminosity estimates because of rapid rotation; for this subset the dispersion is only {approx}2.5%. We find effective temperatures in agreement within a couple of percent for the interferometrically characterized sample of main-sequence stars compared to those derived via the infrared flux method and spectroscopic analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Massive relic galaxies challenge the co-evolution of super-massive black holes and their host galaxies

We study a sample of eight massive galaxies that are extreme outliers (3–5σ) in the M{sub ∙}− M{sub bulge} local scaling relation. Two of these galaxies are confirmed to host extremely large super-massive black holes (SMBHs), whereas the virial mass estimates for the other six are also consistent with having abnormally large SMBHs. From the analysis of their star formation histories and their structural properties, we find that all of these extreme outliers can be considered to be relic galaxies from the early (z ∼ 2) universe: i.e., they are compact (R {sub e}<2 kpc) and have purely old stellar populations (t≳10 Gyr). In order to explain the nature of such deviations from the local relations, we propose a scenario in which the hosts of these über-massive SMBHs are galaxies that have followed a different evolutionary path than the two-phase growth channel assumed for massive galaxies. Once the SMBH and the core of the galaxy are formed at z ∼ 2, the galaxy skips the second phase, remaining structurally untouched and without further mass and size increase. We show that if the outliers had followed the normal evolutionary path by growing in size via merger activity, the expected (mild) growth in mass would place them closer to the observed local relations. Our results suggest that the SMBH growth epoch for the most massive galaxies stopped ∼10 Gyr ago.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Measurements of WH and ZH production in the $$H \rightarrow b\bar{b}$$ decay channel in pp collisions at $$13\,\text {Te}\text {V}$$ with the ATLAS detector

Measurements of the Standard Model Higgs boson decaying into a $$b\bar{b}$$ b b ¯ pair and produced in association with a W or Z boson decaying into leptons, using proton–proton collision data collected between 2015 and 2018 by the ATLAS detector, are presented. The measurements use collisions produced by the Large Hadron Collider at a centre-of-mass energy of $$\sqrt{s} = 13\,\text {Te}\text {V}$$ s = 13 Te , corresponding to an integrated luminosity of $$139\,\mathrm {fb}^{-1}$$ 139 fb - 1 . The production of a Higgs boson in association with a W or Z boson is established with observed (expected) significances of 4.0 (4.1) and 5.3 (5.1) standard deviations, respectively. Cross-sections of associated production of a Higgs boson decaying into bottom quark pairs with an electroweak gauge boson, W or Z , decaying into leptons are measured as a function of the gauge boson transverse momentum in kinematic fiducial volumes. The cross-section measurements are all consistent with the Standard Model expectations, and the total uncertainties vary from 30% in the high gauge boson transverse momentum regions to 85% in the low regions. Limits are subsequently set on the parameters of an effective Lagrangian sensitive to modifications of the WH and ZH processes as well as the Higgs boson decay into $$b\bar{b}$$ b b ¯ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Search for New Physics via EFT in collisions containing a top quark and a boosted Z or Higgs boson

We present a generator-level sensitivity study of physics beyond the Standard Model within the framework of Effective Field Theory (EFT). The targeted signal processes are single top quark production in association with a Lorentz-boosted Higgs or Z boson (tHq and tZq) in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Event selection requires one electron or muon, a high-transverse-momentum, large-radius (AK8) jet reconstructing hadronic H → b̄b or Z → b̄b decays, at least two distinct, non-overlapping small-radius (AK4) jets with one originating from a b quark, and a missing transverse energy greater than 30 GeV. Signal and background samples are generated via Monte Carlo simulation using MadGraph with MadJax to perform EFT matrix-element calculations. Deviations from the Standard Model are parametrized through dimension-six EFT operators that probe modified top quark interactions. This generator-level study identifies kinematic observables with enhanced sensitivity to EFT operators and motivates future reconstruction-level analyses of tHq and tZq channels.

Meshramkar, Daniel [Baylor U., Waco]↗

DOE OSTI2026

Search for New Physics via EFT in collisions containing a top quark and a boosted Z or Higgs boson

Meshramkar, Daniel [Baylor U., Waco]↗

DOE OSTI2016

PARALLAX AND ORBITAL EFFECTS IN ASTROMETRIC MICROLENSING WITH BINARY SOURCES

In gravitational microlensing, binary systems may act as lenses or sources. Identifying lens binarity is generally easy, in particular in events characterized by caustic crossing since the resulting light curve exhibits strong deviations from a smooth single-lensing light curve. In contrast, light curves with minor deviations from a Paczyński behavior do not allow one to identify the source binarity. A consequence of gravitational microlensing is the shift of the position of the multiple image centroid with respect to the source star location — the so-called astrometric microlensing signal. When the astrometric signal is considered, the presence of a binary source manifests with a path that largely differs from that expected for single source events. Here, we investigate the astrometric signatures of binary sources taking into account their orbital motion and the parallax effect due to the Earth’s motion, which turn out not to be negligible in most cases. We also show that considering the above-mentioned effects is important in the analysis of astrometric data in order to correctly estimate the lens-event parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

The effect of an offset polar cap dipolar magnetic field on the modeling of the vela pulsar's γ-ray light curves

We performed geometric pulsar light curve modeling using static, retarded vacuum, and offset polar cap (PC) dipole B-fields (the latter is characterized by a parameter ϵ), in conjunction with standard two-pole caustic (TPC) and outer gap (OG) emission geometries. The offset-PC dipole B-field mimics deviations from the static dipole (which corresponds to ϵ=0). In addition to constant-emissivity geometric models, we also considered a slot gap (SG) E-field associated with the offset-PC dipole B-field and found that its inclusion leads to qualitatively different light curves. Solving the particle transport equation shows that the particle energy only becomes large enough to yield significant curvature radiation at large altitudes above the stellar surface, given this relatively low E-field. Therefore, particles do not always attain the radiation-reaction limit. Our overall optimal light curve fit is for the retarded vacuum dipole field and OG model, at an inclination angle α=78{sub −1}{sup +1{sup {sup ∘}}} and observer angle ζ=69{sub −1}{sup +2{sup {sup ∘}}}. For this B-field, the TPC model is statistically disfavored compared to the OG model. For the static dipole field, neither model is significantly preferred. We found that smaller values of ϵ are favored for the offset-PC dipole field when assuming constant emissivity, and larger ϵ values favored for variable emissivity, but not significantly so. When multiplying the SG E-field by a factor of 100, we found improved light curve fits, with α and ζ being closer to best fits from independent studies, as well as curvature radiation reaction at lower altitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

A Catalog of Quasar Properties from Sloan Digital Sky Survey Data Release 16

We present a catalog of continuum and emission-line properties for 750,414 broad-line quasars included in the Sloan Digital Sky Survey Data Release 16 quasar catalog (DR16Q), measured from optical spectroscopy. These quasars cover broad ranges in redshift (0.1 ≲ z ≲ 6) and luminosity (44 ≲ log(L bol /erg s -1 ) ≲ 48), and probe lower luminosities than an earlier compilation of SDSS DR7 quasars. Derived physical quantities such as single-epoch virial black hole masses and bolometric luminosities are also included in this catalog. We present improved systemic redshifts and realistic redshift uncertainties for DR16Q quasars using the measured line peaks and correcting for velocity shifts of various lines with respect to the systemic velocity. About 1%, 1.4%, and 11% of the original DR16Q redshifts deviate from the systemic redshifts by |ΔV| > 1500 km s -1 , |ΔV| $\in$ [1000, 1500] km s -1 , and |ΔV| $\in$ [500, 1000] km s -1 , respectively; about 1900 DR16Q redshifts were catastrophically wrong (|ΔV| > 10,000 km s -1 ). We demonstrate the utility of this data product in quantifying the spectral diversity and correlations among physical properties of quasars with large statistical samples.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

A comprehensive laboratory study on the immersion freezing behavior of illite NX particles. A comparison of 17 ice nucleation measurement techniques

Immersion freezing is the most relevant heterogeneous ice nucleation mechanism through which ice crystals are formed in mixed-phase clouds. In recent years, an increasing number of laboratory experiments utilizing a variety of instruments have examined immersion freezing activity of atmospherically relevant ice-nucleating particles. However, an intercomparison of these laboratory results is a difficult task because investigators have used different ice nucleation (IN) measurement methods to produce these results. A remaining challenge is to explore the sensitivity and accuracy of these techniques and to understand how the IN results are potentially influenced or biased by experimental parameters associated with these techniques. Within the framework of INUIT (Ice Nuclei Research Unit), we distributed an illite-rich sample (illite NX) as a representative surrogate for atmospheric mineral dust particles to investigators to perform immersion freezing experiments using different IN measurement methods and to obtain IN data as a function of particle concentration, temperature ( T ), cooling rate and nucleation time. A total of 17 measurement methods were involved in the data intercomparison. Experiments with seven instruments started with the test sample pre-suspended in water before cooling, while 10 other instruments employed water vapor condensation onto dry-dispersed particles followed by immersion freezing. The resulting comprehensive immersion freezing data set was evaluated using the ice nucleation active surface-site density, n s , to develop a representative n s ( T ) spectrum that spans a wide temperature range (-37 °C < T < -11 °C) and covers 9 orders of magnitude in n s . In general, the 17 immersion freezing measurement techniques deviate, within a range of about 8 °C in terms of temperature, by 3 orders of magnitude with respect to n s . In addition, we show evidence that the immersion freezing efficiency expressed in n s of illite NX particles is relatively independent of droplet size, particle mass in suspension, particle size and cooling rate during freezing. A strong temperature dependence and weak time and size dependence of the immersion freezing efficiency of illite-rich clay mineral particles enabled the n s parameterization solely as a function of temperature. We also characterized the n s ( T ) spectra and identified a section with a steep slope between -20 and -27 °C, where a large fraction of active sites of our test dust may trigger immersion freezing. This slope was followed by a region with a gentler slope at temperatures below -27 °C. While the agreement between different instruments was reasonable below ~ -27 °C, there seemed to be a different trend in the temperature-dependent ice nucleation activity from the suspension and dry-dispersed particle measurements for this mineral dust, in particular at higher temperatures. For instance, the ice nucleation activity expressed in n s was smaller for the average of the wet suspended samples and higher for the average of the dry-dispersed aerosol samples between about -27 and -18 °C. Only instruments making measurements with wet suspended samples were able to measure ice nucleation above -18 °C. A possible explanation for the deviation between -27 and -18 °C is discussed. Multiple exponential distribution fits in both linear and log space for both specific surface area-based n s ( T ) and geometric surface area-based n s ( T ) are provided. These new fits, constrained by using identical reference samples, will help to compare IN measurement methods that are not included in the present study and IN data from future IN instruments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Effects of interaction strength of associating groups on linear and star polymer dynamics

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. In this study, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead–spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 k B T. We find that, for all melts and blends, interaction of a few k B T between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few k B T and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Measurement of Higgs boson decay into $b$-quarks in associated production with a top-quark pair in $pp$ collisions at $ \sqrt{s} $ = 13 TeV with the ATLAS detector

The associated production of a Higgs boson and a top-quark pair is measured in events characterized by the presence of one or two electrons or muons. The Higgs boson decay into a b-quark pair is used. The analyzed data, corresponding to an integrated luminosity of 139 fb –1 , were collected in proton-proton collisions at the Large Hadron Collider between 2015 and 2018 at a centre-of-mass energy of √s = 13 TeV. The measured signal strength, defined as the ratio of the measured signal yield to that predicted by the Standard Model, is $0.35$ $^{+0.36}_{–0.34}$. This result is compatible with the Standard Model prediction and corresponds to an observed (expected) significance of 1.0 (2.7) standard deviations. The signal strength is also measured differentially in bins of the Higgs boson transverse momentum in the simplified template cross-section framework, including a bin for specially selected boosted Higgs bosons with transverse momentum above 300 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Inclusive search for highly boosted Higgs bosons decaying to bottom quark-antiquark pairs in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for standard model Higgs bosons (H) produced with transverse momentum (p$_{T}$) greater than 450 GeV and decaying to bottom quark-antiquark pairs ($ \mathrm{b}\overline{\mathrm{b}} $) is performed using proton-proton collision data collected by the CMS experiment at the LHC at $ \sqrt{s} $ = 13 TeV. The data sample corresponds to an integrated luminosity of 137 fb$^{−1}$. The search is inclusive in the Higgs boson production mode. Highly Lorentz-boosted Higgs bosons decaying to $ \mathrm{b}\overline{\mathrm{b}} $ are reconstructed as single large-radius jets, and are identified using jet substructure and a dedicated b tagging technique based on a deep neural network. The method is validated with Z →$ \mathrm{b}\overline{\mathrm{b}} $ decays. For a Higgs boson mass of 125 GeV, an excess of events above the background assuming no Higgs boson production is observed with a local significance of 2.5 standard deviations (σ), while the expectation is 0.7. The corresponding signal strength and local significance with respect to the standard model expectation are μ$_{H}$ = 3.7 ± 1.2(stat)$ {}_{-0.7}^{+0.8} $(syst)$ {}_{-0.5}^{+0.8} $(theo) and 1.9 σ. Additionally, an unfolded differential cross section as a function of Higgs boson p$_{T}$ for the gluon fusion production mode is presented, assuming the other production modes occur at the expected rates.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Mitigating cutting-induced plasticity in the contour method, Part 2: Numerical analysis

Cutting-induced plasticity can have a significant effect on the measurement accuracy of the contour method. The present study examines the benefit of a double-embedded cutting configuration that relies on self-restraint of the specimen, relative to conventional edge-crack cutting configurations. A series of finite element analyses are used to simulate the planar sectioning performed during double-embedded and conventional edge-crack contour cutting configurations. The results of numerical analyses are first compared to measured results to validate the cutting simulations. The simulations are then used to compare the efficacy of different cutting configurations by predicting the deviation of the residual stress profile from an original (pre-cutting) reference stress field, and the extent of cutting-induced plasticity. Comparisons reveal that while the double-embedded cutting configuration produces the most accurate residual stress measurements, the highest levels of plastic flow are generated in this process. As a result, this cutting-induced plastic deformation is, however, largely confined to small ligaments formed as a consequence of the sample sectioning process, and as such it does not significantly affect the back-calculated residual stress field.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Planck 2018 results

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E -mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f NL local = -0.9 ± 5.1; f NL equil = -26 ± 47; and f NL ortho = -38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 σ . Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g NL local = (-5.8 ± 6.5) × 10 4 (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Choice of tip, signal stability, and practical aspects of piezoresponse-force-microscopy

Piezoresponse force-microscopy (PFM) has become the standard tool to investigate ferroelectrics on the micro- and nanoscale. However, reliability of PFM signals is often problematic and their quantification is challenging and thus not widely applied. Here, we present a study of the reproducibility of PFM signals and of the so-called PFM background signal which has been reported in the literature. We find that PFM signals are generally reproducible to certain extents. The PFM signal difference between 180° domains on periodically poled lithium niobate (PPLN) is taken as the reference signal in a large number of measurements, carried out in a low frequency regime (30-70 kHz). We show that in comparison to Pt coated tips, diamond coated tips exhibit improved signal stability, lower background signal, and less imaging artifacts related to PFM which is reflected in the spread of measurements. This is attributed to the improved mechanical stability of the conductive layer. The average deviation of the mean PFM signal is 38.3%, for a diamond coated tip. Although this deviation is relatively high, it is far better than values from the literature which showed a deviation of approx. 73.1%. Additionally, we find that the average deviation of the background signal from 0 is 11.6% of the PPLN domain contrast. Thus, the background signal needs to be taken into account when quantifying PFM signals and should be subtracted from PFM signals. Those results are important for quantification of PFM signals, since PPLN might be used for this purpose when PFM signals measured on PPLN are related to its macroscopic d{sub 33} coefficient. Finally, the crucial influence of sample polishing on PFM signals is shown and we recommend to use a multistep polishing route with a final step involving 200 nm sized colloidal silica particles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Magnetic field-induced non-trivial electronic topology in Fe3− x GeTe2

The anomalous Hall, Nernst, and thermal Hall coefficients of the itinerant ferromagnet Fe3−xGeTe2 display anomalies upon cooling that are consistent with a topological transition that could induce deviations with respect to the Wiedemann–Franz (WF) law. This law has not yet been validated for the anomalous transport variables, with recent experimental studies yielding material-dependent results. Nevertheless, the anomalous Hall and thermal Hall coefficients of Fe3−xGeTe2 are found, within our experimental accuracy, to satisfy the WF law for magnetic fields μ0H applied along its c axis. Remarkably, large anomalous transport is also observed for μ0H||a axis with the field aligned along the gradient of the chemical potential generated by thermal gradients or electrical currents, a configuration that should not lead to their observation. These anomalous planar quantities are found to not scale with the component of the planar magnetization (M||), showing instead a sharp decrease beyond μ0H||= 4 T or the field required to align the magnetic moments along μ0H||. We argue that chiral spin structures associated with Bloch domain walls lead to a field-dependent spin chirality that produces a novel type of topological transport in the absence of interaction between the magnetic field and electrical or thermal currents. Locally chiral spin structures are captured by our Monte Carlo simulations incorporating small Dzyaloshinskii–Moriya and biquadratic exchange interactions. These observations reveal not only a new way to detect and expose topological excitations, but also a new configuration for heat conversion that expands the current technological horizon for thermoelectric energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗