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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 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Intrinsic anharmonicity and thermal properties of ultralow thermal conductivity Ba 6 Sn 6 Se 13

Ultralow thermal conductivity materials continue to be of great interest for technologically important applications such as thermal insulators and thermoelectrics. Often, such materials possess constituents with extensive dynamic disorder, or “rattlers,” or structural disorder such as metallic glasses. Nevertheless, targeted crystalline bonding order and anharmonicity can provide effective means for the scattering of the phonons in certain materials. Our combined experimental and theoretical investigation of Ba 6 Sn 6 Se 13 reveals such a material, with ultralow thermal conductivity measured over a large temperature range. Optic phonon modes hybridize with acoustic modes at relatively low energies resulting in strong acoustic-optic scattering and limited phonon lifetimes. Moreover, our investigations reveal various avoided crossings at low energies that contribute to phonon scattering. These are derived from chiral phase symmetries and may result in nontrivial topological behaviors for phonon band crossings in this chiral material. This work contributes to the ongoing research on low thermal conductivity materials and the underlying mechanisms that affect their thermal behaviors. Manipulation of these effects may provide pathways for enhancement of material properties for targeted thermal applications using similar materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Generalized design principles for hydrodynamic electron transport in anisotropic metals

Interactions of charge carriers with lattice vibrations, or phonons, play a critical role in unconventional electronic transport of metals and semimetals. Recent observations of phonon-mediated collective electron flow in bulk semimetals, termed electron hydrodynamics, present new opportunities in the search for strong electron-electron interactions in high carrier density materials. Here we present the general transport signatures of such a second-order scattering mechanism, along with analytical limits at the Eliashberg level of theory. We study electronic transport, using ab initio calculations, in finite-size channels of semimetallic ZrSiS and TaAs 2 with and without topological band crossings, respectively. The order of magnitude separation between momentum-relaxing and momentum-conserving scattering length scales across a wide temperature range make both of them promising candidates for further experimental observation of electron hydrodynamics. More generally, our calculations suggest that the hydrodynamic transport regime does not, to first order, rely on the topological nature of the bands. Finally, we discuss general design principles guiding future search for hydrodynamic candidates, based on the analytical formulation and our ab initio predictions. Further, we find that systems with strong electron-phonon interactions, reduced electronic phase space, and suppressed phonon-phonon scattering at temperatures of interest are likely to feature hydrodynamic electron transport. We predict that layered and/or anisotropic semimetals composed of half-filled d shells and light group V/VI elements with lower crystal symmetry are promising candidates to observe hydrodynamic phenomena in the future.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Thermal properties of the metallic delafossite PdCo⁢O 2 : A combined experimental and first-principles study

Metallic delafossite materials (e.g., PdCo⁢O 2 , PtCo⁢O 2 ), have attracted much recent attention due to record-high oxide conductivities, the origins of which remain unclear. Relatively little attention has been paid to their related thermal properties, however. Here, we address this via wide temperature range experimental studies of the crystal structure, thermal expansion, and specific heat of single-crystal PdCo⁢O 2 , combined with density-functional theory (DFT) calculations of the electronic and phononic densities of states, and thus thermal properties. PdCo⁢O 2 is shown to retain the $R\bar{3}m$ space group from 12 to 1000 K, exhibiting a- and c-axis thermal expansion in good quantitative agreement with DFT-based lattice dynamics calculations. The Co-O bond lengths additionally elucidate the stability of the low-spin state of the nominally Co 3+ ions, which is a notable difference between the edge-shared Co-O octahedra in PdCo⁢O 2 and the corner-shared octahedra in Co-based perovskites. Measurements of specific heat from 1.9 to 400 K provide accurate values for the Debye temperature and Sommerfeld coefficient, the phononic part being describable via a combined Debye-Einstein approach (accounting for high-frequency oxygen-related optical phonons), with excess intermediate-temperature specific heat due to a prominent low-energy peak in the phonon density of states. Most significantly, all electronic and phononic contributions to the specific heat are shown to be remarkably closely reproduced by DFT-based calculations, establishing quantitative understanding of key thermal properties of the metallic delafossite PdCo⁢O 2 .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Theoretical Description of Pump-Probe Experiments in Charge-Density-Wave Materials out to Long Times

We describe coupled nonequilibrium electron-phonon systems semiclassically—Ehrenfest dynamics for the phonons and quantum mechanics for the electrons—using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is expected to be accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds), enabling us to model pump-probe experiments of a charge-density-wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the direct driving of the electrons. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment but never successfully explained by microscopic theory. We also describe the fluence-dependent crossover that inverts the CDW order parameter and changes the phonon dynamics. Finally, we illustrate how this method can examine a number of different types of experiments including photoemission, x-ray diffraction, and two-dimensional (2D) spectroscopy. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Intrinsic Limits of Charge Carrier Mobilities in Layered Halide Perovskites

Layered halide perovskites have emerged as potential alternatives to three-dimensional (3D) halide perovskites due to their improved stability and larger material phase space, allowing fine tuning of structural, electronic, and optical properties. However, their charge carrier mobilities are significantly smaller than those of 3D halide perovskites, which has a considerable impact on their application in optoelectronic devices. Here, we employ state-of-the-art approaches to unveil the electron-phonon mechanisms responsible for the diminished transport properties of layered halide perovskites. Starting from a prototypical A M X 3 halide perovskite, we model the case of n = 1 and n = 2 layered structures and compare their electronic and transport properties to the 3D reference. The electronic and phononic properties are investigated within density functional theory (DFT) and density functional perturbation theory (DFPT), while transport properties are obtained via the Boltzmann transport equation. The vibrational modes contributing to charge carrier scattering are investigated and associated with polar-phonon scattering mechanisms arising from the long-range Fröhlich coupling and deformation-potential scattering processes. Our investigation reveals that the lower mobilities in layered systems primarily originate from the increased electronic density of states at the vicinity of the band edges, while the electron-phonon coupling strength remains similar. Such an increase is caused by the dimensionality reduction and the break in octahedra connectivity along the stacking direction. Our findings provide a fundamental understanding of the electron-phonon coupling mechanisms in layered perovskites and highlight the intrinsic limitations of the charge carrier transport in these materials. Published by the American Physical Society 2024

Cucco, Bruno (ORCID:0000000331564143)↗
DOE OSTI2025

Revealing Fano resonance in the Dirac material ZrTe 5 through Raman scattering

Here, we explore the Fano resonance in ZrTe 5 , using terahertz Raman scattering measurements. We identified two closely spaced B 2⁢g phonon modes, B 2⁢g I and B 2⁢g II, around 9 meV and 11 meV, respectively. Interestingly, only B 2⁢g I exhibited the Fano resonance, an outcome of quantum interference between discrete phonon modes and continuous electronic excitations. This is consistent with the much stronger electron-phonon coupling of B 2⁢g I mode demonstrated by first-principles calculations. Additionally, temperature-dependent measurements highlight an enhanced Fano asymmetry at elevated temperatures, contributed by the thermal renormalization of the band structure and electron-phonon coupling. This study offers insights into the complex interrelation of electron-phonon coupling, thermal effects, and Fano resonances in topological materials.

Cheng, Di [Ames Laboratory (AMES), Ames, IA (Unite↗
DOE OSTI2026

IRMA

IRMA (In)elastic Representation of Materials As S(α,β) evaluations IRMA turns one phonon model into three outputs that usually require three separate tool chains: an evaluated nuclear-data file, predicted neutron-scattering spectra, and scattering kernels for Monte Carlo transport. The three outputs draw on a single, consistent description of the material, so the evaluation, the spectroscopy that can validate it, and the transport that uses it always agree about the physics. Nuclear data. IRMA writes ENDF-6 File 7 thermal scattering evaluations on automatically constructed (α, β) grids. This part reimplements and generalizes NJOY's LEAPR: the classic kernels reproduce freshly generated NJOY2016 tapes digit for digit and published reference tapes to about 1e-4, and the generalized paths add the exact coherent one-phonon term, anisotropic Debye-Waller tensors, coherent elastic for arbitrary crystals, and a per-species partition for polyatomic materials. The tapes feed NJOY, AMPX, FUDGE, and every transport code downstream of them. Neutron spectroscopy. The irma.spectra forward model projects the same physics onto an instrument's kinematics and resolution: INS spectra for VISION and generic indirect geometries, and 2-D S(Q,E) powder maps for direct-geometry spectrometers, from a phonopy model or straight from a phonon DOS. It can be used to predict a proposed measurement before beam time; in analysis, it supplies the calculated single-scattering counterpart of a measured spectrum, from the same material description the evaluation was built from. Monte Carlo transport. The irma.ncrystal exporter writes per-temperature scattering kernels for the companion NCrystal plugin, so McStas, OpenMC, and other NCrystal-aware codes sample the same physics. The exported kernels carry the per-site anisotropic Debye-Waller tensors, keeping directional coherent-elastic physics that NCrystal's standard scalar treatment does not represent. With the same physics inside a transport code, an entire beamline becomes a virtual experiment: IRMA's end-to-end validation ran a custom McStas implementation of the ARCS spectrometer, assembled from the existing McVine and McStas models, against measured data. From a bare crystal structure. The irma mlip front end builds the phonon model itself: a structure file and a choice of potential are enough. Nine pretrained machine-learned interatomic potentials are supported, on a laptop CPU, with no first-principles calculation; an approximate phonon model for a new material costs minutes, not a DFT campaign, and the build emits prefilled inputs for all three outputs. The result is a good starting point rather than a finished evaluation: survey-quality physics with every parameter exposed for review. A converged atomistic calculation enters the same way, as a phonopy model, when higher fidelity is needed.

Ramic, Kemal [Oak Ridge National Laboratory (ORNL)↗
DOE OSTI2020

Violation of the T –1 Relationship in the Lattice Thermal Conductivity of Mg 3 Sb 2 with Locally Asymmetric Vibrations

Most crystalline materials follow the guidelines of T –1 temperature-dependent lattice thermal conductivity (κ L ) at elevated temperatures. Here, we observe a weak temperature dependence of κ L in Mg 3 Sb 2 , T –0.48 from theory and T –0.57 from measurements, based on a comprehensive study combining ab initio molecular dynamics calculations and experimental measurements on single crystal Mg 3 Sb 2 . These results can be understood in terms of the so-called “phonon renormalization” effects due to the strong temperature dependence of the interatomic force constants (IFCs). The increasing temperature leads to the frequency upshifting for those low-frequency phonons dominating heat transport, and more importantly, the phonon-phonon interactions are weakened. In-depth analysis reveals that the phenomenon is closely related to the temperature-induced asymmetric movements of Mg atoms within MgSb 4 tetrahedron. With increasing temperature, these Mg atoms tend to locate at the areas with relatively low force in the force profile, leading to reduced effective 3 rd -order IFCs. The locally asymmetrical atomic movements at elevated temperatures can be further treated as an indicator of temperature-induced variations of IFCs and thus relatively strong phonon renormalization. The present work sheds light on the fundamental origins of anomalous temperature dependence of κ L in thermoelectrics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Reinvestigation of crystal symmetry and fluctuations in La 2 CuO 4

New surprises continue to be revealed about La 2 CuO 4 , the parent compound of the original cuprate superconductor. In this study we present neutron scattering evidence that the structural symmetry is lower than commonly assumed. The static distortion results in anisotropic Cu-O bonds within the CuO 2 planes; such anisotropy is relevant to pinning charge stripes in hole-doped samples. Associated with the extra structural modulation is a soft phonon mode. If this phonon were to soften completely, the resulting change in CuO 6 octahedral tilts would lead to weak ferromagnetism. Hence, we suggest that this mode may be the “chiral” phonon inferred from recent studies of the thermal Hall effect. We also note the absence of interaction between the antiferromagnetic spin waves and low-energy optical phonons, in contrast to what is observed in hole-doped samples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Pressure induced Invar effect in Fe 55 ⁢Ni 45 : An experimental study with nuclear resonant scattering

Pressure-dependent synchrotron x-ray diffraction (XRD), nuclear resonant inelastic x-ray scattering (NRIXS), and nuclear forward scattering (NFS) measurements were made on 57 Fe 55 Ni 45 . XRD measurements were at 298 and 392 K at pressures up to 20 GPa, confirming a pressure-induced Invar effect between 7 and 13 GPa. A decrease of the 57 Fe magnetic moment was found in NFS measurements under pressure, showing an increase in magnetic entropy. The 57 Fe phonon density of states (DOS) was obtained from NRIXS measurements. The low thermal expansion in the high-pressure Invar region originates from a competition between the thermal expansion from spins and phonons as calculated from Maxwell relations. Finally, the longitudinal phonon modes changed their pressure dependence near the Curie transition, which is evidence for a spin-phonon interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamic Rashba-Dresselhaus Effect

The Rashba-Dresselhaus effect is the splitting of doubly degenerate band extrema in semiconductors, accompanied by the emergence of counterrotating spin textures and spin-momentum locking. Here we investigate how this effect is modified by lattice vibrations. We show that, in centrosymmetric nonmagnetic crystals, for which a bulk Rashba-Dresselhaus effect is symmetry-forbidden, electron-phonon interactions can induce a phonon-assisted, dynamic Rashba-Dresselhaus spin splitting in the presence of an out-of-equilibrium phonon population. In particular, we show how Rashba, Dresselhaus, or Weyl spin textures can selectively be established by driving coherent infrared-active phonons, and we perform ab initio calculations to quantify this effect for halide perovskites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Light Dark Matter Detection with Hydrogen-Rich Targets and Low-$T_c$ TES Detectors

Direct detection of nuclear scatterings of sub-GeV dark matter (DM) particles favors low-Z nuclei. Hydrogen nucleus, which has a single proton, provides the best kinematic match. The characteristic nuclear recoil energy is boosted by a factor of a few tens from those for larger nuclei used in traditional Weakly Interacting Massive Particles searches. Furthermore, hydrogen is optimal for detecting spin-dependent nuclear scatterings of sub-GeV DM, where large parameter space still remains unconstrained yet. In this paper, we first introduce several hydrogen-rich targets, which emit two classes of signals under kinetic excitations. One class of the signals is infrared photons, which are from fundamental vibrational and rotational modes of molecules and at several characteristic wavelengths. Another is acoustic phonons and optical phonons that decay into acoustic phonons. Then we discuss the technical status and future researches of low-T c transition-edge sensor (TES) detectors, which measure the infrared photons and acoustic phonons with desirable sensitivities. Utilization of hydrogen-rich targets and ultra-sensitive low-T c TES detectors for light DM detection requires both theoretical modeling and experimental prototyping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Solid breeder material crystal structure evolution due to Li burn up–Loss of crystal stability

Solid breeder materials for fusion power plants are subjected to extreme conditions of radiation damage, high temperature and designed component burn-up. Here, the loss of lattice stability of Li 2 TiO 3 due to Li burn-up was investigated using first principles-based approaches to aid evaluation of upper limit of component lifetime. The lattice stability is analyzed using calculated phonon dispersion in the Li 2 TiO 3 supercell, while Li burn-up is modeled by the introduction of Li-vacancies. It has been determined that the studied ceramic can be structurally stable up to ~40% of Li atoms burn-up. At 50% burn-up, the negative frequency branch in the phonon dispersion spectrum appears indicating the loss of lattice dynamical stability. Moreover, the structure obtained by introduction of unstable frozen phonons with minima energy amplitude also results in a phonon dispersion with negative branches in the structure obtained. Therefore, the system completely loses stability when approximately half of Li atoms are consumed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Structural, Vibrational, and Electronic Properties of 1D-TlInTe 2 under High Pressure: A Combined Experimental and Theoretical Study

Analogous to 2D layered transition-metal dichalcogenides, the TlSe family of quasi-one dimensional chain materials with the Zintl-type structure exhibits novel phenomena under high pressure. In the present work, we have systematically investigated the high-pressure behavior of TlInTe 2 using Raman spectroscopy, synchrotron X-ray diffraction (XRD), and transport measurements, in combination with first principles crystal structure prediction (CSP) based on evolutionary approach. We found that TlInTe2 undergoes a pressure-induced semiconductor-to-semimetal transition at 4 GPa, followed by a superconducting transition at 5.7 GPa (with T c = 3.8 K). An unusual giant phonon mode (A g ) softening appears at ~10–12 GPa as a result of the interaction of optical phonons with the conduction electrons. The high-pressure XRD and Raman spectroscopy studies reveal that there is no structural phase transitions observed up to the maximum pressure achieved (33.5 GPa), which is in agreement with our CSP calculations. In addition, our calculations predict two high-pressure phases above 35 GPa following the phase transition sequence as I4/mcm (B37) → Pbcm → Pm$\bar{3}$m (B2). Electronic structure calculations suggest Lifshitz (L1 & L2-type) transitions near the superconducting transition pressure. Furthermore, our findings on TlInTe 2 open up a new avenue to study unexplored high-pressure novel phenomena in TlSe family induced by Lifshitz transition (electronic driven), giant phonon softening, and electron–phonon coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Resonance Raman Study of Shell Morphology in InP/ZnSe/ZnS Core/Shell/Shell Nanocrystals

Resonance Raman spectra and absolute cross sections of InP/ZnSe/ZnS core/shell/shell nanocrystals have been obtained at excitation wavelengths of 501.7, 457.9, and 410 nm. Eight different structures having nearly the same lowest excitonic absorption wavelength but significantly different stoichiometries are compared. The Raman spectra show phonon features attributable to both the InP core and the ZnSe shell. The largest differences among the structures are seen in the ZnSe phonon region by using excitation at 457.9 nm, on the low-energy edge of the absorption features having significant contributions from the ZnSe shell. Here, structures that are nearly stoichiometric (In:P ratio ≈1.0) show a sharp, strongly polarized peak near the bulk ZnSe phonon frequency (~250 cm –1 ) and a weak lower-frequency shoulder with a higher depolarization ratio. Structures having excess indium show a stronger low-frequency shoulder near 225 cm –1 and lower integrated Raman intensities throughout the ZnSe phonon region. These changes are attributed to the presence of indium atoms in the ZnSe shell. Furthermore, these results support a previous assignment of a slow rise component in the time-resolved photoluminescence spectra of nonstoichiometric structures to transient trapping of holes at indium defects in the shell.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron Nitride

Submicrometer-thick layers of hexagonal boron nitride (hBN) exhibit high in-plane thermal conductivity and useful optical properties, and serve as dielectric encapsulation layers with low electrostatic inhomogeneity for graphene devices. Despite the promising applications of hBN as a heat spreader, the thickness dependence of its cross-plane thermal conductivity is not known, and the cross-plane phonon mean free paths (MFPs) have not been measured. We measure the cross-plane thermal conductivity of hBN flakes exfoliated from bulk crystals. We find that submicrometer thick flakes exhibit thermal conductivities up to 8.1 ± 0.5 W m –1 K –1 at 295 K, which exceeds previously reported bulk values by more than 60%. Surprisingly, the average phonon mean free path is found to be several hundred nanometers at room temperature, a factor of 5 larger than previous predictions. When planar twist interfaces are introduced into the crystal by mechanically stacking multiple thin flakes, the cross-plane thermal conductivity of the stack is found to be a factor of 7 below that of individual flakes with similar total thickness, thus providing strong evidence that phonon scattering at twist boundaries limits the maximum phonon MFPs. These results have important implications for hBN integration in nanoelectronics and improve our understanding of thermal transport in twodimensional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Ligand Controls Excited Charge Carrier Dynamics in Metal-Rich CdSe Quantum Dots: Computational Insights

Small metal-rich semiconducting quantum dots (QDs) are promising for solid-state lighting and single-photon emission due to their highly tunable yet narrow emission line widths. Nonetheless, the anionic ligands commonly employed to passivate these QDs exert a substantial influence on the optoelectronic characteristics, primarily owing to strong electron–phonon interactions. In this work, we combine time-domain density functional theory and nonadiabatic molecular dynamics to investigate the excited charge carrier dynamics of Cd 28 Se 17 X 22 QDs (X = HCOO – , OH – , Cl – , and SH – ) at ambient conditions. These chemically distinct but regularly used molecular groups influence the dynamic surface-ligand interfacial interactions in Cd-rich QDs, drastically modifying their vibrational characteristics. The strong electron–phonon coupling leads to substantial transient variations at the band edge states. The strength of these interactions closely depends on the physicochemical characteristics of passivating ligands. Consequently, the ligands largely control the nonradiative recombination rates and emission characteristics in these QDs. Our simulations indicate that Cd 28 Se 17 (OH) 22 has the fastest nonradiative recombination rate due to the strongest electron–phonon interactions. Conversely, QDs passivated with thiolate or chloride exhibit considerably longer carrier lifetimes and suppressed nonradiative processes. The ligand-controlled electron–phonon interactions further give rise to the broadest and narrowest intrinsic optical line widths for OH and Cl-passivated single QDs, respectively. Finally, obtained computational insights lay the groundwork for designing appropriate passivating ligands on metal-rich QDs, making them suitable for a wide range of applications, from blue LEDs to quantum emitters.

36 MATERIALS SCIENCE↗
DOE OSTI2020

All-Inorganic Halide Perovskites as Potential Thermoelectric Materials: Dynamic Cation off-Centering Induces Ultralow Thermal Conductivity

Halide perovskites are anticipated to impact next generation high performance solar cells because of their extraordinary charge transport and optoelectronic properties. However, their thermal transport behavior has received limited attention. In this work, we studied the thermal transport and thermoelectric properties of the CsSnBr 3–x I x perovskites. We find a strong correlation between lattice dynamics and an ultralow thermal conductivity for series CsSnBr 3–x I x reaching 0.32 Wm –1 K –1 at 550 K. The CsSnBr 3–x I x also possess a decent Seebeck coefficient and controllable electrical transport properties. The crystallography data and theoretical calculations suggest the Cs atom deviates from its ideal cuboctahedral geometry imposed by the perovskite cage and behaves as a heavy atom rattling oscillator. This off-center tendency of Cs, together with the distortion of SnX 6 (X = Br or I) octahedra, produces a highly dynamic and disordered structure in CsSnBr 3–x I x , which gives rise to a very low Debye temperature and phonon velocity. Moreover, the low temperature heat capacity data suggests strong coupling between the low frequency optical phonons and heat carrying acoustical phonons. In conclusion, this induces strong phonon resonance scattering that induces the ultralow lattice thermal conductivity of CsSnBr 3–x I x .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗