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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Pressure effects on lithium anode/nickel-manganese-cobalt oxide cathode pouch cells through fixture design

Applying external pressure to a pouch cell results in improved performance, implicating systems-level design of batteries. Here, different formats and amounts of external pressure to Li-Li x Ni 0.8 Mn 0.1 Co 0.1 O 2 (Li-NMC811) pouch cells were studied under lean electrolyte conditions. Due to the more uniform lithium plating/stripping, a constant gap fixture that retains the distance of the frame during cycling performed greater than a constant pressure fixture that retains applied pressure to the cell. In addition, the use of flexible foam in a constant gap fixture revealed enhanced cycle life at 10 psi; however, at 30 psi, the use of a rigid plate extended cycle life to over 250 cycles, while the foam severely shortened cycle life. This discrepancy with pressure was proven to be driven by stress distribution on cell components. The failure mechanisms and the effects of pressure fixture design on cell components were unveiled, shedding light on improving high-energy battery performance through at-scale fixture design.

25 - ENERGY STORAGE↗
DOE OSTI2025

Chemical versus physical pressure effects on the structure transition of bilayer nickelates

The observation of high-T c superconductivity (HTSC) in concomitant with pressure-induced orthorhombic-tetragonal structural transition in bilayer La 3 Ni 2 O 7 has sparked hopes of achieving HTSC by stabilizing the tetragonal phase at ambient pressure. Chemical pressure, introduced by replacing La 3+ with smaller rare-earth R 3+ has been considered as a potential route. However, our experimental and theoretical investigation reveals that such substitutions, despite causing lattice contraction, actually produce stronger orthorhombic distortions, requiring higher pressures for the structural transition. A linear extrapolation of P c versus the average size of A-site cations (<$r_A$>), yields a putative critical value of (<$r_A$>) ≈ 1.23 Å for P c ≈ 1 bar. The negative correlation between P c and (<$r_A$>) indicates that replacing La 3+ with smaller R 3+ ions is unlikely to reduce P c to ambient pressure. Instead, substituting La 3+ with larger cations like Sr 2+ or Ba 2+ might be a feasible approach. Our results provide guidance for realizing ambient-pressure HTSC in bilayer nickelates.

36 MATERIALS SCIENCE↗
DOE OSTI2024

On the prediction of pressure effects for the combination kinetics of two alkyl radicals with the geometric mean rule

Here, alkyl combination reactions, along with their reverse alkane unimolecular decomposition reactions, are widely present in pyrolysis and combustion systems. These reactions occur mainly at temperatures at which their rate coefficients depend on pressure, and only a few studies have explored this dependence for large size alkyls. The accurate calculation of these kinetic data is limited by the size of the alkyl fragments involved, since the theoretical methods used are computationally expensive. Therefore, little reliable data is available for the modeling of real fuels alkane decomposition kinetics. In this paper, we propose an alternative approach that allows an accurate estimation of pressure-dependent kinetic rates for the combination of long-chain alkyl radicals, based on tabulated reaction models. The rates of combination of linear alkyls radicals forming ethane to pentane were calculated using the CASPT2-F12/cc-pVDZ-F12 level within VRC-TST theory combined with master-equation simulations. The computed high-pressure limit rate coefficients showed that n-propyl could be a minimum-size representative structure for larger n-alkyl chain, but this approach fails to capture the pressure dependence of the reaction that remains size-dependent for larger alkyls. The Geometric Mean Rule (GMR), a simple rule that links the self and cross-reactions of three alkyl radicals, is used to address this issue. Our theoretical calculations show for the first time that the GMR applies not only at the high-pressure limit, but also for every pressure explored. The GMR is shown to be accurate, with a maximum 22 % deviation in the falloff region for the estimation of rates for small alkyl combinations. Using this method, we propose a tabulated reaction rate rule for the combination of alkyl radicals up to C5+C5. The use of computed rate coefficients with the GMR approximation opens ways to develop pressure-dependent reaction rate rules for large n-alkyl combinations, based on accurate and computationally expensive theoretical calculations on smaller alkyl fragments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

High pressure effects on EBC systems in high temperature environments

Environmental barrier coatings (EBCs) are designed to protect SiCfiber/SiCmatrix ceramic matrix composites (CMCs) in turbine engines by mitigating wear in high-temperature water vapor environments. The failure of EBCs is frequently attributed to the accelerated oxidation of the silicon bond coating layer when exposed to high-temperature steam, leading to the formation of a thickened thermally grown oxide (TGO). TGO growth increases interfacial stress, weakens adhesion, and results in coating spallation. Understanding the impact of high-temperature oxidation of EBC systems is essential for developing accurate lifespan models for turbine components, although pressurized oxidation testing is extremely sparse in the open literature. In this work, oxidation tests were performed on rare earth silicate EBCs coated onto SiC substrates under increased pressure conditions. The coated specimens were tested at 1100°C, 1200°C, and 1300°C at both 1 atm and 10 atm total pressure in steam environments. Subsequent characterization focused on the microstructural evolution of the EBC/Si/SiC system. The experimental findings indicated that TGO behavior is dependent on high-pressure conditions, with elevated pressure leading to an increase in oxide scale thickness and modifications in its morphology.

Ardrey, Kristyn [ORNL] (ORCID:0000000184407796)↗
DOE OSTI2025

High-Pressure Effects on an Octa-Hydrated Curium Complex: An Experimental and Theoretical Investigation

An octa-hydrated curium compound [Cm(H 2 O) 8 ](Hdtp)(dtp)·H 2 O (Cm1,H 2 dtp = 2,3-di(tetrazol-5-yl)pyrazine) along with its lanthanide analogues [Ln(H 2 O) 8 ](Hdtp)-(dtp)·H 2 O (Ln1, Ln 3+ = La 3+ –Nd 3+ , Sm 3+ –Lu 3+ ) were synthesized and characterized using single crystal X-ray diffraction and spectroscopic methods. Bond length analysis of VIII Cm(III)–OH 2 (where VIII refers to the coordination number) was compared to VIII Ln(III)–OH 2 (Ln 3+ = Nd 3+ and Sm 3+ ), indicating similar VIII M(III)–OH 2 bond lengths owing to the similar eight-coordinate ionic radii of these VIII M(III) cations. Owing to the reduced coordination number, the VIII Cm(III)–OH 2 bond lengths were shorter than previously reported IX Cm(III)–OH 2 bonds in [Cm(H 2 O) 9 ](CF 3 SO 3 ) 3 . The octa-aquo complexes were also characterized by solid-state UV–vis–NIR spectroscopy in addition to variable-temperature and variable-pressure photoluminescence. Variable-pressure absorption spectra of Cm1 were compared with Ln1 and show that the Cm(III) f → f transitions have a stronger dependence on pressure than that observed in Ln1 (Ln 3+ = Nd 3+ and Sm 3+ ). The experimental and computational analyses reveal that the monotonic decrease in the computed energy difference between the ground state and the first excited state corresponds to the observed red shift of the photoluminescence peak. This is accompanied by a gradual reduction in the average Cm(III)–OH 2 bond length and a delocalization of spin densities, alongside an intensified interaction involving the 5f orbitals under increasing pressure. Furthermore, these changes accommodate the new geometry and collectively modify the energy landscape, resulting in peak broadening and quenching.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Effect of non-stoichiometry and pressure on superconductivity in topological semimetal PdTe

Research into topological superconductivity has been at the forefront of condensed matter physics due to both fundamental interest and potential applications in quantum computing. PdTe, is such a superconductor with a transition temperature T c ∼ 4.5 K and exhibits a nontrivial topological electronic structure, thus receiving significant attention. We report an experimental and theoretical investigation of the pressure effect on superconductivity by applying chemical non-stoichiometry and hydrostatic pressure. While T c decreases with increasing pressure through electrical resistivity, magnetization, and specific heat measurements, chemical pressure has a distinct impact from hydrostatic pressure, which could increase T c by creating negative pressure via non-stoichiometric Pd x Te with x > 1. Accompanied with this is a sign change of the Hall coefficient from negative at x < 1 to positive at x > 1. This indicates extreme sensitivity of the electronic structure to chemical non-stoichiometry, which occurs as a Pd vacancy for x < 1 and Pd interstitial for x > 1.

nonstoichiometry↗
DOE OSTI2025

The Surface Chemistry of Methanol on TiO 2 (110): Effects of Pressure and Temperature on the Stability of C–O and C–H Bonds

Synchrotron-based ambient pressure X-ray photoelectron spectroscopy (AP-XPS) was used to study the surface chemistry of methanol on TiO 2 (110), examining the effects of methanol pressure, oxide temperature, and coadsorption with H 2 . At 300 K, the adsorption of methanol on TiO 2 (110) leads to the formation of CH 3 O on the surface with a minor amount of CH 3 OH present. The easy cleavage of the O–H bond in the alcohol agrees with the predictions of theoretical calculations, and most of the adsorbed CH 3 O was not associated with the presence of Ti 3+ sites in the oxide substrate. The adsorbed CH 3 O was removed from the TiO 2 (110) surface by heating to 600 K without the deposition of CH x fragments or C on the oxide. The results of temperature-programmed desorption (TPD) showed the evolution of methanol and formaldehyde at 360 and 490 K as a result of a disproportionation reaction: 2CH 3 O → CH 3 OH + CH 2 O. This surface chemistry, where there is no rupture of the C–O bond, and only selective cleavage of O–H and C–H bonds, is very different from that found on metals used in catalysts for methanol reforming, where massive conversion of the alcohol into CO, CH x and C species is seen. Furthermore, the TPD data indicate that any CH 3 O formed on the oxide surface can be hydrogenated and desorbed as CH 3 OH at temperatures below 550 K. In this respect, titania is an ideal support for catalysts employed to achieve methanol synthesis through CO 2 hydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Fragile-to-strong transition in liquid As 2 S 3 under pressure: The effect of melt metallization

The well-known classification of glass-forming melts into fragile and strong liquids has several notable exceptions, including water, silica, and certain phase-change materials (PCMs). These exceptional fluid systems exhibit a fragile-to-strong transition (FST) upon cooling: a transformation from a high-temperature liquid with fast atomic dynamics, low viscosity, and low flow activation energy, to a viscous supercooled melt with high energy barriers near the glass transition temperature T g . This behavior is critically important for non-volatile memories, photonic tensor cores, reconfigurable metamaterials, and other devices, that use PCMs, enabling nanosecond-scale crystallization in the fragile regime and long data retention in the strong regime near or below T g . A significant structural transformation is expected between these two viscosity regimes, along with a semiconductor-metal (SC-M) transition upon heating, driven by high internal pressure and associated density increase. By applying high external pressure to the canonical low-conducting chalcogenide melt As 2 S 3 , we observed both the FST and the SC-M transition, occurring simultaneously within the same domain of the P, T−phase space. These findings suggest that the FST is not limited to a few exceptional liquids but is a common phenomenon, at least in systems that exhibit melt metallization within specific regions of their P, T−phase diagrams.

first-principles molecular dynamics↗
DOE OSTI2025

Effect of pressure cycling and compression rate on the bcc-hcp transition in an FeNi alloy

Here, we investigate the body-centered cubic (bcc) to hexagonal close-packed (hcp) phase transition in Fe-10wt. %Ni alloy, combining pressure cycling and fast compression with time-resolved synchrotron x-ray diffraction in a dynamic diamond anvil cell. Three pressure cycles were conducted with compression rates ranging from 0.1 to nearly 10 3 GPa/s. During the first cycle with the slowest compression, the observed orientations in the bcc and hcp phases are consistent with the Burgers mechanism, followed by c-axis rotation of the hcp phase consistent with {$10$ $\bar{1}2$} twinning. During the following cycles with fast compression at 10 2 –10 3 GPa/s, the hcp phase exhibits negligible c-axis rotation with a nearly constant c/a ratio of ∼1.61 up to ∼30 GPa, indicating suppression of plastic deformation (especially, twinning) due to sample confinement from the gasket. Notably, the onset pressure of the transition decreases with additional pressure cycling and faster compression, which normally leads to over-pressurization. This suggests that defects or shear induced from the pressure cycling reduces the transition kinetics even during fast compression. These insights into the deformation and transition behavior in an FeNi alloy under multiple dynamic loading cycles can offer guidance for future design of advanced structural alloys and improve our understanding of planetary core processes.

FeNi alloy↗
DOE OSTI2025

Effects of Pressure on Superconducting Properties and Vortex Pinning of CaKFe 4 As 4 Single Crystals

Measurements of low field magnetization, trapped flux magnetization and 5 K flux creep in single crystal of CaKFe 4 As 4 under pressure up to 7.5 GPa in a diamond pressure cell are presented. Further, the observed evolution of the temperature dependence of the self-field critical current and slowing down of the base temperature flux creep rate are explained within the two sources of pinning hypothesis involving presence of CaFe 2 As 2 intergrowths suggested in the literature. Above the half collapsed tetragonal structural transition under pressure, where superconductivity is non-bulk or absent, critically diminished or no diamagnetism and flux trapped magnetization were observed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

The Effect of Hydrothermal Alteration and Microcracks on Hydraulic Properties and Poroelastic Deformation: A Case Study of the Blue Mountain Geothermal Field

Abstract Geothermal energy plays a vital role in decarbonizing electricity and heat supply. Effective utilization of geothermal resources hinges on identifying or generating permeable reservoir zones and understanding how effective pressure variations affect fluid circulation and reservoir properties by poroelastic deformation. Hydrothermal alteration can modify the petrophysical properties of geothermal reservoir rocks, which may increase or decrease its productivity. Understanding these alteration effects is essential to predict and optimize long‐term sustainable geothermal operations. Here, we investigate the impact of hydrothermal alteration on poroelastic and hydraulic properties of diverse lithologies in a series of deformation tests performed at several confining (0–80 MPa) and pore pressure (10–30 MPa) levels. Experimental results of hydrothermally altered dikes and phyllites obtained from the Blue Mountain geothermal field (Nevada, USA) are compared to thermally cracked La Peyratte granite (France) and correlated with petrophysical properties, mineral composition, and microstructures. Argillic alteration of dikes increases porosity and storage capacity but lowers thermal conductivity and increases pore compressibility. Conversely, silicate precipitation in phyllites increases stiffness and thermal conductivity but also reduces porosity and permeability. Experimentally determined effective pressure coefficients range from 0.1 to 0.9, differ for permeability and volumetric strain and decrease with increasing effective pressure. The presence of compliant microcracks and crack‐like pores significantly increases the stress sensitivity of La Peyratte granite and silicified phyllites. This study demonstrates how thermal and chemical alteration impacts poromechanical and petrophysical characteristics of geothermal targets, which ultimately govern reservoir stability and subsidence, induced seismicity as well as fluid and heat extraction efficiency during geothermal operations.

Schuster, Valerian [Helmholtz Centre Potsdam GFZ G↗
DOE OSTI2025

Structure and Superconductivity of Hydrogenated TiZr Alloys Under High Pressure

The effects of pressure on the structure and electrical transport properties, including electrical resistance and critical magnetic field values for superconductivity in pristine and hydrogenated TiZr alloys, were investigated. As pressure increased from ambient to 55 GPa, the structure of the pristine TiZr alloys transformed from hcp to bcc via an intermediate ω phase. The superconducting transition temperature (T c ) significantly increased from 1.76 K at ambient pressure to 15.5 K at 52.2 GPa, accompanied by an extrapolated upper critical field of 24.5 T at T = 0 K. In contrast, the hydrogenated samples exhibited substantially lower T c values compared to the pristine ones, with a T c of 4.6 K at 50.5 GPa and an extrapolated upper critical field of 1.8 T at T = 0 K. Upon decompression, the superconductivity in the hydrogenated sample persisted down to 25 GPa, disappearing when the pressure was reduced to 19 GPa. Synchrotron X-ray diffractions (XRD) analysis revealed the formation of three hydrides: I4/mmm-(Ti, Zr)H 2 , P6 3 /mmc-(Ti, Zr)H 3 , and I4̅3d-(Ti,Zr) 4 H 15 . Finally, by combining XRD and electrical resistance data, we tentatively propose that the P6 3 /mmc-(Ti, Zr)H 3 predominantly induces superconductivity. In contrast to superhydrides, where electron–phonon interactions increase the superconducting temperature at high pressure, hydrogen atoms in hcp-(Ti, Zr)H 3 reduce T c .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Temperature effect on turbulent burning velocity of lean premixed hydrogen/air flames

Hydrogen has drawn great attention in recent years as a carbon-free fuel. The turbulent burning velocity (S T ) is an important parameter for the design and modeling of hydrogen-fueled engines given the high propagation speed of hydrogen flames. It has been well documented that S T of hydrogen flames can be dramatically increased by thermo-diffusive effects which are sensitive to thermodynamic conditions. Previous studies have mainly focused on the pressure effect on S T of lean hydrogen flames, while the temperature effect has been largely ignored. Here, in the present study, the turbulent burning velocity for a lean hydrogen/air mixture over a wide range of temperatures (300–641 K) and pressures (1–15 atm) is investigated through direct numerical simulations of statistically planar turbulent premixed flames. Results show that the variation of normalized turbulent burning velocity (S T /S L , where S L is the laminar flame speed) with temperature and pressure is mainly controlled by the variation of the stretching factor I 0 . While S T /S L is only marginally dependent on temperature at the atmospheric pressure, it exhibits a decreasing trend with temperature at an elevated pressure (10 atm). This is associated with different temperature dependencies of flame surface area enlargement at the two different pressures, despite the monotonically decreasing trends of I 0 with temperature at both pressures. In addition, under engine-relevant conditions where the temperature and pressure increase simultaneously, the promotion effect of pressure is found to be largely canceled out by the suppression effect of temperature, leading to only a slight increase in I 0 and S T /S L . The observed trends are further explained through detailed flame dynamic analysis. Furthermore, I 0 at different temperatures and pressures is found to correlate very well with the enhancement of fuel consumption rate in the critically strained laminar flames. The present study elucidates the strong impact of temperature on S T of lean premixed hydrogen/air flames at elevated pressures and provides new insights into the modeling of S T , especially for engine-relevant conditions.

Wang, Yiqing [Argonne National Laboratory (ANL), A↗
DOE OSTI2025

Ab initio quantum many-body description of superconducting trends in the cuprates

Using a systematic ab initio quantum many-body approach that goes beyond low-energy models, we directly compute the superconducting pairing order and estimate the pairing gap of several doped cuprate materials and structures within a purely electronic picture. We find that we can correctly capture two well-known trends: the pressure effect, where the pairing order and gap increase with intra-layer pressure, and the layer effect, where the pairing order and gap vary with the number of copper-oxygen layers. From these calculations, we observe that the strength of superexchange and the covalency at optimal doping are the best descriptors for these trends. Our microscopic analysis further identifies that strong short-range spin fluctuations and multi-orbital charge fluctuations drive the development of the pairing order. Our work illustrates the possibility of a material-specific ab initio understanding of unconventional high-temperature superconducting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Effects of screening and pressure ionization on the electron broadening of spectral lines in dense plasmas

Collisions between electrons and radiating atoms broaden spectral absorption and emission lines in dense plasmas. High densities also introduce screening and pressure ionization effects that distort the wave functions of both bound and free electrons. In order to study how dense plasma effects influence the electron broadening of spectral lines, this paper incorporates electron wave functions from an average-atom (AA) model to calculate the linewidth of the B III 2⁢𝑝−2⁢𝑠 transition at 𝑇 = 10 eV for mass densities ranging from 𝜌 = 10 −4 to 0.4⁢ g⁡/cc. The calculation method uses the impact approximation, allowing the linewidth to be written in terms of electron-collision cross sections and an interference term. Compared to an otherwise identical calculation that uses Coulomb free wave functions, the AA method is found to modify both the cross sections and the resulting linewidth at sufficiently high density by introducing screening and pressure-ionized bound states. Screening lowers the cross sections at low energies and near electron excitation thresholds, while pressure-ionized bound states introduce resonances into the continuum. Thus, as the density increases, the relative linewidth between the AA and Coulomb calculations follows a general decrease because of screening, with sharp increases at various intervals due to pressure ionization. Finally, the AA results are also compared with a common approach to introduce screening through the interaction potential and reduced models that use the Bethe formula for the inelastic electron-collision cross sections.

electronic excitation & ionization↗
DOE OSTI2025

Effects of equilibrium pressure on plasma response to RMPs in a spherical tokamak

This study presents a comprehensive analysis of the equilibrium pressure on the plasma response to resonant magnetic perturbations (RMPs) in the spherical tokamak (ST) MAST-U, employing both single-fluid and MHD-kinetic hybrid models (implemented via the MARS-F/K codes). As a key finding, the study identifies two different pressure-driven eigenmodes, exhibiting Sturmian property, that affect the Troyon no-wall limits for the onset of the n = 1 and n = 2 ( n is the toroidal mode number) ideal external kink instabilities as well as the corresponding plasma response to the applied RMP. With increasing equilibrium pressure, the plasma response to RMPs is significantly enhanced in the ST plasma, particularly in the high-pressure regime where kinetic effects strongly stabilize the external kink instability. The Troyon no-wall limit divides the plasma response into two regions: well below the limit, the response amplitudes and trends (versus pressure) are similar between the fluid and kinetic models; as the equilibrium pressure approaches the Troyon limit, the kinetic model predicts significant amplification of the RMP field, up to 30 times for cases considered. A relatively weak dependence of the optimal coil phasing on the equilibrium pressure is computed in this ST plasma, similar to the trend obtained for the conventional aspect ratio devices. These findings underscore the importance of incorporating kinetic effects in accurate prediction of the plasma response to RMPs in high-pressure ST tokamak plasmas and provide a theoretical basis for optimizing RMP-based control of the edge-localized modes in future ST devices.

RMP↗
DOE OSTI2026

Thermal loading effects on chalk hydromechanical behavior for nuclear waste disposal

Safe disposal of heat-generating nuclear waste depends on host rock stability under thermal, hydrological, and mechanical stresses. This study investigates the effect of thermal loading on mechanical behavior of the shallowly buried Ghareb formation chalk through triaxial and hydrostatic constant strain rate and creep tests at temperatures up to 100 ˚C and effective pressures up to 20.7 MPa. Experimental results show that thermal loading reduces the elastic moduli of chalk by 50–75%, and a transition occurs above 60 ˚C where creep rates increase rapidly. Water saturation nearly doubles the thermally induced strain compared to dry conditions and strongly decreases material rigidity. Thermal loading also leads to significant pore pressure increases under undrained conditions and leads to reductions in the apparent permeability during drained conditions. Laboratory experimental data were used to parameterize and develop a preliminary constitutive model for predicting future deformation during repository operations in the Ghareb. The strongly coupled effects – mechanical weakening, fluid pressure fluctuations, and permeability modification – demonstrate that elevated repository temperatures will have a pronounced effect on the near field Ghareb behavior during waste disposal operations. The findings indicate that the coupled interactions must be considered in predictive models and repository design to ensure long-term nuclear waste isolation and safety.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
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↗