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DOE OSTI2021

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

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Stress-induced high- T c <?em> superconductivity in solid molecular hydrogen

Solid molecular hydrogen has been predicted to be metallic and high-temperature superconducting at ultrahigh hydrostatic pressures that push current experimental limits. Meanwhile, little is known about the influence of nonhydrostatic conditions on its electronic properties at extreme pressures where anisotropic stresses are inevitably present and may also be intentionally introduced. In this report we show by first-principles calculations that solid molecular hydrogen compressed to multimegabar pressures can sustain large anisotropic compressive or shear stresses that, in turn, cause major crystal symmetry reduction and charge redistribution that accelerate bandgap closure and promote superconductivity relative to pure hydrostatic compression. Our findings highlight a hitherto largely unexplored mechanism for creating superconducting dense hydrogen, with implications for exploring similar phenomena in hydrogen-rich compounds and other molecular crystals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Switching charge states in quasi-2D molecular conductors

Abstract 2D molecular entities build next-generation electronic devices, where abundant elements of organic molecules are attractive due to the modern synthetic and stimuli control through chemical, conformational, and electronic modifications in electronics. Despite its promising potential, the insufficient control over charge states and electronic stabilities must be overcome in molecular electronic devices. Here, we show the reversible switching of modulated charge states in an exfoliatable 2D-layered molecular conductor based on bis(ethylenedithio)tetrathiafulvalene molecular dimers. The multiple stimuli application of cooling rate, current, voltage, and laser irradiation in a concurrent manner facilitates the controllable manipulation of charge crystal, glass, liquid, and metal phases. The four orders of magnitude switching of electric resistance are triggered by stimuli-responsive charge distribution among molecular dimers. The tunable charge transport in 2D molecular conductors reveals the kinetic process of charge configurations under stimuli, promising to add electric functions in molecular circuitry.

Huang, Yulong (ORCID:0000000296160134)↗

DOE OSTI2026

Mo 4 FeGa 17.25– x Ge x : Complementary Point Substitutions, Buffering Frameworks, and Merging of the 18-n and Octet Bonding Schemes

We present the discovery of Mo 4 FeGa 17.25–x Ge x (x ∼ 2.1(4), based on determination of Ge content), a complex gallide featuring a variety of point substitution phenomena. Its crystal structure is derived from the Ti 2 Ni type, in which a diamond network of face-sharing octahedra is interpenetrated by a second diamond network of vertex-sharing stella quadrangula. However, while in the ideal Ti 2 Ni type these two frameworks run uninterrupted through the crystal, Mo 4 FeGa 17.25–x Ge x shows three variations. First, the inner tetrahedron of every other stella quadrangula is replaced with a main group atom, creating tetrahedra reminiscent of the Zintl phase NaTl. Next, a selection of Ga 6 octahedra are filled with Fe atoms, in a manner analogous to the stuffed AuCu 3 -type phases. Finally, the refined crystal structure shows that in each unit cell a single Ga2 atom in the octahedral network is substituted with a dumbbell of Ga/Ge atoms. Electronic structure calculations on ordered models of Mo 4 FeGa 17.25–x Ge x reveal a narrow band near the Fermi energy, which is explained in terms of the 18-n and octet bonding schemes using reversed approximation Molecular Orbital analysis. A DFT-chemical pressure analysis connects the tetrahedron/atom and atom/dumbbell substitutions to the relief of atomic packing tensions and highlights soft atomic motions within the octahedral framework and driving forces for atom/dumbbell substitution. The combination of soft vibrational modes, disorder, and a narrow band gap could make this phase of interest for potential thermoelectric properties.

Chemical structure↗

DOE OSTI2022

Two Distinct Cu(II)-V(IV) Superexchange Interactions with Similar Bond Angles in a Triangular ?CuV2? Fragment

The strength and sign of superexchange interactions are often predicted on the basis of the bond angles between magnetic ions, but complications may arise in situations with a nontrivial arrangement of the magnetic orbitals. We report on a novel molecular tetramer compound [Cu(H2O)dmbpy]2[V2O2F8] (dmbpy = 4,4 '-dimethyl-2,2 ' bipyridyl) that is composed of triangular "CuV2" fragments and displays a spin gap behavior. By combining first-principles calculations and electronic models, we reveal that superexchange Cu-V interactions carry drastically diHerent coupling strengths along two Cu-F-V pathways with comparable bond angles in the triangular "CuV2" fragment. Counterintuitively, their strong disparity is found to originate from the restricted symmetry of the half-filled Cu dx2-y2 orbital stabilized by the crystal field, leading to one dominating antiferromagnetic Cu-V coupling in each fragment. We revisit the magnetic properties of the reported spin-gapped chain compound [enH2]Cu(H2O)2[V2O2F8] (enH2 = ethylene diammonium) containing similar triangular "CuV2" fragments, and the magnetic behavior of the molecular tetramer and the chain compounds is rationalized as that of weakly coupled spin dimers and spin trimers, respectively. This work demonstrates that fundamentally diHerent magnetic couplings can be observed between magnetic ions with similar bond angles in a single spin motif, thus providing a strategy to introduce various exchange interactions combined with low dimensionality in heterometallic Cu(II)-V(IV) compounds.

Complexes↗

DOE OSTI2021

Orientational Ordering within Semiconducting Polymer Fibrils

Abstract Due to a general paucity of suitable characterization methods, the internal orientational ordering of polymer fibrils has rarely been measured despite its importance particularly for semi‐conducting polymers. An emerging tool with sensitivity to bond orientation is polarized resonant soft X‐ray scattering (P‐RSoXS). Here, P‐RSoXS reveals the molecular arrangement within fibrils (if type I or type II fibrils), the extent of orientation in the fibril crystal, and an explicit crystal‐amorphous interphase. Neat films as well as binary blends with a fullerene derivative are characterized for three different polymers, that are prototypical materials widely used in organic electronics applications. Anisotropic P‐RSoXS patterns reveal two different fibril types. Analysis of the q ‐dependence of the anisotropy from simulated and experimental scattering patterns reveal that neat polymer fibrillar systems likely comprise more than two phases, with the third phase in addition to crystal and amorphous likely being an interphase with distinct density and orientation. Intriguingly, the fibril type correlates to the H‐ or J‐aggregation signature in ultraviolet‐visible (UV–vis) spectroscopy, revealing insight into the fibril formation. Together, the results will open the door to develop more sophisticated structure‐function relationships between chemical design, fibril type, formation pathways and kinetics, interfacial ordering, and eventually device functions.

Mukherjee, Subhrangsu↗

DOE OSTI2024

A Four‐Coordinate Pr 4+ Imidophosphorane Complex

Abstract The imidophosphorane ligand, [NP t Bu 3 ] − ( t Bu= tert ‐butyl), enables isolation of a pseudo‐tetrahedral, tetravalent praseodymium complex, [Pr 4+ (NP t Bu 3 ) 4 ] ( 1‐Pr ), which is characterized by a suite of physical characterization methods including single‐crystal X‐ray diffraction, electron paramagnetic resonance, and L 3 ‐edge X‐ray near‐edge spectroscopies. Variable‐temperature direct‐current magnetic susceptibility data, supported by multiconfigurational quantum chemical calculations, demonstrate that the electronic structure diverges from the isoelectronic Ce 3+ analogue, driven by increased crystal field. The four‐coordinate environment around Pr 4+ in 1‐Pr , which is unparalleled in reported extended solid systems, provides a unique opportunity to study the interplay between crystal field splitting and spin‐orbit coupling in a molecular tetravalent lanthanide within a pseudo‐tetrahedral coordination geometry.

Boggiano, Andrew C.↗

DOE OSTI2024

A Four‐Coordinate Pr 4+ Imidophosphorane Complex

Boggiano, Andrew C.↗

DOE OSTI2020

Electronic structure and small-hole polarons in YTiO 3

As a prototypical Mott insulator with ferromagnetic ordering, YTiO 3 (YTO) is of great interest in the study of strong electron correlation effects and orbital ordering. Here we report the first molecular beam epitaxy (MBE) growth of YTO films, combined with theoretical and experimental characterizations of the electronic structure and charge transport properties. The obstacles of YTO MBE growth are discussed and potential routes to overcome them are proposed. DC transport and Seebeck measurements on thin films and bulk single crystals identify p-type Arrhenius transport behavior with an activation energy of ~0.17 eV in thin films, consistent with the energy barrier for small hole polaron migration from hybrid density functional theory calculations. Hard x-ray photoelectron spectroscopy measurements show the lower Hubbard band at 1.1 eV below the Fermi level, whereas a Mott-Hubbard band gap of ~1.5 eV is determined from photoluminescence measurements. These findings provide critical insight into the electronic band structure of YTO and related materials.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Muonium hydride: The lowest density crystal

A muonium hydride molecule is a bound state of muonium and hydrogen atoms. It has half the mass of a parahydrogen molecule and very similar electronic properties in its ground state. The phase diagram of an assembly of such particles is investigated by first-principles quantum simulations. In the bulk limit, the low-temperature equilibrium phase is a crystal of extraordinarily low density, lower than that of any other known atomic or molecular crystal. Despite the low density and particle mass, the melting temperature is surprisingly high (close to 9 K). No (metastable) supersolid phase is observed. We investigated the physical properties of nanoscale clusters (up to 200 particles) of muonium hydride and found the superfluid response to be greatly enhanced compared to that of parahydrogen clusters. The possible experimental realization of these systems is discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

In situ ion irradiation of amorphous TiO 2 nanotubes

Understanding of structural and morphological evolution in nanomaterials is critical in tailoring their functionality for applications such as energy conversion and storage. Here, we examine irradiation effects on the morphology and structure of amorphous TiO 2 nanotubes in comparison with their crystalline counterpart, anatase TiO 2 nanotubes, using high-resolution transmission electron microscopy (TEM), in situ ion irradiation TEM, and molecular dynamics (MD) simulations. Anatase TiO 2 nanotubes exhibit morphological and structural stability under irradiation due to their high concentration of grain boundaries and surfaces as defect sinks. On the other hand, amorphous TiO 2 nanotubes undergo irradiation-induced crystallization, with some tubes remaining only partially crystallized. The partially crystalline tubes bend due to internal stresses associated with densification during crystallization as suggested by MD calculations. Furthermore, these results present a novel irradiation-based pathway for potentially tuning structure and morphology of energy storage materials.

36 MATERIALS SCIENCE↗

NASA NTRS1991

Protein crystal growth in microgravity

A series of protein-crystal growth experiments were performed on Space Shuttle flight STS-26 in September 1988 and STS-29 in March 1989. These proteins had been studied extensively in crystal-growth experiments on earth prior to the microgravity experiments. For those proteins which produced crystals of adequate size, 3D intensity data sets with electronic area detector systems were collected. Comparisons show that the microgravity-grown crystals of these proteins are larger, display more uniform morphologies, and yield diffraction data to significantly higher resolutions. Analyses of the 3D data sets indicate that the space-grown crystals are more highly ordered at the molecular level than their earth-grown counterparts.

Snyder, Robert↗

DOE OSTI2026

Experimental Quantification of Spin–Phonon Coupling in Molecular Qubits Using Inelastic Neutron Scattering

Electronic spin superposition states enable nanoscale sensing through their sensitivity to the local environment, yet their sensitivity to vibrational motion also limits their coherence times. In molecular spin systems, chemical tunability and atomicscale resolution are accompanied by a dense, thermally accessible phonon spectrum that introduces efficient spin relaxation pathways. Despite extensive theoretical work, there is little experimental consensus on which vibrational energies dominate spin relaxation or how molecular structure controls spin−phonon coupling (SPC). We present a fully experimental method to quantify SPC coefficients by combining temperature-dependent vibrational spectra from inelastic neutron scattering with spin relaxation rates measured by electron paramagnetic resonance. We apply this framework to two model S = 1/2 systems, copper(II) phthalocyanine (CuPc) and copper(II) octaethylporphyrin (CuOEP). Two distinct relaxation regimes emerge: below 40 K, weakly coupled lattice modes below 50 cm −1 dominate, whereas above 40 K, optical phonons above ∼185 cm −1 become thermally populated and drive relaxation with SPC coefficients nearly 3 orders of magnitude larger. Structural distortions in CuOEP that break planar symmetry soften the crystal lattice and enhance anharmonic scattering but also raise the energy of stretching modes at the molecular core where the spins reside. This redistributes vibrational energy toward the molecular periphery and out of plane, ultimately reducing SPC relative to CuPc and enabling room-temperature spin coherence in CuOEP. Although our method does not provide mode-specific SPC coefficients, it quantifies contributions from distinct spectral regions and establishes a broadly applicable, fully experimental link between crystal structure, lattice dynamics, and spin relaxation.

Lohaus, Stefan H. [California Institute of Technol↗

DOE OSTI2022

Ultrafast visualization of incipient plasticity in dynamically compressed matter

Plasticity is ubiquitous and plays a critical role in material deformation and damage; it inherently involves the atomistic length scale and picosecond time scale. A fundamental understanding of the elastic-plastic deformation transition, in particular, incipient plasticity, has been a grand challenge in high-pressure and high-strain-rate environments, impeded largely by experimental limitations on spatial and temporal resolution. Here, we report femtosecond MeV electron diffraction measurements visualizing the three-dimensional (3D) response of single-crystal aluminum to the ultrafast laser-induced compression. We capture lattice transitioning from a purely elastic to a plastically relaxed state within 5 ps, after reaching an elastic limit of ~25 GPa. Our results allow the direct determination of dislocation nucleation and transport that constitute the underlying defect kinetics of incipient plasticity. Large-scale molecular dynamics simulations show good agreement with the experiment and provide an atomic-level description of the dislocation-mediated plasticity.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Facile Tensile Testing Platform for In Situ Transmission Electron Microscopy of Nanomaterials

In situ tensile testing using transmission electron microscopy (TEM) is a powerful technique to probe structure-property relationships of materials at the atomic scale. In this work, a facile tensile testing platform for in situ characterization of materials inside a transmission electron microscope is demonstrated. The platform consists of: 1) a commercially available, flexible, electron-transparent substrate (e.g., TEM grid) integrated with a conventional tensile testing holder, and 2) a finite element simulation providing quantification of specimen-applied strain. The flexible substrate (carbon support film of the TEM grid) mitigates strain concentrations usually found in free-standing films and enables in situ straining experiments to be performed on materials that cannot undergo localized thinning or focused ion beam lift-out. The finite element simulation enables direct correlation of holder displacement with sample strain, providing upper and lower bounds of expected strain across the substrate. The tensile testing platform is validated for three disparate material systems: sputtered gold-palladium, few-layer transferred tungsten disulfide, and electrodeposited lithium, by measuring lattice strain from experimentally recorded electron diffraction data. The results show good agreement between experiment and simulation, providing confidence in the ability to transfer strain from holder to sample and relate TEM crystal structural observations with material mechanical properties.

2D materials↗

DOE OSTI2023

Tuning Organic Semiconductor Packing and Morphology through Non-equilibrium Solution Processing (Final Report)

Organic semiconductors (OSCs) are a promising candidate to produce low-cost, large area, and flexible electronics. There has previously been successful development of organic field effect transistors (OFETs), photovoltaics (OPV), and bioelectronics using OSCs. Solution processing of these materials allows for the fabrication of large-area devices in the kinetic crystallization regime. The charge transport capabilities have been shown to depend on the morphology and molecular packing of the OSC within thin films. Our hypothesis is that solution processing conditions may significantly impact OSC morphology and as a result the charge transport. Therefore, this work has focused on obtaining a fundamental understanding of the morphology and molecular packing of OSCs for optimal device performance. Through our work, we have gained a better understanding of how these structural conditions were influenced by the solution processing conditions. Our studies have led to a more systematic understanding of the various parameters that impact OSC morphology. Solution processing leads to non-equilibrium films, thus allowing for the formation of diverse morphologies that are inaccessible by other fabrication methods. Previously, our group has focused on tuning the morphology of small-molecular OSCs [53, 55-57]. However, little work had been devoted to polymer OSCs. There was a lack of detailed studies characterizing the solution-state of polymer OSCs in terms of their conformation, degree of entanglement, polymer aggregation, and chain relaxation dynamics. The solution state properties are also likely to be influenced by the rigidity and molecular weight of the polymer OSCs investigated. Thus, we have focused our attention on gaining a better insight of polymer OSC films and solution processing methods. Through this proposal, our approach is to investigate the correlation between solution-state properties and the morphology of the resulting polymer OSC films. We worked three specific aims: investigate the effects of 1) polymer OSC solution-state properties on final film morphology; 2) molecular additives on the solution-state and final film properties; 3) controlled pre-aggregation in the solution-state in the final film morphology. More rigid and planar polymer backbones should promote interchain charge transport and more efficient interchain hopping between polymer chains. Through tailoring the polymer backbone, polymer sidechains, and molecular weight, we expected the altered solution-state properties to affect the final film morphology. In addition, reducing the entanglements and promoting chain alignment will likely prevent charge carrier trapping through conformation disorders. We thus studied different mechanisms, such as molecular additives, to reduce entanglements in solution. Devices fabricated from these solutions were expected to have improved charge transport abilities. In addition to tailoring the solution-state characteristics of the polymer OSCs, we investigated the effect of solution processing methods on the molecular packing and morphology of polymer OSC films. Two main solution processing techniques, e.g., spin-coating and solution shearing, were employed to fabricate OFETs. Spin coating was employed to prepare OSC films, which produce isotropic films. This technique creates several parameters to tune such as spin coating speed, acceleration, and time. Additionally, our research group developed the solution shearing method, which consists of the solution initially sandwiched between two plates. By sliding the top plate, the solution front is exposed and drying begins. This technique allows for the creation of aligned large crystalline domains. Solution shearing consists of different processing parameters which can affect the final morphology, such as shearing speed, substrate temperature and temperature gradient, distance between both plates, and the tilt angle of the top plate. Due to the complexity of the polymer systems investigated, numerous techniques were employed to characterize the polymer OSC solution state and films. All the materials were characterized using the DOE supported synchrotron X-ray scattering facilities at the Stanford Synchrotron Radiation Lightsource (SSRL). Using grazing incidence X-ray scattering (GIXS) and Near Edge X-ray Absorption Fine Structure (NEXAFS) techniques, the crystalline structure and molecular orientations of the thin films were measured. Optical absorption (UV-Vis) spectroscopy was employed to determine the aggregation state in solution and films of the polymer systems. Polarized UV-Vis also allowed for the determination of the relative degree of polymer chain alignment for solution sheared films. Additionally, various other techniques were used to investigate other properties within the film, such as atomic force microscopy (AFM) and solution rheology. Finally, the device performance is quantified through the fabrication and characterization of OFETs, which will highlight the effects of morphology on charge transport.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Advances in Molecular Beam Epitaxy Growth of Ultra-Wide Bandgap Ga2O3 Based Alloys

Gallium oxide (Ga2O3) is an emerging ultra-wide bandgap semiconductor material that has attracted attention for its potential to outperform existing SiC and GaN based devices operating at high breakdown voltages and high temperature. Isovalent alloying of In and Al in Ga2O3 provides the ability to engineer bandgap energy and strain of the material. Alloying with Al increases the bandgap energy and the theoretically achievable Baliga's figure of merit, a key measure of a material's ultimate performance limits for high power switching devices. Alloying with In introduces compressive strain and can be used to counteract the tensile strain of Al incorporation. The resulting (AlxGa1-x-yIny)2O3 alloy can be lattice-matched to commercially available Ga2O3 wafers and has a tunable bandgap energy greater than that of Ga2O3, 4.76 eV. Such lattice-matched material can be grown arbitrarily thick without the detrimental effects of elastic strain and relaxation, making it suitable for high voltage diodes and transistors. However, efforts to synthesize isovalent alloys are complicated by their tendency to phase separate into corundum Al2O3 or bixbyite In2O3. Literature reports of the quaternary (AlxGa1-x-yIny)2O3 are limited to <1% unintentional indium incorporation in In-catalyzed (AlxGa1-x)2O3. The primary limitation to quaternary growth is the limited incorporation of indium at elevated growth temperatures. This limited incorporation is due to both the volatility of indium oxide and Al and Ga cation exchange reactions which replace indium in In2O3. We report on the development of a novel high-throughput molecular beam epitaxy (MBE) technique to screen the growth conditions for the ternary alloy (InyGa1-y)2O3, and the application of these findings to the first successful synthesis of phase pure monoclinic (AlxGa1-x-yIny)2O3 by MBE. By leveraging the unique sub-oxide chemistry of Ga2O3 and in-situ monitoring of crystal properties by reflection high-energy electron diffraction (RHEED), a cyclical growth and etch-back method is developed and applied to rapidly characterize the (InyGa1-y)2O3 growth space. This cyclical method provides approximately 10x increase in experimental throughput and up to 46x improvement in Ga2O3 substrate utilization. Appropriate growth conditions for monoclinic (InyGa1- y)2O3 are identified by machine learning analysis of RHEED patterns and targeted growths are characterized ex-situ to confirm improved In incorporation. These growth conditions are then combined with established (AlxGa1-x)2O3 growth conditions to grow quaternary (AlxGa1-x-yIny)2O3 with Al mole fractions ranging from 1.4% - 24.4% and In mole fractions ranging from 3.1% to 15.5%. The chemical and optical properties of the alloys are investigated by XRD, XPS, and spectroscopic ellipsometry. A lattice-matched (AlxGa1-x-yIny)2O3 alloy is examined by 4D-STEM and the chemical and physical uniformity of Al and In incorporation are discussed.

alloy↗

DOE OSTI2020

Magnetic, thermal, and electronic-transport properties of EuMg 2 Bi 2 single crystals

The trigonal compound EuMg 2 Bi 2 has recently been discussed in terms of its topological band properties. These are intertwined with its magnetic properties. In this paper detailed studies of the magnetic, thermal, and electronic-transport properties of EuMg 2 Bi 2 single crystals are presented. The Eu + 2 spins 7/2 in EuMg 2 Bi 2 exhibit an antiferromagnetic (AFM) transition at a temperature T N = 6.7 K, as previously reported. By analyzing the anisotropic magnetic susceptibility χ data below T N in terms of molecular-field theory (MFT), the AFM structure is inferred to be a c -axis helix, where the ordered moments in the hexagonal a b -plane layers are aligned ferromagnetically in the a b plane with a turn angle between the moments in adjacent moment planes along the c axis of ≈ 120 ° . An alternate but less likely magnetic structure is a planar structure with nearest-neighbor Eu spins aligned at ≈ 120 ° with respect to each other, where these ordered-moment layers are stacked along the c axis. The magnetic heat capacity exhibits a λ anomaly at T N with evidence of dynamic short-range magnetic fluctuations both above and below T N . The high- T limit of the magnetic entropy is close to the theoretical value for spins 7/2. The in-plane electrical resistivity ρ ( T ) data indicate metallic character with a mild and disorder-sensitive upturn below T min = 23 K. An anomalous rapid drop in ρ ( T ) on cooling below T N as found in zero field is replaced by a two-step decrease in magnetic fields. The ρ ( T ) measurements also reveal an additional transition below T N in applied fields of unknown origin that is not observed in the other measurements and may be associated with an incommensurate to commensurate AFM transition. The dependence of T N on the c -axis magnetic field H ⊥ was derived from the field-dependent χ ( T ) , C p ( T ) , and ρ ( T ) measurements. This T N ( H ⊥ ) was found to be consistent with the prediction of MFT for a c -axis helix with S = 7 / 2 and was used to generate a phase diagram in the H ⊥ – T plane.

36 MATERIALS SCIENCE↗