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Surface vs Homogeneous Organo-Hafnium Catalyst Ion-Pairing and Ligand Effects on Ethylene Homo- and Copolymerizations

Heterogeneous catalysts have long dominated polyethylene and polypropylene production, but understanding their catalysis is challenged by uncertainties in active site structures and percentages. Surface-bound organometallic catalysts are an emerging strategy to combine successful homogeneous catalysts having well-understood structures, relatively high percentages of active sites, and exceptional control of selectivity, with the attractions of surface catalysts, to transition promising homogeneous systems to large-scale heterogeneous ones. Nevertheless, surface-bound olefin polymerization catalysts typically produce ultrahigh M w ’s but with low activity and comonomer selectivity. Here, we report the systematic synthesis and characterization of a series of pyridylamido–Hf complexes and their corresponding surface catalysts chemisorbed on sulfated alumina (AlS) and zirconia (ZrS). Comparative ethylene homo- and 1-octene copolymerizations reveal similar activity and 1-octene selectivity trends in the homogeneous and heterogeneous systems. For the surface pyridylamido–Hf catalyst series, large variations in activity (up to 10×) and 1-octene incorporation (up to 28×) are achieved by ligand and support manipulation. Interestingly, while the homogeneous catalysts exhibit positive comonomer effects in ethylene/1-octene copolymerization, the surface catalysts behave oppositely. Extended X-ray absorption fine structure (EXAFS) reveals significantly elongated Hf···O bond distances vs typical Hf–O covalent bonds (2.06 vs 1.97 Å). Furthermore, density functional theory (DFT) analysis of the heterolytic ion pair separation enthalpies, olefin insertion energetics, and NBO/Bader charges also suggest electrostatic Hf cation–anionic support binding and catalytic patterns, which are modulated by the ion-pairing energetics and ligand architecture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluating Use of Boron- and Hafnium-Modified Polysilazanes for Ceramic Matrix Minicomposites

In this study, the potential of polymer-derived Ceramic Matrix Composites (CMCs) is demonstrated by addition of thin ceramic coatings on Carbon Fiber (CF) bundles. Boron- and hafnium- modified polysilazane liquid precursors were synthesized and used to infiltrate the fiber bundles of CF to fabricate lab-scale Si(B)CN/CF and Si(Hf)CN/CF CMC mini-composites, respectively. The precursor-to-ceramic conversion process was achieved at 800°C with crosslinked precursor to ceramic yield of approx. 90% in Ar environment. The Si(B)CN/CF contained Si-N and B-N bonds, while Si-N and Hf-O-Si bonds were observed for Si(Hf)CN/CF sample with uniform and dense surfaces. Room-temperature tensile tests showed that the Si(Hf)CN/CF sample could reach a tensile strength of ~790 MPa and elastic modulus of 66.88 GPa among the composites. Oxidation study of the Si(Hf)CN/CF mini-composites showed higher stability compared to SiCN/CF and Si(B)CN/CF mini-composites up to 1500°C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparing correlation components and approximations in Hartree–Fock and Kohn–Sham theories via an analytical test case study

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the “traditional” correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Further, our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Accurate Hellmann–Feynman forces from density functional calculations with augmented Gaussian basis sets

The Hellmann–Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upward of 10 eV/Å in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed, and HF forces can be computed as accurately as analytical forces with state-of-the-art basis sets, allowing geometry optimization and molecular dynamics to be reliably performed with HF forces. Our results pave a clear path forward for the accurate and efficient simulation of large systems using ML densities and the HF theorem.

Pathak, Shivesh (ORCID:0000000172798195)↗

Completion of lunar magma ocean solidification at 4.43 Ga

Crystallization of the lunar magma ocean yielded a chemically unique liquid residuum named KREEP. This component is expressed as a large patch on the near side of the Moon and a possible smaller patch in the northwest portion of the Moon’s South Pole-Aitken basin on the far side. Thermal models estimate that the crystallization of the lunar magma ocean (LMO) could have spanned from 10 and 200 My, while studies of radioactive decay systems have yielded inconsistent ages for the completion of LMO crystallization covering over 160 My. Here, we show that the Moon achieved >99% crystallization at 4,429 ± 76 Ma, indicating a lunar formation age of ~4,450 Ma or possibly older. Using the 176 Lu– 176 Hf decay system (t 1/2 = 37 Gy), we found that the initial 176 Hf/ 177 Hf ratios of lunar zircons with varied U–Pb ages are consistent with their crystallization from a KREEP-rich reservoir with a consistently low 176 Lu/ 177 Hf ratio of 0.0167 that emerged ~140 My after solar system formation. The previously proposed younger model age of ~4.33 Ga for the source of mare basalts (240 My after solar system formation) might reflect the timing of a large impact. Our results demonstrate that lunar magma ocean crystallization took place while the Moon was still battered by planetary embryos and planetesimals leftover from the main stage of planetary accretion. The study of Lu–Hf model ages for samples brought back from the South Pole-Aitken basin will help to assess the lateral continuity of KREEP and further understand its significance in the early history of the Moon.

Science & Technology - Other Topics↗

Thermo-Mechanical Distortion of Tungsten-Coated Steel During High Heat Flux Testing Using Plasma Arc Lamps

An experimental setup and a test section were designed and fabricated for high heat flux testing (HHFT) of neutron-irradiated specimens using water-wall plasma arc lamps. Because of the radiological considerations and limitations of reactor irradiation, the size of the test articles was limited to disks less than 10 mm in diameter. The specimen was clamped onto an actively cooled block, and clamping allowed the insertion of several thermocouples on the back surface of the specimen through a copper (Cu) block. Five vacuum plasma sprayed tungsten (W)–coated F82H steel specimens were subjected to HHFT. Surface profilometry measurements, which were conducted after HHFT, revealed central bowing of the top W surface. This type of residual distortion occurred for all of the specimens, and the larger the specimens were, the larger was the distortion.In an attempt to understand specimen distortion and address the science questions related to the testing of subsize specimens during HHFT, a simplified thermo-mechanical model was developed. By using a measured temperature in the Cu as an isothermal boundary condition, the model eliminated the need for coupling cooling fluid flow models with stress models, greatly simplifying the analysis. The main variable in the proposed model is hC, i.e., the thermal contact conductance between the F82H and the Cu washer. Inelastic properties, including hardening properties, were considered for F82H steel and Cu. Numerical simulation results demonstrated a buildup of residual deformation during HHFT and a very complex state of stress and deformation during typical heat flux (HF) cycling. Additionally, hoop stress evolution during a high heat flux cycle reveals that F82H at an interface with W would be mainly in compression during HF application and experienced a transition to a tension state during cooldown. Also, specimen distortion evolves during each HF cycle, as the specimen bows downward during HF application and upward during the cooldown period between HF cycles. The final specimen distortion, i.e., upward bowing of the specimen center, was qualitatively predicted for hC values of 4000 to 5000 W/(m 2 ·K). This hC range of values, for which bulging is obtained, is at the lower spectrum of the range of values for hC, consistent with the low thermal contact conductance expected from the unpolished F82H surface.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Turbulence link to L-mode, I-mode, and H-mode confinement in the DIII-D tokamak

Understanding the physics of low-confinement (L-), improved-confinement (I-), and high-confinement (H-) modes is critical for fusion reactors. The finding herein reports observations of two types of turbulence coexisting near the L-mode edge, one magnetohydrodynamic (MHD)-like and another micro-tearing mode (MTM)-like, linked to the H-mode and I-mode confinement in the DIII-D tokamak. Ion-scale magnetic and density turbulence is measured using a Faraday-effect radial-interferometer-polarimeter and beam-emission-spectroscopy (BES). Broadband turbulence spectra of up to ~600 kHz are observed in two discharges where transitions between L-mode, I-mode, and H-mode occurs. Turbulence is found to be inversely correlated with confinement, meaning lower turbulence power at higher confinement. Distinctively, the high-frequency (HF, >~100 kHz) magnetic turbulence power changes by the most (55%) during transitions primarily involving energy confinement change, whereas the low-frequency (LF, <~100 kHz) magnetic and density turbulence power changes by the most (80%) during transitions primarily involving particle confinement change. The LF turbulence amplitude oscillates with and leads to deuterium-alpha emission oscillations before an H-mode. These results imply that HF turbulence mainly affects energy confinement whereas LF turbulence can affect particle confinement. The magnetic and density turbulence exhibits coherence up to 0.6 and cross-phase magnitude close to π/2 in most cases, suggesting they have a common origin in both the LF and HF ranges. BES suggests that LF turbulence resides at the edge (ρ = 0.95) and HF turbulence can be at the outer core (ρ = 0.8) or edge (ρ = 0.95). Comparisons of measurements, theory, and gyrokinetic simulations suggest that HF turbulence is MTM-like in all cases, whereas LF turbulence is more consistent with MHD-like modes and the exact instability might change during transitions—except that a drift-wave origin is possible in a low collisionality H-mode. These results suggest that the H-mode involves suppressed MHD-like turbulence, whereas the I-mode mitigates MTM-like turbulence along with largely unchanged MHD-like turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics

The Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA) offers an approximate numerical procedure for propagating the two-time nonequilibrium Green's function (NEGF). Here, using the GW self-energy, we compare the HF-GKBA to exact results for a variety of systems with long- and short-range interactions, different two-body interaction strengths, and various nonequilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. Furthermore, this agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, we look at the use of dynamical mode decomposition (DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16% of the total time evolution, we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long-time trajectories in large-scale systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Growth of High-Performance 4-5μm Thick Film REBCO Tapes Doped With Hafnium Using Advanced MOCVD

Advanced metal organic chemical vapor deposition technique (A-MOCVD) was used to grow 4-5 µm thick REBa 2 Cu 3 O 7–δ (REBCO, RE = rare earth) films, doped with 5% and 15% Hf. Thick REBCO films doped with 5% Hf exhibit self-field critical current density (J c ) over 1.8 MA/cm 2 at 77 K and 3 MA/cm 2 at 65 K, 1.5 T. Increasing the Hf content to 15% resulted in J c above 9 MA/cm 2 at 20 K, 9 T. The effect of (Ba+Hf)/Cu content in Hf-added (5 and 15 mol.%) REBCO films on the critical current density at 77 K, 0 T, c-axis lattice parameter and out-of- plane texture has been studied. In addition to growth of thick film REBCO tapes with superior performance, the A-MOCVD reactor has been used to quadruple the precursor-to-film conversion efficiency above 45%. Furthermore, this achievement has a first order impact in lowering the cost of REBCO tapes made by A-MOCVD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Organic carbon enables the biotic engineering of beneficial soil structure in Profundihumic and Haplic Ferralsols

We investigated how organic matter may, directly and indirectly, modify the porosity of Ferralsols, that is, deeply weathered soils of the tropics and subtropics. Although empirical and anecdotal evidence suggests that organic matter accumulation may increase porosity, a mechanistic understanding of the processes underlying this beneficial effect is lacking, especially so for Ferralsols. To achieve our end, we leveraged the fact that the Profundihumic qualifier of Ferralsols (PF) is distinguished from Haplic Ferralsols (HF) by both a much larger average carbon content in the first 1 m of soil depth (19 kg C m -3 in PF vs. 10 kg C m -3 in HF) and a significantly lower bulk density (1.05 ± 0.08 kg L -1 in PF vs. 1.21 ± 0.05 kg L -1 in HF). Through exhaustive modelling of carbon – bulk density relationships, we demonstrate that the lower bulk density of PF cannot be satisfactorily explained by a simple dilution effect. Rather, we found that bulk density correlated with carbon content when combined with carbon: nitrogen ratio (r 2 = 0.51), black carbon content (r 2 = 0.75), and Δ 14 C (r 2 =0.81). Total pore space was greater in PF (61± 3%) than in HF (55 ± 2%), but x-ray computed tomography revealed that pore space inside soil aggregates of 4–5 mm diameter does not vary between the studied Ferralsols. We further observed nearly twice as many roots and burrows in PF compared with HF. We thus infer that the mechanism responsible for the increase in porosity is most likely an enhancement of resource availability (e.g., energy, carbon, and nutrients) for the organisms (earthworms, ants, termites, etc.) that physically displace soil particles and promote soil aggregation. As a result of increased resource availability, soil organisms can create especially the mesoscale structural soil features necessary for unrestricted water flow and rapid gas exchange. In conclusion, this insight paves the way for the development of land management technologies to optimize the physical shape and capacity of the soil bioreactor.

54 ENVIRONMENTAL SCIENCES↗

Plasma proteomic biomarkers of physical frailty in heart failure: a propensity score matched discovery-based pilot study

Background: Physical frailty is highly prevalent in heart failure (HF), but we lack an understanding of the underlying pathophysiology. Proteomics evaluation of plasma samples may elucidate potential mechanisms and biomarkers of physical frailty in HF. We aimed to identify plasma proteomic biomarkers that are differentially expressed between physically frail and non physically frail adults with HF. Methods: This was a secondary analysis of a subset of data and plasma samples from a study of frailty among patients with New York Heart Association (NYHA) Functional Classification I-IV HF. Physical frailty was measured using the Frailty Phenotype Criteria. Propensity score matching was used to match pairs of physically frail (n = 20) vs. non-physically frail (n = 20) patients on clinical characteristics. Plasma samples were processed using a sensitive liquid chromatography mass spectrometry platform, utilizing a multiplexed tandem mass tag-labeled quantitative proteomics approach. Differentially expressed proteins were quantified individually using paired t tests with associated log fold change of 0.3 and Fisher’s combined p values. Results: The sample (n = 40) was 62.8±16.9 years old, 58% female, and 55% NYHA Class III/IV. Proteomics analysis revealed 7 proteins differentially expressed using full differential criteria: matrix metalloproteinase-14 was downregulated in frailty, and copine-1, low affinity immunoglobulin gamma Fc region receptor III-A and III-B, probable non-functional immunoglobulin kappa variable 2D-24, glutathione S-transferase Mu 1, and argininosuccinate lyase were upregulated in frailty. Conclusions: Proteomic biomarkers related to the immune system, stress response, and detoxification were differentially expressed between physically frail and non-physically frail adults with HF.

Biomarkers↗

Geophysical Signatures of Crack Network Coalescence in Rocks at Multiple Length Scales

The main goal of the research project was to identify the geophysical signatures of fracture growth in natural rocks by utilizing novel geophysical techniques. The research objectives were to (a) investigate the potential for geophysical methods to determine when cracks initiate, the types and locations of propagated cracks, and the coalescence of networks of cracks in natural rocks at multiple scales, (b) determine how damage at the microscale evolved into damage at the macroscale and then link the microscopic and macroscopic observations, (c) quantify crack coalescence in rocks under realistic stress conditions using coupled mechanical-geophysical-optical visualization, and (d) identify the precursors in geophysical signals to crack coalescence. The following research thrusts were explored to achieve the research objectives: (1) uniaxial compression testing of rock specimens with and without a set of pre‐existing flaws and (2) triaxial compression testing of natural rock specimens. These thrusts allowed for exploring fracturing in rocks under realistic in situ environments and at multiple scales. This project provided educational opportunities for nine graduate and undergraduate students and resulted in 27 peer-reviewed publications. This first research thrust focused on investigating the micromechanics of fractures in rocks through uniaxial compression testing combined with advanced geophysical and imaging techniques, specifically acoustic emission (AE) monitoring, ultrasonic imaging, and 2-dimensional Digital Image Correlation (2D-DIC). By examining damage processes under time-independent and time-dependent loading conditions, insights into damage localization, crack initiation, and fracturing mechanisms were gained. It was observed that the AE signals and the strain-based measurements directly reflect the state of damage in the rock specimen and could be used to identify the cracking levels, such as the crack initiation (CI) and crack damage (CD), and the mode of deformation. A novel calibration apparatus was developed to enhance the accuracy of AE sensors, allowing for the estimation of key parameters such as magnitude, source dimension, stress drop, and radiated seismic energy associated with the fractures. The findings highlighted significant variations in the temporal evolution of AE source parameters during the primary, secondary, and tertiary stages of creep, identifying tensile cracking as the primary deformation mode. The second research thrust focused on enhancing the understanding of fracturing processes in natural rocks through triaxial compression testing, real-time AE monitoring, and ultrasonic monitoring. We investigated the impact of various factors such as fracture propagation regimes, injection parameters, rock types, and pre-existing conditions on the hydraulic fracture (HF) behavior using scaled true-triaxially loaded specimens of Barre granite and Lyons sandstone. Custom sensor housing facilitated concurrent active and passive monitoring to analyze hydro-mechanical responses and microseismicity associated with different HF scenarios. A coupled investigation of passive microseismicity and active signal attributes permitted a detailed comprehension of the various HF processes (aseismic deformation, fracture initiation and propagation, fluid permeation, and leak-off) and their dependence on the specific rock type. The findings of this research demonstrated the effectiveness of AE monitoring techniques in providing valuable insights into the impact of various factors on the behavior and dynamics of HF processes. The advancements in monitoring techniques, offering a more thorough and precise approach, represent a significant step towards optimizing HF practices and ensuring sustainable resource extraction.

58 GEOSCIENCES↗

Materials Data on HfSi2 by Materials Project

HfSi2 is Zirconium Disilicide structured and crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Hf is bonded in a 10-coordinate geometry to ten Si atoms. There are a spread of Hf–Si bond distances ranging from 2.70–2.96 Å. There are two inequivalent Si sites. In the first Si site, Si is bonded in a 8-coordinate geometry to six equivalent Hf and two equivalent Si atoms. Both Si–Si bond lengths are 2.42 Å. In the second Si site, Si is bonded in a 8-coordinate geometry to four equivalent Hf and four equivalent Si atoms. All Si–Si bond lengths are 2.60 Å.

36 MATERIALS SCIENCE↗

Materials Data on HfGa3 by Materials Project

HfGa3 is Uranium Silicide-like structured and crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Hf is bonded to twelve Ga atoms to form HfGa12 cuboctahedra that share corners with four equivalent HfGa12 cuboctahedra, edges with eight equivalent HfGa12 cuboctahedra, edges with sixteen equivalent GaHf4Ga8 cuboctahedra, faces with four equivalent HfGa12 cuboctahedra, and faces with eight equivalent GaHf4Ga8 cuboctahedra. There are four shorter (2.76 Å) and eight longer (3.00 Å) Hf–Ga bond lengths. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a square co-planar geometry to four equivalent Hf and eight equivalent Ga atoms. All Ga–Ga bond lengths are 3.00 Å. In the second Ga site, Ga is bonded to four equivalent Hf and eight Ga atoms to form distorted GaHf4Ga8 cuboctahedra that share corners with twelve equivalent GaHf4Ga8 cuboctahedra, edges with eight equivalent HfGa12 cuboctahedra, edges with eight equivalent GaHf4Ga8 cuboctahedra, faces with four equivalent HfGa12 cuboctahedra, and faces with ten equivalent GaHf4Ga8 cuboctahedra. All Ga–Ga bond lengths are 2.76 Å.

36 MATERIALS SCIENCE↗

Materials Data on HfGa2 by Materials Project

HfGa2 crystallizes in the tetragonal I4_1/amd space group. The structure is three-dimensional. Hf is bonded in a 10-coordinate geometry to ten Ga atoms. There are a spread of Hf–Ga bond distances ranging from 2.80–3.00 Å. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a distorted square co-planar geometry to four equivalent Hf and four equivalent Ga atoms. There are two shorter (3.03 Å) and two longer (3.06 Å) Ga–Ga bond lengths. In the second Ga site, Ga is bonded in a 12-coordinate geometry to six equivalent Hf and six Ga atoms. Both Ga–Ga bond lengths are 2.77 Å.

36 MATERIALS SCIENCE↗

Materials Data on Hf2Ga3 by Materials Project

Hf2Ga3 crystallizes in the orthorhombic Fdd2 space group. The structure is three-dimensional. Hf is bonded in a 7-coordinate geometry to nine Ga atoms. There are a spread of Hf–Ga bond distances ranging from 2.79–3.16 Å. There are two inequivalent Ga sites. In the first Ga site, Ga is bonded in a 10-coordinate geometry to six equivalent Hf and four equivalent Ga atoms. There are two shorter (2.62 Å) and two longer (2.72 Å) Ga–Ga bond lengths. In the second Ga site, Ga is bonded in a 10-coordinate geometry to six equivalent Hf and four Ga atoms. Both Ga–Ga bond lengths are 2.75 Å.

36 MATERIALS SCIENCE↗

Materials Data on HfGe2 by Materials Project

HfGe2 is Zirconium Disilicide structured and crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Hf is bonded in a 10-coordinate geometry to ten Ge atoms. There are a spread of Hf–Ge bond distances ranging from 2.78–3.13 Å. There are two inequivalent Ge sites. In the first Ge site, Ge is bonded in a 4-coordinate geometry to six equivalent Hf and two equivalent Ge atoms. Both Ge–Ge bond lengths are 2.63 Å. In the second Ge site, Ge is bonded in a 8-coordinate geometry to four equivalent Hf and four equivalent Ge atoms. All Ge–Ge bond lengths are 2.70 Å.

36 MATERIALS SCIENCE↗

Materials Data on HfRe2 by Materials Project

HfRe2 is Hexagonal Laves structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Hf is bonded in a 12-coordinate geometry to twelve Re atoms. There are three shorter (3.08 Å) and nine longer (3.10 Å) Hf–Re bond lengths. There are two inequivalent Re sites. In the first Re site, Re is bonded to six equivalent Hf and six equivalent Re atoms to form a mixture of face, edge, and corner-sharing ReHf6Re6 cuboctahedra. All Re–Re bond lengths are 2.67 Å. In the second Re site, Re is bonded to six equivalent Hf and six Re atoms to form a mixture of face, edge, and corner-sharing ReHf6Re6 cuboctahedra. There are two shorter (2.56 Å) and two longer (2.72 Å) Re–Re bond lengths.

36 MATERIALS SCIENCE↗