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At least 343 records · Page 19

Active Learning Framework

Machine learning (ML) of interatomic potentials show great promise to accelerate scientific simulation, e.g., by emulating expensive computations at a high accuracy but much reduced computational cost. Training datasets are calculated from computationally expensive ab initio quantum mechanics methods, density functional theory (DFT). Trained on this data, an ML model can be very successful in predicting energy and forces for new atomic configurations. A critical factor is the quality and diversity of the training dataset. Thus, a highly automated approach to dataset construction based on active learning framework is designed suitable for material physics. The active learning scheme begins with fully randomized atomic configurations. Then, many Molecular Dynamics (MD) trajectories are simulated using current ML potentials, where each MD trajectory is initialized to a random disordered configuration. The temperature is varied in order to diversify the sampled configuration during these simulations. The variance of predictions for eight neural networks within an ensemble is analyzed to determine whether the model is operating as expected. This helps in determining whether collecting more data would be helpful to the model by checking the ensemble variance is greater than the threshold. In this case, the MD trajectory is terminated and the final atomic configuration is placed on a queue (SQL database) for DFT calculations and added to training dataset. Periodically, ML model is retrained to the updated training model. This Active Learning loop is iterated until the cost of MD simulations becomes prohibitively expensive. The MD simulations will hopefully be sufficiently robust to support nucleation after many active learning iterations. In this sense, active learning scheme must automatically discover the important low energy and nonequilibrium physics.

Nebgen, Benjamin↗

Ab initio studies of the impact of the Debye-Waller factor on the structural and dynamical properties of amorphous semiconductors: The case of a-Si

This paper presents a first-principles study of the Debye-Waller factor and the Debye temperature for amorphous silicon (a-Si) from lattice-dynamical calculations and direct molecular-dynamics simulations using density-functional theory (DFT). The effects of temperature and structural disorder on the intensity of the diffraction maxima and the vibrational mean-square displacement (MSD) of Si atoms are studied in the harmonic approximation, with particular emphasis on the bond-length disorder, the presence of coordination defects, and microvoids in a-Si networks. It has been observed that the MSDs associated with tetrahedrally-bonded Si atoms are considerably lower than their dangling-bond counterparts – originating from isolated and vacancy-induced clustered defects – and those on the surface of microvoids, leading to an asymmetric non-gaussian tail in the distribution of atomic displacements. An examination of the effect of anharmonicity on the MSD at high temperatures using direct ab initio molecular-dynamics simulations (without the harmonic approximation) suggests that the vibrational motion in a-Si is practically unaffected by anharmonic effects at temperatures below 400 K, as far as the present DFT calculations are concerned. The Debye temperature of a-Si is found to be in the range of 488–541 K from specific-heat and MSD calculations using first-principles lattice-dynamical calculations in the harmonic approximation, which matches closely with the experimental value of 487–528 K obtained from specific-heat measurements of a-Si at low temperatures.

36 MATERIALS SCIENCE↗

The u 3 si 2 -H system

U 3 Si 2 is of interest to the nuclear industry as a candidate fuel material due to its high uranium density and high thermal conductivity. However, it has been observed to react with hydrogen, resulting in material decrepitation. As a result, it is important to understand the thermodynamics of the U 3 Si 2 -H system. In this study, the thermodynamics of the hydrogen absorption reaction of USi were determined experimentally using Sievert’s gas absorption and related to crystallographic evolution with hydrogen content using X-ray diffraction. Experimentally-determined thermodynamic parameters were compared with results from density functional theory modeling. Results from this study were also compared with those determined in previous work. Sievert’s gas absorption results were used to develop the pressure-composition-temperature (PCT) curves of the U 3 Si 2 -H system. It was found that the hydride phase exhibited a maximum stoichiometry between U 3 Si 2 H 1.8 and U 3 Si 2 H 2 . The two-phase region for hydride formation from U 3 Si 2 exhibited a miscibility gap with a critical temperature between 623 and 673 K, as calculated from the PCT curves. Analysis of the PCT curves also showed that both the enthalpy and entropy of the hydrogen absorption reaction increased with hydrogen content but were lower than the values for uranium trihydride formation from uranium metal. The enthalpy of reaction for hydrogen absorption was calculated to range between -86.9 and -94.8 kJ mol -1 , while the entropy of reaction was calculated to range between 101.9 and 138.8 J mol -1 K -1 . Furthermore, DFT modeling of the thermoydnamic stability of the USi hydride phases yielded a decomposition temperature of U 3 Si 2 H 2 of approximately 600 K, which was consistent with the experimental results. Similarly, the DFT-calculated enthalpy and entropy of reaction to form USiH were determined to be -106.5kJ mol and 121.8J mol -1 K -1 , respectively, which were both in close agreement with the experimentally-determined values.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Phonon spectrum in the spin-Peierls phase of CuGeO 3

CuGeO 3 has long been studied as a prototypical example of the spin-Peierls transition in a 𝑆 = 1/2 Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.

density functional theory↗

Exploring Spin‐Orbit Effects in a [Cu 6 Tl] + Nanocluster Featuring an Uncommon Tl−H Interaction

Reaction of [CuH(PPh 3 )] 6 with 1 equiv. of Tl(OTf) results in formation of [Cu 6 TlH 6 (PPh 3 ) 6 ][OTf] ([1]OTf]), which can be isolated in good yields. Variable-temperature 1 H NMR spectroscopy, in combination with density functional theory (DFT) calculations, confirms the presence of a rare Tl−H orbital interaction. According to DFT, the 1 H chemical shift of the Tl-adjacent hydride ligands of [1] + includes 7.7 ppm of deshielding due to spin-orbit effects from the heavy Tl atom. In conclusion, this study provides valuable new insights into a rare class of metal hydrides, given that [1][OTf] is only the third isolable species reported to contain a Tl−H interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient computational search for lanthanide-binding additive dopants for advanced U-Zr based fuels

A rational design strategy combining theory and experiment is highly desirable for the development of U-Zr based fuels that are resistant to lanthanide-induced fuel-cladding chemical interaction (FCCI). Here, we performed rapid computational screening of FCCI-mitigating (via strong lanthanide-binding) elements across the periodic table by utilizing three simple criteria and density functional theory (DFT) calculated total energies of relevant elements and compounds retrieved from high-throughput DFT databases. In addition to successfully identifying previously demonstrated additives, our search leads to the discovery of Bi as a highly effective element among all 68 elements screened, and its effectiveness was experimentally confirmed in this study.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Does Chirality Influence the Stability of Amino Acid –Cu Complexes in the Salt-Induced Peptide Formation Reaction? Insights from Density Functional Theory Calculations

The polymerization of amino acids into peptides and ultimately proteins is critical to evolution of life. Ribosomally-synthesized proteins are homochiral, composed entirely of L-amino acids. Abiotic syntheses of amino acids, however, produce racemic mixtures(equal amounts of L and D enantiomers), meaning that the pool of monomers available for abiotic protein synthesis would be racemic or nearly so. There are no prebiotically plausible mechanisms known to yield homochiral peptides from racemic pools of amino acids. While some mechanisms capable of producing or amplifying enantiomeric excesses have been observed, these excesses are small or not applicable to all biologically relevant amino acids. As a result, a prebiotically-feasible mechanism to create enantiopure pools of amino acids has not been identified. However, it is not clear that these enantio-enriched or enantiopure pools are necessary to produce homochiral peptides. Steric and electronic effects, or a combination of both, may influence how different enantiomers interact with each other, potentially leading to homochiral peptides from racemic mixtures. Here, we use density functional theory (DFT) calculations to assess the stability of homochiral and heterochiral reactive complexes produced during polymerization via the salt-induced peptide formation (SIPF) reaction. Experimental studies of the SIPF reaction have shown that it enables the formation of peptides under diverse environmental conditions, making it a plausible pathway to peptide formation on early Earth. In the SIPF reaction, NaCl acts as a condensation reagent while a divalent metal cation, primarily Cu2+, facilitates polymerization by complexing and activating amino acids forming a monochlorocuprate complex. To assess if hetero-or homochiral monochlorocuprate complexes were energetically favored, we compared the stability of LL, DD, and LD enantiomers of Cu2+–(alanine)2and Cu2+–(valine) 2 complexes. Gaussian 09 density DFT energy-minimization calculations were made for each Cu –amino acid complex in the cis and trans configuration. Models were energy minimized using the BH and HLYP/6-31++G(d,p) level of theory and free energies were compared to determine the most stable configuration.

A C Fox↗

Bonding and reactivity of isostructural uranyl and neptunyl peroxide phases

Understanding the reactivity of actinide peroxides is critical for predicting the behavior of spent nuclear fuel in radiolytic environments. Herein, we report the synthesis and characterization of a lithium neptunyl(VI) hydroxo peroxo compound (LiNp), which is isostructural to the uranyl analogue (LiU). Single-crystal X-ray diffraction reveals that LiNp contains both [NpO 2 (O 2 ) 3 ] 4- and [NpO 2 (OH) 4 ] 2- units stabilized by Li + and hydrogen bonding and Raman spectroscopy shows systematic redshifts in neptunyl vibrational modes relative to uranyl. DFT calculations highlight the importance of secondary coordination in reproducing vibrational and structural features, but challenges remain with correctly modeling strong sigma donors. Solid-state EPR spectroscopy and DFT confirm superoxide stabilization within LiU and calculations suggest favorability of the analogous radical species in LiNp. Solution state EPR spectroscopy with the radical spin trap 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide (BMPO) reveal evidence of superoxide in the LiU and LiNp phases and suggests stabilization of superoxide within actinyl triperoxide complexes, forming [AnO 2 (O 2 ) 2 (O) 2 • ] 3- .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High-Energy Hybridized States Enable Long-Lived Hot Electrons in Cobaloxime-Silicon Nanocrystal System

Strong electronic coupling is achieved between the molecular catalyst cobaloxime ([Co]) and silicon nanocrystals (Si NCs) bridged by an ethylenepyridine group derived from vinylpyridine (vpy) covalently bound to the Si NC surface (Si-vpy-[Co]). The ethylenepyridine tether in Si-vpy-[Co] is key to dramatic changes to the system’s physical properties which are not observed in the corresponding formylpyridine (fpy) system (Si-fpy-[Co]) consistent with strong electronic coupling previously observed only in dark electrochemical systems. UV−vis absorption spectroscopy reveals new [Co]-centered electronic states in Si-vpy-[Co], and transient absorption spectroscopy finds a strong absorption feature appearing within 250 fs and persisting for at least 5 ns. Astoundingly, spectroelectrochemical measurements reveal that this absorption feature is consistent with both the singly reduced [Co] − and doubly reduced [Co] 2− complexes, leading to the conclusion that these long-lived charges are derived from high-energy “hot” electrons residing in [Co]-centered states. Detailed analysis using cyclic voltammetry, spectroelectrochemistry, electron paramagnetic resonance spectroscopy, and density functional theory (DFT) calculations provides insight into the unique electronic structure created in Si-vpy-[Co]. DFT reveals that the new electronic states arise from hybridization between deep Si NC band states and high-energy molecular orbitals of the ethylenepyridine tether and the [Co] catalyst and are facilitated by σ-bonding character at the ethylenepyridine linkage. This study demonstrates that strong electronic coupling achieved through precise molecular chemistry can change the paradigm of otherwise fixed energy levels in hybrid photoelectrochemical systems for artificial photosynthesis and related applications.

14 SOLAR ENERGY↗

A Bayesian analysis of nuclear deformation properties with Skyrme energy functionals

In spite of numerous scientific and practical applications, there is still no comprehensive theoretical description of the nuclear fission process based solely on protons, neutrons and their interactions. Furthermore, the most advanced simulations of fission are currently carried out within nuclear density functional theory (DFT). In spite of being fully quantum-mechanical and rooted in the theory of nuclear forces, DFT still depends on a dozen or so parameters characterizing the energy functional. Calibrating these parameters on experimental data results in uncertainties that must be quantified for applications. This task is very challenging because of the high computational cost of DFT calculations for fission. In this paper, we use Gaussian processes to build emulators of DFT models in order to quantify and propagate statistical uncertainties of theoretical predictions for a range of nuclear deformations relevant to describing the fission process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Constrained nuclear–electronic orbital method for periodic density functional theory: Application to H 2 chemisorption on Si(001) surfaces

The nuclear–electronic orbital (NEO) method provides a powerful computational framework for incorporating nuclear quantum effects (NQE) in electronic structure calculations beyond the Born–Oppenheimer approximation. By incorporating additional constraints to the position operator on quantum particles like protons, the NEO method enables calculation of effective potential that accounts for NQE. Here, in this work, we present a new constrained NEO (cNEO) formulation for density functional theory (cNEO-DFT) calculations in the context of extended periodic systems. Using the nudged elastic band method, we discuss an application of the cNEO-DFT approach to studying the adsorption of a hydrogen molecule on the Si(001) surfaces. The calculation shows how NQE impacts the reaction energetics. The proton density changes are computed along the reaction pathways. This work demonstrates the capability of the new cNEO-DFT method to study a wide range of chemical processes, such as surface reactions where the quantum nature of light atoms like protons is non-negligible.

Chemical processes↗

Conventional High-Temperature Superconductivity in Metallic, Covalently Bonded, Binary-Guest C–B Clathrates

Inspired by the synthesis of XB 3 C 3 (X = Sr, La) compounds in the bipartite sodalite clathrate structure, density functional theory (DFT) calculations are performed on members of this family containing up to two different metal atoms. A DFT chemical pressure analysis on systems with X = Mg, Ca, Sr, Ba reveals that the size of the metal cation, which can be tuned to stabilize the B–C framework, is key for their ambient-pressure dynamic stability. High-throughput density functional theory calculations on 105 Pm$\bar{3}$ symmetry XYB 6 C 6 binary-guest compounds (where X, Y are electropositive metal atoms) find 22 that are dynamically stable at 1 atm, expanding the number of potentially synthesizable phases by 19 (18 metals and 1 insulator). Here, the density of states at the Fermi level and superconducting critical temperature, T c , can be tuned by changing the average oxidation state of the metal atoms, with T c being highest for an average valence of +1.5. KPbB 6 C 6 , with an ambient-pressure Eliashberg T c of 88 K, is predicted to possess the highest T c among the studied Pm$\bar{3}$n XB 3 C 3 or Pm$\bar{3}$XYB 6 C 6 phases, and calculations suggest it may be synthesized using high-pressure high-temperature techniques and then quenched to ambient conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ru-promoted perovskites as effective redox catalysts for CO2 splitting and methane partial oxidation in a cyclic redox scheme

The current study reports AxA’1-xByB’1-yO3- perovskite redox catalysts (RCs) for CO2-splitting and methane partial oxidation (POx) in a cyclic redox scheme. Strontium (Sr) and iron (Fe) were chosen as A and B site elements with A’ being lanthanum (La), samarium (Sm) or yttrium (Y), and B’ being manganese (Mn), or titanium (Ti) to tailor their equilibrium oxygen partial pressures (P_(O_2 ) s) for CO2-splitting and methane partial oxidation. DFT calculations were performed for predictive optimization of the oxide materials whereas experimental investigation confirmed the DFT predicted redox performance. The redox kinetics of the RCs improved significantly by 1 wt.% ruthenium (Ru) impregnation without affecting their redox thermodynamics. Ru impregnated LaFe0.375Mn0.625O3 (A=0, A’=La, B=Mn, and B’=0) was the most promising RC in terms of its superior redox performance (CH4/CO2 conversion >90% and CO selectivity~ 95%) at 800oC. Long-term redox testing over Ru impregnated LaFe0.375Mn0.625O3 indicated stable performance during the first 30 cycles following with a ~25% decrease in the activity during the last 70 cycles. Air treatment was effective to reactivate the redox catalyst. Detailed characterizations revealed the underlying mechanism for redox catalyst deactivation and reactivation. Furthermore, this study not only validated a DFT guided mixed oxide design strategy for CO2 utilization but also provides potentially effective approaches to enhance redox kinetics as well as long-term redox catalyst performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4a Raw Data

Calculated formation energy of (0001 ̅) c-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (0001 ̅) c-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4b Raw Data

Calculated formation energy of (1010 ̅) m-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (1010 ̅) m-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗

Multiphase tin equation of state using density functional theory

In this work, we perform density functional theory (DFT) calculations of five solid phases and the liquid phase of tin. The calculations include cold curves of the five solid phases, phonon calculations in the quasiharmonic approximation over a range of volumes for each solid phase, and DFT-based molecular dynamics (DFT-MD) simulations of the liquid phase, including those of the melt curve using the Z method. Using the DFT results, we construct a tabular multiphase sesame equation of state for tin, referred to as sesame 2162. Comparisons to experimental data are made and show a high level of agreement in isobaric data, isothermal data, shock data, and phase boundary measurements, including measurements of the melt curve. The 2162 EOS will be useful for hydrodynamics simulations and has been designed with an eye toward hydrodynamics simulations that incorporate materials strength models and allow for modeling of the kinetics of phase transitions.

3-dimensional systems↗

Electronic structure of the kagome compound CaTi 3⁢ Bi 4 using high-field torque magnetometry and density functional theory

Here, we report systematic torque magnetometry measurements to investigate the electronic properties of the newly discovered kagome compound CaTi 3 ⁢Bi 4 . Electrical transport, magnetic susceptibility, and thermal measurements reveal no evidence of a magnetic ground state in this material. Torque data obtained in magnetic fields up to 41.5 T exhibit clear de Haas–van Alphen (dHvA) oscillations, with nine distinct frequencies ranging from 13 to 6164 T. Angular-dependent dHvA measurements show that, with the exception of the lowest frequency (13 T), all observed frequencies nearly follow a 1/cos ⁡𝜃 dependence, where 𝜃 is the angle between the crystallographic 𝑐 axis and the magnetic field direction. This behavior is characteristic of quasi-two-dimensional Fermi-surface sheets with nearly circular cross sections. To further elucidate the electronic structure, we performed density functional theory (DFT) calculations of the band structure and Fermi surface. The calculated bands reveal the presence of multiple Dirac points (DP), flat bands (FB), and van Hove singularities (VHS) near the Fermi level. The resulting Fermi surface consists of several quasi-two-dimensional cylindrical sheets, consistent with the experimentally observed 1/cos⁡ 𝜃 dependence. Notably, the theoretical dHvA frequencies, derived from extremal Fermi-surface cross-sectional areas, agree well with the experimental values and reproduce their angular dependence. Remarkably, all experimentally observed frequencies are captured by the DFT predictions. Pressure-dependent calculations up to 10 GPa show that the electronic features—DP, FB, and VHS—evolve systematically with pressure. In particular, the VHS shifts closer to the Fermi level, demonstrating that pressure acts as an effective tuning parameter in this material. These combined experimental and theoretical results provide a comprehensive understanding of the electronic structure of CaTi 3 ⁢Bi 4 and demonstrate how pressure can be used to tune its key electronic features, offering valuable guidance for exploring related kagome materials.

Shtefiienko, Kyryl [West Texas A & M University, C↗