Boron Sublattice Research Articles

Hard Copper Boride with Exceptional Conductivity.

Copper and boron seldom engage in reaction at ambient pressure. The few reports on copper-doped boron compounds that exist in the literature often lack definitive stoichiometry. Here, we report successful synthesis of Cu_{2-δ}B_{25} single crystals (δ∼0.03, indicating Cu understoichiometry) via a high-pressure melting method using copper and β-rhombohedral boron as precursors. Crystals thus synthesized are characterized by a tetragonal boron sublattice, within which Cu atoms are either partially or fully situated at different interstices between B_{12} icosahedra. The crystals possess a high Vickers hardness of 26.5GPa and an unusually high electrical conductivity of 1.19×10^{5} S/m-the highest conductivity among the icosahedron-based borides. Hall measurements reveal a notable p-n conduction type transition around 30GPa. This transition, alongside the remarkable conductivity, is potentially modulated by the copper content and its valence states within the structure. The synthesis of Cu_{2-δ}B_{25} not only broadens the spectrum of hard materials but also opens new avenues for innovative modulation of electronic properties in boron-rich compounds, with promising technological implications.

A fresh class of superconducting and hard pentaborides

On the basis of the current theoretical understanding of boron-based hard superconductors under ambient conditions, numerous studies have been conducted with the aim of developing superconducting materials with favorable mechanical properties using boron-rich compounds. In this paper, first-principles calculations reveal the existence of an unprecedented family of tetragonal pentaborides MB5 (M = Na, K, Rb, Ca, Sr, Ba, Sc, and Y), comprising B20 cages and centered metal atoms acting as stabilizers and electron donors to the boron sublattice. These compounds exhibit both superconductivity and high hardness, with the maximum superconducting transition temperature Tc of 18.6 K being achieved in RbB5 and the peak Vickers hardness Hv of 35.1 GPa being achieved in KB5 at 1 atm. The combination of these properties is particularly evident in KB5, RbB5, and BaB5, with Tc values of ∼14.7, 18.6, and 16.3 K and Hv values of ∼35.1, 32.4, and 33.8 GPa, respectively. The results presented here reveal that pentaborides can provide a framework for exploring and designing novel superconducting materials with favorable hardness at achievable pressures and even under ambient conditions.

Boron vacancy-driven thermodynamic stabilization and improved mechanical properties of AlB2-type tantalum diborides as revealed by first-principles calculations

Thermodynamic stability as well as structural, electronic, and elastic properties of boron-deficient AlB2-type tantalum diborides, which is designated as TaB, due to the presence of vacancies at its boron sublattice are studied via first-principles calculations. The results reveal that TaB, where 0.167 0.25, is thermodynamically stable even at absolute zero. On the other hand, the shear and Young’s moduli as well as the hardness of stable TaB are predicted to be superior as compared to those of TaB2. The changes in the relative stability and also the elastic properties of TaB with respect to those of TaB2 can be explained by the competitive effect between the decrease in the number of electrons filling in the antibonding states of TaB2 and the increase in the number of broken bonds around the vacancies, both induced by the increase in the concentration of boron vacancies. A good agreement between our calculated lattice parameters, elastic moduli and hardness of TaB and the experimentally measured data of as-synthesized AlB2-type tantalum diborides with the claimed composition of TaB, available in the literature, suggests that, instead of being a line compound with a stoichiometric composition of TaB2, AlB2-type tantalum diboride is readily boron-deficient, and its stable composition in equilibrium may be ranging at least from TaB to TaB. Furthermore, the substitution of vacancies for boron atoms in TaB2 is responsible for destabilization of WB2-type tantalum diboride and orthorhombic Ta2B3, predicted in the previous theoretical studies to be thermodynamically stable in the Ta−B system, and it thus enables the interpretation of why the two compounds have never been realized in actual experiments.

Low-temperature infrared spectroscopy of the strongly correlated semiconductor Tm0.19Yb0.81B12 with dynamic charge stripes

Tm1–x Yb x B12 dodecaborides represent model objects for the studies of quantum critical behavior, metal–insulator transitions (MITs) and complex charge-spin–orbital–phonon coupling phenomena. In spite of intensive investigations, the mechanism of semiconducting ground state formation both in YbB12 and in the Yb-based strongly correlated electron systems remains a subject of active debates. We have performed first systematic measurements of temperature-dependent spectra of infrared conductivity of Tm0.19Yb81B12 at frequencies 40–35 000 cm−1 and in the temperature range 10–300 K. Analysis of the temperature evolution of the observed absorption resonances is performed allowing to associate these with the cooperative dynamic Jahn–Teller instability of the boron sub-lattice. This ferrodistortive effect of B12-complexes induces the rattling modes of the rare earth ions leading to emergence of both the intra-gap mixed-type collective excitations and the dynamic charge stripes. We estimate the temperature-dependent effective mass of charge carriers and propose the scenario of transformation of the many-body states in the multiple relaxation channels. We attribute the MIT to the localization of electrons at the vibrationally coupled Yb–Yb pairs, which is accompanied by the electronic phase separation and formation of the nanoscale filamentary structure of electron density (stripes) in Tm1–x Yb x B12 compounds.

Crystal-field potential and short-range order effects in inelastic neutron scattering, magnetization, and heat capacity of the cage-glass compound HoB12

The strongly correlated system Ho11B12 with boron sublattice Jahn-Teller instability and nanoscale electronic phase separation (dynamic charge stripes) was studied in detail by inelastic neutron scattering (INS), magnetometry and heat capacity measurements at temperatures in the range 3-300 K. From the analysis of registered INS spectra, we determined parameters of the cubic crystal field at holmium sites, B4=- 0.333 meV and B6= -2.003 meV (in Stevens notations), with an unconventional large ratio B6/B4 pointing on the dominant role of conduction electrons in the formation of a crystal field potential. The molecular field in the antiferromagnetic state, Bloc = (1.75+- 0.1) T has been directly determined from the INS spectra together with short-range order effects detected in the paramagnetic state. A comparison of measured magnetization in diluted Lu0.99Ho0.01B12 and concentrated HoB12 single crystals showed a strong suppression of Ho magnetic moments by antiferromagnetic exchange interactions in holmium dodecaboride. To account explicitly for the short-range antiferromagnetic correlations, a self-consistent holmium dimer model was developed that allowed us to reproduce successfully field and temperature variations of the magnetization and heat capacity in the cage-glass phase of HoB12 in external magnetic fields.

Electronic and magnetic properties of new binary uranium-boron compounds with 2D and 3D boron networks: A revisit of the U:B system

Based on crystal chemistry rationale and calculations within the density functional theory DFT, the U:B system is complemented with additional binary compounds UB3, U2B6, and UB6 possessing two-dimensional 2D and 3D boron substructures. Observations are supported quantitatively with the trends of cohesive energies, charge transfers onto the boron sub-lattice and geometry optimized structures. The results point out to a ‘structure crossover’ from hexagonal (layer B network) to 3D boron network at compositions above UB3 found to be connected with a threshold amount of charge onto boron which is ~0.46. From the energy-volume equation of states EOS considering spin degenerate and spin-polarized configurations, hexagonal UB3, and cubic UB6 were found in a stable ferromagnetic ground state with 1.47 μB and 2.40 μB spin-only moments. The volume variations of magnetization show respectively a smooth and abrupt evolution for UB3 and UB6.

Electron-configuration stabilized (W,Al)B2 solid solutions

By combining experimental and theoretical methods, we have conducted a detailed study of the ternary diboride system (W1-xAlx)1-yB2(1-z). Tungsten rich solid solutions of (W1-xAlx)1-yB2(1-z) were synthesized by physical vapor deposition and subsequently investigated for structure, mechanical properties and thermal stability. All crystalline films show hardness values above 35 GPa, while the highest thermal stability was found for low Al contents. In this context, the impact of point defects on the stabilization of the AlB2 structure type is investigated, by means of ab initio methods. Most notably, we are able to show that vacancies on the boron sublattice are detrimental for the formation of Al-rich (W1-xAlx)1-yB2(1-z), thus providing an explanation why only tungsten rich phases are crystalline.

Maltese cross anisotropy in Ho0.8Lu0.2B12 antiferromagnetic metal with dynamic charge stripes

The model strongly correlated electron system Ho0.8Lu0.2B12 which demonstrates a cooperative Jahn-Teller instability of the boron sub-lattice in combination with rattling modes of Ho(Lu) ions, dynamic charge stripes and unusual antiferromagnetic (AF) ground state has been studied in detail at low temperatures by magnetoresistance, magnetization and heat capacity measurements. Based on received results it turns out that the angular H-fi-T magnetic phase diagrams of this non-equilibrium AF metal can be reconstructed in the form of a Maltese cross. The dramatic AF ground state symmetry lowering of this dodecaboride with fcc crystal structure can be attributed to the redistribution of conduction electrons which leave the RKKY oscillations of the electron spin density to participate in the dynamic charge stripes providing with extraordinary changes in the indirect exchange interaction between magnetic moments of Ho3+ ions and resulting in the emergence of a number of various magnetic phases. It is also shown that the two main contributions to magnetoresistance in the complex AF phase, the (i) positive linear on magnetic field and the (ii) negative quadratic component can be separated and analyzed quantitatively, correspondingly, in terms of charge carrier scattering on spin density wave (5d) component of the magnetic structure and on local 4f-5d spin fluctuations of holmium sites.

Stable and hard hafnium borides: A first-principles study

We investigate the stability of hafnium borides at zero pressure via the evolutionary crystal structure prediction and first-principles calculations. Our results indicate that the well-known P6/mmm-HfB2 is the only thermodynamically stable phase at zero temperature and pressure, and two more phases (Pnma-HfB and Fm3¯m-HfB12) become thermodynamically stable at higher temperatures. We compute the mechanical properties including bulk, shear and Young’s moduli, Vickers hardness, and fracture toughness for all stable and metastable hafnium borides (∼30 phases) and then study in detail the effect of boron concentration and topology of B-sublattice on their mechanical properties. We show that not only the concentration of boron, but also the topology of the boron sublattice is important for the mechanical properties of hafnium borides. Among the predicted stable and low-energy metastable hafnium borides, the highest possible hardness is exhibited by P6/mmm-HfB2 with graphenelike boron sheets and by phases with 3D boron networks and high B/Hf ratios (e.g., Pnnm-HfB5 and Fm3¯m-HfB12).

Morphology, Ordering, Stability, and Electronic Structure of Carbon‐Doped Hexagonal Boron Nitride

Theoretical studies of morphology, stability, and electronic structure of monolayer hexagonal CBN alloys with rich content of h‐BN and carbon concentration not exceeding 50% are presented. The studies are based on the bond order type of the valence force field to account for the interactions between atomic constituents and Monte Carlo method with Metropolis algorithm to establish equilibrium distribution of atoms over the lattice. It is found that the phase separation into graphene and h‐BN domains occurs in the majority of growth conditions. Only in N‐rich growth conditions, it is possible to obtain a quasi uniform distribution of carbon atoms over the boron sublattice. It is been predicted that the energy gap in stoichiometric Cx(BN)1−x alloys exhibits extremely strong bowing.

On the role of isotopic composition in crystal structure, thermal and charge-transport characteristics of dodecaborides LuNB12 with the Jahn-Teller instability

Crystal structures, thermal and charge-transport (resistivity and Seebeck coefficient) characteristics of dodecaborides LuNB12 are studied to determine the role of boron isotopic composition N = 10, 11, natural. Small distortions of the fcc lattice are observed and attributed to cooperative Jahn-Teller effect in the boron sublattice. The Einstein and Debye temperatures, respectively for Lu and B atoms, are determined based on equivalent atomic displacement parameters (ADPs) refined as a part of structure model. Additionally, ADP values are separated into temperature dependent and independent components, arising from (i) thermal and (ii) zero temperature vibrations, together with (iii) static shifts of few atoms from lattice sites. Atomic disordering is most expressed in LunatB12 as follows from its ADP values and the Schottky anomalies in heat capacity. The largest static ADP components of LunatB12 are surprisingly combined with the lower resistivity and thermopower as compared to isotopically pure crystals. One may suppose the static shifts (defects) are centers of pinning facilitating formation of additional conductive channels (dynamic charge stripes), which reveal themselves on difference Fourier maps of electron density.

Observation of dynamic charge stripes in Tm0.19Yb0.81B12 at the metal–insulator transition

Accurate low temperature charge transport measurements in combination with high-precision x-ray diffraction experiments have allowed detection of the symmetry lowering in the single domain Tm0.19Yb0.81B12 crystals that belong to the family of dodecaborides with metal–insulator transition. Based on the fine structure analysis we discover the formation of dynamic charge stripes within the semiconducting matrix of Tm0.19Yb0.81B12. The charge dynamics in these conducting nano-size channels is characterized by broad-band optical spectroscopy that allowed estimating the frequency (~2.4 × 1011 Hz) of quantum motion of the charge carriers. It is suggested that cooperative Jahn–Teller effect in the boron sublattice is a cause of the large-amplitude rattling modes of the Tm and Yb ions responsible for the ‘modulation’ of the conduction band along one of the directions through the variation of 5d-2p hybridization of electron states.

Features of the Crystal Structure of Tm1–xYbxB12 Dodecaborides near a Quantum Critical Point and at a Metal–Insulator Transition

The magnetic phase diagram of Tm1–xYbxB12 antiferromagnets is determined from the specific heat measurements performed at low and ultralow temperatures (0.07–10 K). Precise experimental studies of the features of the crystal structure at room temperature suggest that a metal−insulator transition occurring in Tm1–xYbxB12 with the growth of x is accompanied by a significant (by a factor of 2–6) increase in the amplitude of atomic displacements in the boron and rare-earth sublattices. There is also a signature of an instability arising in the electron configuration of ytterbium ions at this transition. At room temperature, near the quantum critical point at xc ≈ 0.25, anomalies in the structural characteristics of dodecaborides under study are observed.

Nanodomains and local structure in ternary alkaline-earth hexaborides

The local structures of ternary alkaline-earth hexaborides (MB6, M = Ca0.5Sr0.5, Ca0.5Ba0.5 and Sr0.5Ba0.5) have been analysed using X-ray pair distribution function (PDF) analysis, Raman spectroscopy and transmission electron microscopy (TEM). The results show significant local deviations from the average cubic structure within the boron sub-lattice and support the conclusion that rapid synthesis processes lead to the formation of coherent nanodomains over length scales of about 10 nm. Reverse Monte Carlo fitting of the PDFs allows for quantification of the displacement disorder within the boron sub-lattice as a function of sample composition. Detailed Raman spectroscopy studies and high-resolution TEM support the models derived from X-ray scattering. The average magnitude of the static displacement disorder varies by sample composition and positively correlates with the cation radius ratios across the three compositions. The new models form a foundation for future computational and experimental studies aimed at understanding and predicting properties of hexaborides.

Predicting the ground-state structure of sodium boride

Binary borides has been a subject of extensive research. However, the exact compositions and crystal structures of sodium borides remained controversial. Here, using the ab initio variable-composition evolutionary algorithm, a new stable ${\mathrm{Na}}_{2}{\mathrm{B}}_{30}$ with $I{2}_{1}{2}_{1}{2}_{1}$ symmetry ($I{2}_{1}{2}_{1}{2}_{1}\ensuremath{-}{\mathrm{Na}}_{2}{\mathrm{B}}_{30}$) is found, which is $\ensuremath{-}7.38\phantom{\rule{0.28em}{0ex}}\mathrm{meV}/\mathrm{atom}$ lower in energy than the $Imma\ensuremath{-}{\mathrm{Na}}_{2}{\mathrm{B}}_{30}$ structure reported by experimentalists. Interestingly, the $Imma\ensuremath{-}{\mathrm{Na}}_{2}{\mathrm{B}}_{30}$ structure is predicted to be a topological nodal line semimetal, which may result in superior electronic transport. In contrast, $I{2}_{1}{2}_{1}{2}_{1}\ensuremath{-}{\mathrm{Na}}_{2}{\mathrm{B}}_{30}$ is an ultrahard semiconductor with an unprecedented open-framework structure, whose interstitial helical boron sublattice enhances its hardness and energetic stability.

Rattling mode and symmetry lowering resulting from the instability of the B12 molecule in LuB12

The dodecaboride LuB$_{12}$ with cage-glass state and rattling modes has been studied to clarify the nature of the large amplitude vibrations of Lu ions. Discovered anisotropy of charge transport in conjunction with distortions of the conventional \textit{fcc} symmetry of the crystal lattice may be attributed to coherent motion of Lu ions along singular direction in the lattice. Arguments are presented in favor of cooperative dynamic Jahn-Teller effect in the boron sublattice to be the reason of the rattling mode, lattice distortion and formation of the filamentary structure of the conductive channels.

Gap discrete breathers in strained boron nitride

Linear and nonlinear dynamics of hexagonal boron nitride (h-BN) lattice is studied by means of molecular dynamics simulations with the use of the Tersoff interatomic potentials. It is found that sufficiently large homogeneous elastic strain along zigzag direction opens a wide gap in the phonon spectrum. Extended vibrational mode with boron and nitrogen sublattices vibrating in-plane as a whole in strained h-BN has frequency within the phonon gap. This fact suggests that a nonlinear spatially localized vibrational mode with frequencies in the phonon gap, called discrete breather (also often termed as intrinsic localized mode), can be excited. Properties of the gap discrete breathers in strained h-BN are contrasted with that for analogous vibrational mode found earlier in strained graphene. It is found that h-BN modeled with the Tersoff potentials does not support transverse discrete breathers.

Towards a metal-semiconductor transition in two dimensions

Two-dimensional (2D) heterosheets built from silicon and boron may exhibit an intrinsic metallic behavior. From density-functional-theory computer simulations, we have demonstrated that a 2D honeycomb binary compound (h-SiB), which exhibits robust structural and thermal stabilities, maintains its metallicity by increasing hydrogen coverages at 25%, 50%, and 75% on boron or silicon sublattices. However, under a total hydrogenation condition (100%) on B or Si sites, h-SiB opens a well-defined bandgap, meaning that it is possible to obtain a metal-insulator transition at zero temperature in 2D. Additional calculations show that the hydrogenation on B sublattices is energetically more favorable than on silicon.

Coexistence of Superconductivity and Superhardness in Beryllium Hexaboride Driven by Inherent Multicenter Bonding.

Unique multicenter bonding in boron-rich materials leads to the formation of complex structures and intriguing properties. Here global structural searches are performed to unearth the structure of beryllium hexaboride (BeB6) synthesized decades ago. Three BeB6 phases (α, β, and γ) were predicted to be stable at ambient and high pressures. The ground state at ambient pressure, α-BeB6, consists of a strong and uniformly distributed covalent B-B network, which results in exceptional elastic properties and a hardness of 46 GPa comparable to γ-B. Even more surprisingly, α-BeB6 retains credible electron phonon coupling in the boron sublattice, and is predicted to be superconducting at 9 K. Above 4 GPa, β-BeB6 is stabilized with alternating boron slabs and triangular beryllium layers analogous to the structure of MgB2. The β-BeB6 is predicted to be superconducting at 24 K, similar to Nb3(Al,Ge). The γ-BeB6 is stable above 340 GPa. The understanding of intrinsic multicenter-bonding mechanism and related properties demonstrated in the very example of BeB6 provides new insights for the design of tunable multifunctional materials.

Microscopic unravelling of nano-carbon doping in MgB2 superconductors fabricated by diffusion method

We investigated the effects of nano-carbon doping as the intrinsic (B-site nano-carbon substitution) and extrinsic (nano-carbon derivatives) pinning by diffusion method. The contraction of the in-plane lattice confirmed the presence of disorder in boron sublattice caused by carbon substitution. The increasing value in full width half maximum (FWHM) in the X-ray diffraction (XRD) patterns with each increment in the doping level reveal smaller grains and imperfect MgB2 crystalline. The strain increased across the doping level due to the carbon substitution in the MgB2 matrix. The broadening of the Tc curves from low to high doping showed suppression of the connectivity of the bulk samples with progressive dirtying. At high doping, the presence of B4C region blocked the Mg from reacting with crystalline B thus hampering the formation of MgB2. Furthermore, the unreacted Mg acted as a current blocking phase in lowering down the grain connectivity hence depressing the Jc of the 10% nano-carbon doped MgB2 bulk superconductor.