Simulated X-ray Diffraction Patterns Research Articles

Electrochemical stability of biodegradable Zn-Cu alloys through machine-learning accelerated high-throughput discovery.

Zn-Cu alloys have attracted great attention as biodegradable alloys owing to their excellent mechanical properties and biocompatibility, with corrosion characteristics being crucial for their suitability for biomedical applications. However, the unresolved identification of intermetallic compounds in Zn-Cu alloys affecting corrosion and the complexity of the application environment hamper the understanding of their electrochemical behavior. Utilizing high-throughput first-principles calculations and machine-learning accelerated evolutionary algorithms for screening the most stable compounds in Zn-Cu systems, a dataset encompassing the formation energy of 2033 compounds is generated. It reveals that most of the experimentally reported Zn-Cu compounds can be replicated, especially the structure of R32 CuZn5 is first discovered which possesses the lowest formation energy of -0.050 eV per atom. Furthermore, the simulated X-ray diffraction pattern matches perfectly with the experimental ones. By formulating 342 potential electrochemical reactions based on the binary compounds, the Pourbaix diagrams for Zn-Cu alloys are constructed to clarify the fundamental competition between different phases and ions. The calculated equilibrium potential of CuZn5 is higher than that of Zn through the forward reaction Zn + CuZn5 ⇌ CuZn5 + Zn2+ + 2e-, resulting in microcell formation owing to the stronger charge density localization in Zn compared to CuZn5. The presence of chlorine accelerates the corrosion of Zn through the reaction Zn + CuZn5 + 6Cl- + 6H2O ⇌ Cu + 6ZnOHCl + 6H+ + 12e-, where the formation of ZnOHCl disrupts the ZnO passive film and expands the corrosion pH range from 9.2 to 8.8. Our findings reveal an accurate quantitative corrosion mechanism for Zn-Cu alloys, providing an effective pathway to investigate the corrosion resistance of biodegradable alloys.

Ab initio study on changing behaviors of lithium-rich layered composite cathode materials

The lithium-rich composite-layered oxide, xLi2MnO3•(1-x)LiM'O2, where M’ represents transition metals, is a promising cathode material with excellent capacity at high working voltage for lithium-ion batteries (LIBs). Nevertheless, an unusual charge-discharge feature is observed for this material with sloping and plateau regions during the initial charging. In this work, ab initio calculations based on density functional theory were employed to examine the stability of xLi2MnO3•(1-x)Li(Ni1/3Co1/3Mn1/3)O2 composite-layered cathode materials during the first charging. Optimized atomistic models for different compositions (x = 0.0, 0.3, 0.4, 0.5, 0.7, and 1) unveil a pseudo-rhombohedral or monoclinic-like structure within the solid solution phase, with simulated X-ray diffraction patterns closely matching experimental data. Using these atomistic models, the first charging process of the 0.4Li2MnO3•0.6Li(Ni1/3Co1/3Mn1/3)O2 cathode were investigated. There exists phase transition from a layered to a spinel structure. Additionally, Bader charge analysis reveals intriguing trends during the first delithiation process, where the valence states of Ni and Co gradual increase, while that of Mn almost remains unchanged. Simultaneously, significant oxidation of O is observed. This finding leads to further evaluations on oxygen vacancy formation in comparison to the energy required for delithiation. Defect formation energy calculations demonstrate that the plateau in charging curve is resulted from oxygen vacancy formation during the first charging. By empirical fitting oxygen chemical potential at μO = -1.200 eV, the calculated charging-discharging curves aligned well with experimental data during the first and second charging. Furthermore, the pathways of lithium and oxygen deintercalation are elucidated. This work contributes fundamental understandings on the xLi2MnO3•(1-x)LiM'O2 composite-layered oxides as cathode for LIBs, providing valuable guidance for further developments in high-capacity Co-lean cathode materials.

Crystallographic phase identifier of a convolutional self-attention neural network (CPICANN) on powder diffraction patterns.

Spectroscopic data, particularly diffraction data, are essential for materials characterization due to their comprehensive crystallographic information. The current crystallographic phase identification, however, is very time consuming. To address this challenge, we have developed a real-time crystallographic phase identifier based on a convolutional self-attention neural network (CPICANN). Trained on 692 190 simulated powder X-ray diffraction (XRD) patterns from 23 073 distinct inorganic crystallographic information files, CPICANN demonstrates superior phase-identification power. Single-phase identification on simulated XRD patterns yields 98.5 and 87.5% accuracies with and without elemental information, respectively, outperforming JADE software (68.2 and 38.7%, respectively). Bi-phase identification on simulated XRD patterns achieves 84.2 and 51.5% accuracies, respectively. In experimental settings, CPICANN achieves an 80% identification accuracy, surpassing JADE software (61%). Integration of CPICANN into XRD refinement software will significantly advance the cutting-edge technology in XRD materials characterization.

Exploring 2D X-ray diffraction phase fraction analysis with convolutional neural networks: Insights from kinematic-diffraction simulations

Deep-learning models are effective for analyzing the complex information in 2D X-ray diffraction (XRD) patterns. Accurately collecting parameters of the material sample is crucial during model training, significantly impacting model performance. In this study, we employ a kinematic-diffraction simulator to generate simulated 2D XRD patterns for Ti–6Al–4V alloy, allowing precise control of sample parameters. These simulated patterns are used to train convolutional neural networks, predicting β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}-phase volume fractions. The training data set consists exclusively of 2D XRD patterns with pure α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upalpha$$\\end{document}- or pure β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}-phase, while the testing set incorporates patterns with intermediate phase volume fraction. In particular, we investigate how the architectures of the model influence prediction reliability and computational performance. Experimental results reveal that, with appropriate training, the convolutional neural network accurately detects intermediate phase volume fractions even trained with only pure-phase patterns, achieving a mean square error accuracy of 9.4×10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$9.4 \ imes 10^{-4}$$\\end{document}.Graphical abstract

Theoretical Design of Strengthened Nanotwinned γ*-Boron.

The distinctive electron deficiency and unusual multicenter bonding situations of boron give rise to fascinating chemical complexity and imaginative structural polymorphism. Herein, we employ an independently developed method to construct the new twinned γ*-boron based on the well-known hardest elemental boron, γ-B28. Notably, the newly propounded γ*-boron phases exhibit considerably close energy levels with γ-B28 under ambient conditions. The simulated X-ray diffraction patterns of stable twinned structure present excellent agreement with experimental data. First-principles calculations reveal a 7.5% increase in the ideal Vickers shear strength of γ*-boron compared to γ-B28, attributed to diverse bond responses within the twinned slabs. The evaluated hardness of nanotwinned γ*-B reaches 59 GPa in consideration of the size hardening effect. Our research presents an efficient strategy for constructing new polymorphs of boron with improved mechanical properties and expands the knowledge about twinning structures of boron.

Design and investigated a novel BN polymorph in orthorhombic phase

In this work, a new BN polymorph with Pnma symmetry is proposed by RG2 and investigated by density functional theory. Pnma-II BN polymorph is shown to be dynamically and mechanically stable, and the relative enthalpy of Pnma-II BN is 0.187 eV per atom higher than that of c-BN, respectively. Mechanical properties calculations indicate that Pnma-II BN is also a potential superhard material with hardness of 49.7 GPa. The electronic band structures of Pnma-II BN show that the Pnma-II BN is a direct and ultrawide band gap semiconductor (band gap is 5.82 eV). The mechanical anisotropy of Young's modulus of Pnma-II BN and Pnma BN is greater than that of c-BN, while the mechanical anisotropy of shear modulus of Pnma-II BN in the (100), (001) plane is lower than that of c-BN. In addition, simulated X-ray diffraction patterns are provided for experimental confirmation of the predicted structures.

Theoretical design of superhard twinned BC2N

BC2N is an ideal combination of diamond and boron nitride and is expected to exhibit better mechanical properties and thermal stability than boron nitride and diamond, respectively. Recent studies raise exciting prospects of building coherent nanotwinned boundaries to improve performance of ceramics. Herein, we developed a systematic method to construct twin structures of BC2N. The newly identified nanotwinned BC2N variant (τ-BC2N) exhibits better energetic stability and higher mechanical strength than single-crystal BC2N, attributed to the optimized bonding behavior and crystal orientations induced via twinning. The simulated X-ray diffraction patterns of τ-BC2N match those reported in previous experimental data. The nanotwinned BC2N displays superior Vickers hardness of ∼140 GPa, surpassing that of diamond. The computationally tailored approach and results obtained by twin-strengthening strategies offer powerful insights for the rational design and functional optimization of nanotwinned boron–carbon–nitrogen compounds containing intricate multiatomic constituents and structures.

Deciphering the structural evolutions and electronic features of Nd3+:K2YF5 nanocrystals

Neodymium (Nd3+)-doped K2YF5 nanophosphors have attracted considerable attention due to their promising application in fiber lasers, luminescence thermometry and bioimaging. However, the structural evolutions and electronic properties of Nd3+-doped K2YF5 nanocrystals have not been comprehensively studied, which is exactly the basis of spectral formation. In this letter, the ground structure of Nd3+:K2YF5 crystals are first obtained by crystal structure prediction in conjunction with density functional theory. Our results reveal a new stable phase with Pm (No. 6) space group for the Nd3+:K2YF5 nanocrystals, and Nd3+ ions replace the position of Y3+ ions. Additionally, we have identified the presence of a local polyhedron [NdF7]4-, wherein the crystallographic site with Cs symmetry is occupied by Nd3+ ions. The excellent agreement observed between our simulated X-ray diffraction patterns and the experimental data serves as compelling evidence supporting the validity of the ground-state structure. The electronic band structure calculation of Nd3+-doped K2YF5 employing the enhanced modified Becke-Johnson methodology demonstrates a closure of the insulator band gap (4.01 eV). Our analysis of the electron localization function for Nd3+-doped K2YF5 crystal indicates a dominant ionic bond interaction between Nd and F ions. These results offer valuable insights into the structural evolution and enable the exploration of properties when encountering other rare-earth-doped materials.

High Proton Conductivity of the UiO-66-NH2-SPES Composite Membrane Prepared by Covalent Cross-Linking.

A sulfonated poly(ethersulfone) (SPES)-metal-organic framework (MOF) film with excellent proton conductivity was synthesized by anchoring UiO-66-NH2 to the main chain of the aromatic polymer through the Hinsberg reaction. The chemical bond was formed between the amino group in MOFs and the -SO2Cl group in chlorosulfonated poly(ethersulfones) to conduct protons in the proton channel of the membrane, making the membrane have excellent proton conductivity. UiO-66-NH2 is successfully prepared as a result of the consistency of the experimental and simulated powder X-ray diffraction (PXRD) patterns of MOFs. The existence of absorption peaks of characteristic functional groups in Fourier transform infrared (FTIR) spectra proved the successful preparation of SPES, PES-SO2Cl, and a composite film. The results of the AC impedance test indicate that the composite film with a 3% mass fraction has the best proton conductivity of 0.215 S·cm-1, which is 6.2 times higher than that of the blended film without a chemical bond at 98% RH and 353 K. To our knowledge, there are rarely any reports on the preparation of a composite membrane by directly linking MOFs and the membrane matrix with chemical bonds. This work provides a good way to synthesize the highly conductive proton exchange film.

Pseudotetrahedral C2-symmetrical Co/Zn(II)-achiral Schiff base complexes with Δ/Λ-chirality induction at-metal as a racemic mixture

Reaction of achiral Schiff base ligands 1-((X-phenylimino)methyl)naphthalen-2-ol {X = 2-ethyl (HL1) or 4-methyl (HL2)} with cobalt(II) or zinc(II) acetate provided the corresponding bis[1-((X-phenylimino)methyl)naphthalen-2-olato-k2N,O]cobalt(II) or zinc(II) {X = 2-ethyl: M = Co (1) and Zn (2) or X = 4-methyl: M = Co (3) and Zn (4)} complexes. The molecules crystallize in the centrosymmetric space groups R–3 (1) and P–1 (3 or 4). Molecular structures determinations showed coordination of two molecules of the N,O-chelate ligands to the metal ion and formation of pseudotetrahedral complexes with C2-symmetry. Furthermore, coordination of two unsymmetrical achiral N,O-chelates induces Λ/Δ-chirality at the metal atom as a racemic mixture in the centrosymmetric space groups. Structural analyses further reveal that incorporation of 2-ethyl (1) or 4-methyl (3 or 4) group on the N-bound phenyl ring leads to an increase of both the O1-M-O2 and N1-M-N2 bond angles on going from 1 to 3 or 4, with the N1-M-N2 angle increasing to a much greater extent. The fair matching of the experimental and simulated powder X-ray diffraction patterns confirms the phase purity of bulk microcrystalline sample. Differential scanning calorimetry (DSC) results suggest an irreversible phase transformation from solid crystals to isotropic-liquids and subsequent thermal stability of the complexes. Cyclic voltammograms indicate a quasi-reversible two one electron charge transfer processes for 1 or 3 in N,N-dimethylformamide (DMF). Optimized geometry and excited state properties by density functional theory (DFT) and time dependent-density functional theory (TD-DFT) calculations correspond well to the experimental results.

Topological nodal line semimetal with large nodal ring in an all- sp2 hybridized carbon network formed by all-ten-membered carbon rings

Carbon can form versatile allotropes due to its multiple bonding connections and the prediction of new carbon structures and properties has long been a hot topic. In 1983, Hoffmann et al. [J. Am. Chem. Soc. 105, 4831 (1983)] have reported an all-$s{p}^{2}$ hybridized carbon allotrope with a 16-atom body-centered-tetragonal unit cell in $\mathrm{I}{4}_{1}/\mathrm{amd}$ (${D}_{4h}^{19}$) symmetry, which is dubbed as cT16 carbon in this work. Here we report by ab initio calculations a systematical study on the structural, energetic, dynamical, and electronic properties of cT16 carbon. Interestingly, cT16 carbon is linked with all-ten-membered carbon rings. The phonon band spectrum calculations confirm its dynamical stability and ab initio molecular dynamics simulations prove its thermal stability up to 900 K. Previously cT16 carbon was widely considered as a simple metallic carbon. However, our detailed electronic band structures calculations reveal that cT16 is actually a topological nodal line semimetal with a large closed nodal ring centering the high-symmetric $\mathrm{\ensuremath{\Gamma}}$ point. It nearly encloses the entire ${k}_{z}=0$ mirror plane, thus the drumheadlike surface bands can nearly cover the entire projected ($11\overline{1}$) surface Brillouin zone, which makes cT16 carbon an ideal nodal line semimetal. The simulated x-ray diffraction pattern of cT16 carbon matches well with one of the previously unexplained experimental peaks found in the diamond rich coatings grown on the stainless steel substrate. Our findings have provided insight for this well-known cT16 carbon, enriched the family of carbon allotropes with exotic topological electronic properties, suggested a viable route for its synthesis, and also provided an reasonable explanation for previous experimental data.

A pressure-induced high-pressure metallic GeTe phase.

As an important phase-change material, GeTe has many high-pressure phases as well, but its phase transitions under pressure are still lack of clarity. It is challenging to identify high-pressure GeTe crystal structures owing to the phase coexistence in a wide pressure range and the reversibility of phase transitions. Hence, first-principles calculations are required to provide further information in addition to limited experimental characterizations. In this work, a new orthorhombic Cmca GeTe high-pressure phase has been predicted via the CALYPSO method as the most energetically favorable phase in the pressure range between ∼30 and ∼38.5GPa, which would update the GeTe high-pressure phase transition sequence. The crystal structure of the Cmca phase is composed of alternate stacking puckered layers of Ge six-membered rings and Te four-membered rings along the b direction. The high density of states near the Fermi level and delocalization of electrons from the two-dimensional electron localization function indicate a strong metallic property of the Cmca phase. Electron-phonon coupling calculations indicate that the Cmca phase is superconductive below ∼4.2K at 35GPa. The simulated x-ray diffraction pattern of the Cmca phase implies that this phase might coexist with the Pnma-boat phase under high pressure. These results offer further understanding on the high-pressure structural evolution and physical properties in GeTe and other IV-VI semiconductors.

Superhard BC2N in cubic diamondlike structure

Cubic ${\mathrm{BC}}_{2}\mathrm{N}$, a superhard material with a slightly lower hardness than diamond, has been synthesized but the determination of its crystal structure has long been elusive, impeding the further understanding of pertinent physics. Here, by employing a first-principles electronic structure framework, we predicted a cubic ${\mathrm{BC}}_{2}\mathrm{N}$ crystal structure (dia-${\mathrm{BC}}_{2}\mathrm{N}$), marking it as the hitherto cubic phase among all previously proposed structures. Our simulated x-ray diffraction patterns of diamondlike ${\mathrm{BC}}_{2}\mathrm{N}$ agree with the experimental data, implying that our predicted structure is likely to be the high-symmetry ${\mathrm{BC}}_{2}\mathrm{N}$ structure synthesized in experiment. Furthermore, the estimated Vicker's hardness of this structure is 77 GPa, demonstrating its intrinsic superhard nature. Our current findings may begin to clarify the long-term unsolved crystal structure of cubic ${\mathrm{BC}}_{2}\mathrm{N}$, and they may pave the way for further design and discovery of superhard materials.

Globular Phyllosilicates of the Glauconite-Illite Series in the Cambrian and Ordovican Rocks of the Eastern Baltica (North Estonia, Western Lithuania, Western Latvia)

The mineralogical, structural and crystal-chemical features of seven samples of globular phyllosilicates of the glauconite-illite series (GPS) from the Lower Cambrian of Northern Estonia and Western Lithuania, from the Middle Cambrian of Western Latvia, and also from the Lower Ordovician of Northern Estonia and Western Latvia are considered for the first time. The Al index GPS (КAl = VIAl/ [VIFe3+ + VIAl]) varies from 0.27 to 0.59, which allows us to attribute them to the glauconite-illite series, in which GPS are represented mainly by glauconites (the Al index is КAl = 0.27–0.46) and one sample of Al-glauconite (КAl = 0.59). The content of K2O in minerals is from 7.12 to 7.90%. For the first time, the content of expandable layers (4–13%), their types (smectite, vermiculite) and the character of their alternation (R = 0, R = 2) were determined in the studied samples by simulation of experimental X-ray diffraction patterns from oriented preparations. Simulation of X-ray diffraction patterns obtained from nonoriented preparations made it possible to reveal the degree of three-dimensional order, and mean values of the unit-cell parameter b (9.056–9.094 Å) as well as the features of the distribution of their individual micaceous varieties and to establish the heterogeneity of the samples. Based on these data, the microheterogeneity of the Cambrian and Ordovician GSSs was established and compared with the heterogeneity in the previously studied Riphean GPS [Drits et al., 2013]. The obtained Rb-Sr и K-Ar ages for the Middle Cambrian and Lower Ordovician samples, as well as the earlier published dates for the Lower Cambrian samples, are “rejuvenated” compared to age limits accepted for the Cambrian and Lower Ordovician [Gradstein et al., 2020]. The dependence of the Cambrian and Lower Ordovician “rejuvenated” isotopic dates and the discovered GPS heterogeneity, as well as possible reasons for its occurrence, are discussed.

CrystalMELA: a new crystallographic machine learning platform for crystal system determination.

Determination of the crystal system and space group is the first step of crystal structure analysis. Often this turns out to be a bottleneck in the material characterization workflow for polycrystalline compounds, thus requiring manual interventions. This work proposes a new machine-learning (ML)-based web platform, CrystalMELA (Crystallography MachinE LeArning), for crystal systems classification. Two different ML models, random forest and convolutional neural network, are available through the platform, as well as the extremely randomized trees algorithm, available from the literature. The ML models learned from simulated powder X-ray diffraction patterns of more than 280 000 published crystal structures from organic, inorganic and metal-organic compounds and minerals which were collected from the POW_COD database. A crystal system classification accuracy of 70%, which improved to more than 90% when considering the Top-2 classification accuracy, was obtained in tenfold cross-validation. The validity of the trained models has also been tested against independent experimental data of published compounds. The classification options in the CrystalMELA platform are powerful, easy to use and supported by a user-friendly graphic interface. They can be extended over time with contributions from the community. The tool is freely available at https://www.ba.ic.cnr.it/softwareic/crystalmela/ following registration.

First-principles study on stability, electronic and mechanical properties of 4^3T175 carbon allotrope

We present a systemical study on the stability, electronic and mechanical properties of a sp3-bonded carbon allotrope with 4^3T175 topology. This carbon allotrope is composed of a C-centered orthorhombic unit cell with 20 atoms and is mechanically and dynamically stable over a pressure range from ambient conditions to 50 GPa. According to the calculations, 4^3T175 is an indirect band gap semiconductor with band gap of 2.84 eV and also a potential superhard material with Vickers hardness of 73 GPa. The simulated X-ray diffraction pattern can be matched to some of the diffraction peaks of those unidentified carbon phases in detonation soot samples, indicating its possible presence in these specimens. These findings yield a deeper understanding of 4^3T175 and provide a guidance to elucidate the unidentified carbon phase in the high-pressure synthesis products.

First-principles predictions of stable structure of AuAl2 under high pressure

Pressure-induced phase transformation of AuAl2 had been theoretically investigated by using crystal structure searching technique combined with first-principles calculations. The predicted orthorhombic Pbnm structure possesses a larger structural stability with pressure larger than 17 GPa, and transition pressure is consistent with experimental value. The simulated x-ray diffraction patterns of Pbnm structure are in satisfactory agreement with the experimental data. The specific density of states indicate that there are discontinuous changes of electrical resistance accompanying with phase transition, and these are in accordance with experimental observations. Moreover, phonon dispersions and elastic constants reveal that Pbnm structure has dynamical and mechanical stabilities. The directional dependence of Young's modulus was analyzed and Pbnm phase has a larger elastic anisotropy.

Theoretical Study on the Vapochromic Ni(II)-Quinonoid Complex: One-Dimensional Stacking Structure-Based Color Switching.

Vapochromic crystals of Ni(II)-quinonoid complexes were theoretically investigated using density functional theory (DFT) calculations. Kato et al. previously reported that the purple crystals of a four-coordinate Ni(II)-quinonoid complex (1P) exhibited vapochromic characteristics upon exposure to methanol gas, resulting in orange crystals of the six-coordinate methanol-bound complex (1O) [Angew. Chem., Int. Ed.2017, 56, 2345-2349]. However, the authors did not characterize the crystal structure of 1P. In the present study, we computationally predicted the crystal structure of 1P by performing a crystal structure search with classical force-field computations followed by optimization using DFT calculations. The simulated powder X-ray diffraction pattern of the DFT-optimized structure agreed with experimental observations, indicating that our predicted crystal structure is reliable. Investigation of the optimized crystal structure of 1P revealed that its color change arose from changes in its 1D-band structure, which consists of Ni 3d orbitals and quinonoid π-orbitals. Intermolecular interactions were weakened upon the binding of methanol to the Ni(II) center in 1O. Consequently, the intermolecular 3d-π interaction in 1P lowered the band gap and induced the red-shifting of the monomeric four-coordinate Ni(II)-quinonoid complex. Meanwhile, the obtained absorption spectrum of 1O closely corresponded to that of the monomeric six-coordinate Ni(II)-quinonoid complex. Our study provides a new strategy for accurately predicting molecular crystal structures and reveals a new insight into vapochromism based on band structure color switching.

Tunable Multicolor Circularly Polarized Luminescence via Co-assembly of One Chiral Electron Acceptor with Various Donors

Tunable Multicolor Circularly Polarized Luminescence via Co-assembly of One Chiral Electron Acceptor with Various Donors

A DFT study to determine the structure and composition of ε-W2B5−x

There is no consensus in the literature on the structure and composition of the ε phase of the W-B system, variously reported as WB2 and W2B5. We used ab initio calculations at two levels of theory to identify the stable crystal structure and stoichiometry of this phase. Among the sixteen structures investigated in the composition range of 67–71.4 at% B (WB2–W2B5), nine exhibited unfeasibly high formation energies; the remaining seven were dynamically stable (did not exhibit any soft phonon modes), and satisfied mechanical stability criteria. When including the thermal vibrational contribution to the free energy, all structures with the W2B5 composition lay above the convex hull, suggesting that this composition is metastable, while those with WB2 composition lay on the convex hull or within DFT precison of the convex hull. We found that four of the candidate structures exhibit negative vacancy formation energy, suggesting that the structures are unstable, or that they are naturally hypo-stoichiometric. Combining these results with a comparison of simulated and experimental x-ray and neutron diffraction patterns, we concluded that the ε phase is most likely a hypo-stochiometric W2B5−x compound with space group P63/mmc.