Wyckoff Positions Research Articles

Mechanical and electronic properties of transition metal hexa-nitrides in hexagonal structure from density functional theory calculations

We investigated structural, vibrational, mechanical, electronic, and magnetic properties of all 29 nitrogen-rich transition metal nitrides (TMNs) with a stoichiometric 1:6 (M:N) ratio in the hexagonal phase (space group: R3¯m with Wyckoff positions M (3a) and N (18 h)) by utilizing density functional theory-based calculations. Only 13 of these compounds are found to be both mechanically and vibrationally stable. Among them, FeN6 is predicted to be the hardest compound with a Vickers hardness of 22 GPa. Compounds from group 8 elements which have a valence electron concentration of 38 (FeN6, RuN6, and OsN6) are predicted to be the hardest and they also possess the highest densities. In general, hardness increases with decreasing M−M or M−N bond lengths. The calculation of local density of states and electronic band structures further suggests that all 13 stable MN6 compounds have metallic bonding character. Three compounds from group 4 elements are semiconductors, however, they are only mechanically stable. The bonding analysis reveals that hardness is primarily attributed to M−N and M−M interactions. Eight of the investigated MN6 compounds have a magnetic moment.

Delocalized Bi-tetrahedral cluster induced ultralow lattice thermal conductivity in Bi3Ir3O11

Low-frequency cluster vibration plays an important role in reducing the lattice thermal conductivity of a system. Here, we show a new type of cluster vibration called “delocalized cluster vibration” that involves a highly symmetric local structure with lone pair electrons and marked impacts on lattice thermal transport. We take a transition-metal oxide Bi3Ir3O11 (two specific Wyckoff positions for Bi: corner-Bi1 and inner-Bi2) as an example, which exhibits counterintuitive low lattice thermal conductivity in metallic materials. Based on first-principles simulations of phonon transport in the Boltzmann transport formulation, this study shows that the four fourth neighbor Bi2 atoms form a regular Bi-tetrahedral cluster (Bi24), which collectively vibrates in certain intercorrelated patterns strongly and induces low-frequency optical phonon modes (∼0.77 and ∼1.06 THz) along with low group velocities. The Bi24-related optical modes interrupt the acoustic vibrations and thus suppress the lattice thermal conductivity to an ultralow value (calculated value is 1.0 W/m·K at 300 K). Surprisingly, these Bi2–Bi2 have relatively large distances but significant interatomic force constants, indicating delocalized interactions among Bi24. This work demonstrates that the delocalized cluster vibration plays a significant role in lowering lattice thermal conductivity.

To study the synthesis and characterization of photocatalyst TiO2/SiO2 nanocomposite prepared by Co-Precipitation method

We report here the synthesis of Nanocomposites of TiO2/SiO2 by the wet chemical method i.e. Coprecipitation method. The sample of TiO2 and SiO2 and composite of TiO2/SiO2 calcined at 600 °C and were structurally analyzed by X-Ray Diffraction. The values of cell parameter, Wyckoff position, sites etc. of prepared samples were also calculated. The size of the crystal of TiO2/SiO2 nanocomposites was obtained as 33.2 nm. The visualization of crystal structure of both TiO2 and SiO2 were also discussed in this paper.

Magnetic, electric and toroidal polarization modes describing the physical properties of crystals. NdFeO3 case.

The structure and the physical phenomena that occur in a crystal can be described by using a suitable set of symmetry-adapted modes. The classification of magnetic modes in crystals presented in Fabrykiewicz et al. [Acta Cryst. (2021), A77, 327-338] is extended to a classification of electric and toroidal (anapole) modes in crystals. These three classifications are based on magnetic point groups, which are used in two contexts: (i) the magnetic point group of the magnetic crystal class and (ii) the magnetic site-symmetry point group of the Wyckoff position of interest. The classifications for magnetic, electric and toroidal modes are based on the properties of the three generalized inversions: space inversion 1, time inversion 1' and the space-and-time inversion 1'. It is emphasized that none of these three inversions is more important than the other two. A new notation for symmetry operation symbols and magnetic point group symbols is proposed; each operation is presented as a product of one proper rotation and one generalized inversion. For magnetic, electric and toroidal orderings there are 64 modes: three pure ferro(magnetic/electric/toroidal) modes, 13 mixed ferro(magnetic/electric/toroidal) and antiferro(magnetic/electric/toroidal) modes, and 48 pure antiferro(magnetic/electric/toroidal) modes. The proposed classification of modes leads to useful observations: the electric and toroidal modes have many symmetry limitations similar to those already known for the magnetic modes, e.g. a continuous reorientation of the magnetic or electric or toroidal moments is possible only in triclinic or monoclinic symmetry. An antiferro(magnetic/electric/toroidal) ordering with a weak perpendicular ferro(magnetic/electric/toroidal) component is possible only in monoclinic or orthorhombic symmetry. The general classifications of magnetic, electric and toroidal modes are presented for the case of NdFeO3.

The element occupation preference of μ phase in ternary Ni-Cr-Mo model superalloy

Topologically close-packed (TCP) phases seriously endanger the properties of Superalloy. Investigating the microstructure of the TCP phases will provide a crystallographic reference for the design of superalloys with better properties. The μ phase is a common TCP phase in superalloys. It belongs to the space group R-3m, and has a hexagonal structure with five Wyckoff sites of 3a, 18h, 6c1, 6c2 and 6c3. In this paper, occupation of the three kinds of atoms at five Wyckoff sites of the μ phase in Ni-Cr-Mo model superalloy was determined using aberration-corrected High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy (HAADF-STEM), QSTEM software simulation and first-principles calculations. It was found that Mo atoms with larger size and smaller electronegativity tend to occupy 6c3, 6c1 and 6c2 sites in order of priority. Ni atoms mainly occupy the sites with coordination number (CN) of 12 at 3a and 18 h, and 3a sites contain more Cr atoms than 18 h sites.

Annealing‐Free Thioantimonate Argyrodites with High Li‐Ion Conductivity and Low Elastic Modulus

AbstractAlthough Li‐ion superconducting sulfides have been developed as solid electrolytes (SEs) in all‐solid‐state batteries, their high deformability, which is inherently beneficial for room‐temperature compaction, is overlooked and sacrificed. To solve this dilemmatic task, herein, highly deformable Li‐ion superconductors are reported using an annealing‐free process. The target thioantimonate, Li5.2Si0.2Sb0.8S4Br0.25I1.75, comprising bimetallic tetrahedra and bi‐halogen anions is synthesized by two‐step milling tuned for in situ crystallization, and exhibits excellent Li‐ion conductivity (σion) of 13.23 mS cm−1 (averaged) and a low elastic modulus (E) of 12.51 GPa (averaged). It has a cubic argyrodite phase of ≈57.39% crystallinity with a halogen occupancy of ≈90.67% at the 4c Wyckoff site. These increased halogen occupancy drives the Li‐ion redistribution and the formation of more Li vacancies, thus facilitating Li‐ion transport through inter‐cage pathway. Also, the facile annealing‐free process provides a unique glass‐ceramic structure advantageous for high deformability. These results represent a record‐breaking milestone from the combined viewpoint of σion and E among promising SEs. Electrochemical characterization, including galvanostatic cycling tests for 400 h, reveals that this material displays reasonable electrochemical stability and cell performance (150.82 mAh g−1 at 0.1C). These achievements shed light on the synthesis of practical SEs suffice both σion and E requirements.

Defective lithium titanate oxide with stable cycling over a wide voltage window

Spinel lithium titanate oxide (Li4Ti5O12, LTO) is a promising electrode material with a maximum capacity of 295 mAh·g−1 that accommodate 5Li ions at 0.01 V. However, upon accepting 2Li ions at Wyckoff site 8a at low potentials, its capacity and stability significantly decrease because of the short Li-Li distance. To address this issue, we synthesize defective LTO (d-LTO) nanoparticles via the calcination of porous LTO. Notably, the discharge capacity of d-LTO is close to the theoretical value, and does not lead to structural decomposition in the voltage range of 3.0–0.01 V. d-LTO retain 95 % of their initial capacity after 100 cycles with a coulombic efficiency of 99.8 %. In situ synchrotron PXRD analysis and the density functional theory calculations unequivocally demonstrate the high stability of d-LTO during cyclic charge/discharge. Therefore, this simple strategy will provide insight into novel Li-ion electrode materials with high capacity and long-term stability.

Mixed valence nature of the Ce4fstate inCeCo5based on spin-polarizedDFT+DMFTcalculations

Cerium-based intermetallics are currently attracting much attention as highly promising alternatives to conventional permanent magnets that contain a scarce rare earth element like neodymium. In the present work we apply a charge fully self-consistent approach combining density functional theory and dynamical mean-field theory (DFT $+$ DMFT) to investigate the magnetization and electronic structure of the ${\mathrm{CeCo}}_{5}$ system. We treat simultaneously the correlation effects in Ce-$4f$ and Co-$3d$ orbitals while taking the spin polarization into account. The calculated magnetic moment corresponding to the Ce-$4f$ shell using the DFT $+$ DMFT method is found to be drastically reduced as compared to the DFT results. Moreover, the Ce-$4f$ valence state fluctuations are evaluated and compared within ${\mathrm{CeCo}}_{5}$ and $\mathrm{Ce}{({\mathrm{Co}}_{0.8}{\mathrm{Cu}}_{0.2})}_{5}$ on account of the trivalent Ce in ${\mathrm{CeCu}}_{5}$. Regarding the Cu substitutions at two Wyckoff positions of Co (2c and 3g), the substitution at 3g sites slightly enhances the magnetic moment of Ce while the substitution at 2c sites leads to nearly vanishing Ce and Co moments. Such a contrast may contribute to the experimentally reported nonmonotonic change of the magnetic anisotropy with increasing Cu alloying content in $\mathrm{Ce}{({\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x})}_{5}$ alloys.

Structural, elastic, thermodynamic, electronic and magnetic characteristics of FeNbScZ (Z = al, Ga, Ge, Si) heusler alloys: A DFT study

Physical characteristics of Fe based quaternary Heusler alloys (QHAs) FeNbScZ (Z = Al, Ga, Ge, Si) are explored using full potential linearized augmented plane wave (FP-LAPW) method with Generalized Gradient Approximation (GGA) approach. Geometry optimization is determined by using three different Wyckoff positions and type III found to be the most stable for all alloys. Magnetic phase optimization showed that ferro-magnetic (FM) phase is the most stable for all combinations of reported alloys. The mechanical stability is confirmed via elastic parameters which inferred that all alloys possess ductile nature. Debye temperature and melting temperature (Tmelt) are also determined. The electronic band structures and density of states graphs clearly showed that these alloys possess the half metallic character. Calculated total magnetic moment (Mtot) values followed the Slater Pauling rule (SPR). Further bonding and anti-bonding states are also discussed.

Spin-momentum locking from topological quantum chemistry: Applications to multifold fermions

In spin-orbit coupled crystals, symmetries can protect multifold degeneracies with large Chern numbers and Brillouin zone spanning topological surface states. In this work, we explore the extent to which the nontrivial topology of chiral multifold fermions impacts the spin texture of bulk states. To do so, we formulate a definition of spin-momentum locking in terms of reduced density matrices. Using tools from the theory of topological quantum chemistry, we show how the reduced density matrix can be determined from the knowledge of the basis orbitals and band representation forming the multifold fermion. We show how onsite spin-orbit coupling, crystal-field splitting, and Wyckoff position multiplicity compete to determine the spin texture of states near chiral fermions. We compute the spin texture of multifold fermions in several representative examples from space groups $P432$ (207) and $P{2}_{1}3$ (198). We show that the winding number of the spin around the Fermi surface can take many different integer values, from zero all the way to $\ifmmode\pm\else\textpm\fi{}7$. Finally, we conclude by showing how to apply our theory to real materials using the example of PtGa in space group $P{2}_{1}3$.

Hydrogen-Induced Order–Disorder Effects in FePd3

Binary intermetallic compounds, such as FePd3, attract interests due to their physical, magnetic and catalytic properties. For a better understanding of their hydrogenation properties, both ordered FePd3 and disordered Fe0.25Pd0.75 are studied by several in situ methods, such as thermal analysis, X-ray powder diffraction and neutron powder diffraction, at moderate hydrogen pressures up to 8.0 MPa. FePd3 absorbs small amounts of hydrogen at room temperature and follows Sieverts’ law of hydrogen solubility in metals. [Pd6] octahedral voids are filled up to 4.7(9)% in a statistical manner at 8.00(2) MPa, yielding the hydride FePd3H0.047(9). This is accompanied by decreasing long-range order of Fe and Pd atoms (site occupancy factor of Fe at Wyckoff position 1a decreasing from 0.875(3) to 0.794(4)). This trend is also observed during heating, while the ordered magnetic moment decreases up to the Curie temperature of 495(8) K. The temperature dependences of the magnetic moments of iron atoms in FePd3 under isobaric conditions (p(D2) = 8.2(2) MPa) are consistent with a 3D Ising or Heisenberg model (critical parameter β = 0.28(5)). The atomic and magnetic order and hydrogen content of FePd3 show a complex interplay.

Triangular Magnet Emergent from Noncentrosymmetric Sr0.94Mn0.86Te1.14O6 Single Crystals.

We report the successful growth of high-quality single crystals of Sr0.94Mn0.86Te1.14O6 (SMTO) using a self-flux method. The structural, electronic, and magnetic properties of SMTO are investigated by neutron powder diffraction (NPD), single-crystal X-ray diffraction (SCXRD), thermodynamic, and nuclear magnetic resonance techniques in conjunction with density functional theory calculations. NPD unambiguously determined octahedral (trigonal antiprismatic) coordination for all cations with the chiral space group P312 (no. 149), which is further confirmed by SCXRD data. The Mn and Te elements occupy distinct Wyckoff sites, and minor anti-site defects were observed in both sites. X-ray photoelectron spectroscopy reveals the existence of mixed valence states of Mn in SMTO. The magnetic susceptibility and specific heat data evidence a weak antiferromagnetic order at TN = 6.6 K. The estimated Curie-Weiss temperature θCW = -21 K indicates antiferromagnetic interaction between Mn ions. Furthermore, both the magnetic entropy and the 125Te nuclear spin-lattice relaxation rate showcase that short-range spin correlations persist well above the Néel temperature. Our work demonstrates that Sr0.94(2)Mn0.86(3)Te1.14(3)O6 single crystals realize a noncentrosymmetric triangular antiferromagnet.

Fine details of sixfold Dirac fermions in pyrite-structured PdSb2

We report detailed angle-resolved photoemission measurements on the electronic structure of an unconventional multifold Dirac fermionic semimetal ${\mathrm{PdSb}}_{2}$ with a pyrite structure. By exploiting the photon energy and polarization dependence of the matrix element in photoemission intensity and by comparing photoemission data with ab initio band calculations, we experimentally identify the exact electronic structure, including the orbital characters of the electron pockets at the $R$ point in the Brillouin zone of ${\mathrm{PdSb}}_{2}$. Each electron pocket and hole-pocket-like structure consists of three doubly degenerate parabolic bands, respectively, which cross one another at the $R$ point, forming a sixfold Dirac fermion. The overall electronic structure is consistent with the band calculations, but the gap size between two sextuple points is very sensitive to the Wyckoff position of Sb atoms, which is a result of the competition between the band energies and crystal symmetries.

Probing the surface active sites of Ce1−xNixO2-δ for catalytic reduction of NO

Understanding the underlying mechanism of NO reduction on supported metal catalysts has been a long standing challenge. Herein, we report an integrated experimental cum theoretical probe to elucidate the surface active sites vis à vis the plausible reaction mechanism to comprehend the catalytic reduction of NO over solid solutions of Ce1−xNixO2-δ. In the as-prepared solid solutions of phase pure Ce1−xNixO2-δ, minor component of Ni2+ substituted Ce4+ at the Wyckoff sites 4a resulting in a uniform distribution Ni2+ within the crystal lattice of the parent fluorite CeO2. The as-prepared material exhibited a higher catalytic efficacy towards NO reduction in comparison with the Ni or NiO dispersed over CeO2 support. The catalytic efficacy was further enhanced with reduced Ce1−xNixO2-δ due to the presence of excess oxygen vacancies and surface hydroxyl species. The important role of oxygen vacancies and surface hydroxyl species as active sites in the reaction mechanism was further corroborated by DFT calculations. A generalized kinetic model was developed that could identify the rate determining step for the NO reduction mechanism by H2 over supported metal catalysts Ce1−xNixO2-δ.

A novel high entropy perovskite oxide with co-substitution in A and B sites (Ca1/3Sr1/3Ba1/3)(Y1/4Zr1/2Nb1/4)O3 design, synthesis and structural characterization

A novel high-entropy perovskite oxide (HEPO) (Ca1/3Sr1/3Ba1/3)(Y1/4Zr1/2Nb1/4)O3 (CSBYZN) was designed and synthesized by solid-state reaction method by the use of CaCO3, SrCO3, BaCO3, Y2O3, ZrO2 and Nb2O5. Due to the substitution of the cations at both the A and B sites, the configuration entropy of CSBYZN was higher than that of other HEPOs with only one Wyckoff site (A or B site) substituted with 5 elements. The crystal structure of CSBYZN was identified as a cubic structure of the Pm-3m space group by Rietveld refinement. The measured lattice constant a = 4.1242 Å is similar to the value obtained by using the empirical formula (acal = 4.1229 Å). It was proved that the lattice constant of HEPOs can be predicted by the empirical formula. This study provides a new thought for the design of novel HEPOs.

Thermodynamic modeling of the Pd–Zn system with uncertainty quantification and its implication to tailor catalysts

Pd–Zn intermetallic catalysts show encouraging combinations of activity and selectivity on well-defined active site ensembles. Thermodynamic description of the Pd–Zn system, delineating phase boundaries and enumerating site occupancies within intermediate alloy phases, is essential to determining the ensembles of Pd–Zn atoms as a function of composition and temperature. Combining the present extensive first-principles calculations based on density functional theory (DFT) and available experimental data, the Pd–Zn system was remodeled using the CALculation of PHAse Diagrams (CALPHAD) approach. High throughput modeling tools with uncertainty quantification, i.e., ESPEI and PyCalphad, were incorporated in the phase analysis. The site occupancies across the γ phase composition region were given special attention. A four-sublattice model was used for the γ phase owing to its four Wyckoff positions, i.e., the outer tetrahedral (OT) site 8c, the inner tetrahedral (IT) site 8c, the octahedral (OH) site 12e, and the cuboctahedral (CO) site 24g. The site fractions of Pd and Zn calculated from the present thermodynamic model show the occupancy preference of Pd in the OT and OH sublattices in agreement with experimental observations. The force constants obtained from DFT-based phonon calculations further supports the tendency of Pd occupying the OH sublattice compared with the IT and CO sublattice. The catalytic ensembles changing from Pd monomers (Pd1) to trimers (Pd3) on the surface of γ phase are attributed to the increase of Pd occupancy in the OH sublattice.

Silver–Bismuth Halide Double Salts for Lead‐Free Photovoltaics: Insights from Symmetry‐Based Modeling

Ag/Bi halide double salts, also called rudorffites, constitute a promising path to achieve low‐cost, high‐efficiency lead‐free optoelectronic devices, in particular solar cells. These materials present tunable gaps within the visible range, high short‐circuit currents, and interesting efficiencies in outdoor and indoor devices. Herein, a combination of symmetry analysis and first‐principles calculations is used to explore the structural, electronic, and optical properties of prototypical rudorffites solar cell absorbers AgBiI4 and Ag3BiI6. The challenges to model those ternary materials are first established. It is shown that Ag/Bi double salts cannot be modeled as random alloys. Second, a Wyckoff position splitting method is developed leading to the generation of model structures, which are unique for each compound, and agrees with experimental structural data. These structures are used to establish the optoelectronic properties of AgBiI4 and Ag3BiI6. Finally, the ideal photovoltaic performance of the materials is predicted through the spectral limited maximum efficiency approach. It is shown that AgBiI4 presents a slightly higher potential for solar cell applications, and the realized devices are mostly limited by the low open‐circuit voltage. The structural models developed here can help unveiling complex properties of the materials and explore substitutional engineering within halide double salts.

Two-dimensional obstructed atomic insulators with fractional corner charge in the MA2Z4 family

According to topological quantum chemistry (TQC), a class of electronic materials has been called obstructed atomic insulators (OAIs), in which a portion of valence electrons necessarily have their centers located on some empty Wyckoff positions (WPs) without atom occupation in the lattice. The obstruction of centering these electrons coinciding with their host atoms is nontrivial and results in metallic boundary states when the boundary is properly cut. Here, on the basis of first-principles calculations in combination with TQC analysis, we propose two-dimensional ${MA}_{2}{Z}_{4}$ $(M=\mathrm{Cr}, \mathrm{Mo}, and \mathrm{W}; A=\mathrm{Si} \mathrm{and} \mathrm{Ge}; Z=\mathrm{N}, \mathrm{P}, \mathrm{and} \mathrm{As})$ monolayers are all OAIs. A typical case is the recently synthesized ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ (${\ensuremath{\alpha}}_{1}\text{\ensuremath{-}}{\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$). Although both ${\ensuremath{\alpha}}_{1}$- and ${\ensuremath{\alpha}}_{2}\text{\ensuremath{-}}{\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ monolayers are topological trivial insulators, it has valence electrons centering empty WPs and the in-gap corner states at the three vertices of triangle-shaped nanodisk samples respecting ${C}_{3}$ rotation symmetry, which can be explained by the filling anomaly of electrons. In addition, the ${\ensuremath{\alpha}}_{2}\text{\ensuremath{-}}{\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ monolayer exhibits unique OAI-induced metallic edge states along the $(1\overline{1})$ edge. The readily synthesized ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ is quite stable and has a large bulk bandgap of 1.94 eV, which makes the identification of these edge and corner states most possible for experimental clarification.

Ordered metal substitution in Ti3AlC2 and the effect on tribological behaviors in a wide temperature range

In this work, tribological properties of Ti3AlC2, Cr2TiAlC2, and Mo2TiAlC2 MAX are evaluated in a wide temperature range of 25–800 ℃. By replacing the 4 f Wyckoff site Ti atoms of Ti3AlC2 with Cr or Mo, the MAXs deliver lower coefficient of friction (COF) than Ti3AlC2. Interestingly, as confirmed by the morphological, structural, and chemical analyses, the two MAXs are applicable in different temperatures. For Cr2TiAlC2, the lowest wear rate is 2.30 × 10−7 mm3 N−1 m−1 at 800 ℃, while the lowest wear rate of Mo2TiAlC2 is achieved at room temperature of 3.83 × 10−7 mm3 N−1 m−1. These distinct tribological behaviors are ascribed to the altered M-A and M-C bindings, as well as the properties of the produced oxides.

Deep Learning Classification of Crystal Structures Utilizing Wyckoff Positions

In materials science, crystal lattice structures are the primary metrics used to measure the structure–property paradigm of a crystal structure. Crystal compounds are understood by the number of various atomic chemical settings, which are associated with Wyckoff sites. In crystallography, a Wyckoff site is a point of conjugate symmetry. Therefore, features associated with the various atomic settings in a crystal can be fed into the input layers of deep learning models. Methods to analyze crystals using Wyckoff sites can help to predict crystal structures. Hence, the main contribution of our article is the classification of crystal classes using Wyckoff sites. The presented model classifies crystals using diffraction images and a deep learning method. The model extracts feature groups including crystal Wyckoff features and crystal geometry. In this article, we present a deep learning model to predict the stage of the crystal structure–property. The lattice parameters and the structure–property commotion values are used as inputs into the deep learning model for training. The structure–property value of a crystal with a lattice width value of one-half millimeter on average is used for learning. The model attains a considerable increase in speed and precision for the real structure–property prediction. The experimental results prove that our proposed model has a fast learning curve, and can have a key role in predicting the structure–property of compound structures.