The Limited Predictive Power of the Pauling Rules

The Fundamental Disorder Unit in (Si, P)-(O, N) Networks

This study presents the synthesis and characterization of oxonitridosilicate phosphates Sr3SiP3O2N7, Sr5Si2P4ON12, and Sr16Si9P9O7N33 as the first of their kind. These compounds were synthesized under high-temperature (1400 °C) and high-pressure (3 GPa) conditions. A unique structural feature is their common fundamental building unit, a vierer single chain of (Si, P)(O, N)4 tetrahedra. All tetrahedra comprise substitutional disorder which is why we refer to it as the fundamental disorder unit (FDU). We classified four different FDU motifs, revealing systematic bonding patterns. Including literature known Sr5Si2P6N16, three of the four patterns were found in the presented compounds. Common techniques like single-crystal X-ray diffraction (SCXRD), elemental analyses, and 31P nuclear magnetic resonance (NMR) spectroscopy were utilized for structural analysis. Additionally, low-cost crystallographic calculations (LCC) provided insights into the structure of Sr16Si9P9O7N33 where NMR data were unavailable due to the lack of bulk samples. The optical properties of these compounds, when doped with Eu2+, were investigated using photoluminescence excitation (PLE), photoluminescence (PL) measurements, and density functional theory (DFT) calculations. Factors influencing the emission properties, including thermal quenching mechanisms, were discussed. This research reveals the new class of oxonitridosilicate phosphates with unique systematic structural features that offer potential for theoretical studies of luminescence and band gap tuning in insulators.

Facilitating Layered Oxide Cathodes Based on Orbital Hybridization for Sodium-Ion Batteries: Marvelous Air Stability, Controllable High Voltage, and Anion Redox Chemistry

Layered oxides have become the research focus of cathode materials for sodium-ion batteries (SIBs) due to the low cost, simple synthesis process, and high specific capacity. However, the poor air stability, unstable phase structure under high voltage, and slow anionic redox kinetics hinder their commercial application. In recent years, the concept of manipulating orbital hybridization has been proposed to simultaneously regulate the microelectronic structure and modify the surface chemistry environment intrinsically. In this review, the hybridization modes between atoms in 3d/4d transition metal (TM) orbitals and O 2p orbitals near the region of the Fermi energy level (EF) are summarized based on orbital hybridization theory and first-principles calculations as well as various sophisticated characterizations. Furthermore, the underlying mechanisms are explored from macro-scale to micro-scale, including enhancing air stability, modulating high working voltage, and stabilizing anionic redox chemistry. Meanwhile, the origin, formation conditions, and different types of orbital hybridization, as well as its application in layered oxide cathodes are presented, which provide insights into the design and preparation of cathode materials. Ultimately, the main challenges in the development of orbital hybridization and its potential for the production application are also discussed, pointing out the route for high-performance practical sodium layered oxide cathodes.

Hg4(Te2O5)(SO4): A Giant Birefringent Sulfate Crystal Triggered by a Highly Selective Cation

Sulfate crystals are often criticized for their low birefringence. The small anisotropic SO4 group is becoming the biggest bottleneck hindering the application of sulfates in optical functional materials. In this study, we report a new method to significantly enhance the birefringence of sulfates. The title compound increases the birefringence recording of sulfates to 0.542@546 nm, which is significantly larger than that of the commercial birefringent crystal of TiO2 (0.306@546.1 nm). At the infrared wavelength, the birefringence of Hg4(Te2O5)(SO4) can be up to 0.400@1064 nm, which is also much larger than the infrared birefringent crystal of YVO4 (0.209@1064 nm). In addition, it also has a wide transparency range, high thermal stability, and excellent environmental stability, making it a potential birefringent material. Hg4(Te2O5)(SO4) features a novel two-dimensional layered structure composed of [Hg4(Te2O5)]2+ layers separated by isolated (SO4)2- tetrahedra. This compound was designed by introducing a highly selective cation in a tellurite sulfate system. The low valence low coordination cations connect with tellurite groups only, making the sulfate isolated in the structure. The steric repulsive action of the isolated SO4 tetrahedra may regulate the linear and lone pair groups arranged in a way that favors large birefringence. This method can be proven by theoretical calculations. PAWED studies showed that the large birefringence originated from the synergistic effect of (Hg2O2)2-, (Te2O5)2-, and (SO4)2- units, with a contribution ratio of 42.17, 37.92, and 19.88%, respectively. Our work breaks the limitation of low birefringence in sulfates and opens up new possibilities for their application as birefringent crystals.

Rb3MgB5O10 and LiBaAl(BO3)2: covalent tetrahedra MO4-containing borates with deep-ultraviolet cutoff edges

Borates are favored by materials scientists and chemists because of the significant electronegativity difference between B and O atoms and their flexible assembly modes resulting in abundant structures and excellent properties. For the design of deep-ultraviolet (DUV) optical crystals with excellent macroscopic performance, it is crucial to choose appropriate cations and anionic groups and microscopically reasonable assembly patterns. Herein, by introducing covalent tetrahedra ([MO4], M = Mg, Al), two new mixed alkali metal and alkaline earth metal borates, Rb3MgB5O10 and LiBaAl(BO3)2, were synthesized using the melt method and high-temperature solution method. They contain M-B-O two-dimensional (2D) layers (2∞[MgB5O10] and 2∞[Al(BO3)2], respectively) composed of isolated B-O groups ([B5O10]5- and [BO3]3-, respectively) and metal-centered tetrahedral connectors ([MgO4]6- and [AlO4]5-, respectively). Combining experiments and theoretical calculations shows that the two compounds have short cutoff edges (<200 nm) and moderate birefringences. Further analysis manifests that the isolated [MO4] covalent tetrahedra can optimize the arrangement of anion groups, guarantee the balanced optical properties of materials, and point out the direction for further exploration of novel borate structures.

New Halide-Based Sodium-Ion Conductors Na3Y2Cl9 Inversely Designed by Building Block Construction

Due to the excellent ionic conductivity and compatibility with high-voltage cathodes, halide-based superionic conductors as promising electrolytes have received widespread attention. A series of halide-based conductors, including Na₃YCl₆, are investigated aiming to find new solid electrolytes for sodium-ion batteries. However, Na₃YCl₆ with high ionic conductivity is meta-stable in thermostability while the stable phase exhibits poor ionic transport properties. In this work, we find that the coplanar formed anionic group (Y₂Cl₉)^3- is the result of a combination of the structural features of the fast ion phase and stable phase of Na₃YCl₆ by systematic analysis of crystal structures. Aiming to find fast sodium-ion conductors, the three-step structure construction method using functional (Y₂Cl₉)^3- groups as building blocks is proposed, and three new crystal structures in the composition of Na₃Y₂Cl₉ with the space group of P6₃, Cc, and R32 are obtained. Na⁺ transport properties, thermostability, and electrochemical window of these structures with various symmetries are investigated by first-principles calculation methods. The results show that the principle to inverse design crystal structures of halides by basic blocks, e.g., anion groups and mobile cations, is proven to be effective and successful. For P6₃-Na₃Y₂Cl₉ with outstanding transport properties, the simulation results indicate that its superionic behavior is attributed to the coherent diffusion connecting two directions. The synchronization of the migration pathways along the ab plane and the migration pathways along the c direction promotes the Na ion conductivity in Na₃Y₂Cl₉. Our research will promote the understanding of the transport mechanism in halide-based electrolytes, and the structure construction method based on functional basic building blocks and special stacking modes will accelerate the inverse design of inorganic crystal structures.

Crystal structure, electronic structure, and optical properties of the novel Li4CdGe2S7, a wide-bandgap quaternary sulfide with a polar structure derived from lonsdaleite

The novel quaternary thiogermanate Li4CdGe2S7 (tetralithium cadmium digermanium heptasulfide) was discovered from a solid-state reaction at 750 °C. Single-crystal X-ray diffraction data were collected and used to solve and refine the structure. Li4CdGe2S7 is a member of the small, but growing, class of I4–II–IV2–VI7 diamond-like materials. The compound adopts the Cu5Si2S7 structure type, which is a derivative of lonsdaleite. Crystallizing in the polar space group Cc, Li4CdGe2S7 contains 14 crystallographically unique ions, all residing on general positions. Like all diamond-like structures, the compound is built of corner-sharing tetrahedral units that create a relatively dense three-dimensional assembly. The title compound is the major phase of the reaction product, as evidenced by powder X-ray diffraction and optical diffuse reflectance spectroscopy. While the compound exhibits a second-harmonic generation (SHG) response comparable to that of the AgGaS2 (AGS) reference material in the IR region, its laser-induced damage threshold (LIDT) is over an order of magnitude greater than AGS for λ = 1.064 µm and τ = 30 ps. Bond valence sums, global instability index, minimum bounding ellipsoid (MBE) analysis, and electronic structure calculations using density functional theory (DFT) were used to further evaluate the crystal structure and electronic structure of the compound and provide a comparison with the analogous I2–II–IV–VI4 diamond-like compound Li2CdGeS4. Li4CdGe2S7 appears to be a better IR nonlinear optical (NLO) candidate than Li2CdGeS4 and one of the most promising contenders to date. The exceptional LIDT is likely due, at least in part, to the wider optical bandgap of ∼3.6 eV.

Persona of Transition Metal Ions in Solids: A Statistical Learning on Local Structures of Transition Metal Oxides

The local structure of a transition metal (TM) ion is a function of cation elements and valence states. More than that, in this work, by employing a trove of first-principles data of TM oxides, the local structures of TM cations are statistically analyzed to extract detailed information about cation site preference, bond length, site structural distortion, and cation magnetization. It is found that cation radius alone poorly describes the local structure of a transition metal oxide, while the statistics of coordination number as well as the TMO bond length distribution, especially that of the 3d TMs, can provide comprehensive knowledge for understanding the behavior of TM elements. Based on these statistics, the interplay of site distortion due to the Jahn-Teller effect, cation site similarity, and a new set of ionic radii are all obtained to chart the "persona" of transition metal ions in solids.

Li6.58Na7.43Sr4(B9O18)(B12O24)Cl: Unprecedented combination of the largest two highly polymerized isolated B-O Clusters with novel isolated B9O18 FBB

A new borate, Li6.58Na7.43Sr4(B9O18)(B12O24)Cl (LNSBOC), is successfully obtained by spontaneous crystallization method in an open system. LNSBOC crystallizes in a hexagonal crystal system with the centrosymmetric space group of P63/m,...

Cu4MnGe2S7 and Cu2MnGeS4: two polar thiogermanates exhibiting second harmonic generation in the infrared and structures derived from hexagonal diamond

The new, quaternary diamond-like semiconductor (DLS) Cu₄MnGe₂S₇ was prepared at high-temperature from a stoichiometric reaction of the elements under vacuum. Single crystal X-ray diffraction data were used to solve and refine the structure in the polar space group Cc. Cu₄MnGe₂S₇ features [Ge₂S₇]^6- units and adopts the Cu₅Si₂S₇ structure type that can be considered a derivative of the hexagonal diamond structure. The DLS Cu₂MnGeS₄ with the wurtz-stannite structure was similarly prepared at a lower temperature. The achievement of relatively phase-pure samples, confirmed by X-ray powder diffraction data, was nontrival as differential thermal analysis shows an incongruent melting behaviour for both compounds at relatively high temperature. The dark red Cu₂MnGeS₄ and Cu₄MnGe₂S₇ compounds exhibit direct optical bandgaps of 2.21 and 1.98 eV, respectively. The infrared (IR) spectra indicate potentially wide windows of optical transparency up to 25 μm for both materials. Using the Kurtz-Perry powder method, the second-order nonlinear optical susceptibility, χ⁽²⁾, values for Cu₂MnGeS₄ and Cu₄MnGe₂S₇ were estimated to be 16.9 ± 2.0 pm V^-1 and 2.33 ± 0.86 pm V^-1, respectively, by comparing with an optical-quality standard reference material, AgGaSe₂ (AGSe). Cu₂MnGeS₄ was found to be phase matchable at λ = 3100 nm, whereas Cu₄MnGe₂S₇ was determined to be non-phase matchable at λ = 1600 nm. The weak SHG response of Cu₄MnGe₂S₇ precluded phase-matching studies at longer wavelengths. The laser-induced damage threshold (LIDT) for Cu₂MnGeS₄ was estimated to be ∼0.1 GW cm^-2 at λ = 1064 nm (pulse width: τ = 30 ps), while the LIDT for Cu₄MnGe₂S₇ could not be ascertained due to its weak response. The significant variance in NLO properties can be reasoned using the results from electronic structure calculations.

Using collective knowledge to assign oxidation states of metal cations in metal-organic frameworks

Knowledge of the oxidation state of metal centres in compounds and materials helps in the understanding of their chemical bonding and properties. Chemists have developed theories to predict oxidation states based on electron-counting rules, but these can fail to describe oxidation states in extended crystalline systems such as metal-organic frameworks. Here we propose the use of a machine-learning model, trained on assignments by chemists encoded in the chemical names in the Cambridge Structural Database, to automatically assign oxidation states to the metal ions in metal-organic frameworks. In our approach, only the immediate local environment around a metal centre is considered. We show that the strategy is robust to experimental uncertainties such as incorrect protonation, unbound solvents or changes in bond length. This method gives good accuracy and we show that it can be used to detect incorrect assignments in the Cambridge Structural Database, illustrating how collective knowledge can be captured by machine learning and converted into a useful tool.

Triple-Vertex Linkage of (BO4 )-Tetrahedra in a Borosulfate: Synthesis, Crystal Structure, and Quantum-Chemical Investigation of Sr[B3 O(SO4 )4 (SO4 H)]

Borosulfates are classified as silicate analogue materials. The number of crystallographically characterized compounds is still limited, whereas the structural diversity is already impressive. The anionic substructures of borosulfates exhibit vertex-connected (BO₄ )- and (SO₄ )-tetrahedra, whereas bridging between two (SO₄ )- or even between two (BO₄ )-tetrahedra is scarce. The herein presented compound Sr[B₃ O(SO₄ )₄ (SO₄ H)] is the first borosulfate with a triple-vertex linkage of three (BO₄ ) tetrahedra via one common oxygen atom. DFT calculations complement the experimental studies. Bader charges (calculated for all atoms) as well as charge-density calculations give hint to the electron distribution within the anionic substructure and density-of-states calculations support the interpretation of the bonding situation.

Structure motif-centric learning framework for inorganic crystalline systems

Incorporation of physical principles in a machine learning (ML) architecture is a fundamental step toward the continued development of artificial intelligence for inorganic materials. As inspired by the Pauling's rule, we propose that structure motifs in inorganic crystals can serve as a central input to a machine learning framework. We demonstrated that the presence of structure motifs and their connections in a large set of crystalline compounds can be converted into unique vector representations using an unsupervised learning algorithm. To demonstrate the use of structure motif information, a motif-centric learning framework is created by combining motif information with the atom-based graph neural networks to form an atom-motif dual graph network (AMDNet), which is more accurate in predicting the electronic structures of metal oxides such as bandgaps. The work illustrates the route toward fundamental design of graph neural network learning architecture for complex materials by incorporating beyond-atom physical principles.

Symmetry relations in wurtzite nitrides and oxide nitrides and the curious case of Pmc21

Binary and multinary nitrides in a wurtzitic arrangement are very interesting semiconductor materials. The group–subgroup relationship between the different structural types is established.

Binary III–V nitrides such as AlN, GaN and InN in the wurtzite-type structure have long been considered as potent semiconducting materials because of their optoelectronic properties, amongst others. With rising concerns over the utilization of scarce elements, a replacement of the trivalent cations by others in ternary and multinary nitrides has led to the development of different variants of nitrides and oxide nitrides crystallizing in lower-symmetry variants of wurtzite. This work presents the symmetry relationships between these structural types specific to nitrides and oxide nitrides and updates some prior work on this matter. The non-existence of compounds crystallizing in Pmc2₁, formally the highest subgroup of the wurtzite type fulfilling Pauling’s rules for 1:1:2 stoichiometries, has been puzzling scientists for a while; a rationalization is given, from a crystallographic basis, of why this space group is unlikely to be adopted.

Benchmarking Coordination Number Prediction Algorithms on Inorganic Crystal Structures

Coordination numbers and geometries form a theoretical framework for understanding and predicting materials properties. Algorithms to determine coordination numbers automatically are increasingly used for machine learning (ML) and automatic structural analysis. In this work, we introduce MaterialsCoord, a benchmark suite containing 56 experimentally derived crystal structures (spanning elements, binaries, and ternary compounds) and their corresponding coordination environments as described in the research literature. We also describe CrystalNN, a novel algorithm for determining near neighbors. We compare CrystalNN against seven existing near-neighbor algorithms on the MaterialsCoord benchmark, finding CrystalNN to perform similarly to several well-established algorithms. For each algorithm, we also assess computational demand and sensitivity toward small perturbations that mimic thermal motion. Finally, we investigate the similarity between bonding algorithms when applied to the Materials Project database. We expect that this work will aid the development of coordination prediction algorithms as well as improve structural descriptors for ML and other applications.

Metal-Metal Bond in the Light of Pauling's Rules

About 70 years ago, in the framework of his theory of chemical bonding, Pauling proposed an empirical correlation between the bond valences (or effective bond orders (BOs)) and the bond lengths. Till now, this simple correlation, basic in the bond valence model (BVM), is widely used in crystal chemistry, but it was considered irrelevant for metal-metal bonds. An extensive analysis of the quantum chemistry data computed in the last years confirms very well the validity of Pauling's correlation for both localized and delocalized interactions. This paper briefly summarizes advances in the application of the BVM for compounds with TM-TM bonds (TM = transition metal) and provides further convincing examples. In particular, the BVM model allows for very simple but precise calculations of the effective BOs of the TM-TM interactions. Based on the comparison between formal and effective BOs, we can easily describe steric and electrostatic effects. A possible influence of these effects on materials stability is discussed.

Zero-Dimensional Hybrid Organic-Inorganic Indium Bromide with Blue Emission

Low-dimensional hybrid organic-inorganic metal halides have received increased attention because of their outstanding optical and electronic properties. However, the most studied hybrid compounds contain lead and have long-term stability issues, which must be addressed for their use in practical applications. Here, we report a new zero-dimensional hybrid organic-inorganic halide, RInBr₄, featuring photoemissive trimethyl(4-stilbenyl)methylammonium (R⁺) cations and nonemissive InBr₄^- tetrahedral anions. The crystal structure of RInBr₄ is composed of alternating layers of inorganic anions and organic cations along the crystallographic a axis. The resultant hybrid demonstrates bright-blue emission with Commission Internationale de l'Eclairage color coordinates of (0.19, 0.20) and a high photoluminescence quantum yield (PLQY) of 16.36% at room temperature, a 2-fold increase compared to the PLQY of 8.15% measured for the precursor organic salt RBr. On the basis of our optical spectroscopy and computational work, the organic component is responsible for the observed blue emission of the hybrid material. In addition to the enhanced light emission efficiency, the novel hybrid indium bromide demonstrates significantly improved environmental stability. These findings may pave the way for the consideration of hybrid organic In(III) halides for light emission applications.

Structural flexibility in crystalline coordination polymers: a journey along the underlying free energy landscape

In this perspective, we discuss structural flexibility in crystalline coordination polymers. We identify that the underlying free energy landscape unites scientific disciplines, and discuss key areas to advanced the field.

Supertetrahedral polyanionic network in the first lithium phosphidoindate Li3InP2 - structural similarity to Li2SiP2 and Li2GeP2 and dissimilarity to Li3AlP2 and Li3GaP2

Phosphide-based materials have been investigated as promising candidates for solid electrolytes, among which the recently reported Li₉AlP₄ displays an ionic conductivity of 3 mS cm⁻¹. While the phases Li–Al–P and Li–Ga–P have already been investigated, no ternary indium-based phosphide has been reported up to now. Here, we describe the synthesis and characterization of the first lithium phosphidoindate Li₃InP₂, which is easily accessible via ball milling of the elements and subsequent annealing. Li₃InP₂ crystallizes in the tetragonal space group I4₁/acd with lattice parameters of a = 12.0007(2) and c = 23.917(5) Å, featuring a supertetrahedral polyanionic framework of interconnected InP₄ tetrahedra. All lithium atoms occupy tetrahedral voids with no partial occupation. Remarkably, Li₃InP₂ is not isotypic to the previously reported homologues Li₃AlP₂ and Li₃GaP₂, which both crystallize in the space group Cmce and feature 2D layers of connected tetrahedra but no supertetrahedral framework. DFT computations support the observed stability of Li₃InP₂. A detailed geometrical analysis leads to a more general insight into the structural factors governing lithium ion mobility in phosphide-based materials: in the non-ionic conducting Li₃InP₂ the Li ions exclusively occupy tetrahedral voids in the distorted close packing of P atoms, whereas partially filled octahedral voids are present in the moderate ionic conductors Li₂SiP₂ and Li₂GeP₂.

Li₃InP₂ exhibits a polyanionic framework of corner-sharing InP₄ tetrahedra and DFT computations reveal the stability trend for indium in the tetragonal structure compared to the orthorhombic structure of the lighter homologues.

The Crystal Chemistry of Inorganic Hydroborates

The crystal structures of inorganic hydroborates (salts and coordination compounds with anions containing hydrogen bonded to boron) except for the simplest anion, borohydride BH4−, are analyzed regarding their structural prototypes found in the inorganic databases such as Pearson’s Crystal Data [Villars and Cenzual (2015), Pearson’s Crystal Data. Crystal Structure Database for Inorganic Compounds, Release 2019/2020, ASM International, Materials Park, Ohio, USA]. Only the compounds with hydroborate as the only type of anion are reviewed, although including compounds gathering more than one different hydroborate (mixed anion). Carbaborane anions and partly halogenated hydroborates are included. Hydroborates containing anions other than hydroborate or neutral molecules such as NH3 are not discussed. The coordination polyhedra around the cations, including complex cations, and the hydroborate anions are determined and constitute the basis of the structural systematics underlying hydroborates chemistry in various variants of anionic packing. The latter is determined from anion–anion coordination with the help of topology analysis using the program TOPOS [Blatov (2006), IUCr CompComm. Newsl. 7, 4–38]. The Pauling rules for ionic crystals apply only to smaller cations with the observed coordination number within 2–4. For bigger cations, the predictive power of the first Pauling rule is very poor. All non-molecular hydroborate crystal structures can be derived by simple deformation of the close-packed anionic lattices, i.e., cubic close packing (ccp) and hexagonal close packing (hcp), or body-centered cubic (bcc), by filling tetrahedral or octahedral sites. This review on the crystal chemistry of hydroborates is a contribution that should serve as a roadmap for materials engineers to design new materials, synthetic chemists in their search for promising compounds to be prepared, and materials scientists in understanding the properties of novel materials.

ChemEnv: a fast and robust coordination environment identification tool

Coordination or local environments have been used to describe, analyze and understand crystal structures for more than a century. Here, a new tool called ChemEnv, which can identify coordination environments in a fast and robust manner, is presented. In contrast to previous tools, the assessment of the coordination environments is not biased by small distortions of the crystal structure. Its robust and fast implementation enables the analysis of large databases of structures. The code is available open source within the pymatgen package and the software can also be used through a web app available on http://crystaltoolkit.org through the Materials Project.

Predicting short-range order and correlated phenomena in disordered crystalline materials

Disordered crystalline materials are used in a wide variety of energy-related technologies. Recent results from neutron total scattering experiments have shown that the atomic arrangements of many disordered crystalline materials are not random nor are they represented by the long-range structure observed from diffraction experiments. Despite the importance of disordered materials and the impact of disorder on the expression of physical properties, the underlying fundamental atomic-scale rules of disordering are not currently well understood. Here, we report that heterogeneous disordering (and associated structural distortions) can be understood by the straightforward application of Pauling's rules (1929). This insight, corroborated by first principles calculations, can be used to predict the short-range, atomic-scale changes that result from structural disordering induced by extreme conditions associated with energy-related applications, such as high temperature, high pressure, and intense radiation fields.

The Limited Predictive Power of the Pauling Rules

The Pauling rules have been used for decades to rationalise the crystal structures of ionic compounds. Despite their importance, there has been no statistical assessment of the performances of these five empirical rules so far. Here, we rigorously and automatically test all five Pauling rules for a large data set of around 5000 known oxides. We discuss each Pauling rule separately, stressing their limits and range of application in terms of chemistries and structures. We conclude that only 13 % of the oxides simultaneously satisfy the last four rules, indicating a much lower predictive power than expected.