Octahedral Network Research Articles

A new method for computing the vertex PI index with applications to special classes of graphs

The Padmakar-Ivan (PI) index of a graph G is given by PI ( G ) = ∑ e ∈ E ( G ) ( | V ( G ) | − N G ( e ) ) , where N G ( e ) is the number of equidistant vertices for the edge e. This paper presents a triangle cover for a graph, along with a novel method for finding the PI index using this cover. The technique is used to examine some chemical networks, including octahedral and oxide networks, leading to the determination of the exact formula for their PI indices. Additionally, the approach is used to study perfect graphs such as prismatic and chordal graphs. Finally, the PI index of chordal graphs with a diameter of two is investigated, focusing on their induced subgraphs.

Investigation of the Octahedral Network Structure in Formamidinium Lead Bromide Nanocrystals by Low-Dose Scanning Transmission Electron Microscopy.

Metal halide perovskites (MHP) are highly promising semiconductors. In this study, we focus on FAPbBr3 nanocrystals, which are of great interest for green light-emitting diodes. Structural parameters significantly impact the properties of MHPs and are linked to phase instability, which hampers long-term applications. Clearly, there is a need for local and precise characterization techniques at the atomic scale, such as transmission electron microscopy. Because of the high electron beam sensitivity of MHPs, these investigations are extremely challenging. Here, we applied a low-dose method based on four-dimensional scanning transmission electron microscopy. We quantified the observed elongation of the projections of the Br atomic columns, suggesting an alternation in the position of the Br atoms perpendicular to the Pb-Br-Pb bonds. Together with molecular dynamics simulations, these results remarkably reveal local distortions in an on-average cubic structure. Additionally, this study provides an approach to prospectively investigating the fundamental degradation mechanisms of MHPs.

Two-dimensional perovskitoids enhance stability in perovskite solar cells.

Two-dimensional (2D) and three-dimensional (3D) perovskite heterostructures have played a key role in advancing the performance of perovskite solar cells1,2. However, the migration of cations between 2D and 3D layers results in the disruption of octahedral networks, leading to degradation in performance over time3,4. We hypothesized that perovskitoids, with robust organic-inorganic networks enabled by edge- and face-sharing, could impede ion migration. We explored a set of perovskitoids of varying dimensionality and found that cation migration within perovskitoid-perovskite heterostructures was suppressed compared with the 2D-3D perovskite case. Increasing the dimensionality of perovskitoids improves charge transport when they are interfaced with 3D perovskite surfaces-this is the result of enhanced octahedral connectivity and out-of-plane orientation. The 2D perovskitoid (A6BfP)8Pb7I22 (A6BfP: N-aminohexyl-benz[f]-phthalimide) provides efficient passivation of perovskite surfaces and enables uniform large-area perovskite films. Devices based on perovskitoid-perovskite heterostructures achieve a certified quasi-steady-state power conversion efficiency of 24.6% for centimetre-area perovskite solar cells. We removed the fragile hole transport layers and showed stable operation of the underlying perovskitoid-perovskite heterostructure at 85 °C for 1,250 h for encapsulated large-area devices in ambientair.

Chalcogenide perovskite BaZrS3 bulks for thermoelectric conversion with ultra-high carrier mobility and low thermal conductivity

Chalcogenide perovskites are expected to be promising thermoelectric materials, since they not only possess efficient carrier transport and defect tolerance, but also demonstrate unique advantages of high thermodynamic stability, eco-friendly and earth-abundant constituents. Especially, theoretical reports have predicted their “glass-like” thermal conductivities. However, experimental investigation on thermoelectric performances of chalcogenide perovskite BaZrS3 is extremely scarce due to the difficulty in preparing high-quality bulk samples, which originates from the brittle nature, high melting point, and the large difference in melting points between Ba/S and Zr. In this work, pure phase BaZrS3 bulks with high relative density reaching 100 % are realized by optimized sulfurization from low-cost BaZrO3 powders combined with fast spark plasma sintering. A maximum zT value of 0.37 at 623 K in BaZrS3 bulks is achieved, which is the record-high value among the reported sulfide, halide, and hybrid perovskite materials. A room-temperature electron mobility up to 385 cm2V−1s−1 is among the highest values for perovskites due to the high phase purity, dense morphology and corner-sharing ZrS6 octahedral three-dimensional network as effective carrier channels. Meanwhile, a measured low lattice thermal conductivity of 1.11 Wm−1K−1 at 623 K is attributed to the intense phonon scattering from the intrinsic distorted-perovskite structure and the lattice defects by sulfur deficiency. Moreover, the BaZrS3 bulks in this work are stable against moisture/air and high temperature test. This work provides new insights into the fundamental electrical and thermal properties of chalcogenide perovskites, and highlights their great potential in the practical thermoelectric applications.

Low-Dose 4D-STEM Investigations of the Octahedral Network Structure in Formamidinium Lead Bromide Nanocrystals

Low-Dose 4D-STEM Investigations of the Octahedral Network Structure in Formamidinium Lead Bromide Nanocrystals

Structural Dynamics Descriptors for Metal Halide Perovskites.

Metal halide perovskites have shown extraordinary performance in solar energy conversion technologies. They have been classified as "soft semiconductors" due to their flexible corner-sharing octahedral networks and polymorphous nature. Understanding the local and average structures continues to be challenging for both modeling and experiments. Here, we report the quantitative analysis of structural dynamics in time and space from molecular dynamics simulations of perovskite crystals. The compact descriptors provided cover a wide variety of structural properties, including octahedral tilting and distortion, local lattice parameters, molecular orientations, as well as their spatial correlation. To validate our methods, we have trained a machine learning force field (MLFF) for methylammonium lead bromide (CH3NH3PbBr3) using an on-the-fly training approach with Gaussian process regression. The known stable phases are reproduced, and we find an additional symmetry-breaking effect in the cubic and tetragonal phases close to the phase-transition temperature. To test the implementation for large trajectories, we also apply it to 69,120 atom simulations for CsPbI3 based on an MLFF developed using the atomic cluster expansion formalism. The structural dynamics descriptors and Python toolkit are general to perovskites and readily transferable to more complex compositions.

(In)Coherent-bond-networks in Ni-rich layered oxides for durable lithium-ion batteries

An intriguing “coherent-bond-network” effect is suggested here for mitigating anisotropic lattice variations inducing micro-cracks, for durable Ni-rich layered cathodes based on Li[Ni10/12Co1/12Mn1/12]O2 (NCM) and Li[Ni10/12Co1/12Ti1/12]O2 (NCT) oxide models in lithium-ion batteries (LIBs). Upon charging, the c and a lattice strains for NCT are lower than those for NCM, implying that mechanical failures are mitigated in the former. Considering that Ni ions are a major component in compensating for the charge imbalance caused by Li deintercalation, the Ni–O bond populations in the deeply charged state reveal a uniform bond network in NCT, relative to the conventional Ni-rich cathode with NiO6 distortion. For deeper insights, the O–O edge populations are calculated for the two oxide models, and the discretized values over the entire crystal framework are observed for NCM, whereas delocalization is shown in NCT. These results underpin the Ti-induced “coherent-bond-network” that smoothly connects the MO6 octahedral network upon charging for Ni-rich layered oxides, where M denotes a transition metal. In addition, the oxide-model-dependent (in)coherent-bond-networks are consistently identified for the Li–O bond populations of NCT and NCM, and insights into the chemical stiffness of the Ti–O bond reinforces the structural origin of the uniform octahedral environment. The structural concept based on an in-depth understanding of the Ni-rich layered models not only accounts for the fundamental origin of the Ti-doping effect on the anisotropic lattice change but also provides a local-structure-related point of view in restraining the formation of micro-cracks for durable high-energy–density LIBs.

Optimal PMU placement problem in octahedral networks

Power utilities must track their power networks to respond to changing demand and availability conditions to ensure effective and efficient operation. As a result, several power companies employ phase measuring units (PMUs) to check their power networks continuously. Supervising an electric power system with the fewest possible measurement equipment is precisely the vertex covering graph-theoretic problem, in which a set D is defined as a power dominating set (PDS) of a graph if it supervises every components (vertices and edges) in the system (with a couple of rules). The γp(G) is the minimal cardinality of a PDS of a graph G. In this present study, the PDS is identified for octahedral networks.

Local Ionic Displacements and Polarization at the Paraelectric‐Ferroelectric Heterointerface: Effect of Octahedral Distortion

AbstractAt the ferroelectric ABO3 perovskite heterointerface, the broken translational symmetry significantly alters the octahedral network and cation sublattices. Experimentally revealing the interaction between the polarization and atomic structure parameters is beneficial not only for understanding the novel physical phenomena but also for realizing exotic physical functionalities at the materials surface science. Here, it is demonstrated that the induced polarization can be realized by the cooperative interaction between the octahedral distortion and the cation sublattices at the paraelectric‐ferroelectric heterointerface in the (K,Na)NbO3 epitaxial thin film. It is found that the cation–cation displacement scales with the tetragonality of the perovskite unit cell but not with the polarization, which is minimal in the substrate but increases substantially in the thin film. Nevertheless, the oxygen octahedral distortion in the substrate, accompanied by octahedral rotation, is stronger than that in the film, resulting in a translated and stable polarization across the interface. These results demonstrate the octahedral network plays a significant role in the ferroelectric polarization and can also greatly advance the understanding of the heterointerface science for ferroelectrics.

Aqueous sol-gel synthesis, structural, thermoanalytical studies, and conductivity properties of lithium lanthanum titanate

Newly developed aqueous sol-gel preparation technique was applied for the synthesis of lithium lanthanum titanate with the initial composition of Li0.35La0.55TiO3. The influence of hydrochloric acid, which plays a crucial role in the formation of Li–La–Ti–O tartrate gel precursor, was also investigated. The dissolution mechanism of titanium in the concentrated hydrochloric acid and its relation with the corresponding lithium and lanthanum salts was proposed. Besides, the effect of the tartaric acid as a ligand to the formation of transparent sol and homogeneous gel precursor was discussed. X-ray diffraction revealed that below the temperature of 800 °C starts the crystallization of the final tetragonal crystal phase for Li0.3La0.567TiO3 ceramic. Rietveld refinement of the crystalline samples showed the tendency of crystallites growing with the increase of heat-treatment temperature. Besides, the single crystalline ceramic compounds heat-treated at 1000 °C and 1250 °C of temperatures were obtained only for the initial composition of Li0.35La0.55TiO3. The calculated values of the tolerance factor and structural distortion parameters in octahedral coordination of TiO6 octahedral network for tetragonal and orthorhombic crystal structures confirmed the phase transition tendency by the increase of heat treatment temperature. The scanning electron microscopy proved the formation of the dense structure of the sample for Li0.35La55TiO3 ceramic after the additional heat treatment at the temperature of 1,250 °C. In addition, the quality of synthesized ceramic was confirmed by the impedance spectroscopical measurements, which revealed that the conductivity value for bulk at the temperature of 27 °C (300 K) is equal to 0.123 S m–1.

Bonding-unsaturation-dependent superconductivity in P-rich sulfides

The covalent frameworks found in certain compounds, such as the S–H skeleton in H3S and the H cage in LaH10, play an essential role in their superconductivity. These compounds have the feature of bonding unsaturation (a deficiency of electrons in their covalent bonding) in common. Developing an understanding of the relationship between superconductivity and bonding unsaturation in these materials can provide new ideas for the design of superconducting materials. In this work, we explored the high-pressure phase diagram of binary P–S compounds using first-principles swarm structural calculations. In addition to the previously reported P2S and P3S structures, we identified that P5S, P8S, and P11S also have a common structural character of six-coordinated octahedral networks; however, their bonding unsaturation are distinct due to the different valence electron numbers and unequal ratios of P and S atoms. These features provide an ideal model for exploring the bonding-unsaturation dependence of superconductivity. We estimated the average bonding unsaturation of these P-rich compounds based on the valence electron numbers and the coordination numbers of the central P/S atoms. Interestingly, the resultant average bonding unsaturation was found to be proportional to the predicted superconducting transition temperature. This finding was also verified in MH9 (M = Y, Th, and Pr) and doped H3S (Si, C, and P) compounds. Our work provides an opportunity to gain a deeper understanding of bonding-unsaturation-dependent superconductivity.

Bismuth pyrochlores with varying Fe/Co ratio for efficient Multi-functional Catalysis: Structure evolution versus Photo- and Electro-catalytic activities

Bismuth pyrochlores that the crystal structure tolerates lower site misplacements and higher vacancy concentrations exhibit unique stereo-chemical activity, therefore, the manipulation of the property by structural engineering has driven significant research activity, with the goal of realizing their transformative functional potential. Herein, an excellent platform to investigate the role of the strucutre in tuning catalytic activity is provided by varying Fe/Co ratio in a bismuth niobate pyrochlore oxide. Continuous Co-level from 0 to 100% was ingeniously designed on the basis of special phase diagrams and pryocholore-type pure samples were successfully fabricated by a modified sol–gel auto-combustion method. The effect of structural modulation on dielectric property and multi-functional catalytic activities were studied. Significantly, two opposing strucutral shifts were observed with increasing the Co-level, ascribled to the competition between displacive disorders on the Bi sites and strucutral distortions in the octahedral network. Tunable dielectric relaxation was exhibited by electrical modulus spectroscopy and one additional hidden relaxation process implies an outstanding thermal motion of electrons from variable oxidation states of Fe3+/ Co2+ ions when ionized oxygen vacancy becomes weak. For photocatalysis, the low-level Co showed a best visible-light-responsive photocatalytic activity by means of the RhB-dye decomposition, while the high-level Co exhibited a higher photoinduced current density. For electrocatalysis, the sample that maintains its structure with the coexistence of massive oxygen vacancies and low-spin-state Co2+ present a superior oxygen evolution reaction (OER) activity, with a lower OER overpotential (∼300 mV at 10 mA/cm2) and a smaller Tafel slope (∼70 mV/dec). Moreover, the underlying mechanism of the improved performances was analyzed in detail and the new insights were provied for constructing single-phase multi-functioning catalysts.

SmI3:4f5 honeycomb magnet with spin-orbital entangled Γ7 Kramers doublet

We report magnetic properties of a 4f-honeycomb iodide SmI3 made up of edge-shared network of SmI6 octahedra. High temperature magnetic susceptibility indicates {\Gamma}7 Kramers doublet ground state of Sm3+ (4f5) ions stabilized by the spin-orbit coupling and octahedral crystal electric field, which interact with Sm-I-Sm bond angle nearly 90 degree. Magnetization measurements down to 0.1 K detected antiferromagnetic correlations and an anomaly in the magnetization curve before saturation without a sign of long-range order. Relevance between SmI3 and the antiferromagnetic Kitaev material proposed in the 4f-electron system is discussed.

Buffering Octahedra in Mo4Zr9P: Intergrowth as a Solution to the Frustrated Packing of Tricapped Trigonal Prisms and Icosahedra.

Atomic packings based on icosahedra and tricapped trigonal prisms are prone to frustration─indeed, these polyhedra represent common configurations in metallic glasses. In this Article, we illustrate how these packing issues can serve as a driving force for the formation of modular intermetallic structures. Using Density Functional Theory-Chemical Pressure (DFT-CP) analysis, we relate the Hf9Mo4B-type structure of Mo4Zr9P to interatomic pressures experienced by the atoms in two parent structures: Zr3P, whose structure is built from tricapped trigonal prisms, and ZrMo2, a Laves phase containing icosahedra. CP analysis of Zr3P reveals that it has particularly frustrated packing because of the entangling of its tricapped trigonal prisms. In the ternary phase, the frustration is significantly relieved as the units become isolated from each other. Further analysis points to the stabilizing effect of a face-sharing network of octahedra in Mo4Zr9P that largely separates the structure into Zr-Mo and Zr-P domains and serves as a buffering region for the relaxation of interatomic distances. These conclusions are generalized to the broader members of this structure type with the examination of the CP schemes for the isostructural Mo4Zr9B, Al5Co2, and Mg5Pd2 phases. Finally, we screen the structural literature using the ToposPro software to identify three additional structure types that have similar intergrowth patterns: the Dy4CoCd, La23Ni7Mg4, and Gd14Co3In3 types. An analysis of the interatomic distances within the octahedral networks of these structures suggests that these networks commonly facilitate the reconciliation of packing incompatibilities in intermetallic chemistry.

Octahedral oxide glass network in ambient pressure neodymium titanate

Rare-earth titanates form very fragile liquids that can be made into glasses with useful optical properties. We investigate the atomic structure of 83TiO2-17Nd2O3 glass using pair distribution function (PDF) analysis of X-ray and neutron diffraction with double isotope substitutions for both Ti and Nd. Six total structure factors are analyzed (5 neutron + 1 X-ray) to obtain complementary sensitivities to O and Ti/Nd scattering, and an empirical potential structure refinement (EPSR) provides a structural model consistent with the experimental measurements. Glass density is estimated as 4.72(13) g cm−3, consistent with direct measurements. The EPSR model indicates nearest neighbor interactions for Ti-O at overline{r}_{TiO} = 1.984(11) Å with coordination of n_{TiO} = 5.72(6) and for Nd-O at overline{r}_{NdO} = 2.598(22) Å with coordination of n_{NdO} = 7.70(26), in reasonable agreement with neutron first order difference functions for Ti and Nd. The titanate glass network comprises a mixture of distorted Ti-O5 and Ti-O6 polyhedra connected via 71% corner-sharing and 23% edge-sharing. The O-Ti coordination environments include 15% nonbridging O-Ti1, 51% bridging O-Ti2, and 32% tricluster O-Ti3. This structure is highly unusual for oxide glasses melt-quenched at ambient pressure, as it consists of Ti-Ox predominantly in octahedral (with nearly no tetrahedral) coordination.

Strong Edge Stress in Molecularly Thin Organic-Inorganic Hybrid Ruddlesden-Popper Perovskites and Modulations of Their Edge Electronic Properties.

Organic-inorganic hybrid Ruddlesden-Popper perovskites (HRPPs) have gained much attention for optoelectronic applications due to their high moisture resistance, good processability under ambient conditions, and long functional lifetimes. Recent success in isolating molecularly thin hybrid perovskite nanosheets and their intriguing edge phenomena have raised the need for understanding the role of edges and the properties that dictate their fundamental behaviors. In this work, we perform a prototypical study on the edge effects in ultrathin hybrid perovskites by considering monolayer (BA)2PbI4 as a representative system. On the basis of first-principles simulations of nanoribbon models, we show that in addition to significant distortions of the octahedra network at the edges, strong edge stresses are also present in the material. Structural instabilities that arise from the edge stress could drive the relaxation process and dominate the morphological response of edges in practice. A clear downward shift of the bands at the narrower ribbons, as indicative of the edge effect, facilitates the separation of photoexcited carriers (electrons move toward the edge and holes move toward the interior part of the nanosheet). Moreover, the desorption energy of the organic molecule can also be much lower at the free edges, making it easier for functionalization and/or substitution events to take place. The findings reported in this work elucidate the underlying mechanisms responsible for edge states in HRPPs and will be important in guiding the rational design and development of high-performance layer-edge devices.

On 2-domination number in certain octahedral networks

Fault tolerance is the characteristic that facilitates a system to function when some of its components fail. Thus, developing a fault-tolerant system can respond quickly to threats and mitigate operations spontaneously. Fault tolerance and graph theory form a unique and highly desirable combination with the potential to design diverse fault-tolerant networks at the lowest possible cost. This is achieved using a mathematical framework called domination. In a graph, each node has a minimum of one neighbour in a set, and then the set is called a dominating set of a network. The minimum number of elements of a dominating set is called the domination number of that network. If any node in the network has a minimum of two neighbours in the set, then the set is called a 2-dominating set. The minimum number of elements of such a set is called the 2-domination number. In this paper, the 2-domination numbers for various octahedral networks like n-dimensional octahedron, n-dimensional dominated octahedron, and n-dimensional rectangular octahedron of type I and II are computed. The leading actual world application of the 2-dominating set is fault tolerance. The motivation for our work is how the fault tolerance system is applicable in the octahedral network.

On 2-Domination Number in Certain Octahedral Networks

On 2-Domination Number in Certain Octahedral Networks

Characterization of structural and electrical properties of Ca0.61Nd0.26TiO3 ceramic tailored by complex ions (Al0.5Nb0.5)4+

Miniaturization and low power dissipation are a trend for the development of ceramic-based microwave devices. Therefore, the decrease of the dielectric loss properties of microwave dielectric ceramic material compounds with a high dielectric constant is considered a quite important subject. In this work, the Ca0.61Nd0.26TiO3 material configuration with orthorhombic perovskite structure was thoroughly investigated by applying the strategy of (Al0.5Nb0.5)4+ substitution at the B-site. More specifically, the Ca0.61Nd0.26Ti1-x(Al0.5Nb0.5)xO3 sample with a nearly 60% increase in the quality factor (Q×f) was obtained. Also, the relationship between the structural and the electrical properties of Ca0.61Nd0.26Ti1-x(Al0.5Nb0.5)xO3 (0 ≤ x ≤ 0.15) samples were explored via performing X‐ray diffraction (XRD) measurements, Raman spectra, transmission electron microscopy (TEM) and calculation of the insulation resistance, etc. The extracted outcomes divulged that samples at x = 0–0.12 formed a single perovskite-structured phase, while the grain size of samples decreased by increasing the x value, leading to a drop decline of both the dielectric constant (εr) and electrical conductivity. Additionally, insights from the acquired Raman spectra confirmed that the stressed-rigid oxygen octahedral networks could lower the positive τf value of Ca0.61Nd0.26TiO3-based ceramic compounds. Interestingly, as the doping content of (Al0.5Nb0.5)4+ increased, the Ti3+ in samples was restrained at x = 0.04, whereas the insulation properties of the samples increased. Hence, the conductivity loss was declined. Furthermore, the TEM images illustrated the appearance of a 1: 1 ordered structure at the B-site of the (Al0.5Nb0.5)4+-doped samples. As a result, the Q×f value of the samples raised from 11,095GHz at x = 0–17,802 GHz at x = 0.12, enhanced by 60%. On top of that, for the sample with x = 0.15, the existence of the Ca2Nb2O7 phase deteriorated the microwave dielectric properties of the Ca0.61Nd0.26Ti1-x(Al0.5Nb0.5)xO3 samples, and especially Q×f value.

Chemical Control of the Dimensionality of the Octahedral Network of Solar Absorbers from the CuI-AgI-BiI3 Phase Space by Synthesis of 3D CuAgBiI5.

A newly reported compound, CuAgBiI5, is synthesized as powder, crystals, and thin films. The structure consists of a 3D octahedral Ag+/Bi3+ network as in spinel, but occupancy of the tetrahedral interstitials by Cu+ differs from those in spinel. The 3D octahedral network of CuAgBiI5 allows us to identify a relationship between octahedral site occupancy (composition) and octahedral motif (structure) across the whole CuI–AgI–BiI3 phase field, giving the ability to chemically control structural dimensionality. To investigate composition–structure–property relationships, we compare the basic optoelectronic properties of CuAgBiI5 with those of Cu2AgBiI6 (which has a 2D octahedral network) and reveal a surprisingly low sensitivity to the dimensionality of the octahedral network. The absorption onset of CuAgBiI5 (2.02 eV) barely changes compared with that of Cu2AgBiI6 (2.06 eV) indicating no obvious signs of an increase in charge confinement. Such behavior contrasts with that for lead halide perovskites which show clear confinement effects upon lowering dimensionality of the octahedral network from 3D to 2D. Changes in photoluminescence spectra and lifetimes between the two compounds mostly derive from the difference in extrinsic defect densities rather than intrinsic effects. While both materials show good stability, bulk CuAgBiI5 powder samples are found to be more sensitive to degradation under solar irradiation compared to Cu2AgBiI6.