Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

One-Electron-Addition to Pentavalent Phosphorus with the Phosphorus-Chlorine Bond as Acceptor Introducing a Fundamental Distinction in Substitution Mechanism between S_N2(P) and S_N2(C)

An electron-addition, under single-crystal conditions, to pentavalent phosphorus compounds as Cl-P (=O, S) Y, Z with the P-Cl bond as electron-accepting group, is selected as an additional model for SN2(P) like reactions. It is demonstrated that the geometric information stored in the tetrahedral configuration (substrate) can be transmitted in the corresponding trigonal bipyramidal (TBP) state for nucleophilic substitution. In this article, we focus on these specific mechanistic aspects of carbon and phosphorus. We consider our study as a contribution to the significance of these (bio)chemical intermediates.

In situ atomic-scale observation of size-dependent (de) potassiation and reversible phase transformation in tetragonal FeSe anodes

Potassium-ion batteries(PIBs)are considered promising alternatives to lithium-ion batteries owing to cost-effective potassium resources and a suitable redox potential of-2.93 V(vs.-3.04 V for Li+/Li).However,the exploration of appro-priate electrode materials with the correct size for reversibly accommodating large K+ions presents a significant challenge.In addition,the reaction mecha-nisms and origins of enhanced performance remain elusive.Here,tetragonal FeSe nanoflakes of different sizes are designed to serve as an anode for PIBs,and their live and atomic-scale potassiation/depotassiation mechanisms are revealed for the first time through in situ high-resolution transmission electron micros-copy.We found that FeSe undergoes two distinct structural evolutions,sequen-tially characterized by intercalation and conversion reactions,and the initial intercalation behavior is size-dependent.Apparent expansion induced by the intercalation of K+ions is observed in small-sized FeSe nanoflakes,whereas unexpected cracks are formed along the direction of ionic diffusion in large-sized nanoflakes.The significant stress generation and crack extension originating from the combined effect of mechanical and electrochemical interactions are elucidated by geometric phase analysis and finite-element analysis.Despite the different intercalation behaviors,the formed products of Fe and K_(2)Se after full potassiation can be converted back into the original FeSe phase upon depotassiation.In particular,small-sized nanoflakes exhibit better cycling perfor-mance with well-maintained structural integrity.This article presents the first successful demonstration of atomic-scale visualization that can reveal size-dependent potassiation dynamics.Moreover,it provides valuable guidelines for optimizing the dimensions of electrode materials for advanced PIBs.

Multi-scale Simulation on Bonding Mechanism of Solid-Liquid Cast-Rolling of Cu/Al Cladding Strip based on FEM and MD

To explore the complex thermal-mechanical-chemical behavior in the solid-liquid cast-roll bonding(SLCRB) of Cu/Al cladding strip, numerical simulations were conducted from both macro and micro scales. In macro-scale, with birth and death element method, a thermo-mechanical coupled finite element model(FEM) was set up to explore the temperature and contact pressure distribution at the Cu/Al bonding interface in the SLCRB process. Taking these macro-scale simulation results as boundary conditions, we simulated the atom diffusion law of the bonding interface by molecular dynamics(MD) in micro-scale. The results indicate that the temperature in Cu/Al bonding interface deceases from 700 to 320 ℃ from the entrance to the exit of caster, and the peak of contact pressure reaches up to 140 MPa. The interfacial diffusion thickness depends on temperature and rolling reduction, higher temperature results in larger thickness, and the rolling reduction below kiss point leads to significant elongation deformation of cladding strip which yields more newborn interface with fresh metal and make the diffusion layer thinner. The surface roughness of Cu strip was found to be benefit to atoms diffusion in the Cu/Al bonding interface. Meanwhile, combined with the SEM-EDS observation on the microstructure and composition in the bonding interface of the experimental samples acquired from the castrolling bite, it is revealed that the rolling reduction and severe elongation deformation in the solid-solid contact zone below kiss point guarantee the satisfactory metallurgical bonding with thin and smooth diffusion layer. The bonding mechanisms of reactive diffusion, mechanical interlocking and crack bonding are proved to coexist in the SLCRB process.

Oxidation Kinetics of Aluminum Powders in a Gas Fluidized Bed Reactor in the Potential Application of Surge Arresting Materials

In this technical paper, the oxidation mechanism and kinetics of aluminum powders are discussed in great details. The potential applications of spherical aluminum powders after oxidation to be part of the surging arresting materials are discussed. Theoretical calculations of oxidation of spherical aluminum powders in a typical gas fluidization bed are demonstrated. Computer software written by the author is used to carry out the basic calculations of important parameters of a gas fluidization bed at different temperatures. A mathematical model of the dynamic system in a gas fluidization bed is developed and the analytical solution is obtained. The mathematical model can be used to estimate aluminum oxide thickness at a defined temperature. The mathematical model created in this study is evaluated and confirmed consistently with the experimental results on a gas fluidization bed. Detail technical discussion of the oxidation mechanism of aluminum is carried out. The mathematical deviations of the mathematical modeling have demonstrated in great details. This mathematical model developed in this study and validated with experimental results can bring a great value for the quantitative analysis of a gas fluidization bed in general from a theoretical point of view. It can be applied for the oxidation not only for aluminum spherical powders, but also for other spherical metal powders. The mathematical model developed can further enhance the applications of gas fluidization technology. In addition to the development of mathematical modeling of a gas fluidization bed reactor, the formation of oxide film through diffusion on both planar and spherical aluminum surfaces is analyzed through a thorough mathematical deviation using diffusion theory and Laplace transformation. The dominant defects and their impact to oxidation of aluminum are also discussed in detail. The well-controlled oxidation film on spherical metal powders such as aluminum and other metal spherical powders can potentially become an important part of switch devices of surge arresting materials, in general.

Role of methoxy and C_(α)-based substituents in electrochemical oxidation mechanisms and bond cleavage selectivity of β-O-4 lignin model compounds

In order to better understand the specific substituent effects on the electrochemical oxidation process of β-O-4 bond, a series of methoxyphenyl type β-O-4 dimer model compounds with different localized methoxyl groups, including 2-(2-methoxyphenoxy)-1-phenylethanone, 2-(2-methoxyphenoxy)-1-phenylethanol, 2-(2-methoxyphenoxy)-1-(4-methoxyphenyl)ethanone, 2-(2-methoxyphenoxy)-1-(4-methoxyphenyl)ethanol, 2-(2,6-dimethoxyphenoxy)-1-(4-methoxyphenyl)ethanone, 2-(2,6-dimethoxyphenoxy)-1-(4-methoxyphenyl)ethanol have been selected and their electrochemical properties have been studied experimentally by cyclic voltammetry, and FT-IR spectroelectrochemistry. Combining with electrolysis products distribution analysis and density functional theory calculations, oxidation mechanisms of all six model dimers have been explored. In particular, a total effect from substituents of both para-methoxy(on the aryl ring closing to Cα) and Cα-OH on the oxidation mechanisms has been clearly observed, showing a significant selectivity on the Cα-Cβbond cleavage induced by electrochemical oxidations.

Carbon Fiber Breakage Mechanism in Aluminum(Al)/Carbon Fibers(CFs) Composite Sheet during Accumulative Roll Bonding(ARB) Process

We put forward a method of fabricating Aluminum(Al)/carbon fibers(CFs) composite sheets by the accumulative roll bonding(ARB) method. The finished Al/CFs composite sheet has CFs and pure Al sheets as sandwich and surface layers. After cross-section observation of the Al/CFs composite sheet, we found that the CFs discretely distributed within the sandwich layer. Besides, the tensile test showed that the contribution of the sandwich CFs layer to tensile strength was less than 11% compared with annealed pure Al sheet. With ex-situ observation of the CFs breakage evolution with-16%,-32%, and-45% rolling reduction during the ARB process, the plastic instability of the Al layer was found to bring shear damages to the CFs. At last, the bridging strengthening mechanism introduced by CFs was sacrificed. We provide new insight into and instruction on Al/CFs composite sheet preparation method and processing parameters.

A retrospective view on the history of natural sciences in XX-XXI

The presented paper is dedicated to a new ret-rospective view on the history of natural sci-ences in XX-XXI cc, partially including the sci-ence philosophy (mainly, the problems of the scientific realism, i.e. the correspondence of science to reality) and also a novel scheme for different classes of sciences with different ob-jects and paradigms. There are analyzed the chosen “great” and “grand” problems of phys-ics (including the comprehension of quantum mechanics, with a recently elaborated new chapter, connected with time as a quantum obs- ervable and time analysis of quantum processes) and also of natural sciences as a whole. The particular attention is paid to the interpretation questions and slightly to the aspects, inevitably connected with the world- views of the res- earchers (which do often constitute a part of the interpretation questions).

Exploring mechanism of hidden,steep obliquely inclined bedding landslides using a 3DEC model:A case study of the Shanyang landslide in Shaanxi Province,China

Catastrophic geological disasters frequently occur on slopes with obliquely inclined bedding structures(also referred to as obliquely inclined bedding slopes),where the apparent dip sliding is not readily visible.This phenomenon has become a focal point in landslide research.Yet,there is a lack of studies on the failure modes and mechanisms of hidden,steep obliquely inclined bedding slopes.This study investigated the Shanyang landslide in Shaanxi Province,China.Using field investigations,laboratory tests of geotechnical parameters,and the 3DEC software,this study developed a numerical model of the landslide to analyze the failure process of such slopes.The findings indicate that the Shanyang landslide primarily crept along a weak interlayer under the action of gravity.The landslide,initially following a dip angle with the support of a stable inclined rock mass,shifted direction under the influence of argillization in the weak interlayer,moving towards the apparent dip angle.The slide resistance effect of the karstic dissolution zone was increasingly significant during this process,with lateral friction being the primary resistance force.A reduction in the lateral friction due to karstic dissolution made the apparent dip sliding characteristics of the Shanyang landslide more pronounced.Notably,deformations such as bending and uplift at the slope’s foot suggest that the main slide resistance shifts from lateral friction within the karstic dissolution zone to the slope foot’s resistance force,leading to the eventual buckling failure of the landslide.This study unveils a novel failure mode of apparent dip creep-buckling in the Shanyang landslide,highlighting the critical role of lateral friction from the karstic dissolution zone in its failure mechanism.These insights offer a valuable reference for mitigating risks and preventing disasters related to obliquely inclined bedding landslides.

Hydrocarbon generation and storage mechanisms of deepwater shelf shales of Ordovician Wufeng Formation–Silurian Longmaxi Formation in Sichuan Basin, China

As the hydrocarbon generation and storage mechanisms of high quality shales of Upper Ordovician Wufeng Formation– Lower Silurian Longmaxi Formation remain unclear, based on geological conditions and experimental modelling of shale gas formation, the shale gas generation and accumulation mechanisms as well as their coupling relationships of deep-water shelf shales in Wufeng–Longmaxi Formation of Sichuan Basin were analyzed from petrology, mineralogy, and geochemistry. The high quality shales of Wufeng–Longmaxi Formation in Sichuan Basin are characterized by high thermal evolution, high hydrocarbon generation intensity, good material base, and good roof and floor conditions;the high quality deep-water shelf shale not only has high biogenic silicon content and organic carbon content, but also high porosity coupling. It is concluded that:(1) The shales had good preservation conditions and high retainment of crude oil in the early times, and the shale gas was mainly from cracking of crude oil.(2) The biogenic silicon(opal A) turned into crystal quartz in early times of burial diagenesis, lots of micro-size intergranular pores were produced in the same time;moreover, the biogenic silicon frame had high resistance to compaction, thus it provided the conditions not only for oil charge in the early stage, but also for formation and preservation of nanometer cellular-like pores, and was the key factor enabling the preservation of organic pores.(3) The high quality shale of Wufeng–Longmaxi Formation had high brittleness, strong homogeneity, siliceous intergranular micro-pores and nanometer organic pores, which were conducive to the formation of complicated fissure network connecting the siliceous intergranular nano-pores, and thus high and stable production of shale gas.

Genomic Instability in Cancer II: 4N-Skewed (90°) Reductive Division via Fragile Sites to Fitness Increase for Solid and Hematological Cancer Beginnings

The objective herein was to connect the ontogeny process of diplochromosomal, amitotic, 4n-skewed division-system, to cytogenetic deficiency lesions in satellite, repetitive DNAs, especially in the chromosomal fragile sites, some 100 distributed over the genome. These latter studies had shown that chemical induced replication-stress led to un-replicated lesions in these fragile sites, which from inaccurate repair processes caused genomic instability. In the chain of events of the ontogeny process to the special tetraploidy, it was proposed that primary damaged human cells could undergo replication stress from repair-process present during cell replication, a suggestion verified by X-ray damaged cells producing the unstable fragile sites (see text). The cancer-importance for therapy is recognition of cell cycle change for the 4n derivative fitness-gained, diploid progeny cells. An open question is whether RB controlling G1 to S-period is mutated at this suggested tumorigenesis initiating phase, and if so, with what consequences for therapy. The fragile site studies further showed that repair of repetitive DNAs could produce two types of genomic changes: single gene mutations and CNVs, which were here shown to be chromosomally located on “borders” to repairing satellite lesions. This genomic placement was found to correspond to mutations identified in tumor sequencing (p53, Rb, MYC), favoring a bad luck location for their cancer “mutational nature”. The CNVs in cancers, are here seen as molecular expressions of long-known cytogenetic HSRs and DMs also with demonstrated origin from amplifications of single genes. Over-expression of oncogenes was hinted of being from duplications, but Drosophila genetics demonstrated the opposite, gene inactivation. The reduced eye-size from dominant, BAR-Ultra-Bar-eye phenotypes, was caused by duplications, inactivating the genetic system for eye-size. The finding of CNVs showing “evasion” of the immune system suggests, inactivation of immune-determining genetics. Since mutated genes on borders to satellite DNAs are a fact in hematological cancers, the 4n-skewed division-system is suggested to replace debated leukemogenesis with fitness-gain from molecular mutations. For these cancers the question is how normal bone marrow cells attain genomic damage for special tetraploidy, which was referred to studies of cells moving in artificial marrow-like substrate, needing serious attention.

Computational and bioinformatics tools for understanding disease mechanisms

Computational methods have significantly transformed biomedical research,offering a comprehensive exploration of disease mechanisms and molecular protein functions.This article reviews a spectrum of computational tools and network analysis databases that play a crucial role in identifying potential interactions and signaling networks contributing to the onset of disease states.The utilization of protein/gene interaction and genetic variation databases,coupled with pathway analysis can facilitate the identification of potential drug targets.By bridging the gap between molecular-level information and disease understanding,this review contributes insights into the impactful utilization of computational methods,paving the way for targeted interventions and therapeutic advancements in biomedical research.

Pathological mechanism of immune disorders in diabetic kidney disease and intervention strategies

Diabetic kidney disease is one of the most severe chronic microvascular complications of diabetes and a primary cause of end-stage renal disease.Clinical studies have shown that renal inflammation is a key factor determining kidney damage during diabetes.With the development of immunological technology,many studies have shown that diabetic nephropathy is an immune complex disease,and that most patients have immune dysfunction.However,the immune response associated with diabetic nephropathy and autoimmune kidney disease,or caused by ischemia or infection with acute renal injury,is different,and has a complicated pathological mechanism.In this review,we discuss the pathogenesis of diabetic nephropathy in immune disorders and the intervention mechanism,to provide guidance and advice for early intervention and treatment of diabetic nephropathy.

Plasticity of photorespiratory carbon concentration mechanism in Sedobassia sedoides(Pall.)Freitag&G.Kadereit under elevated CO_(2)concentration and salinity

Rising atmospheric CO_(2)(carbon dioxide)concentrations and salinization are manifestations of climate change that affect plant growth and productivity.Species with an intermediate C_(3)-C_(4)type of photosynthesis live in a wide range of precipitation,temperature,and soil quality,but are more often found in warm and dry habitats.One of the intermediate C_(3)-C_(4)photosynthetic type is C_(2)photosynthesis with a carbon concentration mechanism(CCM)that reassimilates CO_(2)released via photorespiration.However,the ecological significance under which C_(2)photosynthesis has advantages over C_(3)and C_(4)plants remains largely unexplored.Salt tolerance and functioning of CCM were studied in plants from two populations(P1 and P2)of Sedobassia sedoides(Pall.)Freitag&G.Kadereit Asch.species with C_(2)photosynthesis exposed to 4 d and 10 d salinity(200 mM NaCl)at ambient(785.7 mg/m^(3),aCO_(2)and elevated(1571.4 mg/m^(3),eCO_(2))CO_(2).On the fourth day of salinity,an increase in Na+content,activity catalase,and superoxide dismutase was observed in both populations.P2 plants showed an increase in proline content and a decrease in photosynthetic enzyme content:rubisco,phosphoenolpyruvate carboxylase(PEPC),and glycine decarboxylase(GDC),which indicated a weakening of C_(2)and C_(4)characteristics under salinity.Treatment under 10 d salinity led to an increased Na^(+)content and activity of cyclic electron flow around photosystem I(PSI CEF),a decreased content of K^(+)and GDC in both populations.P1 plants showed greater salt tolerance,which was assessed by the degree of reduction in photosynthetic enzyme content,PSI CEF activity,and changes in relative growth rate(RGR).Differences between populations were evident under the combination of eCO_(2)and salinity.Under long-term salinity and eCO_(2),more salt-tolerant P1 plants had a higher dry biomass(DW),which was positively correlated with PSI CEF activity.In less salt-tolerant P2 plants,DW correlated with transpiration and dark respiration.Thus,S.sedoides showed a high degree of photosynthetic plasticity under the influence of salinity and eCO_(2)through strengthening(P1 plants)and weakening C_(4)characteristics(P2 plants).

Numerical investigation on detonation cell evolution in a channel with area-changing cross section

The two-dimensional cellular detonation propagating in a channel with area-changing cross section was numerically simulated with the dispersion-controlled dissipative scheme and a detailed chemical reaction model. Effects of the flow ex-pansion and compression on the cellular detonation cell were investigated to illus-trate the mechanism of the transverse wave development and the cellular detona-tion cell evolution. By examining gas composition variations behind the leading shock,the chemical reaction rate,the reaction zone length,and thermodynamic parameters,two kinds of the abnormal detonation waves were identified. To explore their development mechanism,chemical reactions,reflected shocks and rarefac-tion waves were discussed,which interact with each other and affect the cellular detonation in different ways.

Multiscale Characteristics and Connection Mechanisms of Attraction Networks:A Trajectory Data Mining Approach Leveraging Geotagged Data

Urban tourism is considered a complex system,and multiscale exploration of the organizational patterns of attraction networks has become a topical issue in urban tourism,so exploring the multiscale characteristics and connection mechanisms of attraction networks is important for understanding the linkages between attractions and even the future destination planning.This paper uses geotagging data to compare the links between attractions in Beijing,China during four different periods:the pre-Olympic period(2004–2007),the Olympic Games and subsequent‘heat period’(2008–2013),the post-Olympic period(2014–2019),and the COVID-19(Corona Virus Disease 2019)pandemic period(2020–2021).The aim is to better understand the evolution and patterns of attraction networks at different scales in Beijing and to provide insights for tourism planning in the destination.The results show that the macro,meso-,and microscales network characteristics of attraction networks have inherent logical relationships that can explain the commonalities and differences in the development process of tourism networks.The macroscale attraction network degree Matthew effect is significant in the four different periods and exhibits a morphological monocentric structure,suggesting that new entrants are more likely to be associated with attractions that already have high value.The mesoscale links attractions according to the common purpose of tourists,and the results of the community segmentation of the attraction networks in the four different periods suggest that the functional polycentric structure describes their clustering effect,and the weak links between clusters result from attractions bound by incomplete information and distance,and the functional polycentric structure with a generally more efficient network of clusters.The pattern structure at the microscale reveals the topological transformation relationship of the regional collaboration pattern,and the attraction network structure in the four different periods has a very similar importance profile structure suggesting that the attraction network has the same construction rules and evolution mechanism,which aids in understanding the attraction network pattern at both macro and micro scales.Important approaches and practical implications for planners and managers are presented.

On the Isotope-Like Effect for High-T_cSuperconductors in the Scenario of 2-Phonon Exchange Mechanism for Pairing

By generalizing the isotope effect for elemental superconductors (SCs) to the case of pairing in the 2-phonon exchange mechanism for composite SCs, we give here an explanation of the well-known increase in the critical temperature (Tc) of Bi2Sr2CaCu2O8 from 95 K to 110 K and of Bi2Sr2Ca2Cu3O10 from 105 to 115 - 125 K when Bi and Sr in these are replaced by Tl and Ba, respectively. On this basis, we also give the estimated Tcs of some hypothetical SCs, assuming that they may be fabricated by substitutions similar to Bi → Tl and Sr → Ba.

Instability mechanism of mining roadway passing through fault at different angles in kilometre-deep mine and control measures of roof cutting and NPR cables

The angle α between the fault strike and the axial direction of the roadway produces different damage characteristics. In this paper, the research methodology includes theoretical analyses, numerical simulations and field experiments in the context of the Daqiang coal mine located in Shenyang, China. The stability control countermeasure of "pre-splitting cutting roof + NPR anchor cable"(PSCR-NPR) is simultaneously proposed. According to the different deformation characteristics of the roadway, the faults are innovatively classified into three types, with α of type I being 0°-30°, α of type II being 30°-60°, and α of type III being 60°-90°. The full-cycle stress evolution paths during mining roadway traverses across different types of faults are investigated by numerical simulation. Different pinch angles α lead to high stress concentration areas at different locations in the surrounding rock. The non-uniform stress field formed in the shallow surrounding rock is an important reason for the instability of the roadway. The pre-cracked cut top shifted the high stress region to the deep rock mass and formed a low stress region in the shallow rock mass. The high prestressing NPR anchor cable transforms the non-uniform stress field of the shallow surrounding rock into a uniform stress field. PSCR-NPR is applied in the fault-through roadway of Daqiang mine. The low stress area of the surrounding rock was enlarged by 3-7 times, and the cumulative convergence was reduced by 45%-50%. It provides a reference for the stability control of the deep fault-through mining roadway.

草酸根桥联的双核铜髤配合物[Cu_2(phen)_2(H_2O)_2(μ_2-C_2O_4)](NO_3)_2的合成及晶体结构

A new binuclear copper(Ⅱ) complex, [Cu2(phen)2(H2O)2( μ2-C2O4)](NO3)2, has been synthesized and characterized by elemental analysis, IR and UV-Vis spectrum. Its crystal structure was determined by single crystal X-ray diffraction techniques. Crystal data: monoclinic, space group P21/c, a=0.712 21(8) nm, b=1.170 93(14) nm, c=1.783 7(2) nm, β=111.828(2)°, and V=1.380 8(3) nm3, Dc=1.769 Mg·m-3, Z=2, F(000)=744, R1=0.025 4, wR2=0.069 5, Gof=1.077, Δρ=328^-455 e·nm-3. The complex is packed by one centrosymmetry binuclear copper(Ⅱ) unit, oxalate dianion and NO3- anion. In the molecule structure of the title complex, two Cu(Ⅱ) ions are bridged by oxalate dianion and each Cu(Ⅱ) ions coordinates with two nitrogen atoms from 1,10-phenanthroline ligand and one oxygen atom from water to form a five-coordinate distorted square-pyramidal configuration. The hydrogen bonds are observed between coordinated water molecules and NO3- anions. The analysis of the crystal structure indicates that the complex has a two-dimensional stacking network structure, which is formed by intramolecular hydrogen bonds, intermolecular hydrogen bonds and stacking effect of aromatic ring. CCDC: 255345.

Valence electronic structure of tantalum carbide and nitride

The valence electronic structures of tantalum carbide (TaC) and tantalum nitride (TaN) are studied by using the empirical electronic theory (EET). The results reveal that the bonds of these compounds have covalent,metallic and ionic characters. For a quantitative analysis of the relative strength of these components,their ionicities have been calculated by implanting the results of EET to the PVL model. It has been found that the ionicity of tantalum carbide is smaller than that of tantalum nitride. The EET results also reveal that the covalent electronic number of the strongest bond in the former is larger than that of the latter. All these suggest that the covalent bond of TaC is stronger than that of TaN,which coincides to that de-duced from the first-principles method.