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A novel lead zinc titanate tungsten oxide (PbZn${}_{1∕3}$Ti${}_{1∕3}$W${}_{1∕3}$O${}_3)$ single perovskite was synthesized employing a cost-effective solid-state reaction technique. A phase transition occurs from tetragonal (P4mm) to monoclinic (C2/m) after substituting zinc (Zn) and tungsten (W) into the B-site of the pure lead titanate. The average crystallite size and micro-lattice strain are 66.2nm and 0.159%, respectively, calculated by the Williamson–Hall method. The grains are uniformly distributed through well-defined grain boundaries and the average grain size is about 17.8$\mu$m analyzed from the SEM micrograph. Raman spectrum suggests the presence of all constituent elements in the sample. The UV–Visible study suggests that the sample is suitable for photovoltaic applications because of high bandgap energy $E_g=4.17$eV. The dielectric study confirms the negative temperature coefficient resistance (NTCR) behavior of the sample. The activation energy increases from 13.9meV to 142meV with a rise of temperature suggesting that ac conductivity is thermally activated. The thermally activated relaxation process was managed by immobile charge carriers at low temperatures while defects and oxygen vacancies at higher temperatures. The presence of the asymmetrical curves in modulus plots confirms the non-Debye-type behavior. Both Nyquist and Cole–Cole semi-circular arcs confirm the semiconductor nature of the sample.

Vacancy plays a crucial role in mechanical properties of transition metal borides (TMBs). However, the influence of vacancy on hardness of TMBs is unknown. In this paper, the relationship between boron vacancy and mechanical properties of CrB₄ is investigated by first-principle calculations. Two different vacancies including boron monovacancy (MV) and boron bivacancy (BV) are considered. We find that CrB₄ with boron MV is more stable than that of boron BV. The removed atom weakens the deformation resistances, and reduces the elastic stiffness and hardness. The calculated shear modulus, Young’s modulus and theoretical hardness of boron MV are larger than that of boron BV. The reason is that the removed atom weakens the localized hybridization between B and B atoms, and damages the 3D-network B–B covalent bond. However, the bulk modulus of B${}_{\mathrm{\text{-BV4}}}$ is slightly larger than that of perfect CrB₄. This reason is attributed to the formation of triangular pyramid bonding in B${}_{\mathrm{\text{-BV4}}}$ vacancy.

The ferromagnetic (FM) ordering in rutile TiO₂ has been theoretically studied by substituting different $p$-block elements (B, Al, C, Si, N, P and As) doped at oxygen site (B${}_{\mathrm{\text{O}}}$, Al${}_{\mathrm{\text{O}}}$, C${}_{\mathrm{\text{O}}}$, Si${}_{\mathrm{\text{O}}}$, N${}_{\mathrm{\text{O}}}$, P${}_{\mathrm{\text{O}}}$ and As${}_{\mathrm{\text{O}}}$) as well as at titanium site. Ab initio calculations in the frame work of density functional theory indicates that the $p$-block elements (B, C, Al, Si, N, P and As) when substituting the oxygen site give significant amount of magnetic moment, but induce zero magnetic moment in case of substitution at Ti site. Spin–spin interaction for (Ti${}_{12}$O${}_{23}$X)₂ with X = B, Al, C, Si, N, P and As system has also been studied with two different doping distances. Among all the possibilities, carbon substitution at oxygen site (C${}_{\mathrm{\text{O}}}$) results the most stable FM ordering in rutile TiO₂.

Ceramics of the composition BaBiO₃ (BB) were sintered in oxygen to obtain a single phase with monoclinic $I$2/$m$ symmetry as suggested by high-resolution X-ray diffraction. X-ray photoelectron spectroscopy confirmed the presence of bismuth in two valence states — 3$+$ and 5$+$. Optical spectroscopy showed presence of a direct bandgap at $\sim$ 2.2eV and a possible indirect bandgap at $\sim$ 0.9eV. This combined with determination of the activation energy for conduction of 0.25eV, as obtained from ac impedance spectroscopy, suggested that a polaron-mediated conduction mechanism was prevalent in BB. The BB ceramics were crushed, mixed with BaTiO₃ (BT), and sintered to obtain BT–BB solid solutions. All the ceramics had tetragonal symmetry and exhibited a normal ferroelectric-like dielectric response. Using ac impedance and optical spectroscopy, it was shown that resistivity values of BT–BB were orders of magnitude higher than BT or BB alone, indicating a change in the fundamental defect equilibrium conditions. A shift in the site occupancy of Bi to the A-site is proposed to be the mechanism for the increased electrical resistivity.

$(1-y)$(BiFe${}_{1-x}$GdxO₃)–y(PbZrO₃) composites $(y=0.5)$, having four different Gd concentrations ($x=0.05$, 0.1, 0.15, and 0.2), were synthesized and their structural, dielectric, and ferroelectric properties have been studied using different characterization techniques. In addition, to investigate the effect of ion implantation on the microstructure and dielectric properties, these composites were exposed to 2MeV He${}^{+}$-ions. Modifications of the structure, surface morphology and electrical properties of the samples before and after ion exposure were demonstrated using powder X-ray diffraction (XRD), scanning electron microscopy (SEM) technique, and LCR meter. The compositional analysis was carried out using energy dispersive X-ray spectrometry (EDS). XRD results demonstrated a decrease in the intensity profile of the dominant peak by a factor of 6 showing a degradation of the crystallinity. Willliamson–Hall (WH) plots reveal reduction in the grain size after irradiation along with an increase in strain and dislocation density. A decrease in the dielectric constant and loss has been recorded after ion beam exposure with reduction in ac conductivity value. The contribution of grain and grain boundary effect in conduction mechanism has been addressed using Nyquist plots. All the samples demonstrate a lossy ferroelectric loop which shows a clear modification upon irradiation. The role of structural defects modifying the physical properties of the composite materials is discussed in this work.

We develop a rigorous framework for modeling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problem on a discrete energy space and establish qualitatively sharp far-field decay estimates for the equilibrium configuration. This work extends [V. Ehrlacher, C. Ortner and A. Shapeev, Analysis of boundary conditions for crystal defect atomistic simulations, Arch. Ration. Mech. Anal.222 (2016) 1217–1268] by admitting infinite-range interaction which in particular includes some quantum chemistry based interatomic interactions.

In this paper, we study topological defect lines in two character rational conformal field theories. Among them one set of two character theories are commutant pairs in $E_{8,1}$ conformal field theory. Using these defect lines, we construct defect partition function in the $E_8$ theory. We find that the defects preserve only a part of the $E_8$ current algebra symmetry. We also determine the defect partition function in $c=24$ CFTs using these defects lines of two character theories and we find that, with appropriate choice of commutant pairs, these defects preserve all current algebra symmetries of $c=24$ CFTs.

The electrical and thermal properties of extruded samples of Bi${}_{85}$Sb${}_{15}$$〈\mathrm{\text{Te}}〉$ modified with ZrO₂ were investigated depending on the dose of gamma radiation in the temperature range $\sim 80÷300$ K and magnetic field strength (H) $\sim 74\times 10^4$ A/m. It was found that an increase in the mobility in the irradiated modified Bi${}_{85}$Sb${}_{15}$$〈\mathrm{\text{Te}}〉$ is associated with the radiation introduction of acceptor (negatively charged) centers, which at low doses are generated mainly in the regions of the efficiency of impurity scattering of charge carriers and partially neutralized centers and, accordingly, to a certain increase in the mobility. In the extruded modified samples of the Bi${}_{85}$Sb${}_{15}$ solid solution, irradiation with gamma quanta results not only in the generation of radiation defects (RDs) (centers), but also accompanied by their rearrangement. This causes a change in the spectrum of localized states and the electron scattering process, which leads to corresponding changes in the presented electrical and thermal parameters.

Spherical Bi₂S₃ nanoparticles (NPs) were prepared by a facile in situ thermal sulfuration method. Different Bi₂S₃ samples were obtained by controlling the sulfuration time. The products were characterized by X-ray diffractometer (XRD), scanning electron microscopy (SEM), Raman and Fourier-transform infrared (FT-IR) methods. The optical properties were examined by UV-visible-near-infrared (UV-Vis–NIR) and photoluminescence (PL) techniques. The results show that the phase of the products after sulfuration is pure and the spherical shape of Bi NPs has been successfully transmitted to Bi₂S₃ samples. The light absorption edges exhibit red shift to 1060 nm while the light emission displays blue shift to 868 nm, compared with the energy bandgap of bulk Bi₂S₃. The reason for the special optical properties of Bi₂S₃ NPs by this in situ sulfuration route is considered to associate with the defects and quantum size effect of NPs.

Pb(${\text{In}}_{1∕2}$${\text{Nb}}_{1∕2}$)O₃-Pb(${\text{Mg}}_{1∕3}$${\text{Nb}}_{2∕3})$O₃-PbTiO₃ (PIN-PMN-PT) relaxor ferroelectric crystals in 5^″ diameter by 5^″ length were grown by the Bridgman (BR) method for the first time. Typical issues in the crystal growth concerning large volume of the melt, high density of the crystal and corrosion of the melt on the wall of Pt crucible are discussed.

The martensitic transformation is often accompanied by the production of defects either in the austenite, the martensite or in both phases. An interesting example of this is the generation of bulk dislocations and surface defects after pseudoelastic cycling in Cu-Zn-Al single crystals. The involved phases are the cubic (L2₁) of the austenite and the monoclinic 18R martensitic phase. The dislocations arrange in the bulk following crystallographic patterns associated to the habit plane of the transition and the basal plane of the martensite. A microscopic analysis shows that the dislocations are produced by plastic deformation of the martensite. These dislocations have several consequences on the mechanical behavior of the material and on the kinetics of the diffusional processes present in both phases. The formation of intrusions and extrusions at the surface specimens is another important effect of the pseudoelastic cycling. They play a crucial role on the fatigue life of the specimens. Recent results show a strong effect of composition on the nucleation of surface defects. The crystallography of the defects, the origin of the dislocations, their arrangements and their interaction with the specimen surface are discussed.

Surface conditions of aluminum can influence the final arrangement of nano-pores in fabrication of ordered nanoporous anodic alumina membranes (AAMs). This study is mainly focused on the different applied voltages of aluminum electropolishing by keeping all the other parameters constant. After heat treatment (stress relieving and annealing at 500°C) of pure aluminum sheets, the samples were electropolished at different voltages (10-60V) to obtain desirable surface smoothness, while the temperature of the container was kept constant. The current-time curves were recorded during electropolishing process. The surface roughness obtained in each applied voltage was examined using optical microscope and atomic force microscope (AFM). The process was followed by two-step anodization in order to reach ordered nano-pores. Finally, the influence of surface roughness on regularity of nano-pores was observed using scanning electron microscope (SEM). The SEM images were analyzed to investigate the morphology and the degree of self ordering of pores of the samples by using a new designed analytical method aiming MATLAB and fast Fourier transform (FFT) technique. It was concluded that the electropolishing voltage and the resulted surface roughness and also formed defects can competitively affect the arrangement of membrane's nano-pores. A desired smoothness obtained from electropolishing voltage of 30V. Also 40V provided the best order with respect to the other voltages.

Target waves in excitable media such as neuronal network can regulate the spatial distribution and orderliness as a continuous pacemaker. Three different schemes are used to develop stable target wave in the network, and the potential mechanism for emergence of target waves in the excitable media is investigated. For example, a local pacing driven by external periodical forcing can generate stable target wave in the excitable media, furthermore, heterogeneity and local feedback under self-feedback coupling are also effective to generate continuous target wave as well. To discern the difference of these target waves, a statistical synchronization factor is defined by using mean field theory and artificial defects are introduced into the network to block the target wave, thus the robustness of these target waves could be detected. However, these target waves developed from the above mentioned schemes show different robustness to the blocking from artificial defects. A regular network of Hindmarsh–Rose neurons is designed in a two-dimensional square array, target waves are induced by using three different ways, and then some artificial defects, which are associated with anatomical defects, are set in the network to detect the effect of defects blocking on the travelling waves. It confirms that the robustness of target waves to defects blocking depends on the intrinsic properties (ways to generate target wave) of target waves.

Nitrogen (N) is an important impurity in silicon (Si), which associates with impurities as well as with other defects to form defect complexes. The knowledge of the properties and behavior of defect structures containing carbon (C), N and oxygen (O) is important for the Si–based electronic technology. Here, we employ density functional theory (DFT) calculations to investigate the association of nitrogen with carbon and oxygen defects to form the C_iN and C_iNO_i defects. We provide evidence of the formation of these defects and additional details of their structure, their density of states (DOS) and Bader charges. Therefore, C_iN and C_iNO_i defects are now well characterized.

A torsional buckling model of cylindrical shells with asymmetric local thickness defect is established based on the Hamiltonian system. The critical load and torsional buckling mode of cylindrical shells with defects are obtained by the symplectic eigensolution expansion method, which overcomes the difficulty of constructing the deflection function of the traditional semi-inverse method. Local buckling modes can be captured by this new analytical model with the superposition of symplectic eigensolutions. To ensure accuracy and validity of the symplectic method, the analytical solution with torsional buckling of a cylindrical shell is compared with the classical solution and the finite element method (FEM) solution. The results show that the most detrimental position of the defect is only related to the width of the defect, not to the depth. The local defect changes the circumferential buckling wave number of the cylindrical shell and concentrates the torsional corrugation on the side containing the defect. Torque symmetry is broken due to the asymmetric defect, and the most detrimental defect direction for buckling is the same as the direction of torsional buckling wavelet.

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Bäcklund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical r-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.

In this paper, we discuss a new way to get a quantum holonomy around topological defects in $C_{60}$ fullerenes. For this, we use a Kaluza–Klein extra dimension approach. Furthermore, we discuss how an extra dimension could promote the formation of new freedom degrees which would open a discussion about a possible qubits computation.

This study aims to build a new bridge between configurational stress/force and material fracture. The migrating control volume and thermodynamics are used to develop the Eshelby relation, and the relationship between the conservative integral in fracture mechanics and configurational stress/force for elastic or elastic-plastic materials is further clarified. Additionally, the configurational stresses, including circumferential configurational stress at the crack tip taking T-stress into consideration, are determined, and the $J$ integral vector is then calculated further. The results indicate that $J_1$ integral is path-independent while $J_2$ is path-dependent when T-stress is considered. We preliminarily present the relationship between the configurational stress and crack initiation and the zero circumferential configurational stress fracture criterion (ZCCS) is proposed based on the local properties of the crack-tip configurational stress tensor and fracture mechanics. To estimate the fracture loads, we also develop two fracture criteria based on the critical area of crack-tip plastic zone determined by the Mises configurational stress (MCSPA) and the principal configurational stress difference (PCSDPA), respectively. It is found that the initiation angle assessed by the ZCCS fracture criterion is in good agreement with that by both the MTS fracture criterion and experimental observations, as well as T stresses could affect the initiation angles for mixed-mode cracks under tension-shear loads. Furthermore, the fracture loads evaluated by the MCSPA and PCSDPA fracture criteria are consistent with that by both the MTS fracture criterion and experimental results. Finally, the initiation angles determined based on the characteristics of crack-tip plastic zone by configurational stress coincide with that by MTS and ZCCS fracture criteria.

Grain boundary effect on BaTiO₃ has been widely investigated for several decades. However, all of them tailored the grain boundary by grain size of BaTiO₃. In this case, a direct way was introduced to modify the grain boundary by coating technique to investigate the role of grain boundary in ferroelectric materials. Nonferroelectric phase TiO₂ was employed to investigate grain boundary effects on the electrical properties of BaTiO₃ piezoelectric ceramics. TiO₂ coating can result in the reduction of piezoelectric and ferroelectric properties and the annealing process in oxygen can increase piezoelectric behavior of pure BaTiO₃ due to valence state of Ti ions while that remains for Ti-modified composition possibly due to the increased grain boundary effect by impedance analysis. Compared with ferroelectric grain, grain boundary plays a critical role to impact the electrical properties of perovskite-type ferroelectric materials.

This research summarizes the analytical and experimental results of heat-transfer processes influence on defects formation during sapphire crystal growth by horizontal directed crystallization method (HDC). The shape of solid-melt interface significantly influences the process of sapphire crystals growth by this method. We receive the Stefan problem solution for sapphire crystals growth. It allows investigating the crystal growth process and the related factors (thermal stresses on different stages of growth process), their influence on defects formation. We investigate the main reasons for the formation of defective structures of the solid phase of sapphire crystals and the influence of thermal unit construction, the crystal geometry on the quality of the resulting sapphire crystal. We study the structure formation process, impurity distribution, and the nature of the defects in the crystal during it growth.