Distortion Properties Research Articles

Sharp Coefficient Related Results for Nephroid Shaped Domain

In this study, the focus is on two main objectives related to starlike functions associated with a nephroid-shaped domain. Firstly, the aim is to determine sharp bounds for the coefficients of these functions up to the fifth order. These bounds are crucial as they provide a detailed understanding of the behavior of the coefficients, which is important for further analysis and various applications of these functions. The sharp determination of these coefficients can aid in refining mathematical models and theoretical frameworks involving starlike functions. Secondly, the sharp bound for the third order Hankel determinant for functions in this class is also derived. The Hankel determinant is a significant tool in complex analysis, as it provides insights into the growth, distortion, and other important properties of functions. By deriving these sharp bounds, this study improves upon the existing results in the literature, thereby contributing to a more sharp characterization of starlike functions associated with nephroid-shaped domains. This advancement has the potential to lead to enhanced applications, such as in geometric function theory and fluid dynamics, and offers a deeper understanding of these mathematical functions. By addressing these objectives, the study not only fills gaps in the current research but also opens new avenues for future exploration in the field of complex analysis.

Influence of printing parameters on part density in L-BPF of Ti-6Al-4V and correlation with static mechanical properties measured using indentation testing

Abstract A complete workflow of parameter development and process qualification of a part manufactured using laser powder bed fusion (L-PBF) AM technique requires data of porosity, pore morphology, distortion and static mechanical properties. Using a combination of two non-destructive techniques: Computed tomography and indentation testing, the influence of printing parameters on defect types and part density in L-PBF of Ti-6Al-4V is described. In addition, the results using the combined method are compared to conventional testing methods.

Prediction of the structural and magnetic properties of the all-d-metal Heusler alloys Ni–Mn–Cr

In this work, all-d metal Heusler alloys Ni–Mn–Cr were predicted by first principles. Their structure, magnetism, tetragonal distortion and electronic properties were studied. The cubic groud state structures of Ni2MnCr and NiMnCr2 are XA type, and that of NiMn2Cr is L21 type. All of them have magnetism. The change of their lattice constants is closely related to the covalent radius of atoms. Ni2MnCr has a stable tetragonal phase and may undergo martensitic transition. NiMn2Cr has a lower energy tetragonal phase, but is dynamically unstable. The equilibrium volumes of the two compounds expand through tetragonal distortion. NiMnCr2 does not have a lower energy tetragonal phase. In the tetragonal distortion, the atomic magnetic moments are influnced by the interatomic distance and the magnetic moments of neighboring atoms. The origin of the tetragonal distortion and magnetic properties was discussed in terms of the electronic density of states.

Generalized Bounded Distortion Property

Generalized Bounded Distortion Property

Systematic investigation of microstructure, distortion, mechanical and thermal properties of NiB and ZrB2-modified 90W-6Ni-4Co alloys

The present work focuses on the role of NiB and ZrB2 addition on density, structural evolution, mechanical and thermal properties of 90W-6Ni-4Co (wt%) heavy alloys. The investigated tungsten heavy alloys were sintered at 1485 °C and 1500 °C with a holding time of 75 min in H2 atmosphere. Compared to the base alloy 90W-6Ni-4Co, the NiB-substituted alloys showed improved densification at both sintering temperatures. An in-depth study of the phase and microstructure of the 1500 °C sintered samples was carried out. X-ray diffraction analysis confirmed the presence of ZrO2 in ZrB2 containing WHAs. Microstructural analysis affirms that ZrB2 incorporation attributes for grain size refinement in sintered alloys. Furthermore, the elephant foot formation in the sintered samples was avoided by incorporating NiB individually or in combination with ZrB2 dispersoids. The distortion parameter (δ) of the samples sintered at 1500 °C was found to be decreased from 24.83 (0 wt% ZrB2) to 6.36 (2 wt% ZrB2). On the other hand, the combined addition of NiB and ZrB2 provides better shape retention with δ=2.82 for the tungsten heavy alloys with 3 wt% NiB and 2 wt% ZrB2. The maximum compressive stress of ∼2000 MPa was obtained in the 89W-6Ni-4Co-1ZrB2 samples. The maximum and minimum bulk hardness of 432 ± 5 HV3 and 365 ± 9 HV3 was obtained for 88W-3Ni-3NiB-4Co-2ZrB2 and 90W-6Ni-4Co heavy alloys. The coefficient of thermal expansion of the 90W-6Ni-4Co alloy was found to be the highest (7.65 × 10−6 /°C), which was reduced to 7.1 × 10−6 /°C and 6.8 × 10−6 /°C with the incorporation of 1 and 2 wt% ZrB2 respectively. W-rich channels were noticed in the microstructure of 1500 °C sintered samples. Overall, W-Ni/NiB-Co-ZrB2 alloys are very effective in enhancing the mechanical properties and distortion behavior compared to W-Ni-Co alloys.

Ultrastrong Coupling between Polar Distortion and Optical Properties in Ferroelectric MoBr2O2.

Tuning the properties of materials by using external stimuli is crucial for developing versatile smart materials. Strong coupling among the order parameters within a single-phase material constitutes a potent foundation for achieving precise property control. However, cross-coupling is fairly weak in most single materials. Leveraging first-principles calculations, we demonstrate a layered mixed anion compound MoBr2O2 that exhibits electric-field switchable spontaneous polarization and ultrastrong coupling between polar distortion and electronic structures as well as optical properties. It offers feasible avenues of achieving tunable Rashba spin-splitting, electrochromism, thermochromism, photochromism, and nonlinear optics by applying an external electric field to a single domain sample and heating, as well as intense light illumination. Additionally, it exhibits an exceptionally large photostrictive effect. These findings not only showcase the feasibility of achieving multiple order parameter coupling within a single material but also pave the way for comprehensive applications based on property control, such as energy harvesting, information processing, and ultrafast control.

Effects of Ti content on the tensile ductility, lattice distortion and mechanical properties of VNbTaTix refractory high-entropy alloys

Refractory high-entropy alloys (RHEAs) have remarkable properties like high strength and thermal stability at high temperatures. Their practical application is hindered by ambient brittleness and inferior formability. Titanium (Ti) is recognized as a crucial element in improving the ductility and oxidation resistance of RHEAs, but its plasticizing mechanism is still unclear. To address this, a series of body-centered cubic (BCC) single-phase VNbTaTix alloys were designed. The alloys exhibited exceptional ductility and cold-rolling formability at room temperature. Remarkably, the tensile fracture elongation of VNbTaTi alloy was about 26.9%, which surpassed most RHEAs. The major plastic mechanisms of the alloys are a/2<1 1 1>-type dislocation and {1 1 2}<1 1 1>-type twinning. Solid solution strengthening was identified as the primary strengthening mechanism. Although Ti reduced the solid solution strengthening effect, it contributed to weight reduction and enhanced local lattice distortion. This study not only designed several RHEAs with ductility but also provided insights into the effect of Ti content on their phase stability, lattice distortion, and strength mechanisms. These findings have significant implications for designing new RHEAs with ambient ductility.

Study of a generalized subclass of meromorphic functions

This paper is concerned with a new subclass of meromorphic close-to-convex functions defined by means of subordination. various properties of this class such as coefficient estimates, inclusion relationship, distortion property and radius of meromorphic convexity, are established. Some earlier known results follow as special cases.

Mixed cations tin-germanium perovskite: A promising approach for enhanced solar cell applications

Significant progress has been made over the years to improve the stability and efficiency of rapidly evolving tin-based perovskite solar cells (PSCs). One powerful approach to enhance the performance of these PSCs is through compositional engineering techniques, specifically by incorporating a mixed cation system at the A-site and B-site structure of the tin perovskite. These approaches will pave the way for unlocking the full potential of tin-based PSCs. Therefore, in this study, a theoretical investigation of mixed A-cations (FA, MA, EA, Cs) with a tin-germanium-based PSC was presented. The crystal structure distortion and optoelectronic properties were estimated. SCAPS 1-D simulations were employed to predict the photovoltaic performance of the optimized tin-germanium material using different electron transport layers (ETLs), hole transport layers (HTLs), active layer thicknesses, and cell temperatures. Our findings reveal that EA0.5Cs0.5Sn0.5Ge0.5I3 has a nearly cubic structure (t = 0.99) and a theoretical bandgap within the maximum Shockley-Queisser limit (1.34 eV). The overall cell performance is also improved by optimizing the perovskite layer thickness to 1200 nm, and it exhibits remarkable stability as the temperature increases. The short-circuit current density (Jsc) remains consistent around 33.7 mA/cm2, and the open-circuit voltage (Voc) is well-maintained above 1 V by utilizing FTO as the conductive layer, ZnO as the ETL, Cu2O as the HTL, and Au as the metal back contact. This configuration also achieves a high fill factor ranging from 87 % to 88 %, with the highest power conversion efficiency (PCE) of 31.49 % at 293 K. This research contributes to the advancement of tin-germanium perovskite materials for a wide range of optoelectronic applications.

Properties of Nonlinear Distortions and Related Measures in Audio Amplifiers

Properties of Nonlinear Distortions and Related Measures in Audio Amplifiers

Tailoring the crystal distortion and dielectric properties of 0.7CaTiO3-0.3NdAlO3 microwave ceramics by La, Sm and Eu doping into A-site Nd

The TiO6 octahedra titling and rotation play an important role in affecting the microwave properties of 0.7CaTiO3-0.3NdAlO3 microwave ceramics by A-site La, Sm and Eu doping. The oxygen octahedra of Sm-doped 0.7CaTiO3-0.3NdAlO3 ceramics exhibit antiphase tilting, while both in-phase and antiphase tilting coexist in the 0.7CaTiO3-0.3EuAlO3 ceramics. There is an undeniable correlation between the crystal distortion and the tolerance factor t. As the tolerance factor t continues to increase, the crystal structure of A-site doped CTNA ceramics changes from both in-phase tilting and antiphase tilting to untilted structure and the TiO6 octahedra exhibits an inclination to tilt around c axis. The weakening bending vibration of the Ti–O(2)-Ti bond results in the increase of the polarization and the damping coefficient of lattice vibration. The dielectric constant (εr) rises to 48 from 43 and Q × f values decrease to 36,000 GHz from 44,800 GHz (measured at 6 GHz). These findings could be used to guide the tailoring of the crystal distortion and microwave dielectric properties of technologically important perovskite 0.7CaTiO3-0.3NdAlO3 based ceramics.

Mn–Si synergistically co-doping adjusting microstructures and microwave-millimeter-wave dielectric properties of Y3Al5O12 garnet ceramics: Lattice occupancy and ligand distortion perspective

Y3-xMnxAl5-xSixO12 (x = 0.1–0.5) ceramics were fabricated through the high-temperature reaction method. The effects of Mn2+-Si4+ co-doping on lattice occupancy, ligand distortion and microwave dielectric properties of Y3Al5O12 garnet were inquired. Mn2+ ions successively occupy the lattice sites of Y3+ dodecahedron and Al3+ octahedron along with the increase of distortion degree of [AlO6] octahedron. In Y3-xMnxAl5-xSixO12, εr predominantly correlates with ionic polarizability, average bond ionicity (△fi) and Mn2+ ionic lattice occupation. The Q × f is primarily influenced by factors like relative density, lattice energy (U) and atomic packing fraction. Meanwhile, τf is associated with the distortion of octahedra, bond energy (E), and the bond valence between Y/Mn and O. Ultimately, the microwave and millimeter-wave dielectric properties of the Y2.8Mn0.2Al4.8Si0.2O12 ceramics excel with values of εr = 10.89, Q × f = 56,135 GHz@11 GHz (Q × f = 88200 GHz@25 GHz), and τf = -39.35 ppm/°C.

Composition design study of strong and ductile Mo-alloyed CoCrNi medium-entropy alloys

The assistance of alloying elements provides enormous opportunities for the discovery of high-performance face-centered cubic (FCC) medium-entropy alloys (MEAs). In this work, the influence of alloying element Mo on the phase stability, stacking fault energy (SFE), deformation mechanisms, lattice distortion, and mechanical properties of (CoCrNi)100–xMox (0 ≤ x ≤ 10) MEAs was synthetically explored with the first-principles calculations. It indicates that the FCC phase remains metastable at 0 K, and its stability degenerates with increasing Mo content. The monotonous decrease of SFE is revealed with the rise of Mo content, which promotes the activation of stacking faults, deformation twinning, or martensitic transformation. Raising Mo content also causes the aggravation of lattice distortion and thus triggers intense solid solution strengthening. Significantly, the essential criterion for the composition design of FCC (CoCrNi)100–xMo MEAs with superior strength-ductility combination was established based on the synergistic effects between multiple deformation mechanisms and solid solution strengthening. According to the criterion, the optimal composition is predetermined as (CoCrNi)93Mo7 MEA. The criterion is proved to be effective, and it can provide valuable inspiration for the development of alloying-element reinforced FCC multi-principal element alloys.

Designing Quaternary and Quinary Refractory-Based High-Entropy Alloys: Statistical Analysis of Their Lattice Distortion, Mechanical, and Thermal Properties

The rapid evolution in materials science has resulted in a significant interest in high-entropy alloys (HEAs) for their unique properties. This study focuses on understanding both quaternary and quinary body-centered cubic (BCC) of 12 refractory-based HEAs, and on analysis of their electronic structures, lattice distortions, mechanical, and thermal properties. A comprehensive assessment is undertaken by means of density functional theory (DFT)-based first principles calculations. It is well known that multiple constituents lead to notable lattice distortions, especially in quinary HEAs. This distortion, in turn, has significant implications on the electronic structure that ultimately affect mechanical and thermal behaviors of these alloys such as ductility, lattice thermal conductivity, and toughness. Our in-depth analysis of their electronic structures revealed the role of valence electron concentration and its correlation with bond order and mechanical properties. Local lattice distortion (LD) was investigated for these 12 HEA models. M1 (WTiVZrHf), M7 (TiZrHfW), and M12 (TiZrHfVNb) have the highest LD whereas the models M3 (MoTaTiV), M5 (WTaCrV), M6 (MoNbTaW), and M9 (NbTaTiV) have the less LD. Furthermore, we investigated the thermal properties focusing on Debye temperature (ΘD), thermal conductivity (κ), Grüneisen parameter (γα), and dominant phonon wavelength (λdom). The NbTaTiV(M9) and TiVNbHf(M10) models have significantly reduced lattice thermal conductivities (κL). This reduction is due to the mass increase and strain fluctuations, which in turn signify lattice distortion. The findings not only provide an understanding of these promising materials but also offer guidance for the design of next-generation HEAs with properties tailored for potential specific applications.

Effects of quenching and annealing on conductivity and ferroelectric properties of Na0.5Bi0.5TiO3-NaNbO3 ceramics

Quenching procedures are effective in enhancing the low depolarization temperature of sodium bismuth titanate (NBT) relaxor ferroelectrics. In the present work, the influence of thermal processing parameters on the structure and electrical properties of NBT ceramics modified with 5 mol% sodium niobate (NBT-5NN) are evaluated. It is shown that quenching leads to higher electrical conductivity due to reduction at high temperatures, resulting in a higher oxygen vacancy concentration. The quenched materials also exhibit enhanced rhombohedral distortion and ferroelectric properties. The reduction process is largely reversible by reoxidation during annealing at intermediate temperatures in the region of 550 °C, which helps to recover the bulk resistivity to values close to those of the as-sintered materials. On the other hand, the rhombohedral distortion and ferroelectric properties were not affected significantly by the annealing procedure, indicating that the mechanisms responsible for the modification of electrical conductivity and structural distortion/ferroelectric properties have a different origin.

Pressure-Modulated Anomalous Organic-Inorganic Interactions Enhance Structural Distortion and Second-Harmonic Generation in MHyPbBr3 Perovskite.

Organic-inorganic halide perovskites possess unique electronic configurations and high structural tunability, rendering them promising for photovoltaic and optoelectronic applications. Despite significant progress in optimizing the structural characteristics of the organic cations and inorganic framework, the role of organic-inorganic interactions in determining the structural and optical properties has long been underappreciated and remains unclear. Here, by employing pressure tuning, we realize continuous regulation of organic-inorganic interactions in a lead halide perovskite, MHyPbBr3 (MHy+ = methylhydrazinium, CH3NH2NH2+). Compression enhances the organic-inorganic interactions by strengthening the Pb-N coordinate bonding and N-H···Br hydrogen bonding, which results in a higher structural distortion in the inorganic framework. Consequently, the second-harmonic-generation (SHG) intensity experiences an 18-fold increase at 1.5 GPa, and the order-disorder phase transition temperature of MHyPbBr3 increases from 408 K under ambient pressure to 454 K at the industrially achievable level of 0.5 GPa. Further compression triggers a sudden non-centrosymmetric to centrosymmetric phase transition, accompanied by an anomalous bandgap increase by 0.44 eV, which stands as the largest boost in all known halide perovskites. Our findings shed light on the intricate correlations among organic-inorganic interactions, octahedral distortion, and SHG properties and, more broadly, provide valuable insights into structural design and property optimization through cation engineering of halide perovskites.

Extremal properties of Sobolev's Beltrami coefficients and distortion of curvelinear functionals

An important problem in applications of quasiconformal analysis and in its numerical aspect is to establish algorithms for explicit or approximate determination of the basic quasiinvariant curvelinear and analytic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmüller and Grunsky norms, Fredholm eigenvalues and the quasireflection coefficients of associated quasicircles. We prove two general theorems of new type answering this question for univalent functions in arbitrary quasiconformal domains and provide its applications. The results are strengthened in the case of maps of the disk and give rise to extremal Beltrami coefficients of a new type.

Backward and forward Wasserstein projections in stochastic order

Motivated by applications of stochastic orders in statistics and economics, we study metric projections onto cones in the Wasserstein space of probability measures, defined by stochastic orders. Duality theorems for backward and forward projections are established under mild conditions, which lay a foundation for investigating sampling of measures in stochastic orders. To demonstrate applications of these theorems beyond practice, particular attention is given to mathematical properties of convex order and subharmonic order. While backward and forward cones possess distinct geometric properties, strong connections between backward and forward projections can be obtained in the convex order case. Compared with convex order, the study of subharmonic order is subtler, particularly the existence and regularity of optimal mappings. In all cases, Brenier-Strassen type polar factorization theorems are proved, thus providing a full picture of the decomposition of optimal couplings between probability measures given by deterministic contractions (resp. expansions) and stochastic couplings. The factorization of convex order projection completes the decomposition obtained by Gozlan and Juillet, which builds a connection with Caffarelli's contraction theorem. A further noteworthy addition to earlier results is the decomposition in the subharmonic order case where the optimal mappings are characterized by volume distortion properties. To our knowledge, this is the first time in this occasion such results are available in the literature.

Data-driven surrogate modelling of residual stresses in Laser Powder-Bed Fusion

ABSTRACT In order to enable the industrialization of additive manufacturing, it is necessary to develop process simulation models that can rapidly predict part quality. Although multi-physics simulations have shown success at predicting residual stress, distortion, microstructure and mechanical properties of additively manufactured parts, they are generally too computationally expensive to be directly used in applications, such as optimization, controls, or digital twinning. In this study, a critical evaluation is made of how data-driven surrogate models can be used to model the residual stress of parts fabricated by Laser Powder-Bed Fusion. Residual stress data is generated by using an inherent-strain based process simulation for two families of part geometries. Three different models using varying levels of sophistication are compared: a multilayer perceptron (MLP), a convolutional neural network (CNN) based on the U-Net architecture, and an interpolation-based method based on mapping geometries onto a reference. All three methods were found to be sufficient for part design, providing mechanical predictions for a CPU time below 0.2 s, representing a runtime speed-up of at least 3900 × . Neural network-based models are significantly more expensive to train compared to using interpolation. However, the generality of models based on the U-Net architecture is attractive for applications in optimization.

Enhancement of vanadium addition on hydrogen storage properties of high entropy alloys TiZrFeMnCrVx

High Entropy Alloys (HEAs) have attracted increasing attention due to their unique characteristics, of which the lattice distortion property is particularly beneficial for hydrogen storage. Herein, we prepared the TiZrFeMnCrV HEAs with different V contents and elucidated the effect of V on the hydrogen storage properties. The TiZrFeMnCrVx (x = 0.5, 1.0, 1.5, 2.0 at%) alloys rapidly absorb 90% of their hydrogen storage capacity within 76 s at 30 °C. Among the alloys, all the three alloys TiZrFeMnCrVx (x = 1.0, 1.5, 2.0 at%) exhibit higher hydrogen absorption properties, which absorb 1.91, 1.93 and 1.91 wt% of hydrogen at 30 °C, respectively. Among them, the TiZrFeMnCrVx (x = 1.0 at%) alloy shows the best dehydrogenation performance, starting to release hydrogen at 151.33 °C and terminating at 346.36 °C. Meanwhile, the TiZrFeMnCrVx (x = 1.0 at%) exhibits remarkable cycle stability and displays a reversible gravimetric capacity of 98% after 15 cycles.