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Keywords = complete residuated lattice

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30 pages, 4851 KB  
Article
Scalable Production of Boron Nitride-Coated Carbon Fiber Fabrics for Improved Oxidation Resistance
by Cennet Yıldırım Elçin, Muhammet Nasuh Arık, Kaan Örs, Uğur Nakaş, Zeliha Bengisu Yakışık Özgüle, Özden Acar, Salim Aslanlar, Özkan Altay, Erdal Çelik and Korhan Şahin
J. Compos. Sci. 2025, 9(10), 564; https://doi.org/10.3390/jcs9100564 - 14 Oct 2025
Viewed by 271
Abstract
This study aimed to develop an industrially scalable coating route for enhancing the oxidation resistance of carbon fiber fabrics, a critical requirement for next-generation aerospace and high-temperature composite structures. To achieve this goal, synthesis of hexagonal boron nitride (h-BN) layers was achieved via [...] Read more.
This study aimed to develop an industrially scalable coating route for enhancing the oxidation resistance of carbon fiber fabrics, a critical requirement for next-generation aerospace and high-temperature composite structures. To achieve this goal, synthesis of hexagonal boron nitride (h-BN) layers was achieved via a single wet step in which the fabric was impregnated with an ammonia–borane/THF solution and subsequently nitrided for 2 h at 1000–1500 °C in flowing nitrogen. Thermogravimetric analysis coupled with X-ray diffraction revealed that amorphous BN formed below ≈1200 °C and crystallized completely into (002)-textured h-BN (with lattice parameters a ≈ 2.50 Å and c ≈ 6.7 Å) once the dwell temperature reached ≥1300 °C. Complementary XPS, FTIR and Raman spectroscopy confirmed a near-stoichiometric B:N ≈ 1:1 composition and the elimination of O–H/N–H residues as crystallinity improved. Low-magnification SEM (100×) confirmed the uniform and large-area coverage of the BN layer on the carbon fiber tows, while high-magnification SEM revealed a progressive densification of the coating from discrete nanospheres to a continuous nanosheet barrier on the fibers. Oxidation tests in flowing air shifted the onset of mass loss from 685 °C for uncoated fibers to 828 °C for the coating produced at 1400 °C; concurrently, the peak oxidation rate moved ≈200 °C higher and declined by ~40%. Treatment at 1500 °C conferred no additional benefit, indicating that 1400 °C provides the optimal balance between full crystallinity and limited grain coarsening. The resulting dense h-BN film, aided by an in situ self-healing B2O3 glaze above ~800 °C, delayed carbon fiber oxidation by ≈140 °C. Overall, the process offers a cost-effective, large-area alternative to vapor-phase deposition techniques, positioning BN-coated carbon fiber fabrics for robust service in extreme oxidative environments. Full article
(This article belongs to the Section Fiber Composites)
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11 pages, 10889 KB  
Article
Post-Irradiation Annealing of Bi Ion Tracks in Si3N4: In-Situ and Ex-Situ Transmission Electron Microscopy Study
by Anel Ibrayeva, Jacques O’Connell, Ruslan Rymzhanov, Arno Janse van Vuuren and Vladimir Skuratov
Crystals 2025, 15(10), 852; https://doi.org/10.3390/cryst15100852 - 30 Sep 2025
Viewed by 238
Abstract
High-energy (710 MeV) Bi ion track morphology in polycrystalline silicon nitride was investigated during post-irradiation annealing. Using both in-situ and ex-situ transmission electron microscopy, we monitored the recovery of crystallinity within initially amorphous ion track regions. In-situ annealing involved heating samples from room [...] Read more.
High-energy (710 MeV) Bi ion track morphology in polycrystalline silicon nitride was investigated during post-irradiation annealing. Using both in-situ and ex-situ transmission electron microscopy, we monitored the recovery of crystallinity within initially amorphous ion track regions. In-situ annealing involved heating samples from room temperature to 1000 °C in 50 °C increments, each held for 10 s. We observed a steady decrease in both the size and number of tracks, with only a small number of residual crystalline defects remaining at 1000 °C. Ex-situ annealing experiments were conducted at 400 °C, 700 °C, and 1000 °C for durations of 10, 20, and 30 min. Complete restoration of the crystalline lattice occurred after 30 min at 700 °C and 20 min at 1000 °C. Due to inherent differences in geometry, heat flow, and stress conditions between thin lamella and bulk specimens, in-situ and ex-situ results cannot be compared. Molecular dynamics simulations further revealed that track shrinkage begins in cells within picoseconds, supporting the notion that recrystallization can start on very short timescales. Overall, these findings demonstrate that thermal recrystallization of damage induced by swift heavy ion irradiation in polycrystalline Si3N4 is possible. This study provides a foundation for future research aimed at better understanding radiation damage recovery in this material. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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23 pages, 3820 KB  
Article
Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras
by Xingna Zhang, Eunsuk Yang and Xiaohong Zhang
Axioms 2024, 13(11), 799; https://doi.org/10.3390/axioms13110799 - 18 Nov 2024
Viewed by 1008
Abstract
As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the [...] Read more.
As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the ‘semi-Θ-Ξ function’, which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures. Full article
(This article belongs to the Special Issue Fuzzy Systems, Fuzzy Decision Making, and Fuzzy Mathematics)
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12 pages, 6413 KB  
Article
Approach towards the Purification Process of FePO4 Recovered from Waste Lithium-Ion Batteries
by Liuyang Bai, Guangye Liu, Yufang Fu, Wenbin Sun, Xiaomao Zeng, Rumeng Shao, Huiming Ou, Yunting Liang and Fangli Yuan
Processes 2024, 12(9), 1861; https://doi.org/10.3390/pr12091861 - 31 Aug 2024
Cited by 3 | Viewed by 3465
Abstract
The rapid development of new energy vehicles and Lithium-Ion Batteries (LIBs) has significantly mitigated urban air pollution. However, the disposal of spent LIBs presents a considerable threat to the environment. Recycling these waste LIBs not only addresses the environmental issues but also compensates [...] Read more.
The rapid development of new energy vehicles and Lithium-Ion Batteries (LIBs) has significantly mitigated urban air pollution. However, the disposal of spent LIBs presents a considerable threat to the environment. Recycling these waste LIBs not only addresses the environmental issues but also compensates for resource shortages and generates substantial economic benefits. Current recycling processes primarily focus on the extraction of valuable metals, often overlooking the treatment of residual waste post-extraction. This project targets the iron phosphate (FePO4) derived from waste lithium iron phosphate (LFP) battery materials, proposing a direct acid leaching purification process to obtain high-purity iron phosphate. This purified iron phosphate can then be used for the preparation of new LFP battery materials, aiming to establish a complete regeneration cycle that recovers lithium carbonate and iron phosphate from waste LFP materials for the production of LFP. The study investigates process parameters such as acid types and concentrations, leaching time, and the number of leaching cycles. The results demonstrate that, after purification, the levels of impurity metals decrease while the iron content increases correspondingly. Under optimized experimental conditions, the dilute sulfuric acid leaching rates of Al, Cu, Ca, and Ni reached 36.0%, 51.4%, 89.5%, and 90.9%, respectively. Furthermore, hydrothermal treatment in dilute phosphoric acid achieved leaching rates of 87.9%, 85.8%, 98.4%, and 99.1% for Al, Ca, Cu, and Ni, respectively. The microstructure characterization revealed significant changes in phase and grain morphology during the leaching process in dilute phosphoric acid, which are likely associated with the liberation of impurity atoms from the lattice. These findings indicate that acid leaching is highly effective in removing impurities from the iron phosphate recycled from waste LIBs. Full article
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15 pages, 5601 KB  
Article
Precipitation Thermodynamics in an Al–Zn–Mg Alloy with Different Grain Sizes
by Zhen Wang, Siqi Huang, Wenkai Zhang, Shunqiang Li and Jizi Liu
Metals 2024, 14(6), 625; https://doi.org/10.3390/met14060625 - 25 May 2024
Cited by 1 | Viewed by 1986
Abstract
In order to gain insight into the influence of grain size on precipitation thermodynamics, bulk materials of coarse-grained (CG), ultrafine-grained (UFG) (with or without dislocations), and nanocrystalline (NC) 7075 Al alloy have been fabricated by solid solution treatment, equal-channel angular pressing (ECAP), or [...] Read more.
In order to gain insight into the influence of grain size on precipitation thermodynamics, bulk materials of coarse-grained (CG), ultrafine-grained (UFG) (with or without dislocations), and nanocrystalline (NC) 7075 Al alloy have been fabricated by solid solution treatment, equal-channel angular pressing (ECAP), or high-pressure torsion (HPT) processes. The precipitation behavior and the corresponding thermal phenomenon were studied by transmission electron microscopy (TEM) and differential scanning calorimetry (DSC) heating. The results indicated that there are significant differences in precipitation thermodynamics among the four bulk materials. In the CG and UFG materials without dislocations, homogeneous nucleation is the primary precipitation mechanism. However, the nucleation of the GP zones is suppressed at lower temperatures due to a reduction in the number of residual vacancies and the supersaturation in the UFG interiors. This is attributed to the absorption of vacancies and solute atoms by a greater volume of grain boundaries. It can be observed that the greater the excess of vacancies remaining in grain interiors, the lower the temperature at which nucleation of GP zones occurs. Defect-assisted heterogeneous nucleation was identified as the predominant precipitation mechanism in the UFG materials with dislocations and the NC materials. These defects encompass dislocations, lattice distortions, and grain boundaries. The decomposition processes of solid solutions were found to be almost complete at a lower temperature. The presence of dislocations, lattice distortions, and grain boundaries enables solute atoms to diffuse at a much faster rate, significantly enhancing the precipitation rate and reducing the nucleation and formation energies of various precipitate phases. Full article
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14 pages, 3786 KB  
Article
Welding Residual Stress Elimination Technique in the Top Chord of Main Truss of Steel Truss Bridge
by Long Piao, Jianfeng Yuan, Niujing Ma, Changqi Yue, Ronghui Wang and Gangbing Zheng
Buildings 2023, 13(5), 1267; https://doi.org/10.3390/buildings13051267 - 12 May 2023
Cited by 3 | Viewed by 2139
Abstract
The large-amplitude fluctuations of ultrasound in high-energy ultrasonic stress relieving cause the crystal grains or lattices in the high residual stress zone to vibrate or creep alternately. This triggers secondary effects such as ultrasonic softening and dislocation movement. The sound field also produces [...] Read more.
The large-amplitude fluctuations of ultrasound in high-energy ultrasonic stress relieving cause the crystal grains or lattices in the high residual stress zone to vibrate or creep alternately. This triggers secondary effects such as ultrasonic softening and dislocation movement. The sound field also produces periodic shock waves or intermittent shock waves, which form local pressure gradients at the wave front. These pressure gradients cause local heating of the grain boundary, accelerating material softening and promoting slip between grains, ultimately resulting in residual stress elimination. This technique was applied to detect the welding residual stress of the upper chord of the main truss of Sanguantang Bridge by using an ultrasonic stress meter. After the measurement, it was found that the welding residual stress in some areas was too large, and the welding residual stress needed to be eliminated. The welding seam was re-inspected after the residual stress relief operation was completed. The test results showed a maximum reduction rate of 63.91% and an average overall reduction rate ranging from 24.52% to 37.23%. The reduction effect is more significant in areas with higher welding residual stress. Full article
(This article belongs to the Special Issue Recent Scientific Developments in Steel Structure)
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21 pages, 384 KB  
Article
The Single Axiomatization on CCRL-Fuzzy Rough Approximation Operators and Related Fuzzy Topology
by Yaoliang Xu, Dandan Zou and Lingqiang Li
Axioms 2023, 12(1), 37; https://doi.org/10.3390/axioms12010037 - 28 Dec 2022
Viewed by 1661
Abstract
It is well known that lattice-valued rough sets are important branches of fuzzy rough sets. The axiomatic characterization and related topology are the main research directions of lattice-valued rough sets. For L=(L,), a complete co-residuated lattice [...] Read more.
It is well known that lattice-valued rough sets are important branches of fuzzy rough sets. The axiomatic characterization and related topology are the main research directions of lattice-valued rough sets. For L=(L,), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on the basis of the L-fuzzy relation. In this article, we give a further study on Qiao’s LFLAO around the axiomatic characterization and induced L-topology. Firstly, we investigate and discuss three new LFLAO generated by ⊛-transitive, ⊛-Euclidean and ⊛-mediated L-fuzzy relations. Secondly, we utilize a single axiom to characterize the LFLAO generated by serial, symmetric, reflexive, ⊛-transitive and ⊛-mediate L-fuzzy relations and their compositions. Thirdly, we present a method to generate Alexandrov L-topology (ALTPO) from LFLAO and construct a bijection between ALTPO and ⊛-preorder (i.e., reflexive and ⊛-transitive L-fuzzy relation) on the same underlying set. Full article
(This article belongs to the Special Issue Non-classical Logics and Related Algebra Systems)
11 pages, 5021 KB  
Article
Effect of Substrate-RF on Sub-200 nm Al0.7Sc0.3N Thin Films
by Michele Pirro, Xuanyi Zhao, Bernard Herrera, Pietro Simeoni and Matteo Rinaldi
Micromachines 2022, 13(6), 877; https://doi.org/10.3390/mi13060877 - 31 May 2022
Cited by 17 | Viewed by 3292
Abstract
Sc-doped aluminum nitride is emerging as a new piezoelectric material which can substitute undoped aluminum nitride (AlN) in radio-frequency MEMS applications, thanks to its demonstrated enhancement of the piezoelectric coefficients. Furthermore, the recent demonstration of the ferroelectric-switching capability of the material gives AlScN [...] Read more.
Sc-doped aluminum nitride is emerging as a new piezoelectric material which can substitute undoped aluminum nitride (AlN) in radio-frequency MEMS applications, thanks to its demonstrated enhancement of the piezoelectric coefficients. Furthermore, the recent demonstration of the ferroelectric-switching capability of the material gives AlScN the possibility to integrate memory functionalities in RF components. However, its high-coercive field and high-leakage currents are limiting its applicability. Residual stress, growth on different substrates, and testing-temperature have already been demonstrated as possible knobs to flatten the energy barrier needed for switching, but no investigation has been reported yet on the whole impact on the dielectric and ferroelectric dynamic behavior of a single process parameter. In this context, we analyze the complete spectrum of variations induced by the applied substrate-RF, from deposition characteristics to dielectric and ferroelectric properties, proving its effect on all of the material attributes. In particular, we demonstrate the possibility of engineering the AlScN lattice cell to properly modify leakage, breakdown, and coercive fields, as well as polarization charge, without altering the crystallinity level, making substrate-RF an effective and efficient fabrication knob to ease the limitations the material is facing. Full article
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16 pages, 333 KB  
Article
ZL-Completions for ZL-Semigroups
by Shuhua Su, Qingguo Li and Qi Li
Symmetry 2022, 14(3), 578; https://doi.org/10.3390/sym14030578 - 15 Mar 2022
Cited by 1 | Viewed by 2025
Abstract
In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where [...] Read more.
In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where L is a complete residuated lattice. For this asymmetric mathematical structure, we define a ZL-completion of it to be a complete residuated L-ordered semigroup together with a join-dense L-ordered semigroup embedding satisfying the universal property. We prove that: (1) For every compositive ZL, the category CSL of complete residuated L-ordered semigroups is a reflective subcategory of the category SZL of ZL-semigroups; (2) for an arbitrary ZL, there is an adjunction between SZL and the category SZLE of weakly ZL-continuous L-ordered semigroup embeddings of ZL-semigroups. By appropriate specialization of ZL, the results can be applied to the DML-completion, certain completions associated with fuzzy subset systems, etc. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
20 pages, 9608 KB  
Article
Spatiotemporal Evolution of Stress Field during Direct Laser Deposition of Multilayer Thin Wall of Ti-6Al-4V
by Sergei Ivanov, Antoni Artinov, Evgenii Zemlyakov, Ivan Karpov, Sergei Rylov and Vaycheslav Em
Materials 2022, 15(1), 263; https://doi.org/10.3390/ma15010263 - 30 Dec 2021
Cited by 11 | Viewed by 2501
Abstract
The present work seeks to extend the level of understanding of the stress field evolution during direct laser deposition (DLD) of a 3.2 mm thick multilayer wall of Ti-6Al-4V alloy by theoretical and experimental studies. The process conditions were close to the conditions [...] Read more.
The present work seeks to extend the level of understanding of the stress field evolution during direct laser deposition (DLD) of a 3.2 mm thick multilayer wall of Ti-6Al-4V alloy by theoretical and experimental studies. The process conditions were close to the conditions used to produce large-sized structures by the DLD method, resulting in specimens having the same thermal history. A simulation procedure based on the implicit finite element method was developed for the theoretical study of the stress field evolution. The accuracy of the simulation was significantly improved by using experimentally obtained temperature-dependent mechanical properties of the DLD-processed Ti-6Al-4V alloy. The residual stress field in the buildup was experimentally measured by neutron diffraction. The stress-free lattice parameter, which is decisive for the measured stresses, was determined using both a plane stress approach and a force-momentum balance. The influence of the inhomogeneity of the residual stress field on the accuracy of the experimental measurement and the validation of the simulation procedure are analyzed and discussed. Based on the numerical results it was found that the non-uniformity of the through-thickness stress distribution reaches a maximum in the central cross-section, while at the buildup ends the stresses are distributed almost uniformly. The components of the principal stresses are tensile at the buildup ends near the substrate. Furthermore, the calculated equivalent plastic strain reaches 5.9% near the buildup end, where the deposited layers are completed, while the plastic strain is practically equal to the experimentally measured ductility of the DLD-processed alloy, which is 6.2%. The experimentally measured residual stresses obtained by the force-momentum balance and the plane stress approach differ slightly from each other. Full article
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23 pages, 4745 KB  
Article
Effect of Al2TiO5 Content and Sintering Temperature on the Microstructure and Residual Stress of Al2O3–Al2TiO5 Ceramic Composites
by Kunyang Fan, Wenhuang Jiang, Jesús Ruiz-Hervias, Carmen Baudín, Wei Feng, Haibin Zhou, Salvador Bueno and Pingping Yao
Materials 2021, 14(24), 7624; https://doi.org/10.3390/ma14247624 - 11 Dec 2021
Cited by 13 | Viewed by 3649
Abstract
A series of Al2O3–Al2TiO5 ceramic composites with different Al2TiO5 contents (10 and 40 vol.%) fabricated at different sintering temperatures (1450 and 1550 °C) was studied in the present work. The microstructure, crystallite structure, [...] Read more.
A series of Al2O3–Al2TiO5 ceramic composites with different Al2TiO5 contents (10 and 40 vol.%) fabricated at different sintering temperatures (1450 and 1550 °C) was studied in the present work. The microstructure, crystallite structure, and through-thickness residual stress of these composites were investigated by scanning electron microscopy, X-ray diffraction, time-of-flight neutron diffraction, and Rietveld analysis. Lattice parameter variations and individual peak shifts were analyzed to calculate the mean phase stresses in the Al2O3 matrix and Al2TiO5 particulates as well as the peak-specific residual stresses for different hkl reflections of each phase. The results showed that the microstructure of the composites was affected by the Al2TiO5 content and sintering temperature. Moreover, as the Al2TiO5 grain size increased, microcracking occurred, resulting in decreased flexure strength. The sintering temperatures at 1450 and 1550 °C ensured the complete formation of Al2TiO5 during the reaction sintering and the subsequent cooling of Al2O3–Al2TiO5 composites. Some decomposition of AT occurred at the sintering temperature of 1550 °C. The mean phase residual stresses in Al2TiO5 particulates are tensile, and those in the Al2O3 matrix are compressive, with virtually flat through-thickness residual stress profiles in bulk samples. Owing to the thermal expansion anisotropy in the individual phase, the sign and magnitude of peak-specific residual stress values highly depend on individual hkl reflection. Both mean phase and peak-specific residual stresses were found to be dependent on the Al2TiO5 content and sintering temperature of Al2O3–Al2TiO5 composites, since the different developed microstructures can produce stress-relief microcracks. The present work is beneficial for developing Al2O3–Al2TiO5 composites with controlled microstructure and residual stress, which are crucial for achieving the desired thermal and mechanical properties. Full article
(This article belongs to the Special Issue Microstructural Design and Processing Control of Advanced Ceramics)
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21 pages, 318 KB  
Article
L-Fuzzy Rough Approximation Operators Based on Co-Implication and Their (Single) Axiomatic Characterizations
by Qiu Jin and Lingqiang Li
Axioms 2021, 10(3), 134; https://doi.org/10.3390/axioms10030134 - 27 Jun 2021
Cited by 3 | Viewed by 2302
Abstract
For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual [...] Read more.
For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual operator of the Qiao–Hu L-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the L-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean L-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively. Full article
19 pages, 11290 KB  
Article
Studies of Post-Fabrication Heat Treatment of L-PBF-Inconel 718: Effects of Hold Time on Microstructure, Annealing Twins, and Hardness
by Wakshum M. Tucho and Vidar Hansen
Metals 2021, 11(2), 266; https://doi.org/10.3390/met11020266 - 4 Feb 2021
Cited by 32 | Viewed by 5292
Abstract
The widely adopted temperature for solid solution heat treatment (ST) for the conventionally fabricated Inconel 718 is 1100 °C for a hold time of 1 h or less. This ST scheme is, however, not enough to dissolve Laves and annihilate dislocations completely in [...] Read more.
The widely adopted temperature for solid solution heat treatment (ST) for the conventionally fabricated Inconel 718 is 1100 °C for a hold time of 1 h or less. This ST scheme is, however, not enough to dissolve Laves and annihilate dislocations completely in samples fabricated with Laser metal powder bed fusion (L-PBF) additive manufacturing (AM)-Inconel 718. Despite this, the highest hardness obtained after aging for ST temperatures (970–1250 °C) is at 1100 °C/1 as we have ascertained in our previous studies. The unreleased residual stresses in the retained lattice defects potentially affect other properties of the material. Hence, this work aims to investigate if a longer hold time of ST at 1100 °C will lead to complete recrystallization while maintaining the hardness after aging or not. For this study, L-PBF-Inconel 718 samples were ST at 1100 °C at various hold times (1, 3, 6, 9, 16, or 24 h) and aged to study the effects on microstructure and hardness. In addition, a sample was directly aged to study the effects of bypassing ST. The samples (ST and aged) gain hardness by 43–49%. The high density of annealing twins evolved during 3 h of ST and only slightly varies for longer ST. Full article
(This article belongs to the Section Additive Manufacturing)
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24 pages, 314 KB  
Article
The Relations between Residuated Frames and Residuated Connections
by Yong Chan Kim and Ju-Mok Oh
Mathematics 2020, 8(2), 295; https://doi.org/10.3390/math8020295 - 21 Feb 2020
Cited by 1 | Viewed by 2321
Abstract
We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. [...] Read more.
We introduce the notion of (dual) residuated frames as a viewpoint of relational semantics for a fuzzy logic. We investigate the relations between (dual) residuated frames and (dual) residuated connections as a topological viewpoint of fuzzy rough sets in a complete residuated lattice. As a result, we show that the Alexandrov topology induced by fuzzy posets is a fuzzy complete lattice with residuated connections. From this result, we obtain fuzzy rough sets on the Alexandrov topology. Moreover, as a generalization of the Dedekind–MacNeille completion, we introduce R-R (resp. D R - D R ) embedding maps and R-R (resp. D R - D R ) frame embedding maps. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
8 pages, 1652 KB  
Article
An Evaluation of the Zeeman Shift of the 87Sr Optical Lattice Clock at the National Time Service Center
by Xiaotong Lu, Mojuan Yin, Ting Li, Yebing Wang and Hong Chang
Appl. Sci. 2020, 10(4), 1440; https://doi.org/10.3390/app10041440 - 20 Feb 2020
Cited by 10 | Viewed by 4281
Abstract
The Zeeman shift plays an important role in the evaluation of optical lattice clocks since a strong bias magnetic field is applied for departing Zeeman sublevels and defining a quantization axis. We demonstrated the frequency correction and uncertainty evaluation due to Zeeman shift [...] Read more.
The Zeeman shift plays an important role in the evaluation of optical lattice clocks since a strong bias magnetic field is applied for departing Zeeman sublevels and defining a quantization axis. We demonstrated the frequency correction and uncertainty evaluation due to Zeeman shift in the 87Sr optical lattice clock at the National Time Service Center. The first-order Zeeman shift was almost completely removed by stabilizing the clock laser to the average frequency of the two Zeeman components of mF = ±9/2. The residual first-order Zeeman shift arose from the magnetic field drift between measurements of the two stretched-state center frequencies; the upper bound was inferred as 4(5) × 10−18. The quadratic Zeeman shift coefficient was experimentally determined as –23.0(4) MHz/T2 and the final Zeeman shift was evaluated as 9.20(7) × 10−17. The evaluation of the Zeeman shift is a foundation for overall evaluation of the uncertainty of an optical lattice clock. This measurement can provide more references for the determination of the quadratic coefficient of 87Sr. Full article
(This article belongs to the Special Issue Optical Trapping)
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