Extensive Lattice Research Articles

Interfacial stability and electronic properties of YBCO/ABO3 heterostructures: A comparative DFT study

In this study, we utilized density functional theory (DFT) to analyze the interfacial properties of YBa2Cu3O7 (YBCO) with perovskite metal oxides LaAlO3 (LAO), KTaO3 (KTO), and SrTiO3 (STO). We focused on surface energies, lattice mismatches, strain energies, and adhesion energies to gauge the stability and compatibility of these interfaces. Our findings indicate that KTO exhibits the highest surface preference due to its lowest surface energy (0.054 eV/Å 2), suggesting superior surface stability. Moreover, LAO and STO show minor lattice mismatches with YBCO, implying effective interface integration, while YBCO/KTO interfaces experience significant strain due to extensive lattice mismatches. STO is distinguished by the lowest strain energy (0.07 eV), indicating minimal energy requirement for lattice mismatch accommodation, unlike KTO, which demonstrates high strain energy (0.42 eV) and potential structural distortions. The strongest interfacial bond, as indicated by an adhesion energy of −2.16 eV, was observed at YBCO/LAO, while the weakest was found at the YBCO/KTO interface, with an adhesion energy of −0.56 eV. Additionally, charge density difference (CDD) analysis highlighted electron density redistribution at the interfaces, predominantly around interfacial oxygen atoms, indicating a mix of ionic and covalent bonding. This study provides comparative insights into the interfacial characteristics of YBCO/ABO3 heterostructures, suggesting pathways for optimizing their design and performance.

Effect of secondary orientation on the tensile behavior of single-crystal superalloys with [001] primary orientation at 760 °C

This study assesses the impact of secondary orientations on the tensile deformation behavior of single-crystal superalloys at mid-temperature of 760 °C. Tensile tests and stress-strain analyses were performed on specimens with primary orientation [001] and secondary orientations [100], [410], and [110]. Stress distributions were modeled using Abaqus software, while fracture behavior, slip system activation, oxidation, lattice rotation, and micro-dislocation movements were investigated using optical microscopy (OM), scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM). Findings reveal that the [100] orientation, due to the activation of coplanar dual slip systems, underwent significant strain hardening, exhibiting the highest strength and lowest ductility due to restricted lattice rotation. In contrast, the [410] and [110] orientations, each with a single primary slip system, showed reduced strength. The [410] orientation demonstrated enhanced ductility due to extensive lattice rotation, whereas the [110] orientation displayed the lowest strength, primarily due to premature cracking aligned with slip lines on the surface oxide film. Dominant deformation microstructures involved isolated stacking faults (SFs) shearing into γ′ precipitates, with the formation of immobile dual Lomer-Cottrell (L-C) locks at intersecting slip planes significantly contributing to microstructural strengthening.

Randomized Quasi-Monte Carlo Methods on Triangles: Extensible Lattices and Sequences

Randomized Quasi-Monte Carlo Methods on Triangles: Extensible Lattices and Sequences

Ab initio generalized Langevin equation

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

Abstract 2009: Novel clinically relevant CLIP-170 variants display an extended conformation microtubule-lattice bound conformation associated with taxane resistance

Abstract Taxanes are microtubule (MT)-stabilizing drugs widely used for the treatment of solid tumors, including the highly prevalent cancers of the breast, the prostate and gastric cancer. However, despite their initial activity, taxane resistance invariably occurs, leaving patients with limited therapeutic options. Currently, the molecular determinants of clinical taxane resistance remain poorly understood. We recently identified CLIP-170S, a novel truncated variant of the MT plus-end binding protein CLIP-170, that confers taxane resistance in vitro and is associated with clinical taxane resistance in patients with gastric cancer. We further showed that CLIP-170S is aberrantly localized along the MT lattice, thus impairing taxane access to its binding site in the MT lumen. However, the mechanism underlying the resistance-inducing extensive lattice localization of CLIP-170S is unknown. The activity and MT binding properties of canonical CLIP-170 are regulated by conformational changes mediated by the interaction of its N- and C-terminal domains. In its inactive, “closed” conformation, CLIP-170 is soluble as the N- and C-terminal domains interact with each other. In the active “open” conformation, CLIP-170’s N- and C-terminal domains are apart, thus exposing its MT-binding domain and allowing MT plus-end binding. As CLIP-170S is missing part of its N-terminal domain, we hypothesized that CLIP-170S is constitutively displayed in an open conformation that promotes its extensive and aberrant localization to the MT lattice. To prove this hypothesis, we used the FKBP-rapalog-FRB system to “force” CLIP-170S to assume a “closed” conformation. We generated a fusion CLIP-170S protein tagged with FKBP and FRB domains in its N- and C-terminal, respectively. The addition of rapalog induced FKBP (N-ter) and FRB (C-ter) domains to interact, promoting CLIP-170S to adopt a “closed” conformation. CLIP-170S in this “closed” conformation resulted in its release from the MT-lattice and restored taxane binding to MTs. We next extended our search to other CLIP-170 clinically prevalent variants with sequence alteration predicted to bind to the MT-lattice and potentially interfere with taxane sensitivity. This search identified CLIP-170IR (an intron retention variant) and several other truncation mutants prevalent in gastric, breast and lung cancer cell lines. Experimentally, we showed that these variants not only phenocopy CLIP-170S binding to the MT- lattice but also confer taxane-resistance. Together, these data demonstrate a novel mechanism of taxane resistance mediated by CLIP-170 mutations that induce CLIP-170 to adopt a constitutively “open” MT-lattice binding conformation, which renders them susceptible to causing taxane resistance. Citation Format: Urko del Castillo, Kiran Kumari Sahu, William G. Stone, Manish A. Shah, Paraskevi Giannakakou. Novel clinically relevant CLIP-170 variants display an extended conformation microtubule-lattice bound conformation associated with taxane resistance [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2009.

Adjoints of matroids

We first show that an adjoint of a loopless matroid is connected if and only if the original matroid is connected. By proving that the opposite lattice of a modular matroid is isomorphic to its extension lattice, we obtain that a modular matroid has only one adjoint (up to isomorphism) which can be given by its opposite lattice. This makes projective geometries become a key ingredient in characterizing the adjoint sequence ad0M,adM,ad2M,… of a connected matroid M. We classify such adjoint sequences into three types: finite, cyclic and convergent. For the first two types, the adjoint sequences eventually stabilize at finite projective geometries except for free matroids. For the last type, the infinite non-repeating adjoint sequences are convergent to infinite projective geometries.

Regular Double p-Algebras: A Converse to a Katriňák Theorem and Applications

ABSTRACT In 1973, Katriňák proved that regular double p-algebras can be regarded as (regular) double Heyting algebras by ingeniously constructing binary terms for the Heyting implication and its dual in terms of pseudocomplement and its dual. In this paper, we prove a converse to Katriňák’s theorem, in the sense that in the variety ℝ D ℙ ℂ ℍ \[\mathbb{R}\mathbb{D}\mathbb{P}\mathbb{C}\mathbb{H}\] of regular dually pseudocomplemented Heyting algebras, the implication operation → satisfies Katriňák’s formula. As applications of this result together with the above-mentioned Katriňák’s theorem, we show that the varieties ℝ D B L ℙ \[\mathbb{R}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{P}\] , ℝ D ℙ ℂ ℍ \[\mathbb{R}\mathbb{D}\mathbb{P}\mathbb{C}\mathbb{H}\] , ℝ ℙ ℂ ℍ d \[\mathbb{R}\mathbb{P}\mathbb{C}{{\mathbb{H}}^{d}}\] and ℝ D B L ℍ \[\mathbb{R}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{H}\] of regular double p-algebras, regular dually pseudocomplemented Heyting algebras, regular pseudocomplemented dual Heyting algebras, and regular double Heyting algebras, respectively, are term-equivalent to each other and also that the varieties ℝ D M ℙ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{P}\] , ℝ D M ℍ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{H}\] , ℝ D M D B L ℍ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{H}\] , ℝ D M D B L ℙ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{P}\] of regular De Morgan p-algebras, regular De Morgan Heyting algebras, regular De Morgan double Heyting algebras, and regular De Morgan double p-algebras, respectively, are also term-equivalent to each other. From these results and recent results of Adams, Sankappanavar and Vaz de Carvalho on varieties of regular double p-algebras and regular pseudocomplemented De Morgan algebras, we deduce that the lattices of subvarieties of all these varieties have cardinality 2 ℵ 0 \[{{2}^{{{\aleph }_{0}}}}\] . We then define new logics, ℛ D P C ℋ \[\mathcal{R}\mathcal{D}\mathcal{P}\mathcal{C}\mathcal{H}\] , ℛ P C ℋ d \[\mathcal{R}\mathcal{P}\mathcal{C}{{\mathcal{H}}^{d}}\] and ℛ D ℳ ℋ \[\mathcal{R}\mathcal{D}\mathcal{M}\mathcal{H}\] , and show that they are algebraizable with ℝ D ℙ ℂ ℍ \[\mathbb{R}\mathbb{D}\mathbb{P}\mathbb{C}\mathbb{H}\] , ℝ ℙ ℂ ℍ d \[\mathbb{R}\mathbb{P}\mathbb{C}{{\mathbb{H}}^{d}}\] and ℝ D M ℍ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{H}\] , respectively, as their equivalent algebraic semantics. It is also deduced that the lattices of extensions of all of the above mentioned logics have cardinality 2 ℵ 0 \[{{2}^{{{\aleph }_{0}}}}\] .

Deformation behavior of LPSO phases with regulated morphology and distribution and their role on dynamic recrystallization in hot-rolled Mg–Gd–Y–Zn–Zr alloy

Three relatively novel initial microstructures of Mg–Gd–Y–Zn–Zr alloy were regulated by heat treatment, the deformation behavior of long period stacking ordered (LPSO) phases with different morphology and distribution and their role on recrystallization during thermal deformation were systematically investigated. The interdendritic block-shaped LPSO phases exhibit higher deformation resistance, and shearing, bending, kinking, tearing, dissolution, together with the breaking of plate-shaped lamellae produced by dissolution, are the main deformation mechanisms for them to coordinate deformation. As for the lamellar LPSO phases, deformation behaviors such as shearing, bending, kinking and breaking mainly occur. The interdendritic block-shaped LPSO promote recrystallization through the particle-stimulated nucleation (PSN) mechanism, and the PSN effect is enhanced with the increasing phase fraction, also, the broken block-shaped LPSO have better PSN effect. Recrystallized grains tend to nucleate at the kink of lamellar LPSO and form recrystallized grains bands along the kink bands; the fragmented fine lamellae have better PSN effect, promoting numerous recrystallization nucleation in the severely deformation zone, meanwhile, the joint pinning effect of the fragmented lamellae and precipitates β-phase results in the smaller recrystallized grains size. However, the intragranular continuous large-sized lamellar LPSO strongly pin the dislocation movement and hinder migration of recrystallized grain boundaries along the basal plane and c-axis of lamellar LPSO, making it difficult to achieve extensive lattice rotation, which is not conducive to the recrystallization nucleation. The most remarkable work in this paper is that we clarified the mechanism of different LPSO phases, especially lamellar LPSO phase, on recrystallization behavior, and these findings will provide microstructure regulation guidance for thermal-deformed Mg–Gd–Y–Zn–Zr alloys containing LPSO.

Laser‐induced Fano interference subsumed by electron–phonon coupling in orthorhombic KNbO3nano‐bricks: An ab initio vibrational and Raman spectroscopic investigation

AbstractHydrothermally prepared potassium niobate (KNbO3) nanoparticles are characterized meticulously to explore various crystallographic, microstructural, morphological, optical, compositional, and lattice‐vibrational properties. Laser power‐dependent Raman spectroscopy is employed to study the Fano effect in asymmetrically broadened optic (LO/TO) phonon modes in the orthorhombic KNbO3system, considering interference with the interband electronic continuum. The phonon softening, alterations in charge‐phonon coupling constant, linewidth and lifetime of phonon modes, and so on are explained in the light of theories formulated by Fano, Allen, and Hui, accompanying factor group analysis of the Raman‐active modes. Under local heating via focused laser irradiation, highly sensitive Raman spectra introspect perturbations in the generic vibrations at the first Brillouin zone center and moderations in the constructive/destructive interference conditions of resonant Fano scattering. Density functional theory (DFT)‐based calculations on phonon dispersion, density of phonon states, and relevant thermodynamic attributes decipher the theoretical background. Amid photoexcited electron plasma, the charge‐phonon coupling for distinct modes is strengthened considerably against strong excitation intensity without any unwanted anharmonicity, extensive lattice thermal expansion, phonon decay, or microscopic phase transformation. Finally, the direction of asymmetry, particle–particle, and particle–quasiparticle interactions are illustrated using Feynman diagrams for the associated and phonon modes.

Electronic, Magnetic, and Elastic Features of Quaternary Heusler Alloys: FeVScSb and FeVYSb

This study employs density functional theory to investigate the structural, elastic, electronic, and magnetic properties of FeVScSb and FeVYSb Heusler compounds. FeVScSb exhibits ferromagnetic properties in its stable state, whereas FeVYSb displays ferrimagnetic behavior. The obtained elastic constants (Cij) indicate that FeVScSb and FeVYSb possess mechanical stability and ductility, while also displaying a significant degree of elastic anisotropy. The aggregate magnetic moment of said alloys is determined to be equivalent to 3 μB, in accordance with the Slater–Pauling principle. The investigation of the impact of uniform strain on electronic and magnetic characteristics is conducted. The findings indicate that FeVScSb and FeVYSb exhibit semiconductivity within extensive lattice parameter intervals, ranging from 5.84 to 6.60 Å for FeVScSb and from 6.11 to 6.70 Å for FeVYSb. The Heusler compounds FeVScSb and FeVYSb exhibit half‐metallic behavior within a range of lattice parameters. Specifically, FeVScSb displays this behavior when the lattice parameter varies from 6.61 to 6.72 Å, while FeVYSb exhibits half‐metallicity within the range of 6.71–6.81 Å. Under the influence of strain, the magnetic moment retains a constant value of 3 μB. Therefore, the potential for spintronics is promising.

Bdellovibrio predation cycle characterized at nanometre-scale resolution with cryo-electron tomography.

Bdellovibrio bacteriovorus is a microbial predator that offers promise as a living antibiotic for its ability to kill Gram-negative bacteria, including human pathogens. Even after six decades of study, fundamental details of its predation cycle remain mysterious. Here we used cryo-electron tomography to comprehensively image the lifecycle of B. bacteriovorus at nanometre-scale resolution. With high-resolution images of predation in a native (hydrated, unstained) state, we discover several surprising features of the process, including macromolecular complexes involved in prey attachment/invasion and a flexible portal structure lining a hole in the prey peptidoglycan that tightly seals the prey outer membrane around the predator during entry. Unexpectedly, we find that B. bacteriovorus does not shed its flagellum during invasion, but rather resorbs it into its periplasm for degradation. Finally, following growth and division in the bdelloplast, we observe a transient and extensive ribosomal lattice on the condensed B. bacteriovorus nucleoid.

HIV-2 Immature Particle Morphology Provides Insights into Gag Lattice Stability and Virus Maturation

Retrovirus immature particle morphology consists of a membrane enclosed, pleomorphic, spherical and incomplete lattice of Gag hexamers. Previously, we demonstrated that human immunodeficiency virus type 2 (HIV-2) immature particles possess a distinct and extensive Gag lattice morphology. To better understand the nature of the continuously curved hexagonal Gag lattice, we have used the single particle cryo-electron microscopy method to determine the HIV-2 Gag lattice structure for immature virions. The reconstruction map at 5.5 Å resolution revealed a stable, wineglass-shaped Gag hexamer structure with structural features consistent with other lentiviral immature Gag lattice structures. Cryo-electron tomography provided evidence for nearly complete ordered Gag lattice structures in HIV-2 immature particles. We also solved a 1.98 Å resolution crystal structure of the carboxyl-terminal domain (CTD) of the HIV-2 capsid (CA) protein that identified a structured helix 12 supported via an interaction of helix 10 in the absence of the SP1 region of Gag. Residues at the helix 10–12 interface proved critical in maintaining HIV-2 particle release and infectivity. Taken together, our findings provide the first 3D organization of HIV-2 immature Gag lattice and important insights into both HIV Gag lattice stabilization and virus maturation.

Extensions and Congruences of Partial Lattices

Abstract For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the one-point extension of a partial lattice need not be a lattice. We describe these two-point extensions and prove several properties of them. We introduce the concept of a congruence on a partial lattice and show its relationship to the notion of a homomorphism and its connections with congruences on the corresponding two-point extension. In particular we prove that the quotient L/E of a partial lattice L by a congruence E on L is again a partial lattice and that the two-point extension of L/E is isomorphic to the quotient lattice of the two-point extension L * of L by the congruence on L * generated by E. Several illustrative examples are enclosed.

A Logic for Dually Hemimorphic Semi-Heyting Algebras and its Axiomatic Extensions

The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras.

Oxide Cathodes: Functions, Instabilities, Self Healing, and Degradation Mitigations.

Recent progress in high-energy-density oxide cathodes for lithium-ion batteries has pushed the limits of lithium usage and accessible redox couples. It often invokes hybrid anion- and cation-redox (HACR), with exotic valence states such as oxidized oxygen ions under high voltages. Electrochemical cycling under such extreme conditions over an extended period can trigger various forms of chemical, electrochemical, mechanical, and microstructural degradations, which shorten the battery life and cause safety issues. Mitigation strategies require an in-depth understanding of the underlying mechanisms. Here we offer a systematic overview of the functions, instabilities, and peculiar materials behaviors of the oxide cathodes. We note unusual anion and cation mobilities caused by high-voltage charging and exotic valences. It explains the extensive lattice reconstructions at room temperature in both good (plasticity and self-healing) and bad (phase change, corrosion, and damage) senses, with intriguing electrochemomechanical coupling. The insights are critical to the understanding of the unusual self-healing phenomena in ceramics (e.g., grain boundary sliding and lattice microcrack healing) and to novel cathode designs and degradation mitigations (e.g., suppressing stress-corrosion cracking and constructing reactively wetted cathode coating). Such mixed ionic-electronic conducting, electrochemically active oxides can be thought of as almost "metalized" if at voltages far from the open-circuit voltage, thus differing significantly from the highly insulating ionic materials in electronic transport and mechanical behaviors. These characteristics should be better understood and exploited for high-performance energy storage, electrocatalysis, and other emerging applications.

A novel two-dimensional C36 fullerene network; an isotropic, auxetic semiconductor with low thermal conductivity and remarkable stiffness

The synthesis of two-dimensional (2D) C60 fullerene network (Nature (2022), 606, 507) with an anisotropic lattice is among the most exciting advances in the field of carbon-based materials, which has the potential to expand and establish a new class of 2D materials. In this work, a novel C36 fullerene 2D network with an isotropic structure is designed by screening of extensive and diverse fullerene lattices. Density functional theory calculations confirm that the herein predicted C36 fullerene network can exhibit an outstanding thermal stability up to 1500 K, an elastic modulus of 266 GPa, a negative Poisson's ratio of −0.05, and an indirect semiconducting electronic nature, with a HSE06(PBE) bad gap of 1.63 (0.97) eV. The phonon dispersion relation, mechanical and failure responses, and lattice thermal conductivity are explored with the aid of machine learning interatomic potentials (MLIPs). MLIP-based calculations close to the ground state confirm the dynamical stability, a negative Poisson's ratio of −0.06, an elastic modulus of 269 GPa, and a high tensile strength of around 26.8 GPa for the predicted 2D network. Room temperature phononic thermal conductivity and tensile strength are also predicted to be 9.8 ± 1 W/m.K and 15.9 GPa, respectively. This study introduces a novel isotropic and auxetic semiconducting full-carbon nanoporous nanosheet, with low thermal conductivity and appealing electronic, optical, and mechanical features, highlighting a bright prospect for the design and synthesis of novel fullerene-based 2D networks.

Whitney numbers of matroid extensions and co-extensions

Crapo found that single-element extensions of matroid are equivalent to modular cuts. This paper will study the single-element extension and co-extension of a matroid and establish the upper semi-continuity for the signless coefficients of Whitney polynomials and Whitney numbers on both extensions via its extension lattice, a lattice of all non-empty modular cuts.

Structural Completeness in Many-Valued Logics with Rational Constants

The logics RŁ, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, RŁ is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q-universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of RP. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of RP, and this is also the case for extensions of RG, where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of RG, we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is Q-universal.

Quantum Defects: What Pairs with the Aryl Group When Bonding to the sp2 Carbon Lattice of Single-Wall Carbon Nanotubes?

Aryl diazonium reactions are widely used to covalently modify graphitic electrodes and low-dimensional carbon materials, including the recent creation of organic color centers (OCCs) on single-wall carbon nanotube semiconductors. However, due to the experimental difficulties in resolving small functional groups over extensive carbon lattices, a basic question until now remains unanswered: what group, if any, is pairing with the aryl sp3 defect when breaking a C═C bond on the sp2 carbon lattice? Here, we show that water plays an unexpected role in completing the diazonium reaction with carbon nanotubes involving chlorosulfonic acid, acting as a nucleophilic agent that contributes -OH as the pairing group. By simply replacing water with other nucleophilic solvents, we find it is possible to create OCCs that feature an entirely new series of pairing groups, including -OCH3, -OC2H5, -OC3H7, -i-OC3H7, and -NH2, which allows us to systematically tailor the defect pairs and the optical properties of the resulting color centers. Enabled by these pairing groups, we further achieved the synthesis of OCCs with sterically bulky pairs that exhibit high purity defect photoluminescence effectively covering both the second near-infrared window and the telecom wavelengths. Our studies further suggest that these diazonium reactions proceed through the formation of carbocations in chlorosulfonic acid, rather than a radical mechanism that typically occurs in aqueous solutions. These findings uncover the unknown half of the sp3 defect pairs and provide a synthetic approach to control these defect color centers for quantum information, imaging, and sensing.

Effects of magnetic and non-magnetic doping on the vortex lattice in MgB2

Small-angle neutron scattering has been used to study the vortex lattice in superconducting MgB2 doped with either manganese or carbon to achieve a similar suppression of the critical temperature. Measurements were performed with the magnetic field applied along the c axis, where the vortex lattice in pure MgB2 is known to undergo a field- and temperature-driven 30° rotation transition. For Mn doping, the vortex lattice phase diagram remains qualitatively similar to that of pure MgB2, indicating only a modest effect on the vortex–vortex interaction. In contrast, the vortex lattice rotation transition is completely suppressed in the C-doped case, probably due to a change in the electronic structure which affects the two-band/two-gap nature of superconductivity in MgB2. The vortex lattice longitudinal correlation length shows the opposite behavior, remaining roughly unchanged between pure and C-doped MgB2 while it is significantly reduced in the Mn-doped case. However, the extensive vortex lattice metastability and related activated behavior, observed in conjunction with the vortex lattice transition in pure MgB2, are also seen in the Mn-doped sample. This shows that the vortex lattice disordering is not associated with a substantially increased vortex pinning.