Weak Lattice Research Articles

Distance functions and filter topological residuated lattices1

In this paper, we firstly extend C. C. chang’s distance functions from MV-algebras into residuated lattices. But in general, the functions may not be a distance function on residuated lattices. We introduce weak involutory residuated lattices, in which Chang’s function is a pseduo distance function. Moreover we prove that the functions become distance functions on involutory residuated lattices. Secondly by use of the function and a lattice filter, we define F-ball on residuated lattices, and we prove that the set of all F-balls forms a base of a topology τLF on an involutory residuated lattice. Moreover we show that the topology τLF on an involutory residuated lattice L makes L to be a topological residuated lattice. At last, we use filters instead of lattice filters to set up filter topologies on an involutory residuated lattice, and study the properties of the filter topologies.

Exploring Quantum Phases of Dipolar Gases through Quasicrystalline Confinement.

The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.

Phases and coherence of strongly interacting finite bosonic systems in shallow optical lattice

We explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function. Two new many-body phases: fragmented or quasi superfluid (QSF) and incomplete fragmented Mott or quasi Mott insulator (QMI) are emerged due to the strong interplay between short-range contact interaction and lattice depth. Fragmentation is utilized as a figure of merit to distinguish these two new phases. We utilize the eigenvalues of the reduced one-body density matrix and define an order parameter that characterizes the pathway from a very weak lattice to a deep lattice. We provide a detailed investigation through the measures of one- and two-body correlations and information entropy. We find that the structures in one- and two-body coherence are good markers to understand the gradual built-up of intra-well correlation and decay of inter-well correlation with increase in lattice depth. For the dipolar interaction, the many-body features become more distinct and true Mott state can appear even in a shallow lattice. Whereas, for incommensurate fraction of particles, incomplete localization happens that exhibits distinct features in the measure of two-body coherence.

Atomistic analysis on implantation effects of hydrogen ions and copper ions into 4H-SiC

The microstructure evolution of 4H-SiC under the implantation of hydron ions and copper ions was investigated using molecular dynamics (MD) simulations and experimental analysis. MD models were developed to simulate the implantation of single Cu2+ and H+ ions into SiC, analyzing lattice damage, amorphous defects, and temperature distribution. H+ ion implantation resulted in a higher number of amorphous atoms compared to Cu2+ ions. The maximum atomic temperature during Cu2+ ion implantation was significantly higher (1635 K) than during H+ ion implantation (950 K), although the volume of the temperature rise region was larger in the H+ model. Cu2+ ions induced more severe lattice vibrations than H+ ions. Atom movement along regions of weak lattice binding energy was observed. The study also examined overlapping multiple ion implantations, considering ion type, initial energy, and incident angle. Cu2+ ions exhibited smaller sputtering yield, projection range, number of amorphous atoms, and energy increment compared to H+ ions. A 0° incident angle resulted in higher sputtering yield and increased amorphous structure formation due to the channeling effect, which was more pronounced in the H+ model. The experimental results demonstrate that compared to Cu2+ ions, H+ ions have a greater impact on the surface peak roughness, sub-surface damage depth, and surface damage of SiC samples. It can provide a reliable guidance for selecting process parameters and the types of ions to implant.

Multifunctional Dual‐Metal‐Salt Derived Ternary Eutectic Electrolyte for Highly Reversible Zinc Ion Battery

AbstractDeep eutectic electrolytes offer opportunities for tailoring solvation structure and interface chemistry in advanced batteries, but developing deep eutectic electrolytes for high‐performance zinc ion batteries (ZIBs) remains a challenge. Herein, multifunctional dual‐metal‐salt derived ternary eutectic electrolytes (DMEEs) are designed via a supporting salt strategy for dendrite‐free and long‐lifespan ZIBs. DMEEs are constructed by zinc trifluoromethanesulfonate (Zn(OTF)2), supporting salt of lithium bis(trifluoromethanesulfonyl)imide, and neutral ligand of N‐methylacetamide. Noticeably, supporting salt with weak lattice energy not only induces the reconstruction of intermolecular interactions to form ion pairs and ion aggregates but also tailors the Zn2+ solvation structure and solid electrolyte interface (SEI). The developed DMEEs possess a dual‐anion‐rich Zn2+ solvation shell and induce an inorganic‐rich hybrid SEI, which effectively suppresses side reactions and obtains a dendrite‐free Zn anode with high reversibility. Remarkably, Zn//Zn cells demonstrate cycling stability for over 3000 h, and Zn//PANI full cells deliver no significant capacity decay after 5000 cycles at a high current density of 5 A g−1. This work opens a new avenue to design advanced deep eutectic electrolytes, and the deep understanding of solvation structure and SEI offers guidelines for developing high‐performance batteries.

Cofinitely weak f-supplemented lattices

In this paper, weakly [Formula: see text]-supplemented and cofinitely weak [Formula: see text]-supplemented lattices are introduced and studied. Let [Formula: see text] be an element of [Formula: see text] such that [Formula: see text]. If [Formula: see text] is weakly [Formula: see text]-supplemented and [Formula: see text] is weakly [Formula: see text]-supplemented, then [Formula: see text] is weakly [Formula: see text]-supplemented. A [Formula: see text]-complemented lattice with [Formula: see text]-small [Formula: see text]-radical is weakly [Formula: see text]-supplemented if and only if [Formula: see text] is [Formula: see text]-semilocal. A lattice [Formula: see text] is cofinitely weak [Formula: see text]-supplemented if and only if every maximal element of [Formula: see text] has a weak [Formula: see text]-supplement in [Formula: see text]. If [Formula: see text] is a cofinitely weak [Formula: see text]-supplemented sublattice of a lattice [Formula: see text] and [Formula: see text] has no maximal element, then [Formula: see text] is cofinitely weak [Formula: see text]-supplemented. Let [Formula: see text] be a compactly generated lattice such that for every compact element [Formula: see text] of [Formula: see text], [Formula: see text]. Then [Formula: see text] is cofinitely weak [Formula: see text]-supplemented if and only if [Formula: see text] is cofinitely [Formula: see text]-supplemented. Let [Formula: see text] be a compact lattice such that for every compact element [Formula: see text] of [Formula: see text], [Formula: see text]. Then [Formula: see text] is weakly [Formula: see text]-supplemented if and only if [Formula: see text] is [Formula: see text]-supplemented.

Effects of loosely bound electrons and electron–phonon interaction on the thermoelectric properties of electrenes

The interstitial charge in 2D HfI2 exhibits high mobility due to weak lattice perturbation, and the high mobility induces a high power factor and ZT value.

Crystal structure and thermophysical properties of (Gd0.25Sm0.25Yb0.25Y0.25)3TaO7 high-entropy oxide

An equimolar quaternary (Gd0.25Sm0.25Yb0.25Y0.25)3TaO7 high-entropy oxide was synthesised using the sol-gel technique and high-temperature calcination technology. The obtained nanopowder and compact bulk sample are all of the single fluorite phase. The relatively low thermal conductivity (1.170‒1.211W·m‒1·K‒1, 50‒1000 °C) of bulk sample is ascribed to the typical phonon scattering mechanisms and high-entropy distortion effect. The high average thermal expansion coefficient reaches 10.855 × 10–6 K−1 (1000–1400 °C) owing to the relatively weak ionic bond strength and lattice energy. The outstanding phase stability up to 1400 °C is in favour of lengthening the service life at high temperatures. These results reveal that (Gd0.25Sm0.25Yb0.25Y0.25)3TaO7 high-entropy oxide can be explored as a promising thermal barrier coating material.

Disentangling Surface Energy and Surface/Interface Stress Effects in Spin Crossover Nanomaterials

AbstractUnderstanding phase transformation processes at the nanoscale is an important step for the integration of phase change materials into functional nanodevices. Here, a numerical method to assess surface energy and surface stress contributions to finite size effects in spin crossover nanomaterials is proposed. Starting from their formal definitions, molecular dynamic simulations combined with continuum mechanics and thermodynamic considerations on model thin films are performed. The surface energy values extracted from the simulations are 71 and 79 mJ m−2 for the high spin (HS) and low spin (LS) states, respectively. In the limit of a weak lattice parameter misfit, the calculated isotropic stresses of a HS/LS interface are 94 and 45 mJ m−2 for the LS and HS states, respectively. From these results, a ≈10 K downshift of the spin transition temperature is predicted with the size reduction. Whereas surface energy favors systematically the HS state, it is not the case for the interface stress. Indeed, it is demonstrated that the anisotropy of mechanical stresses can lead to the stabilization of the LS state. These results confirm the possible control of the phase stability in these smart nanomaterials through interface engineering.

Mechanical Properties of Single Crystal Organic–Inorganic Hybrid Perovskite MAPbX3 (MA = CH3NH3, X = Cl, Br, I)

Mechanical properties are among the crucial parameters for multilayer hybrid perovskite-based devices. Here, the mechanical properties of the high-quality single-crystalline MAPbX3 (MA = CH3NH3, X = Cl, Br, I), including the hardness (H) and Young’s modulus (E), are systematically studied using the three-dimensional nanoindentation (3D nanoindentation) method. In the sequence of Cl, Br, and I, the hardness and Young’s modulus of MAPbX3 decrease gradually. The hardness of MAPbX3 ranges from 0.31 to 0.57 GPa, and Young’s modulus values are less than 30 GPa. The low hardness and Young’s modulus are attributed to the weak lattice framework composed of Pb-X and the weak hydrogen bond between CH3NH3+ and the octahedron. The relationship between the hardness and Young’s modulus of MAPbX3 is also described. Generally, this work provides the favorable parameters required to further support the design and modification of investigations regarding perovskite-based devices.

Polaron with quadratic electron-phonon interaction

We present a numerically exact study of a polaron with quadratic coupling to the oscillator displacement, or ${X}^{2}$ polaron, using two alternative methodological developments. Our results cover both antiadiabatic and adiabatic regimes and the entire range of electron-phonon coupling ${g}_{2}$, from the system's stability threshold at attractive ${g}_{2}=\ensuremath{-}1$ to arbitrary strong repulsion at ${g}_{2}\ensuremath{\gg}1$. The key properties of ${X}^{2}$ polarons prove dramatically different from their linear counterparts. They (i) are insensitive even to large quadratic coupling except in the antiadiabatic limit near the threshold of instability at attraction, (ii) depend only on the adiabatic ratio but are insensitive to the electron dispersion and dimension of space, and (iii) feature weak lattice deformations even at the instability point. Our results are of direct relevance to the properties of electrons at low densities in polar materials, including recent proposals for their superconducting states.

Vanishing of the Anomaly in Lattice Chiral Gauge Theory

AbstractThe anomaly cancellation is a basic property of the Standard Model, crucial for its consistence. We consider a lattice chiral gauge theory of massless Wilson fermions interacting with a non-compact massive U(1) field coupled with left- and right-handed fermions in four dimensions. We prove in the infinite volume limit, for weak coupling and inverse lattice step of the order of boson mass, that the anomaly vanishes up to subleading corrections and under the same condition as in the continuum. The proof is based on a combination of exact Renormalization Group, non-perturbative decay bounds of correlations and lattice symmetries.

On the Uniqueness of Lattice Characterization of Groups

We analyze the problem of the uniqueness of characterization of groups by their weak congruence lattices. We discuss the possibility that the same algebraic lattice L acts as a weak congruence lattice of a group in more than one way, so that the corresponding diagonals are represented by different elements of L. If this is impossible, that is, if L can be interpreted as a weak congruence lattice of a group in a single way, we say that L is a sharp lattice. We prove that groups in many classes have a sharp weak congruence lattice. In particular, we analyze connections among isomorphisms of subgroup lattices of groups and isomorphisms of their weak congruence lattices. Summing up, we prove that there is a one-to-one correspondence between many known classes of groups and lattice-theoretic properties associated with each of these classes. Finally, an open problem is formulated related to the uniqueness of the element corresponding to the diagonal in the lattice of weak congruences of a group.

Lattice characterization of some classes of groups by series of subgroups

In this paper, we characterize several classes of groups by the properties of their weak congruence lattices. Namely, we give necessary and sufficient conditions for the weak congruence lattice of a group, under which this group is a [Formula: see text]-group, [Formula: see text]-group, metacyclic, cocyclic, hyperabelian, polycyclic, [Formula: see text]-group and [Formula: see text]-group. We also discuss groups for which all subgroups are simple, like the Tarski monsters, and we show that they represent a class of non-Dedekind groups with a particular embedding property for lattices of normal subgroups. All the mentioned characterized groups are related to (different) series of subgroups, and we represent these series as chains of intervals in the weak congruence lattice. The corresponding conditions are formulated in a purely lattice-theoretic language.

The Origin of Lattice Rotation during Dendritic Crystallization of Clinopyroxene

AbstractUnderstanding dendritic crystallization is key to obtaining petrological information about rapid crystallization events. Clinopyroxene dendrites from a basaltic rock fulgurite from Nagpur, India, exhibit curved branches with corresponding lattice rotation that exceeds 180° for some branches. This paper combines crystallographic orientation mapping with microstructural observations and compositional information to determine the dendrites’ 3-D morphology and their bending mechanism. Dendrites exhibit a network of branches in the (010) plane, following either {001}* (normal to {001} planes, strong lattice curvature) or < 10–1 > (weak lattice curvature). Three or more orders of branches are observed in the (010) plane, alternating between {001}* and < 10–1>. Side branches with weak lattice curvature extend sub-perpendicular to the (010) plane, following either {021}* (sprouting from {001}* branches) or < 12–1 > (from <10–1 > branches) and defining curved ‘ribbons’ containing their respective central branch. All branches rotate about [010], with a consistent rotation sense regardless of elongation direction in sample or crystal coordinates. Bending must therefore be caused by local asymmetric thermal and compositional fields in the melt, generated by dendritic growth itself, not by sample-scale compositional, thermal or mechanical gradients. The most likely cause of bending is asymmetric distribution of melt supersaturation around branch tips, related to unequal growth rates perpendicular to different facets. Lattice rotation is inferred to occur via preferential incorporation of high densities of [001] (100) edge dislocations of one sign. High inferred dislocation densities imply that the preservation of bent dendrites requires rapid quenching. Higher inferred degree of undercooling (based on microstructural observations) correlates with greater lattice curvature. Bent dendrites can thus potentially be used to deliver information about spatial variations in degree of undercooling and place limits on the history of a sample after dendritic crystallization. Finally, finding lattice rotation exclusively about [010] is a new criterion to identify cryptic dendritic growth stages in euhedral crystals.

On the Paramagnetic-Like Susceptibility Peaks at Zero Magnetic Field in hbox{WSe}_{2-x}hbox{Te}_{x} Single Crystals

A weakly temperature-dependent paramagnetic-like susceptibility peak at zero magnetic field is observed in hbox{WSe}_{2-x}hbox{Te}_{x} with only marginal amount of ferromagnetic impurities. The ferromagnetic hysteresis loop and the magnetic moment splitting between zero-field-cooled and field-cooled processes indicate ferromagnetism in the samples. The paramagnetic-like susceptibility peak height is proportional to the remanent magnetic moment of hysteresis loops. High-resolution transmission electron microscope image supports that the observed ferromagnetic feature originates from lattice distortion. These results imply that the weakly temperature-dependent paramagnetic-like susceptibility peak originates from weak lattice distortion and/or superparamagnetism.

Mictomagnetism and suppressed thermal conduction of the prototype high-entropy alloy CrMnFeCoNi

• CrMnFeCoNi is found to be mictomagnetic. • There is weak lattice anharmonicity in CrMnFeCoNi. • The thermal conductivity is reduced down to about 10% of nickel due to disorder scattering. • Lattice of CrMnFeCoNi is remarkably softened compared to nickel. High-entropy alloys are characteristic of extensive atomic occupational disorder on high-symmetric lattices, differing from traditional alloys. Here, we investigate the magnetic and thermal transport properties of the prototype face-centered-cubic high-entropy alloy CrMnFeCoNi by combining physical properties measurements and neutron scattering. Direct-current and alternating-current magnetizations measurements indicate a mictomagnetic behavior with coexisting antiferromagnetic and ferromagnetic interactions below room temperature and three anomalies are found at about 80, 40, and 20 K, which are related to the paramagnetic to antiferromagnetic transition, the antiferromagnetic to ferromagnetic transition, and the spin freezing, respectively. The electrical and thermal conductivities are significantly reduced compared to Ni, and the temperature dependence of lattice thermal conductivity exhibits a glass-like plateau. Inelastic neutron scattering measurements suggest weak anharmonicity so that the thermal transport is expected to be dominated by the defect scattering.

Cofinitely (Weak) G-Supplemented Lattices

In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated. It is shown that quotient sublattices of cofinitely (weak) g-supplemented lattices are cofinitely (weak) g-supplemented. If 〖{a_i/0} 〗_(i∈I) is a collection of cofinitely (weak) g-supplemented sublattices of L and 1=⋁_(i∈I) a_i, then L is also cofinitely (weak) g-supplemented. It is proved that without loss of generality weak g-supplements of cofinite elements in compactly generated lattices are compact. An example showing that this is not true for lattices which are not cofinitely generated is given. A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented.

Rocksalt-type PrO epitaxial thin film as a weak ferromagnetic Kondo lattice

A unique Kondo lattice praseodymium monoxide PrO was synthesized in the form of an epitaxial thin film. The rocksalt-type PrO thin films with a $4{f}^{2}5{d}^{1}$ electronic configuration showed metallic conduction with a local resistivity minimum at 7 K as a result of the Kondo effect. In contrast to the other paramagnetic praseodymium monochalcogenides, PrO showed weak ferromagnetism below 28 K, followed by a transition to a more ferromagneticlike phase around 5 K. Emergence of the weak ferromagnetism probably originated from the enhanced $4f\text{\ensuremath{-}}4f$ exchange interaction by the short Pr-Pr distance. For the ferromagneticlike phase below 5 K, magnetic hysteresis of the anomalous Hall effect was significantly larger than that of magnetization, probably due to competing magnetic ordering.

Cекционные методы рентгеновской дифракционной топографии (обзор)

X-ray topography is a group of methods for obtaining diffraction images of structural defects in crystals. Among them, section topography techniques are distinguished by their abilities in acquiring quantitative information about defects based on the analysis of the images. For this purpose, special applications of the dynamic theory of X-ray diffraction are being developed. The interference of wave fields excited in a crystal by an X-ray beam is the basis of the section methods. Their sensitivity to weak lattice distortions is much higher than that of other X-ray methods. This review describes the physical foundations and implementation of the section topography techniques, as well as the results of computer simulating the wave field in a crystal. We present some examples of solving materials science and microelectronics problems and briefly describe the section topography using synchrotron radiation.