A linear operator T between two lattice-normed spaces is said to be p-compact if, for any p-bounded net xα, the net Txα has a p-convergent subnet. p-Compact operators generalize several known classes ...of operators such as compact, weakly compact, order weakly compact, AM-compact operators, etc. Similar to M-weakly and L-weakly compact operators, we define p-M-weakly and p-L-weakly compact operators and study some of their properties. We also study up-continuous and up-compact operators between lattice-normed vector lattices.
The derivation of a crystal structure and its phase‐specific parameters from a single wide‐angle backscattered Kikuchi diffraction pattern requires reliable extraction of the Bragg angles. By means ...of the first derivative of the lattice profile, an attempt is made to determine fully automatically and reproducibly the band widths in simulated Kikuchi patterns. Even under such ideal conditions (projection centre, wavelength and lattice plane traces are perfectly known), this leads to a lattice parameter distribution whose mean shows a linear offset that correlates with the mean atomic number Z of the pattern‐forming phase. The consideration of as many Kikuchi bands as possible reduces the errors that typically occur if only a single band is analysed. On the other hand, the width of the resulting distribution is such that higher image resolution of diffraction patterns, employing longer wavelengths to produce wider bands or the use of higher interference orders is less advantageous than commonly assumed.
The lattice parameters of more than 350 phases have been determined from simulated backscatter Kikuchi patterns. The deviations correlating with the mean atomic number correspond to those observed previously for experimental electron backscatter diffraction patterns.
Thermal transport phenomena are ubiquitous and play a critical role in the performance of various microelectronic and energy-conversion devices. Binary rocksalt and zinc blende compounds, despite ...their rather simple crystal structures, exhibit an extraordinary range of lattice thermal conductivity (κL) spanning over 3 orders of magnitude. A comprehensive understanding of the underlying heat transfer mechanism through the development of microscopic theories is therefore of fundamental importance, yet it remains elusive because of the challenges arising from explicitly treating higher-order anharmonicity. Recent theoretical and experimental advances have revealed the essential role of quartic anharmonicity in suppressing heat transfer in zinc blende boron arsenide (BAs) with ultrahighκL. However, critical questions concerning the general effects of higher-order anharmonicity in the broad classes and chemistries of binary solids are still unanswered. Using our recently developed high-throughput phonon framework based on first-principles density functional theory calculations, we systematically investigate the lattice dynamics and thermal transport properties of 37 binary compounds with rocksalt and zinc blende structures at room temperature, with a particular focus on unraveling the impacts of quartic anharmonicity onκL. Our advanced theoretical model for computingκLembraces current state-of-the-art methods, featuring a complete treatment of quartic anharmonicity for both phonon frequencies and lifetimes at finite temperatures, as well as contributions from off-diagonal terms in the heat-flux operator. We find the impacts of quartic anharmonicity onκLto be strikingly different in rocksalt and zinc blende compounds, owing to the countervailing effects on finite-temperature-induced shifts in phonon frequencies and scattering rates. By correlatingκLwith the phonon scattering phase space, we outline a qualitative but efficient route to assess the importance of four-phonon scattering from harmonic phonon calculations. Among notable examples, in zinc blende HgTe, we identify an unprecedented sixfold reduction inκLdue to four-phonon scattering, which dominates over the three-phonon scattering in the acoustic region at room temperature. We also demonstrate a possible breakdown of the phonon gas model in rocksalt AgCl, wherein the phonon states are significantly broadened due to strong intrinsic anharmonicity, inducing off-diagonal contributions toκLcomparable to the diagonal ones. The deep physical insights gained in this work can be used to guide the rational design of thermal management materials.
The S-wave ΛΛ and NΞ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point (mπ≃146MeV and mK≃525MeV). Lattice QCD potentials in four different ...spin-isospin channels are extracted by using the coupled-channel HAL QCD method and are parametrized by analytic functions to calculate the scattering phase shifts. The ΛΛ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The NΞ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the NΞ system near unitarity. Relevance to the strangeness = −2 hypernuclei as well as to two-baryon correlations in proton-proton, proton-nucleus and nucleus-nucleus collisions is also discussed.
This paper describes the distributivity, the modularity, the semimodularity and the lower semimodularity of compactly generated lattices from a view of cut sets of
L
-valued sets, respectively. ...Applying terms of cut sets of
L
-valued sets, it gives some sufficient and necessary conditions which can be used to determine whether a compactly generated lattice is distributive, modular, semimodular and lower semimodular, respectively.
Combining spatially resolved x-ray Laue diffraction with atomic-scale simulations, we observe how ion-irradiated tungsten undergoes a series of nonlinear structural transformations with increasing ...radiation exposure. Nanoscale defect-induced deformations accumulating above 0.02 displacements per atom (dpa) lead to highly fluctuating strains at ∼0.1 dpa, collapsing into a driven quasisteady structural state above ∼1 dpa. The driven asymptotic state is characterized by finely dispersed vacancy defects coexisting with an extended dislocation network and exhibits positive volumetric swelling, due to the creation of new crystallographic planes through self-interstitial coalescence, but negative lattice strain.
Strut-based lattice structures (SLSs) have been widely used in modern industries including aerospace, automobile and biological implant, due to their unique properties such as lightweight, good ...energy absorption capability and high specific strength. However, the obtainable mechanical performance is significantly limited by the monotonous strut-based feature without any reinforcement topology. The inherent strengthening mechanisms and atom-scale models in material science may be crucial and valuable to optimize the complex structures with desired properties. Inspired by the solid solution strengthening mechanisms in crystal microstructure, a series of novel crystal-inspired hybrid structures, i.e., the common face-center cubic with Z-strut (FCCZ) structure, the face-center substitutional lattice (FCSL) structure, the edge-center interstitial lattice (ECIL) structure and the vertex-node substitutional lattice (VNSL) structure were designed and fabricated by laser powder bed fusion (LPBF) additive manufacturing in this work. The effect of node location on the LPBF formability, mechanical performance, stress distribution, deformation modes and failure mechanisms of the crystal-inspired components was systematically investigated. The computational fluid dynamics (CFD) method was used to understand the dynamics of molten pool to reveal the formation mechanism and control methods of the dross defect attached to overhanging surfaces. Finite element model (FEM) was established to show the stress distribution and deformation behavior of these hybrid structures during compression. Results showed that the ECIL structure possessed the highest specific energy absorption (SEA) of 13.7 J/g, which increased by 17% compared with the initial FCCZ structure. The crush force efficiency (CFE) of VNSL structure reached the peak value of 66% with a unique axisymmetric shear band during deformation, which increased by 14% compared to the FCCZ structure. The underlying mechanism analysis revealed that the as-designed spherical node could redistribute the stress and the performance of the lattice structures could be manipulated by tailoring the position of the spherical nodes. The present approach suggested that the hardening principles of crystalline materials could inspire the design of novel lattice structures with desired properties.
•Hybrid lattice structures inspired by crystal microstructure are designed and fabricated.•Dross formation mechanism induced by suspension condition is investigated.•High specific energy absorption (13.7J/g) and crush force efficiency of 66% are obtained.•Strengthening mechanism at micro scale is also applicable to enhancement of macro lattice structure.
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