arXiv subjects

Chunxiao Zhang

Publications and source records attributed to Chunxiao Zhang.

13 recordsLinked to original sources

arXiv2024

Supercloseness of the DDG method for a singularly perturbed convection diffusion problem on Shishkin mesh

This paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical difficulties lie in controlling the diffusion term inside the layer, the convection term outside the layer, and the inter element jump term caused by the discontinuity of the numerical solution. The main idea is to design a new composite interpolation, in which a global projection is used outside the layer to satisfy the interface conditions determined by the selection of numerical flux, thereby eliminating or controlling the troublesome terms on the unit interface; and inside the layer, Gauß Lobatto projection is used to improve the convergence order of the diffusion term. On the basis of that, by selecting appropriate parameters in the numerical flux, we obtain the supercloseness result of almost $k+1$ order under an energy norm. Numerical experiments support our main theoretical conclusion.

math.NA↗

arXiv2023

Atomistic simulations of thermodynamic properties of liquid gallium from first principles

In the research of condensed matter, atomistic dynamic simulations play a crucial role, particularly in revealing dynamic processes, phase transitions and thermodynamic statistics macroscopic physical properties in systems such as solids and liquids. For a long time, simulating complex and disordered liquids has been a challenge compared to ordered crystalline structures. The primary reasons for this challenge are the lack of precise force field functions and the neglect of nuclear quantum effects. To overcome these two limits in simulation of liquids, we use a deep potential (DP) with quantum thermal bath (QTB) approach. DP is a machine learning model are sampled from density functional theory and able to do large-scale atomic simulations with its precision. QTB is a method which incorporates nuclear quantum effects by quantum fluctuation dissipation. The application of this first principles approach enable us to successfully describe the phase transition processes in solid and liquid Gallium (Ga) as well as the associated dynamic phenomena. More importantly, we obtain the thermodynamic properties of liquid Ga, such as internal energy, specific heat, enthalpy change, entropy and Gibbs free energy, and these results align remarkably well with experiments. Our research has opened up a new paradigm for the study of dynamics and thermodynamics in liquids, amorphous materials, and other disordered systems, providing valuable insights and references for future investigations.

cond-mat.mtrl-sci↗

arXiv2023

Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh

In this paper, we focus on analyzing the supercloseness property of a two-dimensional singularly perturbed convection-diffusion problem with exponential boundary layers. The local discontinuous Galerkin (LDG) method with piecewise tensor-product polynomials of degree k is applied to Bakhvalov-type mesh. By developing special two-dimensional local Gauss-Radau projections and establishing a novel interpolation, supercloseness of an optimal order k+1 can be achieved on Bakhvalov-type mesh. It is crucial to highlight that this supercloseness result is independent of the singular perturbation parameter.

math.NA↗

arXiv2023

Uniform convergence of finite element method on Bakhvalov-type mesh for a 2-D singularly perturbed convection-diffusion problem with exponential layers

On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The primary challenges are the width of the mesh subdomain in the layer adjacent to the transition point, the restriction of the Dirichlet boundary condition, and the structure of exponential layers. To address these challenges, a novel analysis technique is introduced for the first time, which takes full advantage of the characteristics of interpolation and the connection between the smooth function and the layer function on the boundary. Utilizing this technique in conjunction with a new interpolation featuring a simple structure, uniform convergence of optimal order k+1 under an energy norm can be proven for finite element method of any order k. Numerical experiments confirm our theoretical results.

math.NA↗

arXiv2023

Supercloseness of finite element method for a singularly perturbed convection-diffusion problem on Bakhvalov-type mesh in 2D

For singularly perturbed convection-diffusion problems, supercloseness analysis of finite element method is still open on Bakhvalov-type meshes, especially in the case of 2D. The difficulties arise from the width of the mesh in the layer adjacent to the transition point, resulting in a suboptimal estimate for convergence. Existing analysis techniques cannot handle these difficulties well. To fill this gap, a novel interpolation is designed delicately for the first time for the smooth part of the solution, bringing about the optimal supercloseness result of almost order 2 under an energy norm for finite element method. Our theoretical result is uniformly in the singular perturbation parameter and is supported by the numerical experiments.

math.NA↗

arXiv2022

I4/mcm-Si$_{48}$: An Ideal Topological Nodal-Line Semimetal

Topological semimetals (TSMs) have attracted numerous attention due to their exotic physical properties and great application potentials. Silicon-based TMSs are of particularly importance because of their high abundance, nontoxicity and natural compatibility with current semiconductor industry. In this work, an ideal low-energy topological nodal-line semimetal (TNLSM) silicon (I4/mcm-Si$_{48}$) with a clean band crossing at Fermi level is screened from thousands of silicon allotropes by the transferable tight-binding and DFT-HSE calculations. The results of formation energy, phonon dispersion, ab initio molecular dynamics and elastic constants show that I4/mcm-Si48 possesses good stability and is more stable than several synthetized silicon structures. By analyzing the symmetry, it reveals that the topological nodal-line of I4/mcm-Si48 is protected by mirror symmetry and inversion, time-reversal and SU(2) spin-rotation symmetries, and the nearly flat drumhead-like surface spectrum is observed. Furthermore, I4/mcm-Si48 exhibits exotic photoelectric properties and the Dirac fermions with high Fermi velocity (3.4$\sim$4.36$\times$10$^5$ m/s) can be excited by low energy photons. Our study provides a promising topological nodal-line semimetal for fundamental research and potential practical applications in semiconductor-compatible high-speed photoelectric devices.

cond-mat.mtrl-sci↗

arXiv2021

Ground state configuration of hydrogenated Biphenylene sheet: structure, stabilities, electronic and mechanical properties from first-principles calculations

Based on first-principles calculations, the ground state configuration (Cmma-CH) of hydrogenated Biphenylene sheet (Science, 372, 852, 2021) is carefully identified from hundreds of possible candidates generated by RG2 code (Phys. Rev. B., 97, 014104, 2018). Cmma-CH contains four benzene molecules in its crystalline cell and all of them are inequivalent due to its Cmma symmetry. The hydrogen atoms in Cmma-CH bond to carbon atoms in each benzene with a boat-like (boat-1:DDUDDU) up/down sequence and reversed boat-1 (UUDUUD) sequence in adjacent benzene rings. It is energetically less stable than the previously proposed allotropes (chair, tricycle, stirrup, boat-1, boat-2 and twist-boat) of hydrogenated graphene, but its formation energy from hydrogenating Biphenylene sheet is remarkably lower than those for hydrogenating graphene to graphane. Our results confirm that Cmma-CH is mechanically and dynamically stable 2D hydrocarbon phase which is expectable to be experimentally realized by hydrogenating the synthesized Biphenylene sheet. The HSE06 based band structures show that Cmma-CH is an indirect band gap insulators with a gap of 4.645 eV.

cond-mat.mtrl-sci↗

arXiv2020

New structure canditates for the experimentally synthesized heptazine-based and triazine-based two dimensional graphitic carbon nitride

The widely used crystal structures for both heptazine-based and triazine-based two-dimensional (2D) graphitic carbon nitride (g-C$_3$N$_4$) are the flat P-6m2 configurations. However, the experimentally synthesized 2D g-C$_3$N$_4$ possess thickness ranging in 0.2-0.5 nm, indicating that the theoretically used flat P-6m2 configurations are not the correct ground states. In this work, we propose three new corrugated structures P321, P3m1 and Pca21 with energies of 66 (86), 77 (87) and 78 (89) meV/atom lower than that of the corresponding heptazine-based (triazine-based) g-C$_3$N$_4$ in flat P-6m2 configuration, respectively. These corrugated structures have very similar periodic patterns to the flat P-6m2 ones and they are difficult to be distinguished from each other according to their top-views. The optimized thicknesses of the three corrugated structures ranging in 1.347-3.142 Å are in good agreement with the experimental results. The first-principles results show that these corrugated structural candidates are also semiconductors with band gaps slightly larger than those of the correspondingly flat P-6m2 ones. Furthermore, they possess also suitable band edge positions for sun-light-driven water-splitting at both $pH=0$ and $pH=7$ environments. Our results show that these three new structures are more promising candidates for the experimentally synthesized g-C$_3$N$_4$.

cond-mat.mtrl-sci↗

arXiv2019

Stone-Wales graphene: A Two Dimensional Carbon Semi-Metal with Magic Stability

A two-dimensional carbon allotrope, Stone-Wales graphene, is identified in stochastic group and graph constrained searches and systematically investigated by first-principles calculations. Stone-Wales graphene consists of well-arranged Stone-Wales defects, and it can be constructed through a 90$^\circ$ bond-rotation in a $\sqrt{8}$$\times$$\sqrt{8}$ super-cell of graphene. Its calculated energy relative to graphene, +149 meV/atom, makes it more stable than the most competitive previously suggested graphene allotropes. We find that Stone-Wales graphene based on a $\sqrt{8}$ super-cell is more stable than those based on $\sqrt{9} \times \sqrt{9}$, $\sqrt{12} \times \sqrt{12}$ and $\sqrt{13} \times \sqrt{13}$ super-cells, and is a "magic size" that can be further understood through a simple "energy splitting and inversion" model. The calculated vibrational properties and molecular dynamics of SW-graphene confirm that it is dynamically stable. The electronic structure shows SW-graphene is a semimetal with distorted, strongly anisotropic Dirac cones.

cond-mat.mtrl-sci↗

arXiv2018

Complex low energy tetrahedral polymorphs of group IV elements from first-principles

The energy landscape of carbon is exceedingly complex, hosting diverse and important metastable phases, including diamond, fullerenes, nanotubes and graphene. Searching for structures, especially those with large unit cells, in this landscape is challenging. Here we use a combined stochastic search strategy employing two algorithms (AIRSS and RG2) to apply connectivity constraints to unit cells containing up to 100 carbon atoms. We uncover three low energy carbon polymorphs (Pbam-32, P6/mmm and I-43d) with new topologies, containing 32, 36 and 94 atoms in their primitive cells, respectively. Their energies relative to diamond are 96 meV/atom, 131 meV/atom and 112 meV/atom, respectively, which suggests potential metastability. These three carbon allotropes are mechanically and dynamically stable, insulating carbon crystals with superhard mechanical properties. The I43d structure possesses a direct band gap of 7.25 eV, which is the widest gap in the carbon allotrope family. Silicon, germanium and tin versions of Pbam-32, P6/mmm and I-43d also show energetic, dynamical and mechanical stability. The computed electronic properties show that they are potential materials for semiconductor and photovoltaic applications.

cond-mat.mtrl-sci↗

arXiv2018

Prediction of two-dimensional nodal-line semimetal in a carbon nitride covalent network

Carbon nitride compounds have emerged recently as a prominent member of 2D materials beyond graphene. The experimental realizations of 2D graphitic carbon nitride g-C$_3$N$_4$, nitrogenated holey grahpene C$_2$N, polyaniline C$_3$N have shown their promising potential in energy and environmental applications. In this work, we predict a new type of carbon nitride network with a C$_9$N$_4$ stoichiometry from first principle calculations. Unlike common C-N compounds and covalent organic frameworks (COFs), which are typically insulating, surprisingly C$_9$N$_4$ is found to be a 2D nodal-line semimetal (NLSM). The nodal line in C$_9$N$_4$ forms a closed ring centered at $Γ$ point, which originates from the pz orbitals of both C and N. The linear crossing happens right at Fermi level contributed by two sets of dispersive Kagome and Dirac bands, which is robust due to negligible spin-orbital-coupling (SOC) in C and N. Besides, it is revealed that the formation of nodal ring is of accidental band degeneracy in nature induced by the chemical potential difference of C and N, as validated by a single orbital tight-binding model, rather than protected by crystal in-plane mirror symmetry or band topology. Interestingly, a new structure of nodal line, i.e., nodal-cylinder, is found in momentum space for AA-stacking C$_9$N$_4$. Our results imply possible functionalization for a novel metal-free C-N covalent network with interesting semimetallic properties.

cond-mat.mtrl-sci↗

arXiv2017

New allotropes of phosphorene with remarkable stability and intrinsic piezoelectricity

In this letter, we show that a new class of two-dimensional phosphorus allotropes can be constructed via assembling the previously proposed ultrathin metastable phosphorus nanotube into planar structures in different stacking orientations. Based on first-principles method, the structures, stabilities and fundamental electronic properties of these new two-dimensional phosphorus allotropes are systematically investigated. These two-dimensional phosphorus allotropes possess remarkable stabilities due to the strong inter-tube van der Waals interactions, which cause an energy release of about 30-70 meV/atom depending on their stacking manners. Our results show that most of these two-dimensional van der Waals phosphorene allotropes are energetically more favorable than the experimentally viable black alpha-P and blue beta-P. Three of them showing relatively higher probability to be synthesized in future are further confirmed to be dynamically stable semiconductors with strain-tunable band gaps and remarkable piezoelectricity, which may have potential applications in nano-sized sensors, piezotronics, and energy harvesting in portable electronic nano-devices.

cond-mat.mtrl-sci↗

arXiv2016

New Boys and Girls in Phosphorene Family from Gene Recombination: Different from Parents, Excellent than Parents

Based on the crystal structures of the previously proposed low energy phosphorene allotropes η-P and θ-P (Nano. Lett. 2015, 15, 3557), we propose five new structural stable phosphorene boys (XX-XY or XY-XY) and girls (XX-XX) through gene (XY from η-P and XX from θ-P) recombination methods. All of these five new phosphorene allotropes are obviously different from their parents, showing very different and fascinating two-dimensional patterns between each other. The dynamical stabilities of these phosphorene allotropes are confirmed positive and some of them are confirmed energetically more favorable than their parents (η-P and θ-P). Especially, the XX-XX type girl G1-P is confirmed energetically more favorable than all the previously proposed phosphorene allotropes, including black phosphorene (α-P, ACS Nano, 2014, 8, 4033) and blue phosphorene (β-P, Phys. Rev. Lett. 2014, 112, 176802), which is expected to be synthesized in future experiment through vapor deposition. Our results show that such a new promising phosphorene allotrope G1-P is an excellent candidate for potential applications in nano-electronics according to its middle band gap about 1.58 eV from DFT-HSE06 calculation.

cond-mat.mtrl-sci↗