L1_(2)precipitates are known to significantly enhance the strength and ductility of single-phase face-centered cubic(FCC)medium-or high-entropy alloys(M/HEAs).However,further improvements in mechanical properties rema...L1_(2)precipitates are known to significantly enhance the strength and ductility of single-phase face-centered cubic(FCC)medium-or high-entropy alloys(M/HEAs).However,further improvements in mechanical properties remain untapped,as alloy design has historically focused on systems with specific CrCoNi-or FeCoCrNi-based FCC matrix and Ni_(3)Al L1_(2)phase compositions.This study introduces novel Co-Ni-Mo-Al alloys with L1_(2)precipitates by systematically altering Al content,aiming to bridge this research gap by revealing the strengthening mechanisms.The(CoNi)_(81)Mo_(12)Al_(7)alloy achieves yield strength of 1086 MPa,tensile strength of 1520 MPa,and ductility of 35%,demonstrating an impressive synergy of strength,ductility,and strain-hardening capacity.Dislocation analysis via transmission electron microscopy,supported by generalized stacking fault energy(GSFE)calculations using density functional theory(DFT),demonstrates that Mo substitution for Al in the L1_(2)phase alters dislocation behavior,promoting the formation of multiple deformation modes,including stacking faults,super-dislocation pairs,Lomer-Cottrell locks,and unusual nano-twin formation even at low strains.These behaviors are facilitated by the low stacking fault energy(SFE)of the FCC matrix,overlapping of SFs,and dislocation dissociation across anti-phase boundaries(APBs).The increased energy barrier for superlattice intrinsic stacking fault(SISF)formation compared to APBs,due to Mo substitution,further influences dislocation activity.This work demonstrates a novel strategy for designing high-performance M/HEAs by expanding the range of FCC matrix and L1_(2)compositions through precipitation hardening.展开更多
We report high throughput computational screening for magnetic ground state order in 2D materials.The workflow is based on spin spiral calculations and yields the magnetic order in terms of a twodimensional ordering v...We report high throughput computational screening for magnetic ground state order in 2D materials.The workflow is based on spin spiral calculations and yields the magnetic order in terms of a twodimensional ordering vector Q.We then include spin-orbit coupling to extract the easy and hard axes for collinear structures and the orientation of spiral planes in non-collinear structures.Finally,for all predicted ferromagnetswe compute the Dzyaloshinskii-Moriya interactions and determine whether or not these are strong enough to overcome the magnetic anisotropy and stabilise a chiral spin spiral ground state.We find 58 ferromagnets,21 collinear anti-ferromagnets,and 85 non-collinear ground states of which 15 are chiral spin spirals driven byDzyaloshinskii-Moriya interactions.The results show that non-collinear order is in fact as common as collinear order in these materials and emphasise the need for detailed investigation of the magnetic ground state when reporting magnetic properties of new materials.展开更多
High-energy–density lithium-ion batteries(LIBs)that can be safely fast-charged are desirable for electric vehicles.However,sub-optimal lithiation potential and low capacity of commonly used LIBs anode cause safety is...High-energy–density lithium-ion batteries(LIBs)that can be safely fast-charged are desirable for electric vehicles.However,sub-optimal lithiation potential and low capacity of commonly used LIBs anode cause safety issues and low energy density.Here we hypothesize that a cobalt vanadate oxide,Co_(2)VO_(4),can be attractive anode material for fast-charging LIBs due to its high capacity(~1000 mAh g^(−1))and safe lithiation potential(~0.65 V vs.Li^(+)/Li).The Li+diffusion coefficient of Co2VO4 is evaluated by theoretical calculation to be as high as 3.15×10^(-10) cm^(2) s^(−1),proving Co_(2)VO_(4) a promising anode in fast-charging LIBs.A hexagonal porous Co2VO4 nanodisk(PCVO ND)structure is designed accordingly,featuring a high specific surface area of 74.57 m^(2) g^(−1) and numerous pores with a pore size of 14 nm.This unique structure succeeds in enhancing Li^(+) and electron transfer,leading to superior fast-charging performance than current commercial anodes.As a result,the PCVO ND shows a high initial reversible capacity of 911.0 mAh g^(−1) at 0.4 C,excellent fast-charging capacity(344.3 mAh g^(−1) at 10 C for 1000 cycles),outstanding long-term cycling stability(only 0.024% capacity loss per cycle at 10 C for 1000 cycles),confirming the commercial feasibility of PCVO ND in fast-charging LIBs.展开更多
We perform a computational screening for two-dimensional(2D)magnetic materials based on experimental bulk compounds present in the Inorganic Crystal Structure Database and Crystallography Open Database.A recently prop...We perform a computational screening for two-dimensional(2D)magnetic materials based on experimental bulk compounds present in the Inorganic Crystal Structure Database and Crystallography Open Database.A recently proposed geometric descriptor is used to extract materials that are exfoliable into 2D derivatives and we find 85 ferromagnetic and 61 antiferromagnetic materials for which we obtain magnetic exchange and anisotropy parameters using density functional theory.For the easy-axis ferromagnetic insulators we calculate the Curie temperature based on a fit to classical Monte Carlo simulations of anisotropic Heisenberg models.We find good agreement with the experimentally reported Curie temperatures of known 2D ferromagnets and identify 10 potentially exfoliable 2D ferromagnets that have not been reported previously.In addition,we find 18 easy-axis antiferromagnetic insulators with several compounds exhibiting very strong exchange coupling and magnetic anisotropy.展开更多
Computational materials science and engineering has emerged as an interdisciplinary subfield spanning materials science and engineering,condensed matter physics,chemistry,mechanics and engineering in general.Modern ma...Computational materials science and engineering has emerged as an interdisciplinary subfield spanning materials science and engineering,condensed matter physics,chemistry,mechanics and engineering in general.Modern materials research often requires a close integration of computation and experiments in order to fundamentally understand the materials structures and properties and their relation to synthesis and processing.A number of computational methods and tools at different spatiotemporal scales are now well established,ranging from electronic structure calculations based on density functional theory,1,2 atomic molecular dynamics3,4 and Monte Carlo techniques,5 phase-field method6–9 to continuum macroscopic approaches.Over the last few years,computational materials activities have been steadily moving from technique development and purely computational studies of materials towards discovering and designing new materials guided by computation,machine learning and data mining or by a closely tied combination of computational predictions and experimental validation.This movement is being further accelerated by the recent initiatives by various government agencies in the United States,Europe,China and other countries to pursue the materials genome initiative,10 integrated computational materials engineering11–13 as well as the‘Big Data’initiative.展开更多
High-and medium-entropy alloys(HEAs and MEAs)possess high solid-solution strength.Numerous investigations have been conducted on its impact on yield strength,however,there are limited reports regarding the relation be...High-and medium-entropy alloys(HEAs and MEAs)possess high solid-solution strength.Numerous investigations have been conducted on its impact on yield strength,however,there are limited reports regarding the relation between solid-solution strengthening and strain-hardening rate.In addition,no attempt has been made to account for the dislocation-mediated plasticity;most works focused on twinning-or transformation-induced plasticity(TWIP or TRIP).In this work we reveal the role of solidsolution strengthening on the strain-hardening rate via systematically investigating evolutions of deformation structures by controlling the Cr/V ratio in prototypical V_(1-x)Cr_(x)CoNi alloys.Comparing the TWIP of CrCoNi with the dislocation slip of V_(0.4)Cr_(0.6)CoNi,the hardening rate of CrCoNi was superior to slip-band refinements of V_(0.4)Cr_(0.6)CoNi due to the dynamic Hall-Petch effect.However,as V content increased further to V_(0.7)Cr_(0.3)CoNi and VCoNi,their rate of slip-band refinement in V_(0.7)Cr_(0.3)CoNi and VCoNi with high solid-solution strength surpassed that of CrCoNi.Although it is generally accepted in conventional alloys that deformation twinning results in a higher strain-hardening rate than dislocation-mediated plasticity,we observed that the latter can be predominant in the former under an activated huge solid-solution strengthening effect.The high solid-solution strength lowered the cross-slip activation and consequently retarded the dislocation rearrangement rate,i.e.,the dynamic recovery.This delay in the hardening rate decrease,therefore,increased the strain-hardening rate,results in an overall higher strain-hardening rate of V-rich alloys.展开更多
We present the magnetic Moment Tensor Potentials(mMTPs),a class of machine-learning interatomic potentials,accurately reproducing both vibrational and magnetic degrees of freedom as provided,e.g.,from first-principles...We present the magnetic Moment Tensor Potentials(mMTPs),a class of machine-learning interatomic potentials,accurately reproducing both vibrational and magnetic degrees of freedom as provided,e.g.,from first-principles calculations.The accuracy is achieved by a two-step minimization scheme that coarse-grains the atomic and the spin space.The performance of the mMTPs is demonstrated for the prototype magnetic system bcc iron,with applications to phonon calculations for different magnetic states,and molecular-dynamics simulations with fluctuating magnetic moments.展开更多
Efficient algorithms to generate candidate crystal structures with good stability properties can play a key role in data-driven materials discovery.Here,we show that a crystal diffusion variational autoencoder(CDVAE)i...Efficient algorithms to generate candidate crystal structures with good stability properties can play a key role in data-driven materials discovery.Here,we show that a crystal diffusion variational autoencoder(CDVAE)is capable of generating two-dimensional(2D)materials of high chemical and structural diversity and formation energies mirroring the training structures.Specifically,we train the CDVAE on 26152D materials with energy above the convex hullΔH_(hull)<0.3 eV/atom,and generate 5003 materials that we relax using density functional theory(DFT).We also generate 14192 new crystals by systematic element substitution of the training structures.We find that the generative model and lattice decoration approach are complementary and yield materials with similar stability properties but very different crystal structures and chemical compositions.In total we find 11630 predicted new 2D materials,where 8599 of these haveΔH_(hull)<0.3 eV/atom as the seed structures,while 2004 are within 50 meV of the convex hull and could potentially be synthesised.The relaxed atomic structures of all the materials are available in the open Computational 2D Materials Database(C2DB).Our work establishes the CDVAE as an efficient and reliable crystal generation machine,and significantly expands the space of 2D materials.展开更多
Atomically thin two-dimensional(2D)materials are ideal host systems for quantum defects as they offer easier characterisation,manipulation and read-out of defect states as compared to bulk defects.Here we introduce th...Atomically thin two-dimensional(2D)materials are ideal host systems for quantum defects as they offer easier characterisation,manipulation and read-out of defect states as compared to bulk defects.Here we introduce the Quantum Point Defect(QPOD)database with more than 1900 defect systems comprising various charge states of 503 intrinsic point defects(vacancies and antisites)in 82 different 2D semiconductors and insulators.The Atomic Simulation Recipes(ASR)workflow framework was used to perform density functional theory(DFT)calculations of defect formation energies,charge transition levels,Fermi level positions,equilibrium defect and carrier concentrations,transition dipole moments,hyperfine coupling,and zero-field splitting.Excited states and photoluminescence spectra were calculated for selected high-spin defects.In this paper we describe the calculations and workflow behind the QPOD database,present an overview of its content,and discuss some general trends and correlations in the data.We analyse the degree of defect tolerance as well as intrinsic dopability of the host materials and identify promising defects for quantum technological applications.The database is freely available and can be browsed via a web-app interlinked with the Computational 2D Materials Database(C2DB).展开更多
We address the problem of predicting the zero-temperature dynamical stability (DS) of a periodic crystal without computing its fullphonon band structure. Here we report the evidence that DS can be inferred with good r...We address the problem of predicting the zero-temperature dynamical stability (DS) of a periodic crystal without computing its fullphonon band structure. Here we report the evidence that DS can be inferred with good reliability from the phonon frequencies atthe center and boundary of the Brillouin zone (BZ). This analysis represents a validation of the DS test employed by theComputational 2D Materials Database (C2DB). For 137 dynamically unstable 2D crystals, we displace the atoms along an unstablemode and relax the structure. This procedure yields a dynamically stable crystal in 49 cases. The elementary properties of these newstructures are characterized using the C2DB workflow, and it is found that their properties can differ significantly from those of theoriginal unstable crystals, e.g., band gaps are opened by 0.3 eV on average. All the crystal structures and properties are available inthe C2DB. Finally, we train a classification model on the DS data for 3295 2D materials in the C2DB using a representation encodingthe electronic structure of the crystal. We obtain an excellent receiver operating characteristic (ROC) curve with an area under thecurve (AUC) of 0.90, showing that the classification model can drastically reduce computational efforts in high-throughput studies.展开更多
The repeated slab approach has become a de facto standard to accurately describe surface properties of materials by density functional theory calculations with periodic boundary conditions.For materials exhibiting spo...The repeated slab approach has become a de facto standard to accurately describe surface properties of materials by density functional theory calculations with periodic boundary conditions.For materials exhibiting spontaneous polarization,we show that the conventional scheme of passivation with pseudo hydrogen is unable to realize a charge-neutral surface.The presence of a net surface charge induces via Gauss’s law a macroscopic electric field through the slab and results in poor size convergence with respect to the thickness of the slab.We propose a modified passivation method that accounts for the effect of spontaneous polarization,describes the correct bulk limits and boosts convergence with respect to slab thickness.The robustness,reliability,and superior convergence of energetics and electronic structure achieved by the proposed method are demonstrated using the example of polar ZnO surfaces.展开更多
Shift current photovoltaic devices are potential candidates for future cheap,sustainable,and efficient electricity generation.In the present work,we calculate the solar-generated shift current and efficiencies in 326 ...Shift current photovoltaic devices are potential candidates for future cheap,sustainable,and efficient electricity generation.In the present work,we calculate the solar-generated shift current and efficiencies in 326 different 2D materials obtained from the computational database C2DB.We apply,as metrics,the efficiencies of monolayer and multilayer samples.The monolayer efficiencies are generally found to be low,while the multilayer efficiencies of infinite stacks show great promise.Furthermore,the out-of-plane shift current response is considered,and material candidates for efficient out-of-plane shift current devices are identified.Among the screened materials,MXY Janus and MX_(2) transition metal dichalchogenides(TMDs)constitute a prominent subset,with chromium based MXY Janus TMDs holding particular promise.Finally,in order to explain the band gap dependence of the PV efficiency,a simple gapped graphene model with a variable band gap is established and related to the calculated efficiencies.展开更多
This study investigates the effect of defect engineering on the catalytic activity of a NiPS3 monolayer catalyst for the hydrogen evolution reaction(HER).Three different types of vacancies on the basal plane of the mo...This study investigates the effect of defect engineering on the catalytic activity of a NiPS3 monolayer catalyst for the hydrogen evolution reaction(HER).Three different types of vacancies on the basal plane of the monolayer are explored through a multi-step mechanism involving the dissociative adsorption of a water molecule and subsequent electrochemical adsorption of the dissociated proton.Co-formation of vacancies in both Ni and S sites is found to be the most effective in enhancing the catalytic performance of the monolayer.A key resource for the reaction thermodynamics is the S-substitution-like physisorption of a water molecule on a vacant S site,followed by the dissociative occupation of OH and H into vacant sites of S and Ni elements,boosted by the NiS di-vacancy configuration with low activation energy barriers.Investigation reveals the highest contribution of bonding orbitals to the monolayer-H bond makes it the most desirable defect engineering approach for transition metal phosphorus chalcogenides with high HER activities.Overall,this study highlights the significance of controlled defect engineering in augmenting the catalytic performance of NiPS3 monolayer catalysts for HER.展开更多
The impact ofmagnetism on chemical ordering in face-centered cubic CrCoNi medium entropy alloy is studied by a combination of ab initio simulations,machine learning potentials,and Monte Carlo simulations.Large magneti...The impact ofmagnetism on chemical ordering in face-centered cubic CrCoNi medium entropy alloy is studied by a combination of ab initio simulations,machine learning potentials,and Monte Carlo simulations.Large magnetic energies are revealed for some mixed L1_(2)/L1_(0) type ordered configurations,which are rooted in strong nearest-neighbor magnetic exchange interactions and chemical bonding among the constituent elements.展开更多
Melting properties are critical for designing novel materials,especially for discovering highperformance,high-melting refractory materials.Experimental measurements of these properties are extremely challenging due to...Melting properties are critical for designing novel materials,especially for discovering highperformance,high-melting refractory materials.Experimental measurements of these properties are extremely challenging due to their high melting temperatures.Complementary theoretical predictions are,therefore,indispensable.One of the most accurate approaches for this purpose is the ab initio free-energy approach based on density functional theory(DFT).However,it generally involves expensive thermodynamic integration using ab initio molecular dynamic simulations.The high computational cost makes high-throughput calculations infeasible.Here,we propose a highly efficient DFT-based method aided by a specially designed machine learning potential.As the machine learning potential can closely reproduce the ab initio phase-space distribution,even for multi-component alloys,the costly thermodynamic integration can be fully substituted with more efficient free energy perturbation calculations.The method achieves overall savings of computational resources by 80%compared to current alternatives.We apply the method to the high-entropy alloy TaVCrW and calculate its melting properties,including the melting temperature,entropy and enthalpy of fusion,and volume change at the melting point.Additionally,the heat capacities of solid and liquid TaVCrW are calculated.The results agree reasonably with the CALPHAD extrapolated values.展开更多
Recently,high-entropy alloys(HEAs)have attracted wide attention due to their extraordinary materials properties.A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge com...Recently,high-entropy alloys(HEAs)have attracted wide attention due to their extraordinary materials properties.A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space.Ab initio calculations have emerged as a powerful approach that complements experiment.However,for multicomponent alloys existing approaches suffer from the chemical complexity involved.In this work we propose a method for studying HEAs computationally.Our approach is based on the application of machine-learning potentials based on ab initio data in combination with Monte Carlo simulations.The high efficiency and performance of the approach are demonstrated on the prototype bcc NbMoTaW HEA.The approach is employed to study phase stability,phase transitions,and chemical short-range order.The importance of including local relaxation effects is revealed:they significantly stabilize single-phase formation of bcc NbMoTaW down to room temperature.Finally,a so-far unknown mechanism that drives chemical order due to atomic relaxation at ambient temperatures is discovered.展开更多
Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation hightemperature applications.At high temperatures,materials properties are strongly affected by...Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation hightemperature applications.At high temperatures,materials properties are strongly affected by lattice vibrations(phonons).Phonons critically influence thermal stability,thermodynamic and elastic properties,as well as thermal conductivity.In contrast to perfect crystals and ordered alloys,the inherently present mass and force constant fluctuations in multi-component random alloys(high entropy alloys)can induce significant phonon scattering and broadening.Despite their importance,phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys.We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys,from binaries up to 5-component high entropy alloys,addressing the key question of how chemical complexity impacts phonons.We find that it is crucial to include both mass and force constant fluctuations.If one or the other is neglected,qualitatively wrong results can be obtained such as artificial phonon band gaps.We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities,specifically the vibrational entropy.Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations.The set of studied alloys includes MoTa,MoTaNb,MoTaNbW,MoTaNbWV,VW,VWNb,VWTa,VWNbTa,VTaNbTi,VWNbTaTi,HfZrNb,HfMoTaTiZr.展开更多
The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines.The vast compositional parameter spac...The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines.The vast compositional parameter space makes these alloys a unique area of exploration by means of computational design.However,as of now a method to compute efficiently,yet with high accuracy the thermodynamic properties of such alloys has been missing.One of the underlying reasons is the lack of accurate and efficient approaches to compute vibrational free energies—including anharmonicity—for these chemically complex multicomponent alloys.In this work,a density-functional-theory based approach to overcome this issue is developed based on a combination of thermodynamic integration and a machine-learning potential.We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.展开更多
The physical origins of the mechanical properties of Fe-rich Si alloys are investigated by combining electronic structure calculations with statistical mechanics means such as the cluster variation method,molecular dy...The physical origins of the mechanical properties of Fe-rich Si alloys are investigated by combining electronic structure calculations with statistical mechanics means such as the cluster variation method,molecular dynamics simulation,etc,applied to homogeneous and heterogeneous systems.Firstly,we examined the elastic properties based on electronic structure calculations in a homogeneous system and attributed the physical origin of the loss of ductility with increasing Si content to the combined effects of magneto-volume and D03 ordering.As a typical example of a heterogeneity forming a microstructure,we focus on grain boundaries,and segregation behavior of Si atoms is studied through high-precision electronic structure calculations.Two kinds of segregation sites are identified:looser and tighter sites.Depending on the site,different segregation mechanisms are revealed.Finally,the dislocation behavior in the Fe-Si alloy is investigated mainly by molecular dynamics simulations combined with electronic structure calculations.The solid-solution hardening and softening are interpreted in terms of two kinds of energy barriers for kink nucleation and migration on a screw dislocation line.Furthermore,the clue to the peculiar work hardening behavior is discussed based on kinetic Monte Carlo simulations by focusing on the preferential selection of slip planes triggered by kink nucleation.展开更多
We review the theory and application of adiabatic exchange–correlation(xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection f...We review the theory and application of adiabatic exchange–correlation(xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations,respectively.Various different xc-kernels,which are all rooted in the homogeneous electron gas,are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels,in particular the rALDA and rAPBE.The kernels drastically improve the description of short-range correlations as compared to the random phase approximation(RPA),resulting in significantly better correlation energies.This effect greatly reduces the reliance on error cancellations,which is essential in RPA,and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions.For quasiparticle energies,the xc-kernels account for vertex corrections that are missing in the GW self-energy.In this context,we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter.The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.展开更多
基金financially supported by the National Research Foundation of Korea grant funded by the Korea government(MSIT)(Nos.NRF-2022R1A5A1030054,NRF-RS-2024-00345498,and NRFRS-2023-00281508)by Korea Institute for Advancement of Technology(KIAT)grant funded by the Korea Government(MOTIE)(HRD Program for Industrial Innovation-No P0023676)+1 种基金funded by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)-No 519607530funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program(Grant Agreement No 865855).
文摘L1_(2)precipitates are known to significantly enhance the strength and ductility of single-phase face-centered cubic(FCC)medium-or high-entropy alloys(M/HEAs).However,further improvements in mechanical properties remain untapped,as alloy design has historically focused on systems with specific CrCoNi-or FeCoCrNi-based FCC matrix and Ni_(3)Al L1_(2)phase compositions.This study introduces novel Co-Ni-Mo-Al alloys with L1_(2)precipitates by systematically altering Al content,aiming to bridge this research gap by revealing the strengthening mechanisms.The(CoNi)_(81)Mo_(12)Al_(7)alloy achieves yield strength of 1086 MPa,tensile strength of 1520 MPa,and ductility of 35%,demonstrating an impressive synergy of strength,ductility,and strain-hardening capacity.Dislocation analysis via transmission electron microscopy,supported by generalized stacking fault energy(GSFE)calculations using density functional theory(DFT),demonstrates that Mo substitution for Al in the L1_(2)phase alters dislocation behavior,promoting the formation of multiple deformation modes,including stacking faults,super-dislocation pairs,Lomer-Cottrell locks,and unusual nano-twin formation even at low strains.These behaviors are facilitated by the low stacking fault energy(SFE)of the FCC matrix,overlapping of SFs,and dislocation dissociation across anti-phase boundaries(APBs).The increased energy barrier for superlattice intrinsic stacking fault(SISF)formation compared to APBs,due to Mo substitution,further influences dislocation activity.This work demonstrates a novel strategy for designing high-performance M/HEAs by expanding the range of FCC matrix and L1_(2)compositions through precipitation hardening.
基金The authors acknowledge support from the Villum foundation Grant No.00029378.
文摘We report high throughput computational screening for magnetic ground state order in 2D materials.The workflow is based on spin spiral calculations and yields the magnetic order in terms of a twodimensional ordering vector Q.We then include spin-orbit coupling to extract the easy and hard axes for collinear structures and the orientation of spiral planes in non-collinear structures.Finally,for all predicted ferromagnetswe compute the Dzyaloshinskii-Moriya interactions and determine whether or not these are strong enough to overcome the magnetic anisotropy and stabilise a chiral spin spiral ground state.We find 58 ferromagnets,21 collinear anti-ferromagnets,and 85 non-collinear ground states of which 15 are chiral spin spirals driven byDzyaloshinskii-Moriya interactions.The results show that non-collinear order is in fact as common as collinear order in these materials and emphasise the need for detailed investigation of the magnetic ground state when reporting magnetic properties of new materials.
基金supported by the National Key Research and Development Project(2018YFE0124800)the National Nature Science Foundation of China(51702157,51873086,51673096).
文摘High-energy–density lithium-ion batteries(LIBs)that can be safely fast-charged are desirable for electric vehicles.However,sub-optimal lithiation potential and low capacity of commonly used LIBs anode cause safety issues and low energy density.Here we hypothesize that a cobalt vanadate oxide,Co_(2)VO_(4),can be attractive anode material for fast-charging LIBs due to its high capacity(~1000 mAh g^(−1))and safe lithiation potential(~0.65 V vs.Li^(+)/Li).The Li+diffusion coefficient of Co2VO4 is evaluated by theoretical calculation to be as high as 3.15×10^(-10) cm^(2) s^(−1),proving Co_(2)VO_(4) a promising anode in fast-charging LIBs.A hexagonal porous Co2VO4 nanodisk(PCVO ND)structure is designed accordingly,featuring a high specific surface area of 74.57 m^(2) g^(−1) and numerous pores with a pore size of 14 nm.This unique structure succeeds in enhancing Li^(+) and electron transfer,leading to superior fast-charging performance than current commercial anodes.As a result,the PCVO ND shows a high initial reversible capacity of 911.0 mAh g^(−1) at 0.4 C,excellent fast-charging capacity(344.3 mAh g^(−1) at 10 C for 1000 cycles),outstanding long-term cycling stability(only 0.024% capacity loss per cycle at 10 C for 1000 cycles),confirming the commercial feasibility of PCVO ND in fast-charging LIBs.
基金D.T.and T.O.were funded by the Danish Independent Research Foundation,Grant number 6108-00464BK.W.J.and H.M.acknowledge support from the VILLUM Center for Science of Sustainable Fuels and Chemicals,which is funded by the VILLUM Fonden research grant 9455.
文摘We perform a computational screening for two-dimensional(2D)magnetic materials based on experimental bulk compounds present in the Inorganic Crystal Structure Database and Crystallography Open Database.A recently proposed geometric descriptor is used to extract materials that are exfoliable into 2D derivatives and we find 85 ferromagnetic and 61 antiferromagnetic materials for which we obtain magnetic exchange and anisotropy parameters using density functional theory.For the easy-axis ferromagnetic insulators we calculate the Curie temperature based on a fit to classical Monte Carlo simulations of anisotropic Heisenberg models.We find good agreement with the experimentally reported Curie temperatures of known 2D ferromagnets and identify 10 potentially exfoliable 2D ferromagnets that have not been reported previously.In addition,we find 18 easy-axis antiferromagnetic insulators with several compounds exhibiting very strong exchange coupling and magnetic anisotropy.
文摘Computational materials science and engineering has emerged as an interdisciplinary subfield spanning materials science and engineering,condensed matter physics,chemistry,mechanics and engineering in general.Modern materials research often requires a close integration of computation and experiments in order to fundamentally understand the materials structures and properties and their relation to synthesis and processing.A number of computational methods and tools at different spatiotemporal scales are now well established,ranging from electronic structure calculations based on density functional theory,1,2 atomic molecular dynamics3,4 and Monte Carlo techniques,5 phase-field method6–9 to continuum macroscopic approaches.Over the last few years,computational materials activities have been steadily moving from technique development and purely computational studies of materials towards discovering and designing new materials guided by computation,machine learning and data mining or by a closely tied combination of computational predictions and experimental validation.This movement is being further accelerated by the recent initiatives by various government agencies in the United States,Europe,China and other countries to pursue the materials genome initiative,10 integrated computational materials engineering11–13 as well as the‘Big Data’initiative.
基金financially supported by the POSCO Science Fellowship of POSCO TJ Park Foundation,the National Research Foundation of Korea(No.NRF-2020R1C1C1003554)the Creative Materials Discovery Program of the National Research Foundation of Korea(NRF)funded by the Ministry of Science and ICT(No.NRF2016M3D1A1023384)+1 种基金the Korea Institute for Advancement of Technology(KIAT)grant funded by the Korea Government(MOTIE,P0002019,The Competency Development Program for Industry Specialist)support from the German Research Foundation(Deutsche Forschungsgemeinschaft,DFG)under the priority program 2006"CCA-HEA"。
文摘High-and medium-entropy alloys(HEAs and MEAs)possess high solid-solution strength.Numerous investigations have been conducted on its impact on yield strength,however,there are limited reports regarding the relation between solid-solution strengthening and strain-hardening rate.In addition,no attempt has been made to account for the dislocation-mediated plasticity;most works focused on twinning-or transformation-induced plasticity(TWIP or TRIP).In this work we reveal the role of solidsolution strengthening on the strain-hardening rate via systematically investigating evolutions of deformation structures by controlling the Cr/V ratio in prototypical V_(1-x)Cr_(x)CoNi alloys.Comparing the TWIP of CrCoNi with the dislocation slip of V_(0.4)Cr_(0.6)CoNi,the hardening rate of CrCoNi was superior to slip-band refinements of V_(0.4)Cr_(0.6)CoNi due to the dynamic Hall-Petch effect.However,as V content increased further to V_(0.7)Cr_(0.3)CoNi and VCoNi,their rate of slip-band refinement in V_(0.7)Cr_(0.3)CoNi and VCoNi with high solid-solution strength surpassed that of CrCoNi.Although it is generally accepted in conventional alloys that deformation twinning results in a higher strain-hardening rate than dislocation-mediated plasticity,we observed that the latter can be predominant in the former under an activated huge solid-solution strengthening effect.The high solid-solution strength lowered the cross-slip activation and consequently retarded the dislocation rearrangement rate,i.e.,the dynamic recovery.This delay in the hardening rate decrease,therefore,increased the strain-hardening rate,results in an overall higher strain-hardening rate of V-rich alloys.
基金We acknowledge support from the collaborative DFG-RFBR Grant(Grants no.DFG KO 5080/3-1,DFG GR 3716/6-1,and RFBR 20-53-12012)B.G.acknowledges the support by the Stuttgart Center for Simulation Science(SimTech)and funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation programme(grant agreement No.865855).
文摘We present the magnetic Moment Tensor Potentials(mMTPs),a class of machine-learning interatomic potentials,accurately reproducing both vibrational and magnetic degrees of freedom as provided,e.g.,from first-principles calculations.The accuracy is achieved by a two-step minimization scheme that coarse-grains the atomic and the spin space.The performance of the mMTPs is demonstrated for the prototype magnetic system bcc iron,with applications to phonon calculations for different magnetic states,and molecular-dynamics simulations with fluctuating magnetic moments.
基金We acknowledge funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation programme Grant No.773122(LIMA)Grant agreement No.951786(NOMAD CoE).K.S.T.is a Villum Investigator supported by VILLUM FONDEN(grant no.37789).
文摘Efficient algorithms to generate candidate crystal structures with good stability properties can play a key role in data-driven materials discovery.Here,we show that a crystal diffusion variational autoencoder(CDVAE)is capable of generating two-dimensional(2D)materials of high chemical and structural diversity and formation energies mirroring the training structures.Specifically,we train the CDVAE on 26152D materials with energy above the convex hullΔH_(hull)<0.3 eV/atom,and generate 5003 materials that we relax using density functional theory(DFT).We also generate 14192 new crystals by systematic element substitution of the training structures.We find that the generative model and lattice decoration approach are complementary and yield materials with similar stability properties but very different crystal structures and chemical compositions.In total we find 11630 predicted new 2D materials,where 8599 of these haveΔH_(hull)<0.3 eV/atom as the seed structures,while 2004 are within 50 meV of the convex hull and could potentially be synthesised.The relaxed atomic structures of all the materials are available in the open Computational 2D Materials Database(C2DB).Our work establishes the CDVAE as an efficient and reliable crystal generation machine,and significantly expands the space of 2D materials.
基金The Center for Nanostructured Graphene (CNG) is sponsored by The Danish National Research Foundation (project DNRF103)We acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program Grant No.773122 (LIMA) and Grant agreement No.951786 (NOMAD CoE)K.S.T.is a Villum Investigator supported by VILLUM FONDEN (grant no.37789).
文摘Atomically thin two-dimensional(2D)materials are ideal host systems for quantum defects as they offer easier characterisation,manipulation and read-out of defect states as compared to bulk defects.Here we introduce the Quantum Point Defect(QPOD)database with more than 1900 defect systems comprising various charge states of 503 intrinsic point defects(vacancies and antisites)in 82 different 2D semiconductors and insulators.The Atomic Simulation Recipes(ASR)workflow framework was used to perform density functional theory(DFT)calculations of defect formation energies,charge transition levels,Fermi level positions,equilibrium defect and carrier concentrations,transition dipole moments,hyperfine coupling,and zero-field splitting.Excited states and photoluminescence spectra were calculated for selected high-spin defects.In this paper we describe the calculations and workflow behind the QPOD database,present an overview of its content,and discuss some general trends and correlations in the data.We analyse the degree of defect tolerance as well as intrinsic dopability of the host materials and identify promising defects for quantum technological applications.The database is freely available and can be browsed via a web-app interlinked with the Computational 2D Materials Database(C2DB).
基金The Center for Nanostructured Graphene(CNG)is sponsored by the Danish National Research Foundation,Project DNRF103This project has received funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program grant agreement no.773122(LIMA)K.S.T.is a Villum Investigator supported by VILLUM FONDEN(grant no.37789).
文摘We address the problem of predicting the zero-temperature dynamical stability (DS) of a periodic crystal without computing its fullphonon band structure. Here we report the evidence that DS can be inferred with good reliability from the phonon frequencies atthe center and boundary of the Brillouin zone (BZ). This analysis represents a validation of the DS test employed by theComputational 2D Materials Database (C2DB). For 137 dynamically unstable 2D crystals, we displace the atoms along an unstablemode and relax the structure. This procedure yields a dynamically stable crystal in 49 cases. The elementary properties of these newstructures are characterized using the C2DB workflow, and it is found that their properties can differ significantly from those of theoriginal unstable crystals, e.g., band gaps are opened by 0.3 eV on average. All the crystal structures and properties are available inthe C2DB. Finally, we train a classification model on the DS data for 3295 2D materials in the C2DB using a representation encodingthe electronic structure of the crystal. We obtain an excellent receiver operating characteristic (ROC) curve with an area under thecurve (AUC) of 0.90, showing that the classification model can drastically reduce computational efforts in high-throughput studies.
基金This work is supported by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy—EXC 2033—Projekt-nummer 390677874This project has received funding from the ECSEL Joint Undertaking(JU)project UltimateGaN under grant agreement No.826392The J.U.receives support from the European Union’s Horizon 2020 research and innovation program and Austria,Belgium,Germany,Italy,Slovakia,Spain,Sweden,Norway,Switzerland D.W.and C.Vd.W.were supported by the US Department of Energy(DOE),Office of Science,Basic Energy Sciences(BES)under award No.DE-SC0010689.
文摘The repeated slab approach has become a de facto standard to accurately describe surface properties of materials by density functional theory calculations with periodic boundary conditions.For materials exhibiting spontaneous polarization,we show that the conventional scheme of passivation with pseudo hydrogen is unable to realize a charge-neutral surface.The presence of a net surface charge induces via Gauss’s law a macroscopic electric field through the slab and results in poor size convergence with respect to the thickness of the slab.We propose a modified passivation method that accounts for the effect of spontaneous polarization,describes the correct bulk limits and boosts convergence with respect to slab thickness.The robustness,reliability,and superior convergence of energetics and electronic structure achieved by the proposed method are demonstrated using the example of polar ZnO surfaces.
基金M.O.S.,A.T.,K.S.T.,and T.G.P.are supported by the CNG center under the Danish National Research Foundation,project DNRF103U.P.acknowledges funding from the European Union’s Next Generation EU plan through the María Zambrano programme(MAZAM21/19)+2 种基金T.O.is supported by the Villum foundation,Grant No.00028145K.S.T.acknowledge funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program Grant No.773122(LIMA)and Grant agreement No.951786(NOMAD CoE)K.S.T.is a Villum Investigator supported by the Villum foundation(Grant No.37789).
文摘Shift current photovoltaic devices are potential candidates for future cheap,sustainable,and efficient electricity generation.In the present work,we calculate the solar-generated shift current and efficiencies in 326 different 2D materials obtained from the computational database C2DB.We apply,as metrics,the efficiencies of monolayer and multilayer samples.The monolayer efficiencies are generally found to be low,while the multilayer efficiencies of infinite stacks show great promise.Furthermore,the out-of-plane shift current response is considered,and material candidates for efficient out-of-plane shift current devices are identified.Among the screened materials,MXY Janus and MX_(2) transition metal dichalchogenides(TMDs)constitute a prominent subset,with chromium based MXY Janus TMDs holding particular promise.Finally,in order to explain the band gap dependence of the PV efficiency,a simple gapped graphene model with a variable band gap is established and related to the calculated efficiencies.
基金This work was supported by the National Research Foundation of Korea(NRF),funded by the Ministry of Science and ICT(NRF-2020R1A2C1009177)This work was also supported in part by Human Resources Development Program of the Korea Institute of Energy Technology Evaluation and Planning(KETEP)grant funded by the Ministry of Trade,Industry and Energy,Republic of Korea(No.RS-2023-00237035).
文摘This study investigates the effect of defect engineering on the catalytic activity of a NiPS3 monolayer catalyst for the hydrogen evolution reaction(HER).Three different types of vacancies on the basal plane of the monolayer are explored through a multi-step mechanism involving the dissociative adsorption of a water molecule and subsequent electrochemical adsorption of the dissociated proton.Co-formation of vacancies in both Ni and S sites is found to be the most effective in enhancing the catalytic performance of the monolayer.A key resource for the reaction thermodynamics is the S-substitution-like physisorption of a water molecule on a vacant S site,followed by the dissociative occupation of OH and H into vacant sites of S and Ni elements,boosted by the NiS di-vacancy configuration with low activation energy barriers.Investigation reveals the highest contribution of bonding orbitals to the monolayer-H bond makes it the most desirable defect engineering approach for transition metal phosphorus chalcogenides with high HER activities.Overall,this study highlights the significance of controlled defect engineering in augmenting the catalytic performance of NiPS3 monolayer catalysts for HER.
文摘The impact ofmagnetism on chemical ordering in face-centered cubic CrCoNi medium entropy alloy is studied by a combination of ab initio simulations,machine learning potentials,and Monte Carlo simulations.Large magnetic energies are revealed for some mixed L1_(2)/L1_(0) type ordered configurations,which are rooted in strong nearest-neighbor magnetic exchange interactions and chemical bonding among the constituent elements.
基金funding by the Deutsche Forschungsgemeinschaft(DFG,493417040)funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program(grant agreement No.865855)F.K.acknowledges the LRP and MC simulation packages by Alexander Shapeev.
文摘Melting properties are critical for designing novel materials,especially for discovering highperformance,high-melting refractory materials.Experimental measurements of these properties are extremely challenging due to their high melting temperatures.Complementary theoretical predictions are,therefore,indispensable.One of the most accurate approaches for this purpose is the ab initio free-energy approach based on density functional theory(DFT).However,it generally involves expensive thermodynamic integration using ab initio molecular dynamic simulations.The high computational cost makes high-throughput calculations infeasible.Here,we propose a highly efficient DFT-based method aided by a specially designed machine learning potential.As the machine learning potential can closely reproduce the ab initio phase-space distribution,even for multi-component alloys,the costly thermodynamic integration can be fully substituted with more efficient free energy perturbation calculations.The method achieves overall savings of computational resources by 80%compared to current alternatives.We apply the method to the high-entropy alloy TaVCrW and calculate its melting properties,including the melting temperature,entropy and enthalpy of fusion,and volume change at the melting point.Additionally,the heat capacities of solid and liquid TaVCrW are calculated.The results agree reasonably with the CALPHAD extrapolated values.
基金This collaboration might not have been possible had the authors not met at a number of research programs at the Institute of Pure and Applied Mathematics,UCLA.T.K.and A.S.were supported by the Russian Science Foundation(Grant number 18-13-00479)F.K.acknowledges funding from the Deutsche Forschungsgemeinschaft(SPP 2006)+1 种基金the Netherlands Organization for Scientific Research NWO/STW(VIDI grant 15707)J.N.acknowledges financial support by the DFG under project number NE 428/19-1.
文摘Recently,high-entropy alloys(HEAs)have attracted wide attention due to their extraordinary materials properties.A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space.Ab initio calculations have emerged as a powerful approach that complements experiment.However,for multicomponent alloys existing approaches suffer from the chemical complexity involved.In this work we propose a method for studying HEAs computationally.Our approach is based on the application of machine-learning potentials based on ab initio data in combination with Monte Carlo simulations.The high efficiency and performance of the approach are demonstrated on the prototype bcc NbMoTaW HEA.The approach is employed to study phase stability,phase transitions,and chemical short-range order.The importance of including local relaxation effects is revealed:they significantly stabilize single-phase formation of bcc NbMoTaW down to room temperature.Finally,a so-far unknown mechanism that drives chemical order due to atomic relaxation at ambient temperatures is discovered.
基金Funding by the Deutsche Forschungsgemeinschaft(DFG)through the scholarship KO 5080/1-1by the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation programme(Grant agreement No.639211)+1 种基金by the Ministry of Education,Culture,Sports,Science and Technology(MEXT),Japan,through the Elements Strategy Initiative for Structural Materials(ESISM)of Kyoto Universityby the Japan Society for the Promotion of Science(JSPS)KAKENHI Grant-in-Aid for Young Scientist(B)(Grant No.16K18228)are gratefully acknowledged.
文摘Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation hightemperature applications.At high temperatures,materials properties are strongly affected by lattice vibrations(phonons).Phonons critically influence thermal stability,thermodynamic and elastic properties,as well as thermal conductivity.In contrast to perfect crystals and ordered alloys,the inherently present mass and force constant fluctuations in multi-component random alloys(high entropy alloys)can induce significant phonon scattering and broadening.Despite their importance,phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys.We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys,from binaries up to 5-component high entropy alloys,addressing the key question of how chemical complexity impacts phonons.We find that it is crucial to include both mass and force constant fluctuations.If one or the other is neglected,qualitatively wrong results can be obtained such as artificial phonon band gaps.We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities,specifically the vibrational entropy.Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations.The set of studied alloys includes MoTa,MoTaNb,MoTaNbW,MoTaNbWV,VW,VWNb,VWTa,VWNbTa,VTaNbTi,VWNbTaTi,HfZrNb,HfMoTaTiZr.
基金We thank Jan Janssen and Konstantin Gubaev for fruitful discussions.Funding by the Deutsche Forschungsgemeinschaft(SPP 2006)the European Research Council(ERC)under the EU’s Horizon 2020 Research and Innovation Programme(Grant no.639211)is gratefully acknowledged+1 种基金F.K.acknowledges NWO/STW(VIDI grant 15707)A.S.was supported by the Russian Science Foundation(Grant no.18-13-00479)。
文摘The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific disciplines.The vast compositional parameter space makes these alloys a unique area of exploration by means of computational design.However,as of now a method to compute efficiently,yet with high accuracy the thermodynamic properties of such alloys has been missing.One of the underlying reasons is the lack of accurate and efficient approaches to compute vibrational free energies—including anharmonicity—for these chemically complex multicomponent alloys.In this work,a density-functional-theory based approach to overcome this issue is developed based on a combination of thermodynamic integration and a machine-learning potential.We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.
基金supported by the JST Industry-Academia Collaborative Programs,“Materials Strength from Hamiltonian”,and by the Elements Strategy Initiative for Structural Materials(ESISM)through MEXT,Japansupported by a Grant-in-Aid for Scientific Research on Innovative Area“Bulk Nanostructured Metals”and by the Computational Materials Science Initiative(CMSI),MEXT,Japanthe K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project(Project ID:hp130016,hp140233,hp150235).
文摘The physical origins of the mechanical properties of Fe-rich Si alloys are investigated by combining electronic structure calculations with statistical mechanics means such as the cluster variation method,molecular dynamics simulation,etc,applied to homogeneous and heterogeneous systems.Firstly,we examined the elastic properties based on electronic structure calculations in a homogeneous system and attributed the physical origin of the loss of ductility with increasing Si content to the combined effects of magneto-volume and D03 ordering.As a typical example of a heterogeneity forming a microstructure,we focus on grain boundaries,and segregation behavior of Si atoms is studied through high-precision electronic structure calculations.Two kinds of segregation sites are identified:looser and tighter sites.Depending on the site,different segregation mechanisms are revealed.Finally,the dislocation behavior in the Fe-Si alloy is investigated mainly by molecular dynamics simulations combined with electronic structure calculations.The solid-solution hardening and softening are interpreted in terms of two kinds of energy barriers for kink nucleation and migration on a screw dislocation line.Furthermore,the clue to the peculiar work hardening behavior is discussed based on kinetic Monte Carlo simulations by focusing on the preferential selection of slip planes triggered by kink nucleation.
基金K.S.T.acknowledges funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program(grant agreement No 773122,“LIMA”)The work of A.R.was supported by National Science Foundation under Grant No.DMR-1553022.J.E.B.acknowledges the A.R.Smith Department of Chemistry and Fermentation Sciences for support.
文摘We review the theory and application of adiabatic exchange–correlation(xc)-kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin’s equations,respectively.Various different xc-kernels,which are all rooted in the homogeneous electron gas,are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels,in particular the rALDA and rAPBE.The kernels drastically improve the description of short-range correlations as compared to the random phase approximation(RPA),resulting in significantly better correlation energies.This effect greatly reduces the reliance on error cancellations,which is essential in RPA,and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions.For quasiparticle energies,the xc-kernels account for vertex corrections that are missing in the GW self-energy.In this context,we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter.The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.
