The surface diffusion of Pt dimers on Wulff polyhedral clusters with 586-12934 atoms was studied by the embedded atom method. The minimum energy diffusion path and the corresponding energy barrier for dimer diffusion ...The surface diffusion of Pt dimers on Wulff polyhedral clusters with 586-12934 atoms was studied by the embedded atom method. The minimum energy diffusion path and the corresponding energy barrier for dimer diffusion on cluster surfaces were determined through a combination of the quenched Molecular Dynamics and the Nudged Elastic Band method. It was found that the diffusion of a dimer across the step-edge by dissociation and consecutive single-atom exchange with the edge atoms, rather than diffusion over the edge as a unit. Therefore, the step can enhance the dissociation of the dimer. For small Wulff polyhedral clusters containing up to 2000 atoms, the energy barrier for dimer diffusion from the {111} to the {100} facet is almost equal to that for the single adatom diffusion on the flat {111} surface. From the calculated cluster size dependence of the energy barrier, we conclude that the Wulff polyhedral cluster is stable, as the cluster has more than about 2000 atoms.展开更多
We establish the mean width inequalities for symmetric Wulff shapes by a direct approach.We also yield the dual inequality along with the equality conditions.These new inequalities have Barthe’s mean width inequaliti...We establish the mean width inequalities for symmetric Wulff shapes by a direct approach.We also yield the dual inequality along with the equality conditions.These new inequalities have Barthe’s mean width inequalities for even isotropic measures and its dual form as special cases.展开更多
Cobalt nanoparticles(NPs)catalysts are extensively used in heterogeneous catalytic reactions,and the addition of alkali metal promoters is a common method to modulate the catalytic performance because the catalyst'...Cobalt nanoparticles(NPs)catalysts are extensively used in heterogeneous catalytic reactions,and the addition of alkali metal promoters is a common method to modulate the catalytic performance because the catalyst's surface structures and morphologies are sensitive to the addition of promoters.However,the underlying modulation trend remains unclear.Herein,the adsorption of alkali metal promoters(Na and K)on the surfaces of face-centered-cubic(FCC)and hexagonal-closest packed(HCP)polymorphous cobalt was systematically investigated using density functional theory.Furthermore,the effect of alkali promoters on surface energies and nanoparticle morphologies was revealed on the basis of Wulff theory.For FCC-Co,the exposed area of the(111)facet in the nanoparticle increases with the adsorption coverage of alkali metal oxide.Meanwhile,the(311),(110),and(100)facets would disappear under the higher adsorption coverage of alkali metals.For HCPCo,the Wulff morphology is dominated by the(0001)and(1011)facets and is independent of the alkali metal adsorption coverage.This work provides insights into morphology modulation by alkali metal promoters for the rational design and synthesis of cobalt-based nanomaterials with desired facets and morphologies.展开更多
基金Tianyuan Fund for Mathematics of NSFC (Grant No.10526030)Grant No.10531090 of the NSFCDoctoral Program Foundation of the Ministry of Education of China (2006)
文摘在 S <SUP 上给积极功能 F > n </SUP > 它满足一个凸状条件，我们介绍 r-th 各向异性的吝啬的弯曲 M <SUB > r </SUB > 为在是平常的 r-th 的归纳的 ℝ
<SUP> n+1 </SUP> 的亢奋的表面意味着弯曲 H <SUB > r </SUB> 。我们在 R <SUP 为紧缩的亢奋的表面得到 Minkowski 类型的不可分的公式 > n+1 </SUP> 。我们由我们 Minkowski 的公式打的积分的使用给一些 Wulff 形状的新描述，以防 F = 1 哪个到一些著名结果的还原剂。
基金supported by the National Natural Science Foundation of China (Grant No. 50971058)the Hunan Provincial Natural Science Foundation of China (Grant No. 10JJ3050)
文摘The surface diffusion of Pt dimers on Wulff polyhedral clusters with 586-12934 atoms was studied by the embedded atom method. The minimum energy diffusion path and the corresponding energy barrier for dimer diffusion on cluster surfaces were determined through a combination of the quenched Molecular Dynamics and the Nudged Elastic Band method. It was found that the diffusion of a dimer across the step-edge by dissociation and consecutive single-atom exchange with the edge atoms, rather than diffusion over the edge as a unit. Therefore, the step can enhance the dissociation of the dimer. For small Wulff polyhedral clusters containing up to 2000 atoms, the energy barrier for dimer diffusion from the {111} to the {100} facet is almost equal to that for the single adatom diffusion on the flat {111} surface. From the calculated cluster size dependence of the energy barrier, we conclude that the Wulff polyhedral cluster is stable, as the cluster has more than about 2000 atoms.
基金supported by National Natural Science Foundation of China (Grant No. 11271244)Shanghai Leading Academic Discipline Project (Grant No. S30104)
文摘We establish the mean width inequalities for symmetric Wulff shapes by a direct approach.We also yield the dual inequality along with the equality conditions.These new inequalities have Barthe’s mean width inequalities for even isotropic measures and its dual form as special cases.
基金financial support from the National Natural Science Foundation of China (Nos.21972157,21972160,and 22202224)the CAS Project for Young Scientists in Basic Research (No.YSBR-005)+2 种基金the Key Research Program of Frontier Sciences CAS (No.ZDBS-LY-7007)the CAS Project for Internet Security and Information Technology (No.CAS-WX2021SF0110)the funding support from Beijing Advanced Innovation Center for Materials Genome Engineering,Synfuels China,Co.Ltd.and Inner Mongolia University of Technology。
文摘Cobalt nanoparticles(NPs)catalysts are extensively used in heterogeneous catalytic reactions,and the addition of alkali metal promoters is a common method to modulate the catalytic performance because the catalyst's surface structures and morphologies are sensitive to the addition of promoters.However,the underlying modulation trend remains unclear.Herein,the adsorption of alkali metal promoters(Na and K)on the surfaces of face-centered-cubic(FCC)and hexagonal-closest packed(HCP)polymorphous cobalt was systematically investigated using density functional theory.Furthermore,the effect of alkali promoters on surface energies and nanoparticle morphologies was revealed on the basis of Wulff theory.For FCC-Co,the exposed area of the(111)facet in the nanoparticle increases with the adsorption coverage of alkali metal oxide.Meanwhile,the(311),(110),and(100)facets would disappear under the higher adsorption coverage of alkali metals.For HCPCo,the Wulff morphology is dominated by the(0001)and(1011)facets and is independent of the alkali metal adsorption coverage.This work provides insights into morphology modulation by alkali metal promoters for the rational design and synthesis of cobalt-based nanomaterials with desired facets and morphologies.
基金Projects(11102164,11304243)supported by the National Natural Science Foundation of ChinaProject(2014JQ1039)supported by the Natural Science Foundation of Shannxi Province,China+1 种基金Project(3102016ZY027)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(13GH014602)supported by the Program of New Staff and Research Area Project of NWPU,China
基金The project was supported by the National Natural Science Foundation of China(21972170,22072184)the Fundamental Research Funds for the Central Universities,and South-Central Minzu University(CZY13005,CZT20010).
