Calculation of the surface energy of fcc metals with modified embedded-atom method

The surface energies for 38 surfaces of fcc metals Cu, Ag, Au, Ni, Pd, Pt, A1, Pb, Rh and Ir have been calculated by using the modified embedded-atom method. The results show that, for Cu, Ag, Ni, A1, Pb and Ir, the average values of the surface energies are very close to the polycrystalline experimental data. For all fcc metals, as predicted, the close-packed (111) surface has the lowest surface energy. The surface energies for the other surfaces increase linearly with increasing angle between the surfaces (hkl) and (111). This can be used to estimate the relative values of the surface energy.     

Ni,Pd和Pt的表面应力

半经验的修正嵌入原子方法用于Ni，Pd和Pt的低指数面的表面应力计算，得到了与第一原理计算相符合的结果．给出了（110）表面［110］方向的应力是［001］方向应力的两倍左右；阐明了应力各向异性是所有fc金属（110）面的一般特性．预言了Pd和Pt（100）的表面应力的大小． 关键词：     

Relaxation and electronic states of Au(100), (110) and (111) surfaces

Using a first-principles method based on density functional theory, we investigate the surface relaxation and electronic states of Au(100), (110) and (111) surfaces. The calculated results show that the relaxations of the (100) and (110) surfaces of the metal are inward relaxations. However, the Au(111) surface shows an ‘anomalous’ outward relaxation, although several previous theoretical studies have predicted inward relaxations that are contrary to the experimental measurements. Electronic densities of states and the respective charge density distribution along the Z-axis of the relaxed surfaces are analyzed, and the origin of inward and outward relaxation is discussed in detail.     

Surface relaxation and thermal expansion for the (001) face of α-Fe and Cu

The surface relaxation and the near-surface enhancement of thermal expansion have been calculated for the (001) face of a bcc crystal, α-Fe, and an fcc crystal, Cu. The calculations make use of the anharmonic perturbation formalism of Dobrzynski and Maradudin; the results for certain equal-time vibrational correlation functions which arise in this formalism are also presented. The crystal potential is described in terms of several kinds of short-range empirical interatomic potentials, such as have been used in studies of defects in bulk; in the near-surface region, the effects of surface redistribution of the electron distribution are modelled by the addition of a simple surface Madelung (SSM) force. The effect of the SSM force is to limit severely the usual outward relaxation driven by short-range interatomic potentials. For Fe(001), the five and one-half percent outward static relaxation driven by the short-range potentials acting alone is changed to a one percent inward static relaxation when the SSM force is incorporated; for Cu(001), the comparable change is from a one percent outward relaxation to a one-half percent outward relaxation. On the other hand, the SSM force makes only a small effect on the surface-enhanced thermal expansion coefficients (STEC) for interplanar spacings. The STEC for the outermost spacing is between 2.5. and 3.0 times of that for the bulk at the Debye temperature for both Fe(001) and Cu(001); for the second interplanar spacing, the STEC is smaller than 1.5 times of that of the bulk at the Debye temperature. The ratios of the near-surface mean-square amplitudes (MSA) to those of the bulk at high temperatures are, for Fe(001), about 1.75 for z-components (normal to surface) and 1.55 for x-components (parallel to surface) in the surface layer; for Cu(001), about 1.95 for z-components and 1.30 for x-components. The interplanar correlation functions, while smaller than the MSA on an absolute scale, do show considerable surface-enhancement, particularly for the zz-compoments. For example, the zz-correlation between an atom in the outermost layer and its nearest neighbor in the next layer is nearly twice the comparable bulk correlation above the Debye temperature for both Fe(001) and Cu(001).     

Ab-initio calculation of the electronic structure and energetics of the unreconstructed Au(001) surface

The electronic structure, surface and relaxation energies, and the electric field gradient for the unreconstructed Au(001) surface were calculated by means of the ab-initio all-electron full-potential linearized augmented plane wave slab method. The valence states were calculated within the standard semi-relativistic approach whereas the core states are treated in a fully relativistic way. The Au(001) surface was modelled by free slabs of 5, 7, and 9 layers. From the 9-layer calculation a work function of 5.39 eV was obtained. For the surface energy a value of 1.30 J/m² for the unrelaxed geometry was derived from the total energies of the 7- and the 9-layer slabs. From total energy minimization of the 7-layer slab, a negative, inward relaxation of −2.6% and a relaxation energy of 14.3 × 10⁻³ J/m² were derived. To discuss a mechanism of reconstruction, particular surface states were analyzed in detail in terms of the band structure, layer-dependent density of states and the charge density distribution. Differences of surface and central-layer charge densities show a gain of charge in z-direction localised below and also, to a smaller extent, above the surface atoms. We find a very small gain of delocalised charge in the surface plane between the nearest neighbour positions at the expense of more localised s-d hybridised states. The electric field gradient component Φ_zz was obtained in a two energy window calculation for which the Au5p states were also treated as band states. The resulting Φ_zz values are −16.50 × 10¹⁷ V/cm² surface layer, and −3.3 × 10¹⁷ V/cm² for the subsurface layer.     

VC(001)弛豫表面构型与电子结构第一性原理研究

用第一性原理方法对VC(001)清洁表面的构型和电子结构进行了详细研究，与TiC(001)面类似，VC(001)面弛豫后形成表面皱褶，其表层V原子和C原子分别朝体相和真空方向移动. 能带计算结果表明，过渡金属碳化物(001)面的能带结构符合刚性带理论模型. 对于VC(001)面，表面态主要处在-30eV附近，其主要成分为表层C原子的2pz轨道. 此外，以表层V原子的3d轨道成分为主的表面态出现在费米能级附近，由于这些表面态以表面法线方向的轨道(3d２z和3dxz/dyz)为主要成分，因此在表面反应中将起到重要作用，从而体现出与TiC(001)面不同的反应性质. 关键词： 过渡金属碳化物 表面态 能带结构     

Lattice relaxation at alkali metal surfaces

The surface relaxation of the first interlayer spacing for both the (110) and (100) faces of alkali metals has been calculated selfconsistently using the density functional formalism and a new density matrix method which obviates the use of wavefunctions. For the (110) surfaces of all alkali metals we find no or only very small relaxation. The (100) surfaces show bigger relaxation effects and these vary from 3.5% inward for Li to 1% outward for Cs. These findings are consistent with general trends found in LEED or Ion scattering studies. Force constants for the movement of the last atomic layer are also determined.     

The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

The three-dimensional equilibrium crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb crystal state is in support of the experimental ECS of Pb at 320–350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies. PACS 05.70.Np; 61.50.Jr; 68.35.Md; 71.15.Mb     

Effects of surface relaxation on the surface modes of a CsCl (001) slab shaped crystal

The vibrational frequencies of a 24-layer CsCl (001) slab have been calculated with an eleven-parameter shell model. Without surface relaxation, the results exhibit an instability in the form of a pair of imaginary-frequency Rayleigh modes for wave vectors over most of the surface Brillouin zone. To investigate the effects of relaxation on this dynamic instability, two kinds of relaxation have been used; (i) an inward relaxation of the two outermost planes, and (ii) an expansion of the entire slab in the z-direction (i.e. normal to the surfaces), followed by an inward relaxation of the two outermost planes. In the first case, the imaginary frequencies are removed for most wave vectors except for those very close to the zone center. In the second case, the imaginary frequencies are removed for all wave vectors. Due to the occurrence of two different surfaces of the slab, one containing only Cs⁺ ions, the other only Cl^? ions, two classes of surface modes are found: one with the vibrational amplitudes decreasing from the top layer to the bottom layer, the other vice versa. Longitudinal and transverse optical, and transverse accoustical surface modes are found in both classes. The frequencies of these surface modes are strongly dependent on the surface relaxations.     

BiOCl{001}表面原子与电子结构的第一性原理研究

基于密度泛函理论的第一性原理方法研究了BiOCl{001}的三种不同终端面({001}-1Cl, {001}-BiO 和{001}-2Cl)的表面弛豫、能带结构、电子态密度和表面能. 计算结果表明: {001}-1Cl, {001}-BiO和{001}-2Cl表面均发生明显弛豫, 而在双Cl原子层处的层间距变化较大, 但未出现振荡弛豫现象, 其中{001}-1Cl表面弛豫较小. 与体相BiOCl电子结构相比, BiOCl{001}面具有较窄的带隙宽度, 并呈现较强局域性:对于{001}-BiO表面, 其导带与价带均往低能方向发生较大移动, 并且在导带底部出现表面态; 而{001}-2Cl表面的表面态主要出现在价带顶; {001}-1Cl表面的带隙中则无表面态产生; 表面态的出现导致{001}-BiO面和{001}-2Cl面带隙明显减小. BiOCl{001}三种终端表面的表面能分析结果表明, {001}-1Cl表面的表面能最小(0.09206 J·m^-2), 结构最稳定, 而{001}-BiO表面和{001}-2Cl表面的表面能分别为2.392和2.461 J·m^-2. 理论预测{001}-BiO表面和{001}-2Cl表面具有较高的活性, 但在BiOCl晶体生长过程中不易暴露. 本文计算结果为实验获得BiOCl高活性面{001}给予了基础理论解释, 进一步为BiOCl新型光催化材料的应用研究提供理论指导. 关键词： BiOCl{001}表面 表面弛豫 表面能 第一性原理     

Thickness induced structural transition in suspended fcc metal nanofilms

Recent experiments show that at a critical thickness, surface forces can dominate the bulk coercing suspended Au nanofilms to globally reconstruct from the (001) to the (111) orientation. Here we perform molecular dynamics simulations demonstrating that such transformations are generic to other fcc metals. This contrasts with surface reconstruction on the bulk occurring only in 5d metals. We show that this phenomenon occurs once a small energy barrier is overcome and discuss the relation of such a barrier and the critical thickness to film surface area and boundary conditions.     

N_2在Co掺杂Ru(001)表面吸附的DFT研究

采用密度泛函理论与周期性平板模型相结合的方法,对N_2在Ru(001)表面top、fcc、hcp、bridge四个吸附位和Ru-Co(001)表面Ru-top、Co-top、Ru(Ru)Ru-bridge、Co(Co)Co-bridge、Ru(Co)Co-bridge、Ru(Ru)Co-bridge、Ru_2Co-hcp、RuCo_2-hcp、Ru_2Co-fcc、RuCo_2-fcc十个吸附位的14种吸附模型进行了构型优化、能量计算,得到了N_2较有利的吸附位;并对清洁表面进行能带分析,对最佳吸附位进行总态密度分析.结果表明:掺杂Co后,Ru催化剂的能带变宽,催化活性增强;N_2在Ru(001)表面的最稳定吸附位top的吸附能是-88.94 kJ·mol~(-1),在Ru-Co(001)表面的最稳定吸附位Ru-top的吸附能是-95.71 kJ·mol~(-1),而且N_2与金属表面成键,属于化学吸附.     

Al表面的多层弛豫——修正嵌入原子势的应用

利用修正的嵌入原子方法计算了Al低指数面（100），（110），（111）和高指数面（210），（211），（310），（311），（331）的多层弛豫，所得到的结果都与实验及第一原理计算结果符合得很好．尤其是这种半经验方法给出了与实验结果相符的Al（100）和（111）表面最外层向外膨胀的理论结果，并提出这种膨胀主要是由于最外层与第二层的键中s态电子增加而p态电子减少引起的． 关键词：     

Structural,electronic and magnetic properties of the (001), (110) and (111) surfaces of rocksalt sodium sulfide: A first-principles study

First principles study of the structural, electronic and magnetic properties of the (111), (110) and (001) surfaces of rocksalt sodium sulfide (rs-NaS) are reported. The results show that the bulk half-metallicity of this compound is well preserved on the surfaces considered here except for Na-terminated (111) surface. The spin-flip gap at the S-terminated (111), (001) and (110) surfaces are close to the bulk value. Using ab-initio atomistic thermodynamics, we calculate the surface energies as a function of chemical potential to find the most stable surface. We find that the Na-terminated (111) surface is the most stable one over the whole allowed range of chemical potential, while the surface energies of the (001) and (110) surfaces approach the most stable surface energy at the sulfur rich environment. We have also calculated the interlayer exchange interaction in bulk and Na-terminated (111) surface by classical Heisenberg model and we found that the surface effects do not change these kinds of interactions significantly.     

Atomistic structure of stepped surfaces

Atomistic computer simulation with embedded atom method (EAM) interatomic forces was used to study the structure of surface steps on the {111} unreconstructed surface in fcc metallic materials. The energetics and local atomic relaxation behavior of ledges parallel to the 110 direction were studied using a potential describing lattice properties of Au. The vacancy formation energies in the stepped surfaces was also studied, and it was found that the energy of formation of a vacancy in a terrace is the same as that in the perfect unstepped surface. This value is 30% lower than that of the bulk. The vacancy formation energy in the ledge is reduced by a factor of two with respect to that of the terraces. The structure of the “up ledge” (A step) is different from the “down ledge” (B step). These differences do not significantly affect the energy of the ledges, although they do affect the vacancy formation energies in sites in the second surface layer near the ledge. The implications of the results for the formation of kinks and the general structure of high index surfaces are discussed.     

Buried interfaces studied by photoelectron diffraction

Angle- and energy-scanned photoelectron diffraction data can be used to investigate structures below surfaces. The modulations in photoelectron intensity result from diffraction of the emitted electron wave at neighbor atoms. In the past, scanned-energy photoelectron diffraction had been mainly used to determine the adsorption site of molecules at surfaces. Recent data show, however, that the technique can also be employed to obtain information about the upper substrate layer(s). At low kinetic energies, backward scattering is strong and in scanned-angle photoelectron diffraction the recorded patterns result from backward- and multiple-scattering effects. For a structural analysis, the intensity modulations have to be compared with the results for simulations performed for model clusters. As an example, recent angle-scanned photoelectron diffraction patterns recorded for the technologically important silicon oxide/silicon interface were compared with simulations. At the Si(001) surface orientation, the interface is extended over a few layers, whereas at the Si(111) surface orientation the transition is rather abrupt and occurs within one or two layers. Received: 9 September 2002 / Accepted: 2 October 2002 / Published online: 5 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-231/755-3657, E-mail: carsten.westphal@physik.uni-dortmund.de     

Analysis of ground states of fcc thin film of binary alloy under confinement

In this paper, we have investigated the ground states of a few-layered fcc thin film of binary alloy with two surfaces in the (001) direction under symmetric surface confinement. The phase diagram of the ground states is given according to the energy analysis of binary alloy thin film composed of six atomic layers in the (001) direction. Surface confinement field (SC field) is introduced as a term to describe the confinement on the two surfaces in the (001) direction. Using Monte Carlo simulation, we have found that there are 17 different ground states occurring when both SC field and chemical potential vary from - ∞ to + ∞. Antiphase boundary(APB) was found in 12 of the 17 ground states, and only nine configurations with different symmetry were found among the 17 ground states. Received 6 November 2001 and Received in final form 25 January 2002     

fcc金属表面能的各向异性分析及表面偏析的预测

本文将元素变量(φ^*和n_WS)和MAEAM相结合,从原子尺度上对10种fcc金属Cu,Ag,Au,Ni,Pd,Pt,Rh,Al,Ir和Pb的38个不同晶面的表面能进行模拟计算及各向异性分析. 结果表明,fcc金属的密排面(111)的表面能最小,则该晶粒取向优先生长,与实验结果和第一原理的LMTO-ASA计算结果一致;各个晶面的表面能均随着其他晶面与(111)晶面的夹角cosθ_(hkl)的增长而呈线性 关键词： FCC金属 MAEAM 表面能 表面偏析     

立方相Ag_3PO_4(111)面原子几何及弛豫结构的第一性原理计算

采用平面波超软赝势方法研究了立方相Ag_3PO_4(111)面的表面能和表面原子弛豫结构.首先对Ag_3PO_4(111)面的八种不同原子终止结构的体系总能量进行计算,结果表明B种表面模型被证实为最稳定的(111)面原子几何结构.针对该表面结构,探讨了表面能和原子弛豫与模型中原子层数和真空厚度的关系,当原子层数为24层,真空厚度为0.6 nm时,表面能收敛于1.41 J/m2(LDA-CAPZ)和1.39 J/m2(GGA-PBE).表面原子弛豫后,表面两个三配位的Ag原子均向里移动,超过0.06 nm,而表面次层的O原子则均向外移动约0.0042 nm,导致弛豫后暴露在最表面的是O原子,同时表面原子的核外电子向表面内部发生转移,结构趋于稳定.这些结果为进一步深入研究Ag_3PO_4表面的光催化活性起源提供理论支持.