Calculation of the surface energy of fcc-metals with the empirical electron surface model

The empirical electron surface model (EESM) based on the empirical electron theory and the dangling bond analysis method has been used to establish a database of surface energy for low-index surfaces of fcc-metals such as Al, Mn, Co, Ni, Cu, Pd, Ag, Pt, Au, and Pb. A brief introduction of EESM will be presented in this paper. The calculated results are in agreement with experimental and other theoretical values. Comparison of the experimental results and calculation values shows that the average relative error is less than 10% and these values show a strong anisotropy. As we predicted, the surface energy of the close-packed plane (1 1 1) is the lowest one of all index surfaces. For low-index planes, the order of the surface energies is γ_(1 1 1) < γ_(1 0 0) < γ_(1 1 0) < γ_(2 1 0). It is also found that the dangling bond electron density and the spatial distribution of covalent bonds have a great influence on surface energy of various index surfaces.     

The peculiarities of the low-energy ion scattering by polycrystal targets

In the present work, experimental and computer simulation studies of low-energy (E₀ = 80-500 eV) Cs⁺ ions scattering on Ta, W, Re target surfaces and K⁺ ions scattering on Ti, V, Cr target surfaces have been performed for more accurate definition of mechanism of scattering, with a purpose of evaluation of an opportunity of use of slow ions scattering as a tool of surface layers analysis. The choice of the targets was based on the fact that the ratios of atomic masses of target atoms and ions μ = m₂/m₁ were almost the same for all cases considered and greater than 1 (direct mass ratio) however, the difference of binding energies of target atoms in the cases of Cs⁺ and K⁺ scattering was almost twice as much. It has been noticed that the dependencies of the relative energy retained by scattering ions at the maximum of energy distribution versus the initial energy E_m/E₀ (E₀) have a similar shape in all cases. The relative energy retained by scattering ions increases while the initial energy of incidence ions decreases. The curves are placed above each other relative to the binding energies of target atoms, to show what this says about the influence of binding energy on a process of scattering of low-energy ions. The correlation between value of energy change maintained by an ion for different values of E₀ in the case of scattering by targets with different masses of atoms and its binding energies is experimentally established. The contrary behavior of the E_m/E₀ (E₀) dependencies concerning the target atom binding energy quantity E_b for cases with direct (μ > 1) and inverse (μ < 1) mass ratio of colliding particles is established. The comparison of experimental energy distributions with calculated histograms shows that the binary collision approximation cannot elucidate the abnormally great shift in the maxima of relative energy distributions towards greater energy retained by scattering ions.     

Ab initio calculations of generalized-stacking-fault energy surfaces and surface energies for FCC metals

The ab initio calculations have been used to study the generalized-stacking-fault energy (GSFE) surfaces and surface energies for the closed-packed (1 1 1) plane in FCC metals Cu, Ag, Au, Ni, Al, Rh, Ir, Pd, Pt, and Pb. The GSFE curves along (1 1 1) direction and (1 1 1) direction, and surface energies have been calculated from first principles. Based on the translational symmetry of the GSFE surfaces, the fitted expressions have been obtained from the Fourier series. Our results of the GSFEs and surface energies agree better with experimental results. The metals Al, Pd, and Pt have low γ_us/γ_I value, so full dislocation will be observed easily; while Cu, Ag, Au, and Ni have large γ_us/γ_I value, so it is preferred to create partial dislocation. From the calculations of surface energies, it is confirmed that the VIII column elements Ni, Rh, Ir, Pd, and Pt have higher surface energies than other metals.     

Calculation of the surface energy of hcp metals by using the modified embedded atom method

With MEAM, the surface energies of three kinds of representative surfaces, (h 0 l), (h h l) and (h k 0) belong to [0 1 0], [] and [0 0 1] crystal band, respectively, have been calculated for 13 closed-packed hexagonal (hcp) metals Co, Dy, Er, Gd, Ho, Mg, Nd, Pr, Re, Sc, Tb, Tl and Zr. For all 13 hcp metals, the basal plane (0 0 1) has the minimum surface energy. So from surface energy minimization, the (0 0 1) texture should be favored in the hcp films, this is consistent with the experimental results. The fact that the short termination corresponds to much lower surface energy than long one implies the former is more stable for those surfaces having two possible terminations. Such as the prism plane (1 0 0), only the short termination was observed in experiment.     

A theoretical study of FeCN in the Δ electronic ground state

The three-dimensional potential energy and dipole moment surfaces for the electronic ground state ⁶Δ of FeCN have been computed at the MR-SDCI + Q + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, where MR-SDCI means ‘multi-reference single and double excitation configuration interaction’ and ANO means ‘atomic natural orbital’. Based on these potential energy and dipole moment surfaces, the spectroscopic parameters, rovibronic energies, structural parameters, vibrational transition moments, and the wavenumbers and intensities of selected rotation-vibration transitions have been calculated. The equilibrium structure is linear with r_e(Fe-C) = 2.048 Å and r_e(C-N) = 1.168 Å, and the zero-point averaged structure is bent with 〈r(Fe-C)〉₀ = 2.082 Å, 〈r(C-N)〉₀ = 1.172 Å, and 〈∠(Fe-C-N)〉₀ = 170(5)°. At all the MR-SDCI + Q and the size-extensive multi-reference averaged quadratic coupled-cluster (MR-AQCC) levels of theory, with and without relativistic correction E_rel, that were employed in the present work, ⁶Δ FeCN is predicted to be slightly more stable than ⁶Δ FeNC. For example, the energy difference between the two isomers is approximately 150 cm⁻¹ at the highest level of theory employed, MR-AQCC + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] with zero-point energy correction. The electronic structure of ⁶Δ FeCN has also been compared with that of ⁶Δ FeNC. At present, no experimental spectroscopic data are available for ⁶Δ FeCN. It is hoped that the present work will stimulate experimental investigations of this molecule.     

A kinetic study of the thermal decomposition process of potassium metabisulfite: Estimation of distributed reactivity model

The thermal decomposition kinetics of potassium metabisulfite was studied by thermogravimetric (TG) and differential thermogravimetric (DTG) techniques using non-isothermal experiments. The apparent activation energy (E_a) is determined using the differential (Friedman) isoconversional method. The results of the Friedman's isoconversional analysis of the TG data suggests that the investigated decomposition process follows a single-step reaction and the observed apparent activation energy was determined as 122.4±2.1 kJ mol⁻¹. A kinetic rate equation was derived for the decomposition process of potassium metabisulfite with contracting area model, f(α)=2(1−α)^1/2, which is established using the Malek's kinetic procedure. The value of pre-exponential factor (A) is also evaluated and was found to be A=1.37×10¹² min⁻¹. By applying the Miura's procedure the distributed reactivity model (DRM) for investigated decomposition process was established. From the dependence α versus E_a, the experimental distribution curve of apparent activation energies, f(E_a), was estimated. By applying the non-linear least-squares analysis, it was found that the Gaussian distribution model (with distribution parameters E₀=121.3 kJ mol⁻¹ and σ=1.5 kJ mol⁻¹) represents the best reactivity model for describing the investigated process. Using the Miura's method, the A values were estimated at five different heating rates and the average A values are plotted against E_a. The linear relationship between the A and E_a values was established (compensation effect). Also, it was concluded that the E_a values calculated by the Friedman's method and estimated distribution curve, f(E_a), are correct even in the case when the investigated decomposition process occurs through the single-step reaction mechanism.     

Kinetics of slow collapse process: Thermodynamic description of rate constants

Insoluble monolayer formed at the air/water interface compressed at a surface pressure above the equilibrium spreading pressure is unstable. In presented paper the classical theory for homogeneous nucleation is modified adding the activation energy term. It allows quantitative thermodynamic interpretation of the slow collapse phase transformation. The collapse of stearic acid Langmuir films has been carried out by systematic measurements of the area loss-time isobaric dependencies at various temperatures and isothermal dependencies at various pressures. Activation energies (activation enthalpies) and activation entropies have been evaluated for the nucleation (E_α = 1.32 eV) and the growth (E_β = 1.55 eV) processes. The experimental data for various pressures are discussed on the basis of the Gibbs energy analysis.     

Investigation of energy band gap and optical properties of cubic CdS epilayers

High quality cubic CdS epilayers were grown on GaAs (1 0 0) substrates by the hot-wall epitaxy method. The crystal structure of the grown epilayers was confirmed to be the cubic structure by X-ray diffraction patterns. The optical properties of the epilayers were investigated in a wide photon energy range between 2.0 and 8.5 eV using spectroscopic ellipsometry (SE) and were studied in the transmittance spectra at a wavelength range of 400-700 nm at room temperature. The data obtained by SE were analyzed to find the critical points of the pseudodielectric function spectra, 〈?(E)〉 = 〈?₁(E)〉 + i〈?₂(E)〉, such as E₀, E₁, E₂, E^′₀, and E^′₁ structures. In addition, the optical properties related to the pseudodielectric function of CdS, such as the absorption coefficient α(E), were investigated. All the critical point structures were observed, for the first time, at 300 K by ellipsometric measurements for the cubic CdS epilayers. Also, the energy band gap was determined by the transmittance spectra of the free-standing film, and the results were compared with the E₀ structure obtained by SE measurement.     

Energy expression of the chemical bond between atoms in metal oxides

The chemical bond between atoms in metal oxides is expressed in an energy scale. Total energy is partitioned into the atomic energy densities of constituent elements in the metal oxide, using energy density analysis. The atomization energies, ΔE_M for metal atom and ΔE_O for O atom, are then evaluated by subtracting the atomic energy densities from the energy of the isolated neutral atom, M and O, respectively. In this study, a ΔE_O vs. ΔE_M diagram called atomization energy diagram is first proposed and used for the understanding of the nature of chemical bond in various metal oxides. Both ΔE_M and ΔE_O values reflect the average structure as well as the local structure. For example their values vary depending on the vertex, edge or face sharing of MO₆ octahedron, and also change with the overall density of binary metal oxides. For perovskite-type oxides it is shown that the ΔE_O value tends to increase by the phase transition from cubic to tetragonal phase, regardless of the tilting-type or the 〈1 0 0〉 displacement-type transition. The bond formation in spinel-type oxides is also understood with the aid of the atomization energies. The present approach based on the atomization energy concept will provide us a new clue to the design of metal oxides.     

On the mechanical stability of bcc transition elements and alloys

A volume independent and a volume dependent lattice energy function involving short-range interatomic potentials were able to be fitted to the elastic constants, cohesive energy, lattice parameter and for the latter function to the vacancy formation energy and bcc-fcc lattice stability energy, as well, for fcc metals and bcc alkali metals, but not to the cohesive energy and C' elastic constant of bcc transition metals. The assumption that directional, but partial, covalent bonds exist between nearest-neighbors in the bcc transition elements provides an explanation for the latter results and in addition explains the identical dependence of C' and the bcc-fcc lattice stability upon N_d, where N_d is the average number of d electrons, for the bcc transition metals and alloys. Both the mechanical and thermodynamic stability of the bcc structure for transition metals and all transition metal alloys disappears for 5 ? N_d > 2 and <?1.     

Atomistic modeling of β-Sn surface energies and adatom diffusivity

Energies for low number Miller index surfaces of β-Sn (b.c.t. structure) were computed and the (1 0 0) plane was found to have the lowest un-relaxed energy of 0.0497 eV/Ų. We then used the Dimer method to find mechanisms and corresponding activation energies, E_A, for a Sn adatom moving on a β-Sn (1 0 0) surface. After extensive dimer searches and comparison to long molecular dynamics simulations, we conclude that two simple hopping mechanisms dominate transitions on this surface. For each, we determined hopping rates of the adatom using transition state theory and computed its tracer diffusivity. A hop of the adatom in the lattice c-direction gives D_300 K = 1.893 × 10⁻⁰⁶ cm²/s (E_A = 0.1493 eV), while in the lattice a-direction D_300 K = 3.994 × 10⁻⁰⁶ cm²/s (E_A = 0.1138 eV). When compared to studies on the existence of low energy multi-atom adatom diffusion on Cu and Al (1 0 0), we assert that β-Sn's successive (2 0 0) plane layering in the [1 0 0] direction provides for significantly lower activation energies and may contribute to the inability to locate any concerted atomic motion mechanisms.     

The adsorption of CO on Cu surfaces studied by electron energy loss spectroscopy

Electron energy loss spectroscopy (ELS) in the energy range of electronic transitions (primary energy 30 < E₀ < 50 eV, resolution ΔE ≈ 0.3 eV) has been used to study the adsorption of CO on polycrystalline surfaces and on the low index faces (100), (110), (111) of Cu at 80 K. Also LEED patterns were investigated and thermal desorption was analyzed by means of the temperature dependence of three losses near 9, 12 and 14 eV characteristic for adsorbed CO. The 12 and 14 eV losses occur on all Cu surfaces in the whole coverage range; they are interpreted in terms of intramolecular transitions of the CO. The 9 eV loss is sensitive to the crystallographic type of Cu surface and to the coverage with CO. The interpretation in terms of d(Cu) → 2π¹(CO) charge transfer transitions allows conclusions concerning the adsorption site geometry. The ELS results are consistent with information obtained from LEED. On the (100) surface CO adsorption enhances the intensity of a bulk electronic transition near 4 eV at E₀ < 50 eV. This effect is interpreted within the framework of dielectric theory for surface scattering on the basis of the Cu electron energy band scheme.     

Surface structure and solidification morphology of aluminum nanoclusters

Classical molecular dynamics simulation with embedded atom method potential had been performed to investigate the surface structure and solidification morphology of aluminum nanoclusters Al_n (n=256, 604, 1220 and 2048). It is found that Al cluster surfaces are comprised of (1 1 1) and (0 0 1) crystal planes. (1 1 0) crystal plane is not found on Al cluster surfaces in our simulation. On the surfaces of smaller Al clusters (n=256 and 604), (1 1 1) crystal planes are dominant. On larger Al clusters (n=1220 and 2048), (1 1 1) planes are still dominant but (0 0 1) planes cannot be neglected. Atomic density on cluster (1 1 1)/(0 0 1) surface is smaller/larger than the corresponding value on bulk surface. Computational analysis on total surface area and surface energies indicates that the total surface energy of an ideal Al nanocluster has the minimum value when (0 0 1) planes occupy 25% of the total surface area. We predict that a melted Al cluster will be a truncated octahedron after equilibrium solidification.     

CO2 adsorption on Cr(1 1 0) and Cr2O3(0 0 0 1)/Cr(1 1 0)

We attempt to correlate qualitatively the surface structure with the chemical activity for a metal surface, Cr(1 1 0), and one of its surface oxides, Cr₂O₃(0 0 0 1)/Cr(1 1 0). The kinetics and dynamics of CO₂ adsorption have been studied by low energy electron diffraction (LEED), Aug er electron spectroscopy (AES), and thermal desorption spectroscopy (TDS), as well as adsorption probability measurements conducted for impact energies of E_i = 0.1-1.1 eV and adsorption temperatures of T_s = 92-135 K. The Cr(1 1 0) surface is characterized by a square shaped LEED pattern, contamination free Cr AES, and a single dominant TDS peak (binding energy E_d = 33.3 kJ/mol, first order pre-exponential 1 × 10¹³ s⁻¹). The oxide exhibits a hexagonal shaped LEED pattern, Cr AES with an additional O-line, and two TDS peaks (E_d = 39.5 and 30.5 kJ/mol). The initial adsorption probability, S₀, is independent of T_s for both systems and decreases exponentially from 0.69 to 0.22 for Cr(1 1 0) with increasing E_i, with S₀ smaller by ∼0.15 for the surface oxide. The coverage dependence of the adsorption probability, S(Θ), at low E_i is approx. independent of coverage (Kisliuk-shape) and increases initially at large E_i with coverage (adsorbate-assisted adsorption). CO₂ physisorbs on both systems and the adsorption is non-activated and precursor mediated. Monte Carlo simulations (MCS) have been used to parameterize the beam scattering data. The coverage dependence of E_d has been obtained by means of a Redhead analysis of the TDS curves.     

Effect of kink-rounding barriers on step edge fluctuations

The effect that an additional energy barrier E_kr for step adatoms moving around kinks has on equilibrium step edge fluctuations is explored using scaling arguments and kinetic Monte Carlo simulations. When mass transport is through step edge diffusion, the time correlation function of the step fluctuations behaves as C(t)=A(T)t^1/4. At low temperatures the prefactor A(T) shows Arrhenius behavior with an activation energy (E_det+3?)/4 if E_kr<? and (E_det+E_kr+2?)/4 if E_kr>?, where ? is the kink energy and E_det is the barrier for detachment of a step adatom from a kink. We point out that the assumption of an Einstein relation for step edge diffusion has lead to an incorrect interpretation of step fluctuation experiments, and explain why such a relation does not hold. The theory is applied to experimental results on Pt(1 1 1) and Cu(1 0 0).     

Reconstructed (1 1 0) surfaces of FCC transition metals

The energies of the ideal, missing row (MR) and missing column (MC) (1 1 0) surfaces have been calculated by using modified embedded atom method (MEAM) for seven face centered cubic (FCC) transition metals Au, Pt, Ag, Pd, Rh, Cu and Ni. The results, that the MC reconstruction can not be formed for all metals, while the MR reconstruction can be formed naturally for Au and Pt, inductively for Ag, Pd, Rh and Cu and difficultly for Ni, are better than EAM calculated results in comparing with experimental results. In addition to the surface energy explanation, the results are also related to the surface topography and valence electron structure.     

The effect of ferroelectric polarization on the interaction of water and methanol with the surface of LiNbO3(0 0 0 1)

Water and methanol temperature programmed desorption (TPD) measurements were performed on the positive (c⁺) and negative (c⁻) surfaces of poled ferroelectric lithium niobate (LiNbO₃) single crystals. The results indicate that the molecule-surface interactions are both coverage and polarization-dependent. From a comparison of the TPD spectra for the positive and negative surfaces, it is shown that the desorption temperatures of water and methanol are consistently lower on the negative surface by 15 K and 20 K, respectively. The TPD spectra were simulated using the Polanyi-Wigner equation with a coverage-dependent energy term. These calculations show that the polarization dependence of the desorption temperature is due to a difference in the zero-coverage desorption energies on the two surfaces equal to a few kJ per mole. The mechanism for the polarization effect is explored with in situ pyroelectric voltage measurements, which indicate that a surface voltage of ±2 mV develops in the LiNbO₃(0 0 0 1) samples during TPD measurements. The magnitude of the pyroelectric-induced surface charge is heating rate dependent.     

Interaction of alkali metals with the Fe3O4(1 1 1) Surface

The adsorption and interaction of alkali metals (Li, Na, K, Rb and Cs) with the Fe_tet1-terminated Fe₃O₄(1 1 1) surface have been computed at the level of density functional theory. At low coverage, adsorption of alkali metals on site-1 (O_a-O_c-O_d) is energetically more favorable than on site-2 (O_a-O_c-O_d). Li has the strongest adsorption energy, followed by K, Rb, Cs and Na. The computed net charges show that the alkali metals can donate electrons to surface Fe and O atoms in the order of Li < Na < K ≈ Rb ≈ Cs. It is also noted that increasing the coverage does not significantly improve the promoting effect of alkali metals. In addition, alkali metals can move facilely on the Fe₃O₄(1 1 1) surface.     

Surface state density distribution at vacuum-annealed InP(1 0 0) surface as derived from the rigorous analysis of photoluminescence efficiency

The surface state density distribution N_SS(E) and surface Fermi level E_Fs position on a sequentially ultra-high vacuum-annealed n-InP(1 0 0) sample are investigated using rigorous computer analysis of dependences of the room temperature band-edge photoluminescence efficiency (Y_PL) on the photon flux density (Φ). We have found that the minimum density of a U-shaped N_SS(E) distribution as well as the donor-like surface state density are reduced by one order of magnitude after the annealing at 250 and 300 °C. This can be assigned to the decrease in the disorder in the unintentionally formed InP native oxides. On the other hand, we demonstrate that the annealing simultaneously generates discrete surface states probably due to missing group V element (P) in the interface region which may account for electrical interface instabilities observed in InP-based devices. The results are discussed quantitatively and compared to other reports.