Energy calculation for symmetrical tilt grain boundaries in iron

An atomic study of [0 0 1] symmetrical tilt grain boundary (STGB) in iron has been made with modified analytical embedded atom method (MAEAM). The energies of two rigid-body crystals joined together directly are unrealistically high due to very short distance between atoms near grain boundary (GB) plane in either crystal. For each of 27 (h k 0) GB planes, a relative slide between grains could result in a decrease in GB energy and a minimum value could be obtained at specific translation distance L_min/L_(h k 0). Three lowest minimum-energies are corresponding to (3 1 0), (5 3 0) and (5 1 0) boundary successively, from minimization of GB energy, these boundaries should be preferable in (h k 0) boundaries. In addition, the minimum energy increases with increasing ∑, but decreases with increasing interplanar spacing.     

Silver grain boundary diffusion in Pd

Two to ten nanometer thick polycrystalline Pd films were prepared on the (1 1 1) surface of Ag single crystal and investigations of the Ag diffusion along Pd grain boundaries were carried out using the Hwang-Balluffi method. The samples were monitored by Auger electron spectroscopy (AES) during isothermal heat treatments in the 438-563 K temperature range. Using plausible simplifying assumptions, the activation energy of the product of the grain boundary (GB) diffusion coefficient and k′ (k′ = c_s/c_gb; c_s and c_gb are the surface and GB concentration, respectively) was calculated (0.99 ± 0.08 eV) from the evaluated saturation coefficients of the surface accumulation. This energy, for weak temperature dependence of k′, is approximately equal to the activation energy of the GB diffusion.     

The energy and structure of (0 0 1) twist grain boundary in noble metals

The relaxed energy and structure of (0 0 1) twist grain boundary (GB) in noble metals Au, Ag and Cu are simulated by the MAEAM. In-boundary translation between two adjacent grains results in a periodic energy variation and the period is a square with the side length L_Σ/Σ. The lowest energy appears when the two grains are translated relatively to either corner or center of the periodic square. The relaxed GB energy increases smoothly for low-angle boundaries and levels off for larger-angle boundaries except a cusp appeared at θ = 36.87° (Σ = 5). After relaxation, the symmetry of the GB structure is not changed but the displacement of the atoms parallel to the GB plane decreases with increasing the distance of the atoms from the GB plane.     

A DFT study the solvent effects of H2 adsorption on Cu(h k l) surface

Density functional theory (DFT) combined with conductor-like solvent model (COSMO) have been performed to study the solvent effects of H₂ adsorption on Cu(h k l) surface. The result shows H₂ can not be parallel adsorbed on Cu(h k l) surface in gas phase and only vertical adsorbed. At this moment, the binding energies are small and H₂ orientation with respect to Cu(h k l) surfaces is not a determining parameter. In liquid paraffin, when H₂ adsorbs vertically on Cu(h k l) surface, solvent effects not only influences the adsorptive stability, but also improves the ability of H₂ activation; When H₂ vertical adsorption on Cu(h k l) surface at 1/4 and 1/2 coverage, H-H bond is broken by solvent effects. However, no stable structures at 3/4 and 1 ML coverage are found, indicating that it is impossible to get H₂ parallel adsorption on Cu(h k l) surfaces at 3/4 and 1 ML coverages due to the repulsion between adsorbed H₂ molecules.     

Effective biaxial modulus and strain energy density of ideally (h k l)-fiber-textured cubic polycrystalline films

The effective biaxial modulus (M_eff) and strain energy density (W) of cubic polycrystalline films with ideally (h k l) fiber textures are estimated using Vook-Witt (VW) grain interaction model and the data are compared with those derived from Voigt, Reuss and Voigt-Reuss-Hill (VRH) models. Numerical results show that the VW average of M_eff for ideally (1 0 0)- or (1 1 1)-fiber-textured films is identical to the VRH average of M_eff. For (1 1 0) and (1 1 2) planes, however, the VW average of M_eff for (1 1 0)-fiber-textured film is larger than that of (1 1 2)-fiber-textured film when the Zener anisotropic factor (A_R) is not equal to 1. Furthermore, M_eff and W exhibit incremental tendencies with the increase of the orientation factor (Γ_h k l) for the [h k l] axis when A_R > 1, implying that M_eff and W have the minimums on the (1 0 0) plane. Reversely, M_eff and W decrease with the increasing Γ_h k l when A_R < 1. This means that M_eff and W on (1 1 1) plane have the minimums.     

Calculation of the surface energy of bcc transition metals by using the second nearest-neighbor modified embedded atom method

The surface energies for 24 surfaces of all bcc transition metals Fe, Cr, Mo, W, V, Nb and Ta have been calculated by using the second nearest-neighbor modified embedded atom method. The results show that, for all bcc transition metals, the order among three low-index surface energies E_(1 1 0) < E_(1 0 0) < E_(1 1 1) is in agreement with experimental results and E_(1 1 0) is also the lowest surface energy for various surfaces. So that from surface energy minimization, the (1 1 0) texture should be favorable in the bcc films. This is also consistent with experimental results. The surface energy for the other surfaces increases linearly with increasing angle between the surfaces (h k l) and (1 1 0). Therefore, a deviation of a surface orientation from (1 1 0) can be used to estimate the relative values of the surface energy.     

Anisotropy analysis of the surface energy of hcp (c/a < 1.633) metals

In this paper, anisotropy of the surface energy of 5 hcp metals Be, Hf, Ru, Ti and Y have been analyzed. 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 using the modified embedded atom method. For all 5 hcp metals, the (1 1 0) plane has the minimum surface energy in all 35 surfaces studied. Considering surface energy minimization solely, the (1 1 0) texture should be favorable in the hcp films. 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.     

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.     

The periodicity in translation of Ag (0 0 1) and (1 1 0) twist grain boundary

The energies of Ag (0 0 1) and (1 1 0) twist grain boundary (GB) in translation have been calculated with the modified analytical embedded atom method (MAEAM). The energy period corresponds exactly to the DSC lattice unit cell and the area of the energy period referred to the CSL unit cell is 1/Σ². The ‘energy grooves’ are parallel to the sides of the CSL or DSC lattice unit cell. The most preferable sliding direction is parallel to identical sides of the square CSL unit cell for (0 0 1) boundaries and to the short side of the rectangular CSL unit cell for (1 1 0) boundaries. From energy minimization, the stable configuration appears when two adjacent grains are translated relatively to the corners, centre or sides’ midpoint of the DSC lattice unit cell.     

Dependence of the strain energies on grain orientations in HCP metal films

A thin polycrystalline film bonded tightly to a thick substrate of different thermal expansion coefficients will experience thermal strain when the temperature is changed. Calculations of the strain energies for grains having various crystallographic orientations (h k l) relative to the film surface were made for a polycrystalline film composed of the close-packed hexagonal (HCP) metal Be, Cd, Co, Hf, Mg, Re, Ru, Sc, Ti, Y, Zr and Zn, respectively. From strain energy minimization, the (0 0 1), (0 1 3), (0 4 5), (1 2 3), (2 5 8), (0 5 7), (0 3 5), (0 5 7), (0 1 0), (5 5 8), (1 4 7) and (0 0 1) textures should be favorable in Be, Cd, Co, Hf, Mg, Re, Ru, Sc, Ti, Y, Zr and Zn film, respectively.     

Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

In this paper, we develop two new upwind difference schemes for solving a coupled system of convection–diffusion equations arising from the steady incompressible MHD duct flow problem with a transverse magnetic field at high Hartmann numbers. Such an MHD duct flow is convection-dominated and its solution may exhibit localized phenomena such as boundary layers, namely, narrow boundary regions where the solution changes rapidly. Most conventional numerical schemes cannot efficiently solve the layer problems because they are lacking in either stability or accuracy. In contrast, the newly proposed upwind difference schemes can achieve a reasonable accuracy with a high stability, and they are capable of resolving high gradients near the layer regions without refining the grid. The accuracy of the first new upwind scheme is O(h + k) and the second one improves the accuracy to O(ε²(h + k) + ε(h² + k²) + (h³ + k³)), where 0 < ε ? 1/M ? 1 and M is the high Hartmann number. Numerical examples are provided to illustrate the performance of the newly proposed upwind difference schemes.     

Metrological orientation-confirmation of Si(h h k) using scanning tunneling microscopy

For the periodicity-modulation of the Si(h h k) template between (0 0 1) and (1 1 1), it is necessary to prepare the surface with any orientation within this range, most especially for fabricating useful one-dimensional nanostructures. Especially, when there are no strong X-ray signals using the standard Cu K-α source in the vicinity of any arbitrarily chosen (H H K), it turns out that the line-profile analysis on the topographic image of scanning tunneling microscopy can be a unique way for confirming the orientation of the prepared surface. Though there are a number of small-width facets on the reconstructed surface, if any of well-defined facets, such as (1 1 1), (3 3 7), (1 1 2), and (3 3 5), are included in these facets it is possible to determine the orientation using the weighted-average method.     

Surface nano-structural modifications and characteristics in nitrogen ion implanted W as a function of temperature and N energy

The surface modifications of tungsten massive samples (0.5 mm foils) made by nitrogen ion implantation are studied by SEM, XRD, AFM, and SIMS. Nitrogen ions in the energy range of 16-30 keV with a fluence of 1 × 10¹⁸ N⁺ cm⁻² were implanted in tungsten samples for 1600 s at different temperatures. XRD patterns clearly showed WN₂ (0 1 8) (rhombohedral) very close to W (2 0 0) line. Crystallite sizes (coherently diffracting domains) obtained from WN₂ (0 1 8) line, showed an increase with substrate temperature. AFM images showed the formation of grains on W samples, which grew in size with temperature. Similar morphological changes to that has been observed for thin films by increasing substrate temperature (i.e., structure zone model (SZM)), is obtained. The surface roughness variation with temperature generally showed a decrease with increasing temperature. The density of implanted nitrogen ions and the depth of nitrogen ion implantation in W studied by SIMS showed a minimum for N⁺ density as well as a minimum for penetration depth of N⁺ ions in W at certain temperatures, which are both consistent with XRD results (i.e., I_{W (2 0 0)}/I_{W (2 1 1)}) for W (bcc). Hence, showing a correlation between XRD and SIMS results.     

Energy calculation of (0 1 1) twist grain boundary in noble metals

With modified analytical embedded atom method (MAEAM), the energy of (0 1 1) twist grain boundary (GB) has been calculated for three noble metals Cu, Ag and Au. The results show that the unrelaxed energy keeps almost constant with twist angle θ except several cusps at low Σ boundaries. The GB energies drop significantly after expansion perpendicular to the boundary. In-boundary translation results in a periodic energy variation and the rectangular period is 1/Σ of their own CSL smallest unit cell. Three specific positions, the corners or centre of the periodic rectangle, or the midpoints of the sides, are preferable in GB translation.     

Temperature and N energy dependence on nano-structural modifications and characteristics of Mo surface

The surface modifications of Mo massive samples (0.5 mm foils) made by nitrogen ion implantation are studied by SEM, XRD, AFM, and SIMS. Nitrogen ions in the energy range of 16-30 keV with a fluence of 1 × 10¹⁸ N⁺ cm⁻² were implanted in molybdenum samples for 1600 s at different temperatures. XRD patterns clearly showed MoN (0 3 1) (hcp) very close to Mo (2 0 0) line. Crystallite sizes (coherently diffracting domains) obtained from MoN (0 3 1) line, showed an increase with substrate temperature. AFM images showed the formation of grains on Mo samples, which grew in size with temperature. Similar morphological changes to that has been observed for thin films by increasing substrate temperature (i.e., structure zone model (SZM)), is obtained. The density of implanted nitrogen ions and the depth of nitrogen ion implantation in Mo studied by SIMS showed a minimum for N⁺ density as well as a minimum for penetration depth of N⁺ ions in Mo at certain temperatures, which are both consistent with XRD results (i.e., I_{Mo (2 0 0)}/I_{Mo (2 1 1)}) for Mo (bcc). Hence, showing a correlation between XRD and SIMS results. This phenomenon is explained on the basis of residual gas, substrate temperature, dissociation of water in the chamber and the ion energy.     

Epitaxial growth of boron nitride on a Rh(1 1 1) multilayer system: Formation and fine tuning of a BN-nanomesh

The epitaxial growth of boron nitride on the surface of a Rh-YSZ-Si(1 1 1) multilayer system by CVD of borazine (HNBH)₃ was investigated by low energy electron diffraction (LEED). The formation of a (14 × 14) h-BN on (13 × 13) Rh-YSZ-Si(1 1 1) superstructure was observed, which is different in size from an already reported (13 × 13) h-BN on (12 × 12) Rh(1 1 1) superstructure grown on a Rh(1 1 1) single crystal substrate (“h-BN-nanomesh”). We found hints that differences between the thermal expansion behaviour of the multilayer substrates and the single crystal substrate can be the reason for the formation of different sized superstructures.     

The forbidden rotational Q branch of CH3SiF3: A study in internal rotation

The pure rotational spectrum driven by the small dipole moment produced perpendicular to the symmetry axis by centrifugal distortion has been investigated for CH₃SiF₃ in the ground vibrational state using a Fourier transform waveguide spectrometer. Between 10.9 and 17.0 GHz, four (k + 3 ← k) series in the Q branch have been measured in the lowest torsional state v₆ = 0 for k = 4, 5, 6, and 7 with 54 ? J ? 65. In each transition, the quantum number σ = 0, +1, −1 labelling the different torsional sub-levels is conserved. For given (J,k), splittings from ∼10 to ∼45 MHz have been observed between lines with different values of σ. The global data set includes the anticrossing molecular beam energy differences of [W.L. Meerts, I. Ozier, Chem. Phys. 71 (1982) 401-415] as well as the mm-wave R branch frequencies and (A₁ − A₂) splittings of [P. Dréan, J.-M. Colmont, J. Demaison, L. Dore, C. Degli Esposti, J. Mol. Spectrosc. 176 (1996) 23-27]). A good fit was obtained by varying 15 molecular parameters characterizing the torsion-rotation Hamiltonian H_TR for the vibrational ground state. Because of the strong correlation between two of the quartic torsion-distortion parameters (F_0,3K and D_0,Km) and a redundancy connecting the centrifugal distortion constants, four models were obtained yielding comparable fits. In each case, effective values were determined for the A-rotational constant and the height of the potential hindering the internal rotation. A high precision determination of the structural parameter ρ was made that is the same in all four models. For the off-diagonal quartic centrifugal distortion constant ε₀ and the sextic constants H_0,J, H_0,JK, H_0,KJ, and h_0,3, the differences in the values obtained in the two different reductions used have been explained in terms of the redundancy connecting these parameters. For σ = 0, +1, −1, the energy level pattern for (|k| = 3) is discussed for the case where the pure torsional energy splitting and the matrix elements off-diagonal in k are of comparable magnitude. A method is described of using an R branch study of the resulting σ-splittings for (|k| = 3) to probe the zeroth-order torsional Hamiltonian.     

Effects of crystallographic orientation on the oxygen exchange rate of La0.7Sr0.3MnO3 thin films

The oxygen surface exchange of La_0.7Sr_0.3MnO₃ (LSM) thin films was investigated using the electrical conductivity relaxation (ECR) method. Epitaxial (100)-, (110)-, and (111)-oriented LSM films were fabricated on corresponding SrTiO₃ (STO) substrates using pulsed laser deposition. The LSM films had well-controlled surface qualities, exhibited bulk-like steady-state electrical properties, and exhibited surface dominated responses in ECR. The chemical surface exchange coefficients (k_chem) were determined and varied from ≈ 1 × 10^− 6 to 65 × 10^− 6 cm/s, depending on temperature and orientation, with activation energies of between 0.8 and 1.2 eV. At 800 °C, a four fold variation is observed in the k_chem values, with (110)/(100) being the highest/lowest, explained well by the high activation energy for (110), ≈ 1.16 eV, and the low energy for (111) and (100), ≈0.83 eV.     

Exotic superconducting state embedded in the hidden order state of URu2Si2

The heavy-fermion compound URu₂Si₂ has mystified researchers since the superconducting state (T_c = 1.45 K) is embedded within the enigmatic ‘‘hidden order” phase (T_h = 17.5 K). Here, we report charge and thermal transport measurements on ultraclean single crystals of URu₂Si₂ with very large residual-resistivity-ratio down to 30 m K (∼T_c/50), which reveal a number of unprecedented superconducting properties. The results provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology. We propose a gap function with chiral d-wave form Δ(k) = Δ₀k_z(k_x + ik_y). We also demonstrate that a distinct flux line lattice melting transition with outstanding characters occurs well below the upper critical fields even at sub-Kelvin temperature. The intriguing superconducting state of URu₂Si₂ adds a unique and exciting example to the list of unconventional superconductors.     

Island coalescence and diffusion along kinked steps on Cu(0 0 1): Evidence for a large kink Ehrlich-Schwoebel barrier

Using temperature-variable scanning tunneling microscopy, we studied the coalescence of vacancy islands on Cu(0 0 1) in ultra-high vacuum. From the temperature dependence of the relaxation of merged vacancy islands to the equilibrium shape we obtain an activation energy of the island coalescence process of 0.76 eV. From that value we deduce an activation energy for the atomic hopping coefficient of E_Γh=0.89 eV. Comparing our result with previous STM data on step fluctuations with dominant diffusion along straight step segments (E_Γh=0.68 eV; [M. Giesen, S. Dieluweit, J. Mol. Catal. A: Chem. 216 (2004) 263]) and step fluctuations with kink crossing (E_Γh=0.9 eV; [M. Giesen-Seibert, F. Schmitz, R. Jentjens, H. Ibach, Surf. Sci. 329 (1995) 47]), we conclude that there is a large extra barrier for diffusion of atoms across kinks on Cu(0 0 1) of the order of 0.23 eV. This is the first direct experimental evidence for the existence of a large kink Ehrlich-Schwoebel barrier on Cu(0 0 1).