Surface self-diffusion studied by microscopic measurements of crystallite profile evolutions

Dendritic gold crystallites on graphite are heated in ultra high vacuum up to less than 0.5 of the melting point (T_m). Electron microscopy shows that the gold crystallites change their shapes by surface self-diffusion. The dendritic contours round off while the crystallite remains very flat (20 to 40 Å). The increase with time of the radii of dendrite tips is measured statistically. Such an evolution can be described by analogy to the blunting of either metal tips (Nichols and Mullins) or monoatomic cleavage tips (Höche and Bethge). Using this result, a new technique to measure surface self-diffusion coefficients (D) is proposed. Test measurements have shown that this is an interesting, very sensitive method to measure D (down to 10^?13 cm^?2 s^?1) which enables measurements to be made in an unusual low temperature range (0.25 T_m < T < 0.5T_m). In special cases the dendrites are split by the surface self-diffusion which is qualitatively in agreement wih the theory.     

Effect of impurities on surface self-diffusion and surface structure

Measurements using field emission techniques of the activation energy for surface selfdiffusion of several of the refractory transition metals when carbon or silicon is present on the surface show large increases which are dependent on the degree of surface coverage. Maximum values obtained were: 8.5 eV for carbon on tungsten, 7.0 eV for silicon on tungsten, 4.9 eV for carbon on tantalum, 4.5 eV for carbon on molybdenum and 2.8 eV for silicon on molybdenum. In addition, two anomalous effects have been observed in which surface changes occur at critical temperatures, (a) Sharp discontinuities occur in the plots of activation energy versus temperature for carbon on tungsten at about 2300 °K and for silicon on tungsten at about 2000 °K. In both cases the activation energy drops from the respective high value to that for the clean substrate material of 3.0 eV. Concomitant with this transition the emission patterns change in appearance from those typical of a contaminated surface to those typical of a clean surface, (b) For carbon on tungsten and silicon on tungsten, (433) planes are observed which decrease in size with temperature and suddenly disappear at a very sharp critical temperature. It is suggested that the presence of these impurities causes a restructuring of the surface layers even when present in much less than stoichiometric amounts and that surface phase changes occur independent of bulk changes.     

BFKL and CCFM evolutions with saturation boundary

We perform numerical studies of the BFKL and CCFM equations for the unintegrated gluon distribution supplemented with an absorptive boundary which mimics saturation. For BFKL, this procedure yields the same results for the saturation momentum and the gluon distribution above saturation as the non-linear BK equation, for both fixed and running coupling, and for all the considered energies. This similarity goes beyond expectations based on the correspondence with statistical physics, which hold only for fixed coupling and asymptotically high energies. For the CCFM equation, whose non-linear generalization is not known, our method provides the first study of the approach towards saturation. We find that, in the running-coupling case, the CCFM and BFKL predictions for the energy dependence of the saturation momentum are identical within our numerical accuracy.     

Measurement of gold surface self-diffusion by scanning tunneling microscopy

Measurement of gold surface self-diffusion by the method of surface profile decay, using a scanning tunneling microscope (STM) have been done on a polycrystalline gold film deposited on a glass substrate. The peak-to-peak surface roughness was measured as a function of annealing time after annealing at 170 °C with a special pan-cake furnace in the STM. The gold surface diffusion coefficient at 170 °C can then be extracted from these measurements.     

Grain boundary migration initiated by diffusion

A review is presented of work related to two new processes which arise in crystalline materials when impurities diffuse along grain boundaries from the surface of the material: diffusion-initiated grain boundary migration and recrystallization. We analyze the conditions under which DIGM occurs, the kinetics of the process, its driving forces, and also the changes in the grain fine structure and the near-grain regions, as well as the nucleation of new grains on the migrating boundaries, caused by an uncompensated impurity atom flux. We consider the mechanisms for DIGM. It is shown that not one of the mechanisms proposed to describe DIGM is capable of explaining all the experimentally observed properties of grain boundary migration under DIGM conditions. We note that changes in the grain boundary structure caused by the impurity atoms diffusing along it are due to diverse grain-boundary processes, which have important technological implications.V. D. Kuznetsov Physicotechnical Institute, Tomsk State University, Siberia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 34–57, May, 1992.     

Channel plasmon-polariton in a triangular groove on a metal surface

One-dimensional localized plasmons (channel polaritons) guided by a triangular groove on a metal substrate are investigated numerically by means of a finite-difference time-domain algorithm. Dispersion, existence conditions, and dissipation of these waves are analyzed. In particular, it is demonstrated that the localization of the predicted plasmons in acute grooves may be substantially stronger than what is allowed by the diffraction limit. As a result, the predicted waves may be significant for the development of new subwavelength waveguides and interconnectors for nano-optics and photonics.     

Influence of adsorbed sulfur on surface reaction kinetics and surface self-diffusion on iron

The nitrogenation of iron in N₂ and the carburization of iron in CH₄H₂ mixtures were studied in a flow apparatus by a resistance method in the presence of adsorbed sulfur. From these measurements the adsorption isotherm for sulfur on iron was obtained at 850°C and the change of the surface energy in dependence on the sulfur activity could be calculated. These results and measurements of the growth of grain boundary grooves were used to determine the influence of adsorbed sulfur on the surface self-diffusion of iron, which is enhanced by a factor of 3 to 5 in the presence of a saturated layer of adsorbed sulfur.     

Investigation of surface self-diffusion of Ni atoms on the Ni(100) plane by means of work function measurements and Monte Carlo calculations

A novel method is presented to study migration of adsorbed metal atoms on a clean (hkl) surface of a metal substrate. The system used was Ni on Ni(100). We make use of the assumption that each single step of random walk motion of an individual adatom on the metal substrate refers to an activation energy ΔE_if (indices i and f giving the number of occupied nearest neighbour sites in the initial and final position respectively). Furthermore, we assume that the dipole moment p_v of an adatom is determined by the number v of occupied nearest neighbour sites. Via their dipole moments the adsorbed atoms induce a change of work function ΔΦ of the substrate metal, ΔΦ being related to the average dipole moment per unit area by the Helmholtz equation. To measure ΔΦ we use a pendulum device. At fixed low coverage θ the variation of ΔΦ with temperature T has been calculated numerically within the framework of a Monte Carlo simulation (MCS) model, using various activation energies ΔE_if and dipole moments p_v as input parameters. By fitting these data to the experimental curves we could derive the following dipole moments and activation energies: p₀ = 0.45 ± 0.05 D, p₁ = 0.36 ± 0.05 D, p₂ = 0.27 ± 0.05 D, p₃ = 0.18 ± 0.05 D, ΔE₀₀ 0.60 ± 0.02 eV, ΔE₁₀ = 0.70 ± 0.025 eV, ΔE₂₁ = 0.80 ± 0.05 eV, ΔE₂₀ = 0.90 ± 0.05 eV. We compare these results with those of other workers.     

Diffraction of a plane surface electromagnetic wave incident on a half plane

An integral representation and asymptotic expressions are derived for the diffraction field produced at an arbitrary angle of incidence on a half-plane representing an impedance. Some features of the field are discussed.     

Influence of groove depth and surface profile on fluorescence enhancement by grating-coupled surface plasmon resonance

The fluorescence intensity of a sample placed on a metal grating pattern is enhanced due to excitation by the electric field of the grating-coupled surface plasmon resonance (GC-SPR). The dependence of the enhancement on groove depth and surface profile was studied with the aim of improving the sensitivity of fluorescence detection. The enhancement was found to depend on the groove depth, with intensity most enhanced on grating substrate of about 20 nm depth, which produced an intensity about 30 times greater than that on a flat borosilicate glass substrate. Rigorous coupled wave analysis calculation showed that the shape of the groove influenced GC-SPR, suggesting that controlling not only the depth but also the shape of the grating surface profile can be an important factor in improving the sensitivity of detection by fluorescence microscopy.     

Electromagnetic plane-wave scattering from a sectorial groove in a perfectly conducting plane

Scattering characteristics of plane waves by a sectorial groove in a perfectly conducting plane are investigated. Both the transverse magnetic (TM) and transverse electric (TE) polarizations of the incident wave are considered. Judicious use of the region-matching technique provides a rigorous series solution to the problem. The analyzed region is separated into two sub-regions by choosing a semi-circular auxiliary boundary. Thefield in each sub-region is expanded as a summationof proper wave functions with unknown coefficients. Enforcing the matching of conditions on the auxiliary boundary and of boundary condition on the circular-arc surface of the groove leads to a linear set of equations and the unknown coefficients are then determined. Numerical results demonstrate the influence of central angles of the sectorial groove on echo width, far-field pattern and near-field distribution. The presented geometry is easily applicable to the design and fabrication of a grating structure for optical switches and tunable filters.      

Admittance of a groove on a rigid surface under a grazing flow

The problem of sound diffraction by a groove on a rigid surface in the presence of a grazing flow is considered. The input admittance of the groove is calculated, and its real part is shown to be negative.     

Anomalous effects of hydrostatic pressure on ice surface self-diffusion

This paper presents an experimental study of the formation time of the groove that occurs at the intersection of a grain boundary and the free surface of a pure ice sample immersed in silicone oil at a pressure of approximately 10 MPa and temperature higher than ? 25 °C. Using the theoretical approach presented by Mullins (1957) [14], the surface diffusion coefficient is obtained. It is shown that, at 10 MPa, the ice surface diffusion coefficient is more than twice that observed at atmospheric pressure.     

Phase-dependent electron transport through a quantum wire on a surface

Electron transport through a quantum wire in the presence of external periodic energy-level modulations with different on-site phases is studied within the time evolution operator method for a tight-binding Hamiltonian. It is found that in the presence of spatial symmetry of the system and no source-drain and static gate voltages the pumping current can be generated. Moreover, for a wire which is tunnel-coupled to the underlying substrate, the current flowing through an unbiased wire does not fade away but increases with the wire-surface coupling. For randomly chosen phases at every wire site two regimes of the phase-averaged current are found which are related to small and high wire density of states.     

Elastic waves excited by a plane source on the surface of a multilayered medium

Elastic waves excited by a plane piezoelectric source with an arbitrary shape on the surface of a multilayered medium have been studied for the first time in this paper. On the basis of Abzo-zena [Geophys. J. R. Astron. Soc. 58, 91-105 (1979)] and Menke [Geophys. J. R. Astron. Soc. 59, 315-323 (1979)], the propagator matrix for the elastic wave field in multilayered medium is extended from two- to three-dimensional (3D) space. 3D elastic wave field is investigated and the displacement-stress response for the boundary conditions is obtained. The propagation of elastic wave in multilayered media is analyzed in 3D space in the frequency domain. The P-SV and SH modes corresponding to the poles are studied. The excitation and propagation of the modes are analyzed further. It is found that the propagation velocities of the P-SV and SH modes do not depend on the propagation azimuth theta in the plane parallel to the free surface of the multilayered medium while the displacement amplitudes are strongly dependent on the azimuth theta. The directional distribution functions of the modes are independent of the medium parameters and the modes and dependent on the shape and excitation fashion of the source. Finally, as an example, the displacement fields of the P-SV and SH modes excited by a rectangle source are analyzed. The displacement representation and numerical results of the directivity distribution functions for the P-SV and SH modes are obtained.     

Grain boundary grooving in bi-crystal thin films induced by surface drift-diffusion driven by capillary forces and applied uniaxial tensile stresses

Grain boundary (GB) grooving, induced by surface drift-diffusion and driven by the combined actions of capillary forces and applied uniaxial tensile stresses, is investigated in bi-crystal thin films using self-consistent dynamical computer simulations. A physico-mathematical model, based on the irreversible thermodynamics treatment of surfaces and interfaces with singularities allowed auto-control of the otherwise free-motion of the triple junction at the intersection of the grooving surface and the GB, without having any a priori assumption on the equilibrium dihedral angles. In the present theory, the generalised driving forces for stress-induced surface drift-diffusion arise not only from the usual elastic strain energy density (ESED), but also much stronger elastic dipole tensor interactions (EDTI) between the applied stress field and the mobile atomic species situated at the surface layer and in the GB regions. Accelerated groove-deepening kinetics shows that the surface drift-diffusion enhanced by the applied uniaxial tensile stresses through EDTI is dominant over the GB flux leakage at the triple junction. At high uniaxial stress levels (≥500?MPa for a 100-nm thick copper film), a sequential time-frame for micro-crack nucleation and growth is recorded just before specimen failure took place. These non-equilibrium thermokinetics discoveries (kinetics and energetics) contradict or at least do not support the hypothesis of the steady-state diffusive GB micro-crack formation and propagation due to ‘constant’ flux drainage through GB enhanced by tensile stresses acting normal to it.     

半无界分层介质表面任意面源激发的弹性波场

研究了半无界层状介质自由表面任意形状的面源产生的弹性波场。首先,我们将层状介质中的传递矩阵理论从二维推向三维空间,在频率域研究了任意面源激发的三维弹性波理论问题。然后,深入研究了Rayleigh波和Love波的激发与传播特性,发现Rayleigh波和Love波的传播速度在与自由表面平行的平面内与传播方位角θ无关,但其激发强度却强烈地依赖于传播方位角θ。最后,我们具体研究了矩形源、无穷长条形源和圆盘激励出的弹性波场,并通过数值计算给出了Rayleigh波和Love波的位移指向性分布图。     

Directional anisotropy of surface self-diffusion on Pt(110)

The rate of surface self-diffusion on a Pt(110) single crystal in the [1$\text{1}$0] and [001] directions was measured at 1200–1750 K by monitoring the decay of a sinusoidal surface profile. The surface diffusion rate in the [1$\text{1}$o] direction was much faster than in the [001] direction. The activation energy of surface self-diffusion was 1.70 and 3.16 eV for the [1$\text{1}$0] and [001] directions, respectively, in good agreement with theoretical estimates. For large amplitudes of the profile the decay rate for the [001] direction was also dependent on the amplitude. This behavior can be explained by the appearance of (111) facets on the profile, which cause a retardation of the profile decay.