The kinetics of grain growth in real systems is influenced by several unknown factors, making a theoretical treatment very difficult. Idealized grain growth, assuming all grain boundaries to have the same energy and mobility (mobility M = k/ρ, where k is a constant and ρ is grain boundary curvature) can be treated theoretically, but the results obtained can only be compared to numerical grain growth simulations, as ideal grain growth scarcely exists in nature. The validity of the simulation techniques thus becomes of great importance. In the present investigation computer simulations of grain growth in two dimensions using Monte Carlo simulations and the grain boundary tracking technique have been investigated and compared in small grain systems, making it possible to follow the evolution of each grain in the system.

We report measurements of the optical reflectance anisotropy (RA) of the Ag(110) surface as a function of temperature and we find evidence for contributions to the RA spectrum from bulk band transitions that are modified by the anisotropic (110) surface. A comparison is made between temperature-induced shifts in the energy of RA peaks and thermovariation optical spectroscopy results of the temperature dependence of transition energies between bands at the L symmetry point. A three phase model based on the energy derivative of the bulk dielectric function is found to simulate the RA response from well-ordered and Ar ion bombarded surfaces. We conclude that there is a general trend of surface-modified bulk band contributions to the RA response of the noble metal (110) surfaces.

Magnetization-induced second-harmonic generation (SHG) has been used for the study of thin garnet films. The strong optical absorption of these films at the second harmonic frequency provides a unique possibility to study magnetic and structural properties of the film surface and film/substrate interface separately. When studied in transmission at normal incidence all relevant elements of the crystallographic part of the nonlinear optical susceptibility tensor vanish identically, while a magnetization-induced contribution remains. The purely magnetic origin of SHG from the interface is unambiguously demonstrated. From measurements of the SHG rotational anisotropy and magnetic field dependence, the surface is found to have inclusions which act as nonmagnetic sources of SHG, while the anisotropy causing easy in-plane magnetization is found to be stronger at the interface with the substrate than at the surface of the film.

A series of iron garnet films of composition Lu3-xBixFe5-yGayO12 grown on (100) oriented GGG substrates have been studied using variable angle spectroscopic ellipsometry and polar Keff spectroscopy (MOKE). The diagonal and off-diagonal components of the permittivity tensor have been determined in the range 1-5 eV Our results seem to be in accordance with previously reported measurements on similar systems. We find that the optical absorption is reduced as the gallium content is increased. With increased Ga doping we also see an increase in the real part of epsilon(0) above 3.7 eV, but a decrease for lower energies. In the spectra of the off-diagonal permittivity tensor components we observe bismuth enhancement and gallium dilution effects. (C) 2003 Elsevier B.V. All rights reserved.

A key element of analytical models for curvature-driven grain growth is the formulation of a growth law for individual grains. Grain size distributions can be derived through the use of such growth laws. The present paper reviews some recent progress in developing a mean-field statistical theory of normal grain growth. A paradox related to curvilinear polygons is shown to support the expectation that the grain size distribution has a finite cutoff. The circumference of the circumscribing circle and the perimeter of the curvilinear polygon become exactly equal when the number of sides is 12. The boundary of an average 12-sided grain has an integral curvature that is equal in magnitude to the integral boundary of a completely circular grain. For this reason, grains with more than 12 sides are suggested to be energetically unfavourable, a result which is in excellent agreement with simulation data. In the concluding part, finite circle packings are employed to interpret a topological relationship found for Potts-model-type simulations of 2D grain growth. It is briefly indicated how spherical packings may help to develop some intuition about topological relationships found for normal grain growth in three dimensions.

Computer simulations of 2D normal grain growth have shown that size correlations between adjacent grains exist in 2D grain structures. These correlations prevail during the coarsening process and influence on the kinetics of the process and on the grain size distribution. Hillert’s analysis starts with the assumption that all grains in the structure have the same environment. Since computer simulations contradict this assumption, the mean-field theory for normal grain growth needs to be modified. A first attempt was made by Hunderi and Ryum, who modified Hillert’s growth law to include the effect of spatial grain size correlations. In the 1D case the distributions derived by means of the modified growth law agreed well with simulation data. However, the distribution derived for 2D grain growth retained unwanted properties of the Hillert distribution. We review some recent progress in developing a mean-field statistical theory. A paradox related to curvilinear polygons is shown to support the expectation that the grain size distribution has a finite cutoff.

The phase change caused by excitation of surface plasmons (SP) in a Kretschmann configuration was measured by a rotating analyzer scheme. The set-up was used to determinate the optical constants at 632.8 nm of an indium tin oxide (ITO) film with a thickness of 20 nm on a gold film. The numerical values n=0.182, k=3.427 for the Au film, and n=1.91, k=0.01 for ITO were obtained by a best-fit procedure to experimental data for several gold thicknesses. Poynting's vector calculations show that the energy of the plasmon field is redistributed after deposition of the ITO layer. This causes a shift in both the surface plasmon resonance minimum and the turning point of the phase curve. From model calculations it is argued that in thin-film cases SP phase measurements give more precise values for the optical constants than conventional ellipsometry and SP amplitude methods.

The optical properties of the below band-gap uniaxial dielectric function are studied as a function of the degree of hexagonality. The polytypes investigated were lightly doped 4H, 6H, 15R, and 21R silicon carbide. The ordinary component of the dielectric function is extracted from phase modulated spectroscopic ellipsometric measurements including mathematical removal of the overlayer. Accurate spectroscopic birefringence measurements are performed using a θ–2θ ellipsometric setup. The resulting birefringence varies as a third order polynomial as a function of the degree of hexagonality, with a turning point at 50% hexagonality. Furthermore, birefringence resulting from the intraconduction band transitions is studied both directly from the variation in the measured birefringence, and through Kramers–Kronig analysis of the extinction coefficient measured by p and s polarized transmission spectroscopy at 70° incidence. The second derivative of the dielectric function of the strongest below band-gap transition in the extraordinary component fit a one-dimensional critical point, while its energy position appears to be a linear function of the degree of hexagonality of the polytypes under investigation.

A theory of diffusion-controlled growth and dissolution of precipitates in binary alloys, taking account of temperature variations, is proposed. Analytical solutions are derived for planar and spherical interfaces by a method which assumes chemical equilibrium to prevail at the moving interface. The diffusion equations are solved by using the stationary-interface approximation, which restricts the concentration field to have no memory of the past motion of the interface. Predictions of growth and dissolution rates for plate-shaped and spherical particles are formulated and compared using data from the Al-Si equilibrium phase diagram. Solutions by analytical methods are compared with results obtained more easily by using the additivity rule. Conditions for additivity are discussed on the basis of numerical examples. Since the exact moving-boundary solution is unknown, the validity of the stationary-interface approximation could not be discussed. However, isothermal results imply that this approximation is reasonable when precipitates with relatively high concentrations are growing or shrinking in dilute solutions.

This paper first reviews and highlights a relatively large number of distributions and correlation functions that are characteristic for normal grain growth. Attention is then paid to the correlation between the average size of an n-sided grain and the average size of a grain next to an n-sided grain. Size correlations between neighbouring grains are examined using a nearest-neighbour Q=40 Potts model on a triangular 500x500 lattice. We show that few-sided grains tend to be surrounded by large grains, while the neighbours of six-sided grains are typically average-sized. The neighbours of many-sided grains tend to be somewhat smaller than an average-sized grain. This confirms the existence of spatial grain size correlations, which have previously been reproduced by the use of a fundamentally different simulation technique. Finally, the robustness of the stationary correlation functions, is examined by incorporating artificial correlations into the starting pattern. (C) 2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

The Kerr rotation and ellipticity of Bi1.8Y1.2Fe5O12 films (Bi:YIG) with the easy axis of magnetization perpendicular to the film plane was investigated in a Kretschmann setup at the wavelength 1.31 μm. The sample was coated by a thin Au film in order to excite plasmons at the free Au surface. An ellipsometric setup, supplemented with a magnetic field oriented perpendicularly to the film plane was used to measure the reflected p and s components of an incoming p polarized wave. The phase difference between the outgoing p and s waves was found by an indirect procedure. A minimum in Kerr rotation and a maximum in Kerr ellipticity could be observed at the surface plasmon resonance angle. Using the Berreman formalism, the experimental curves for the prism/Bi:YIG/Au system could be reproduced by bulk optical constants of the constituents. The asymmetry of the ellipticity curve is demonstrated to arise from a sudden variation in the phase. The effects of the field distribution and the surface roughness are discussed.

Enhanced scattering of laser light from polished and ion bombarded Ag(110) surfaces is reported. Ar+ ions with energy 500 eV were directed against the sample at angles of incidence between 30degrees and 45degrees. The ion current was about 4-6 muA. The experiments were made with a diode pumped solid-state green laser that emitted at 532 nm, with a continuous wave power output around 5 mW. In a controlled series of experiments a sudden increase in scattered intensity could be observed at a fluence of about 2 x 1017 ions/cm(2). The scatterograms showed radially oriented intensity streaks, superimposed on a diffuse and isotropic background intensity. No correlations with low-index crystallographic directions were found. The surface structure was studied by means of optical interferometry and atomic force microscopy. The scattered light was found to be dominated by the contribution from shallow surface indentations and scratches remaining from the polishing process. It is demonstrated that the sputtering creates a surface topography with correlation length of a few mum. A mechanism based on surface plasmons is proposed to be responsible for the observed increase in scattered intensity.

The local-field theory is applied to the (1×1) and the (1×2) reconstructed (110) surfaces of noble metals. Calculated curves for the unreconstructed and reconstructed Au(110) surfaces are compared. In both cases, a dispersion-shaped profile is present at 2.55eV. The spectrum for the (1×2) case shows a significantly stronger anisotropy than in the unreconstructed case. An experimental study has been made of the reflection anisotropy for the clean Au(110) surface at room temperature, where a (1×2) reconstruction is present, in order to test the validity of the calculations. The measured spectrum has a broad minimum in the range 2–4eV with two sharp structures at 2.4 and 3.4eV, respectively. The feature at 2.4eV and the broad minimum is attributed to the effect of the screened local-field on d-band transitions at the surface. The influence of broadening and shifts in critical-point energies for the surface principal directions is discussed.

The cut-off effect in slightly asymmetric systems prevent the wider practical usage of long range surface polaritons (LRSP) in the infrared region. Due to asymmetry caused by the presence of even a few nanometers wide air gap the LRSP mode disappear. We propose a solution of this problem by using an effective medium approach. The basic idea is to compensate for the airgap induced asymmetry by introducing an additional layer into the system. That allows us to shift the cut-off to values sufficiently for experimental observation of LRSP. FTIR spectra of end-fire coupled LRSPs in the GaAs/Au/GaAs multilayer system were measured in the (800 - 3000) cm(-1) range. Various geometric and polarization sensitive effects of the infrared system capable of influencing the LRSP coupling is discussed. A pronounced increase in the p and s polarized light transmission ratio at long-wavelengths is explained as an increase in the propagation distance L of LRSPs. A fairly good at between experimental and calculated curves was achieved at long wavelengths. The width of the air gap was used as a parameter in the calculations.

The normalized reflection difference Δr/r between the [1̄10] and the [001] directions of the Cu(110) surface is presented. Several features in the spectra, which are taken between 1.3 and 3 eV and includes the Δ5→Δ1 edge region, can be reproduced by approximating the difference between the surface tensorial components by the derivative of the bulk dielectric function. The data show that below the edge the effective electron mass is smaller for electron transport along the [1̄10] chain direction than in the [001] direction. The lifetime for electrons is largest in the [1̄10] direction. Using expressions for the screened dipole–dipole interaction we have found that around 2 eV the local-field effect is responsible for a part of the derivation effect. Another contribution comes from the joint-density-of-states for the bands at the Ȳ point of the surface Brillouin zone.

The effect of low-energy sputtering on the surface electronic structure of Cu(110) was studied under room temperature conditions by means of reflection-anisotropy spectroscopy (RAS) at photon energies between 1.6 and 6eV. Sputtering times varied from 0 to 60min, and the energy of the Ar+ ions was 500eV. Spectral changes that depended on fluence in a reproducible manner were observed. We argue that vacancies in the top layer are responsible for some of the strongest changes, at least for short sputtering times. The spectra could be reproduced by local-field calculations where the screened dipole–dipole interaction coefficients between the top layer and the underlying ones were reduced by a factor proportional to the vacancy concentration. Both components of the surface dielectric tensor are calculated. The behaviour of the RAS signal for longer sputtering times is discussed.

We have calculated the screened surface local-field effect for the f.c.c. (110) case, and applied the results to Cu and Ag. Theoretical reflection anisotropy spectra are compared with experimental ones for both clean and oxygen covered surfaces between 1.8 and 5.5 eV. In the Cu(110) case, there is a satisfactory agreement. For the clean Ag(110) surface, the surface seems to exist in two different states resulting in two qualitatively different RAS spectra. Only one of them can be modelled reasonably well by surface local-field effect theory. In addition, we investigate how the variation in model parameters change the form of the spectra of Ag(110).

Real time control by multiwavelength phase modulated ellipsometry (PME), as applied to the growth of optical coatings deposited on various substrates, is reviewed. The structures consist of plasma deposited SiO2 and SiNx stacks and SiOxNy gradient-index coatings. A feedback method is used for growth control of a standard quarterwave filter on c-Si and on glass, the latter achieved by incorporating incoherent modelling of the transparent substrate. The feedback control method is based on a comparison between the real time PME measurements and pre-computed target trajectories. The resulting optical coatings characterised by spectroscopic PME and transmission measurements show reproducible spectral characteristics, with less than 1% deviation between the target and measured spectral responses. The feedback control method is further generalised to the control of gradient-index coatings.

Fast computer algorithms for calculating the reflection coefficients of inhomogeneous films are developed. The applications of such algorithms are aimed at real-time monitoring and control of the growth of gradient index optical coatings. Inhomogeneous films with a refractive index varying along the direction normal to the surface are generally treated by dividing the film into a large number of homogeneous layers and using an iterative or transfer-matrix method to calculate reflectivities. We develop alternative methods. We show that the elements of the transfer matrix and the reflection coefficients can be written in terms of single, double, and higher-dimensional integrals over the films. In most cases it is sufficient to include only the first term, i.e., the single integrals, and the calculation of reflection coefficients is then between 1 and 2 orders of magnitude faster than that for the transfer-matrix and iteration methods. This gives the possibility of real-time determination of optical parameters of inhomogeneous layers for growth monitoring and opens up feedback control. (C) 1997 Optical Society of America.