Atomic Transport Properties Research Articles

Approaching the limits of high resolution depth profiling

Depth profiling by ion sputtering in combination with surface analysis methods such as AES, XPS, ISS and SIMS is commonly applied to characterize thin films and interfaces with high depth resolution. Frequently, degradation of the depth resolution is observed due to changes of surface topography and composition of the sample during sputtering. Recent progress in sputter profiling of bilayers, multilayers and delta marker profiles of different materials and with different methods has revealed a more detailed knowledge about the limiting factors which impede the attainment of high resolution. In many cases, ion bombardment induced surface topography has been shown to be considerably reduced when using sample rotation during depth profiling. The depth resolution is mainly governed by the altered layer generated during sputtering and depends on ion beam characteristics (ion mass, ion energy and angle of incidence) as well as on thermochemical and atomic transport properties of the sample components. Under favorable conditions, the physical limits of depth resolution of the order of a few atomic monolayers can be approached. Comparison of theoretical modelling of depth profiles with experimental data in many cases allows an estimation of the resolution function and enables deconvolution of the measured profile. The predictability of the depth resolution function for given materials and experimental conditions mainly depends on a detailed understanding of the physico-chemical processes during ion sputtering.

Viscosity of molten Pd82Si18 and the scaling of viscosities of glass forming systems

The viscosity of molten Pd82Si18 was measured from 1045 to 1210 K by capillary flow method. When the molten specimen was not purified in advance and during the experiment, its viscosity could not be determined for temperatures below the liquidus. On the other hand, in the presence of boron oxide flux, the viscosity could be measured up to an undercooling of 58 K below its liquidus and the entire viscosity can be described very well by the following Vogel–Fulcher equation: ln η=−3.779+(1102.135/T−684), where T is in K. No discontinuity is found at the liquidus. The present data were compared with those of other glass forming systems to test the validity of the principle of corresponding states for atomic transport properties.

Viscosity of molten Pd77Cu6.5Si16.5 and the principle of corresponding states

The viscosity of Pd77Cu6.5Si16.5 was measured from 995 to 1183 K by capillary flow method. In the experiment, fluxing of the molten specimen by boron oxide was necessary in order to inhibit the formation of crystallites at temperatures near its liquidus. It was found that the viscosity can be described very well by the following Vogel–Fulcher equation: ln η=−3.764+938.543/(T−726), where T is in K. No discontinuity in viscosity was observed at the thermodynamic melting temperature. Recently Tsao and Spaepen [Amorphous Materials: Modeling of Structure and Properties, edited by V. Vitek (The Metallurgical Society of AIME, New York, 1983), p. 323] determined the equilibrium viscosity of the same system near the glass transition temperature. It turned out that the viscosity data from the two regimes cannot be joined together by a single Vogel–Fulcher equation of constant parameters. Finally the present results were compared with those earlier viscosity data of Pd40Ni40P20 and Au77Ge13.6Si9.4 [D. E. Polk and D. Turnbull, Acta Metall. 20, 493 (1972)] to test the validity of the principle of corresponding states for atomic transport properties.

A molecular dynamics study of liquid copper near the melting point

Molecular dynamic calculations of liquid copper at 1423K are reported. An effective pair potential extracted from the low-angle structure factor data(wavenumber k:from 0.1Å −1 to 2.38Å −1) is used in this study. Results for the pair distribution functions, the thermodynamic properties and the atomic transport properties are presented in comparison with experimental data.

Atomic Transport in Liquids

Abstract The topics discussed are: We conclude that along the saturated vapour pressure curve the temperature dependence of the shear viscosity coefficient, η, for liquid metals is not the same as that of its counterpart in the inert gas liquids, according to the available experimental data. In addition, for the data examined a power law in T is a more appropriate description than an Arrhenius expression. The situation is more confused for the self-diffusion coefficient, D. For the saturated liquid, a linear dependence can be claimed for Ar and some liquid metal data, but the evidence is not conclusive. To develop a coherent and comprehensive understanding of the transport mechanism more extensive diffusion data is essential. The representation of experimental atomic transport coefficient data in simple liquids with respect to temperature and density, the emphasis being on self-diffusion and shear viscosity. The theoretical framework and the derivation of expressions for the coefficients in terms of Green-Kubo integrands. Computer simulation data for the rigid sphere, Lennard-Jones and liquid metal-like systems. Rigid sphere dynamics and the rigid sphere fluid as a reference system for atomic transport in liquids. Mode-coupling theory and interrelationships between coefficients. We suggest, also, a more systematic approach to the determination of transport coefficients in computer simulation studies, particularly for liquid metal-like systems. On the theoretical front, in spite of an established framework, realistic calculations of atomic transport properties of liquids (on the scale required) are rare. Mode-coupling theory, we believe, offers the opportunity of progress here. We comment, finally, on interrelationships between coefficients and give a derivation of the Stokes-Einstein relation between D and η from a microscopic viewpoint.

Atomic transport properties in UO2 and mixed oxides (U, Pu)O2

Atomic diffusion processes in UO2 and in the fast-breeder reactor fuel, (U, Pu)O2 are reviewed. Emphasis is given to the slower-moving species. i.e. U and Pu. Self-diffusion, chemical diffusion, diffusion in a thermal gradient, enhancement of diffusion by radiation and fission and the operative diffusion mechanisms are discussed. The main parameter, besides the temperature, is the oxygen-to-metal ratio (O/M ratio) of the oxide. The experimental results are compared with recent calculations reported elsewhere in this volume. Also treated are effects of the possible λ-transition at ca. 2600 K in UO2 on high-temperature kinetic processes.

Temperature dependence of atomic transport in less-simple liquid metals.

We report on the atomic transport properties viz. the coefficients of shear viscosity and self-diffusion for certain less-simple liquid metals at various temperatures. The basic assumption made is that these properties of a liquid metal resemble those of an appropriate hard-sphere system. The temperature dependence of the basic ingredients, i.e., the hard-sphere diameters and packing fraction, is considered via a full thermodynamic perturbation theory. The optimal values of these basic ingredients are employed in calculating the atomic transport coefficients of Cu, Cd, ln, and Pb. The calculated results are found to be in good agreement with the experimental and available theoretical results.

Liquid Metals: An Introduction to the Physics and Chemistry of Metals in the Liquid State

Mitsuo Shimoji London: Academic 1977 pp xv + 391 price £16.50 This is an important book for all interested in liquid metals, containing as it does a fairly complete account of developments up to about 1974–5. Perhaps the best way to indicate the flavour and approach is to give the chapter headings in order: thermal properties of liquid metals, thermal properties of liquid alloys, static structure of liquid metals and alloys, electron–ion interaction and cohesive energy of liquid metals, electron states in liquid metals and alloys, atomic transport properties, electron transport properties, transition to the nonmetallic states, heterogeneous equilibria and surface properties.

Electrical conductivity and charge compensation in Nb doped TiO2 rutile

The electrical conductivity of rutile doped with 0.04–3 at.% niobium is reported as a function of oxygen pressure in the temperature range 1273–1623 K. The charge compensation is discussed in terms of a point defect model, under the assumption of a substitutional incorporation of niobium into the titanium rutile sublattice. Two kinds of charge compensation occur according to the temperature and the oxygen pressure, via an electronic or a lattice defect, in a Ti1−yNbyO2 or a Ti1−yNbyO2+y/2 solid solution, respectively. In the overstoichiometric range of the oxide, the data, when applied to undoped rutile, allow some conclusions about the atomic or electronic transport properties, both in the high and low temperature regimes.

Atomic Transport Properties in Liquid Metals and Alloys

AbstractThe atomic transport properties of liquid metals are reviewed, with principal emphasis on self‐diffusion. Experimental methods are surveyed, and published data are compared with the predictions of various models and theories.

Hard-sphere results and atomic transport properties of liquid-metals

Experimental data on the shear viscosity of liquid metals have been used in combination with the results of hard-sphere model calculations in order to determine a hard-core size. By using the known density at the melting point and the result of applying Lindemann's law it turns out that the shear viscosity of high-melting refractory metals can be predicted. From temperature- dependent viscosity data interpreted in terms of hard-sphere results if follows that application of a corresponding-states principle to atomic transport in liquid metals is questionable.

Atomic and electronic transport properties and the molar volume of monatomic liquids

Experimental data on the coefficients of self-diffusion and shear viscosity of liquid argon and methane at saturated vapour pressure and on the thermal conductivity of argon expressed as D|T 1 2 , T 1 2 |η and T 1 2 |λ , respectively, are shown to obey a linear increase with the molar volume in a substantial fraction of the liquid range. Though the linear relationships are consistent with the interpretation of transport properties in terms of an appropriate hard-sphere fluid, the calculated diffusion and thermal conductivity in argon are too large by about 20% compared with the experimental values. This is most likely due to the fact that non-uniformities in the attractive- potential energy surface are not taken into account in the hard-sphere model. The atomic-mass transport coefficients of the liquid alkali metals and mercury behave in a similar way, though in this case the calculated diffusion is too small by about 15% compared with experiment. For the liquids, the relationship between D and η in combination with the temperature-dependent hard-core size that can be derived from either transport coefficient is found to be in nearly quantitative agreement with the Stokes-Einstein equation. It turns out that also the electrical resistivity and the thermal conductivity of the alkalis expressed as ϱ|T 1 2 and T 1 2 |λ increase linearly with the molar volume over a substantial range of temperatures, which in the case of cesium extends from room temperature (solid Cs) up to at least 0.9 T c (liquid Cs at saturated vapour pressure). The ratio of electrical and thermal conductivity closely resembles the Lorenz number for free electrons. A remarkable feature is that electron transport properties in the liquid alkalis meet relationships with the molar volume similar to those derived for atomic transport coefficients in hard-sphere kinetic theory.

Atomic distribution and electronic transport properties in liquid alloys studied by X-ray diffraction

Abstract The distribution of atoms in liquid alloys is obtained by Fourier transform of the measured interference function I(K). The density function ρ(r), thus obtained, is the weighted sum of the atomic densities ρ ij (r) which specify the number of j-type atoms per unit volume at the distance r from the i-type atom. The weighting factors depend not only on the atomic concentration ci but also on the atomic scattering factors fi of the atoms. In binary alloys three radial density functions are needed to determine the atomic distribution. In general, three interference functions I a(K), I b(K) and I ab(K) must be determined to obtain these densities. The electronic transport properties depend on these three interference functions and on the Fourier transform U a(K) and U b(K) of the pseudopotentials of the atoms. The coherently scattered intensity I e.u. coh(K) per atom in electron units can be written as: If f a≃f b, the Laue monotonic scattering c a c b(f a-f b)2 will be small and This relation can be applied to determine ρ(r)≃c aρa(r)+c bρb (r) in Ag-Sn, Hg-Tl and Al-Mg alloys. In these systems the interatomic distances r 1 and the coordination numbers were obtained as a function of concentration from the radial distribution function (RDF) 4πr 2 ρ(r). Negative deviation from a linear law (Vegard's law) was observed in Ag-Sn, and positive deviation in Hg-Tl. In Hg-In, f Hg > f In, and the density function ρ(r) is dominated by the more strongly scattering Hg atoms. The interatomic distances as obtained from the weighted RDF show a slight negative deviation from Vegard's law. The atomic distribution in Au-Sn, Al-Mg and Ag-Mg are also briefly discussed. The predicted electrical resistivity in Hg-Tl and Hg-In follow the decreasing trend at higher Tl or In concentration as observed for the measured resistivities. There is however discrepancy between the observed and calculated values of the resistivity for Hg and the dilute Hg alloys. The calculated resistivities of the Ag-Sn alloys agree with the experimental values. The thermoelectric powers were also calculated for these three alloy systems.