[en] Molecular collision cross-section has always been measured by the beam scattering method, or by the measurements of thermal conductivity and/or viscosity coefficient, etc. The cross-section thus obtained has been found to be different, qualitatively, from that of the self-scattering of the molecules moving within a molecular beam. By perturbing the zeroth order solution of the Boltzmann equation with a B-G-K kinetic model for the gas upstream to the orifice, and performing particle scattering calculation for molecules within the beam downstream to the orifice, such self-scattering collision cross-section can be determined from the experimental data of velocity distribution functions of molecules in the beam

[en] Measurements of the isotope effect for impurity diffusion of iron in niobium and of the enhancement of niobium self diffusion by iron addition, taken with the previous measurements of self-diffusion coefficients for niobium and impurity diffusion coefficients for iron in niobium, allow us to demonstrate that neither a short- nor a long-range vacancy model gives a satisfactory explanation of the fast diffusion of iron in niobium. It is also shown that diffusion models based on linear or plane defects, interstitials, simple interchange or ring mechanisms are not in agreement with experimental results. By analogy with a mechanism suggested for high diffusivities in lead, a dissociative mechanism, involving an equilibrium between substitutional iron atoms and interstitial iron atoms, is judged acceptable. Iron diffusion is then effected by vacancy-interstitial pairs. This mechanism, which gives a completely satisfactory explanation of experimental results, is shown to be responsible also for the abnormally high impurity diffusivities for iron, cobalt and nickel in γ uranium, β titanium and β zirconium. (author)

[en] A Comment on the Letter by Lu-Jing Hou, Alexander Piel, and P. K. Shukla, Phys. Rev. Lett. 102, 085002 (2009). The authors of the Letter offer a Reply.

[en] Recent and current work has shown that self- and substitutional diffusion in α-Zr is enhanced by the presence of the ultra-fast, interstitially-diffusion solute, Fe. The bulk of the data indicates that the diffusion coefficients scale directly with the Fe concentration. This work considers the nature of the Fe-enhancement mechanism in terms of vacancies strongly bound to either substitutional or interstitial Fe atoms. Experimental evidence from diffusion experiments, as well as from electron microscopy and positron annihilation spectroscopy investigations, is considered. It is concluded that the experimentally observed substitutional diffusion enhancements are most readily interpreted in terms of transport via an interstitial Fe/vacancy pair. (orig.)

[en] Self-diffusion in an α-zirconium single crystal was investigated over the temperature range 779 to 1128 K. The measurements were made by simultaneous diffusion of ⁹⁵Zr and its radioactive daughter ⁹⁶Nb and by subsequent ion-beam-sputter sectioning (IBS). The activity of ⁹⁵Zr in each section was determined from the 724 keV γ peak using a Ge-Li spectrometer. Gaussian penetration curves were observed. The present results are compared with previous studies of self-diffusion in α- and β-Zr. The Arrhenius plot of self-diffusion coefficients in α-Zr is strongly curved downward. This means that an anomalous behaviour of self-diffusion is observed not only in the β- but also in the α-phase of Zr. Some results on the diffusion of ⁹⁵Nb in α-Zr are reported in an Appendix. (orig./RK)

[en] In this paper, a recent combined isotope and interdiffusion analysis is adapted to the case of binary liquid alloys. Shear-cell interdiffusion experiments with a layer enriched in ⁶⁵Cu sandwiched between the interdiffusion couple ends have been performed on liquid Al-Cu that is suitable for demonstration of the application of this analysis. (Note that the analysis is not limited to the use of the shear-cell technique.) The self-diffusion coefficient of Cu is then obtainable as a function of composition. Results of the new analysis are in good agreement with an independently measured Cu self (tracer) diffusion coefficient at two compositions.

[en] Ion implantation always induces the creation of dislocation loops. When the damage profile is determined by a backscattering technique, the dechanneling by these loops is implicitely at the origin of these measurements. The dechanneling of alpha particles by dislocation loops produced by the coalescence of quenched-in vacancies in aluminium is studied. The dechanneling and the concentration of loops were determined simultaneously. The dechanneling width around dislocation was found equal to lambda=6A, both for perfect and imperfect loops having a mean diameter d=250A. In the latter case, a dechanneling probability chi=0.34 was determined for the stacking fault, in good agreement with previous determination in gold. A general formula is proposed which takes into account the variation of lambda with the curvature (or the diameter d) of the loops. Finally, by a series of isothermal anneals, the self-diffusion energy ΔH of aluminium was measured. The value obtained ΔH=1.32+-0.10eV is in good agreement with the values obtained by other methods

[en] Previously published Monte Carlo molecular-dynamics data on the velocity autocorrelation function of the hard-sphere fluid are supplemented by data for the time-dependent transport coefficient to yield estimates for the self-diffusion coefficient throughout the fluid regime, from 25 to 1.6 times the close-packed volume. The dependence on system size is explored through results for 108--4000 particles. It is found essential to include long-time contributions to the Green-Kubo integral based on the previously validated mode-coupling theory. It is shown that the calculations of Easteal, Woolf, and Jolly [Physica 121A, 286 (1983)] fall significantly below the current estimates, which are in qualitative agreement with the Alder, Gass, and Wainwright [J. Chem. Phys. 53, 3813 (1970)] values

[en] To interpret anomalous self-diffusion in α-Zr, we propose the existence of two kinds of monovacancy mechanisms. The less important one operates via free monovacancies. The other operates via monovacancies associated to interstitially dissolved iron atoms. This mechanism enhances the diffusion coefficient compared with normal diffusion in compact metals. At temperatures over 1003 K, we postulate the existence of the β-phase. We explain how small amounts of β-phase affect the diffusion measurements. (orig.)

[en] The Boltzmann-Hilbert equation for the self diffusion coefficient in a binary hard sphere mixture described by concentration csub(A) = nsub(A)/n, mass ratio α = msub(A)/msub(B) and size ratio γ = sigma²sub(AB)/sigma²sub(AA) is solved by an iterative technique using the method of 'successive uncorrelated binary collisions' (SUBC-model). In the numerical procedure the contribution of each of N collisions of a tagged particle (say A) with particles of either species A or B to the solution of the integro-differential equation is calculated for hard spheres for a wide range of mass ratios (10^-3) less than or equal to α less than or equal to 10³), 0.33 less than or equal to γ less than or equal to 16 and the full concentration range 0 less than or equal to csub(A) less than or equal to 1 in steps of 0.1. A brief discussion for Maxwell-molecules, other forms of potentials and the limiting cases for a Lorentz gas (csub(A) → 0, α → 0) and the quasi Lorentz gas or Rayleigh gas (csub(A) → 0, α → infinity) are included. The self diffusion coefficient is calculated for the mixture using the time integral over the velocity autocorrelation function in the Kubo-Green formalism. The results are compared with a highly accurate Sonine poloynominal type approximation of the Boltzmann equation (for csub(A) → 0) and it is shown that the Chapman-Enskog method is more effective for α → 0 while the SUBC-model is more effective for α → infinity. The SUBC-model is used to calculate a simple 'two collision approximation' and to compare it with the numerical solution of the Boltzmann-Hilbert equation and the results obtained for the self diffusion coefficient. The 'exact' results of the self diffusion coefficient are reproduced by the 'two collision approximation' to better than +- 1% in the investigated range of (csub(A), α, γ) values. (Author)