Diffusion In Wide Grain Boundaries

The rigorous solution of the grain-boundary diffusion problem has been approximated by a series expansion method. The calculations show that higher-order terms may be neglected in the bulk adjacent to the grain boundary. Thus, in this region Whipple\u27s and Suzuoka\u27s solutions represent a close approximation to the problem. Inside the grain boundary, however, higher-order approximations have to be taken into account. These approximations gain importance in the case of wide grain boundaries. The solutions obtained for an instantaneous source have been fitted to available grain-boundary diffusion data of Ni2+ in MgO at 1200°C. Numerical calculations give for the bulk diffusion coefficient D=2.9x10-12 cm2 sec -1, the ratio of diffusion coefficient Δ=1.5 and for the grain-boundary width a=75 μ. © 1970 The American Institute of Physics

Colloquium: Statistical mechanics of money, wealth, and income

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio

CALCULATIONS OF DISLOCATION PIPE DIFFUSION

Les mesures de profils de diffusion ont été interprétées à partir de la solution complète de l'équation de la diffusion dans le canal des dislocations. Deux paramètres ont été ajustés : la diffusivité dans le canal des dislocations D', et le rayon du canal des dislocations a. Les valeurs obtenues pour D' se trouvent en bon accord avec celles déjà données par d'autres auteurs. Par contre les valeurs obtenues pour a sont souvent plus élevées, à cause des erreurs expérimentales dans la détermination de la densité de dislocations. Cependant, la zone de concentration élevée n'est pas limitée au coeur des dislocations ; elle dépend de la diffusivité en volume D, et peut être caractérisée par le rayon effectif de la diffusion le long des dislocations, R = 2√Dt.Experimental diffusion profiles have been analyzed by a complete solution of the pipe diffusion equations, using two fitting parameters, pipe diffusivity D' and dislocation pipe radius a. The pipe diffusivity D' agrees well with values obtained by other authors. The pipe radius often turns out very large due to the inaccuracy of the experimental dislocation density. However, the area of high concentration along the dislocation is not confined to the dislocation core, but depends on the diffusivity D of the bulk and may be characterized by an effective diffusion pipe radius R = 2√Dt

Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution

Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a log-normal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in conjunction with detailed evidence from the UK and Japanese income data, a strong case is made for the mathematically separate treatment of waged and unwaged income. The authors present a case for preferring the use of the Boltzmann distribution over the log-normal function, this leads to a brief review of the work of a number of researchers, which shows that a coherent theory for the distribution of all income can be postulated.

Anion Grain-boundary Diffusion In Soidum Chloride

The grain-boundary diffusion of 131I in Harshaw pure and Ca-doped NaCl was investigated in the temperature range between 430 and 560°C. The Arrhenius plot of the grain-boundary diffusivity parameter Dδ displays a marked dip at around 510°C. It is proposed that this dip is due to a phase transformation occurring at the grain boundary, possibly calcium segregation