Martin Schwind

σ-PHASE PRECIPITATION IN STABILIZED AUSTENITIC STAINLESS STEELS

Experimental observations of sigma-phase precipitation in two stabilized austenitic stainless steers, AISI 321 and AISI 347, aged up to 80,000 h at temperatures between 500 and 800 degrees C, are c ...

ON ZIGZAG SHAPED DIFFUSION PATHS IN MULTI-PHASE DIFFUSION COUPLES

Department of Materials Science and Engineering, Royal Institute of Technology,SE-100 44 Stockholm, Sweden(Received June 6, 2000)(Accepted July 24, 2000)Keywords: Diffusion; Multi-phase diffusionIntroductionSome time ago, Hopfe and Morral (1) proposed and investigated a simple model for multicomponentdiffusion in multi-phase diffusion couples. In their model, the multi-phase equilibrium requirementleads to a singular effective diffusion matrix, which in case of a constant diffusivity gives rise topeculiar zigzag shaped diffusion paths. More recently, Chen and Morral (2) investigated the possibleinfluence of a concentration dependent diffusion matrix and they found, when comparing theiranalytical result with numeric calculations performed with the DICTRA software on realistic modelsystems, that the difference was so small that it was of no practical importance. The minute differencebetween the numeric and analytic results was by the authors mainly considered due to the discretisationerrors in the numerical solution. If the numerical calculations are applied to other alloy systems, thefeatures of the diffusion paths are drastically altered and paths like the one in Fig. 1 are obtained. In thispaper, we therefore illustrate how a concentration dependent diffusion matrix may cause significantdeviations from the ideal zigzag shaped diffusion paths.The ModelIn their model Hopfe and Morral consider an idealized diffusion couple that consists of two multi-phasematerials of different composition brought in contact with each other. In their examples they focus onternary Ni-Cr-Al alloys with a matrix phasegand a secondary phase b, the latter in which no long rangediffusion takes place. Instead the bphase serves as point sources or sinks, the composition of which arehomogeneous and in equilibrium with the surrounding gphase in each point in the system. They usethese assumptions to derive a modified diffusion equation for the average composition c# of gand bina differential volume element›c#›t5››xD

A random walk approach to Ostwald ripening

We investigate a numerical model of Ostwald ripening in which matter is discretised. The model is based on transport by random walk and certain rules at the phase interfaces which mimic the continuous solution of the diffusion and moving boundary problem. In the limit of low volume fractions the results from our simulations agree quantitatively with the results predicted by the Lifshitz-Slyosov-Wagner theory. In contrast to the LSW model, the volume fraction of particles enters our model as part of the diffusion problem and it may therefore be confidently used to investigate what happens when the volume fraction of particles increases.

Trapping of vacancies by rapid solidification

A model has been developed for the process of trapping of vacancies in rapid solidification of pure metals, which includes the effect of solute drag where vacancies play the role of solute. Within a reasonable range of parameter values it predicts that substantial trapping cannot occur unless the solidification velocity is 1 m/s or higher. It is demonstrated that the intrinsic mobility of the liquid/solid interface should not be evaluated without considering the effects of vacancy trapping and solute drag caused by vacancies. The model is applied to copper and unknown parameters are evaluated from information on the solidification velocity as a function of undercooling.

Some remarks on boundary conditions for random walk––the Söderholm condition

Abstract This paper illustrates how the Soderholm process for simulation of diffusion by random walk tends to Dirichlet conditions when the duration of the time steps decreases. The convergence is rather slow which underlines the importance to keep the time step small in random walk simulations.