Section 'Trapping kinetics' is still under construction!!

# TechPaper #2016002: Trapping kinetics

## Compatibility

MatCalc version: 6.0100 - …

Author: Y. Shan

Created: 2016-08-09

Revisions:

## Objectives

This paper describes how trapping for kinetics is evaluated in *MatCalc*. It serves as a basis for the discussion for the trapping model.

# Main document

## Thermodynamics

The kinetics for trapped elements are obtained by the thermodynamic extremal principle [1]

The dissipation at dislocations of an element due to diffusion can be approximated by [2]

with being the acting radius of a dislocation (sites within this radius are considered as trap positions) in a cylindrical unit cell of radius . the diffusion coefficient of element . is the molar volume for trap sites in dislocations and is given by

with being the dislocation density.

Using the thermodynamic extremal principle, this leads to the following evolution of trapped elements

The dissipation at grain boundaries due to diffusion is given by [2]

and the molar volume of trap positions for grain boundaries

with being the grain radius in a unit cell and the grain boundary thickness, which is considered to be the positions for trapping.

The evolution of trapped elements at grain boundaries is finally given by

## References

[1] J. Svoboda, I. Turek, F.D. Fischer, Application of the thermodynamic extremal principle to modelling of thermodynamic processes in material science, Phil. Mag. 85 (2005) 3699-3707.

[2] J. Svoboda, G.A. Zickler, E. Kozeschnik, F.D. Fischer, Kinetics of interstitial segregation in Cottrell atmospheres and grain boundaries, Phil. Mag. Lett. 95 (2015) 458-465.