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Fabien Carrara

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge CB2 3QZ, U.K.

E-mail: carrarafabien@yahoo.fr

Added to MAP: June 2003.

Describes the evolution of the thickness of a grain boundary precipitate, assumed to have an infinite radius of curvature, as a function of the time, in the presence of a distribution of spherical particles present in the center of the grain. Essentially a coarsening process.

Language: | FORTRAN |

Product form: | Source Code |

Complete program.

This program is about the coarsening stage, that is to say the phenomenon in which little particles disappear and larger ones become bigger. In this case the large particles are represented by a single particle with an infinite radius of curvature and symbolising the grain boundary, whereas the little precipitates have a finite initial radius rad0, and are arranged randomly within the material.The material is divided virtually in slices, and within those slices the precipitates are assumed as being in equilibrium with the surrouding matrix. Cbulk(i), the average concentration in solute in ith slice is initially taken equal to cmpr0, that is the concentration in solute in the matrix in equilibrium with the precipitate corrected and accounting for the Gibbs-Thomson effect. Since the interface matrix-precipitate at the grain boundary is assumed to be plane Cmpinf the concentration in solute in equilibrium with the precipitate at this interface is given by the value without the capillarity correction.

Two phenomena occurs at the same time in the material. On the one hand, the diffusion of the solute between adjacent slices, on the other hand, the dissolution of precipitates. They are closely linked in the sense that the matter coming from dissolution of the particles provides the matrix with solute which is then conveyed through the slices and as far as the grain boundary thanks to diffusion.

Concentration profile is calculated step by step with the finite difference method.

- A. Iserles, 1996,
*A First Course in the Numerical Analysis of Differential Equations*, Cambridge University Press, 105. - J.W. Christian, 1975,
*Theory of Transformations in Metals and Alloys*, Pergamon Press, Oxford . - F. Carrera, 2003,
*Report describing the present work, 2003*, Cambridge University Press.

**Temp**- db- Absolute temperature (K).
**D**- db- Diffusion coefficient of the solute in the matrix (m2/s).
**Smp**- db- Interfacial energy for the interface prec-matrix (J/m2).
**Vmol**- db- Volume molaire of the prec (m3/mol).
**rad0**- db- Initial radius of the precipitates (m).
**SizeG**- db- Grain size (m).
**Xpm**- db- Mole fraction of solute in the prec in equilibrium with the matrix.
**Xmp**- db- Mole fraction of solute in the matrix in equilibrium with the prec.
**Xbulk**- db- Bulk mole fraction.
**dt**- db- Time step (s).
**dx**- db- Thickness of the slices (m).

**deltx**- db- Thickness of the GB precipitate (m).

None.

No information supplied.

None.

Complete program.

Results are in the file Radm

coarsening, grain boundary

**
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
**