Materials Algorithms Project
Program Library

Program MAP_KINETIC_PARAMETER_R1

Provenance of code.
Purpose of code.
Specification.
Description of subroutine's operation.
References.
Parameter descriptions.
Error indicators.
Accuracy estimate.
Any additional information.
Example of code
Auxiliary subroutines required.
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Provenance of Source Code

P. E. J. Rivera Díaz del Castillo
Phase Transformations and Complex Properties Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

To obtain the variation of functions N1, N2, R1, R2 with Péclet number. These values can be used to calculate the needle lengthening rate using Trivedi's kinetics.

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Specification

This is a self-contained program.

Language:	FORTRAN
Product form:	Source code

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Description

The program obtains the variation of N1, N2, R1, R2 functions when the Péclet number is varied. The expressions for those functions can be found in the references.

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References

P. E. J. Rivera Díaz del Castillo and H. K. D. H. Bhadeshia, 'Growth of needle and plate shaped particles: theory for small supersaturations, maximum velocity hypothesis', Materials Science and Technology, 17 25-29 2001.
P. E. J. Rivera Díaz del Castillo, Kinetics of Precipitation Reactions, Ph.D. Thesis, University of Cambridge.
R. Trivedi, 'Growth of dendritic needles from a supercooled melt', Acta Metallurgica, 18 287-296 1970.

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Parameters

Input parameters

none.

Output parameters

N1, N2 - double precision: N1, N2 functions for needle growth.
R1, R2 - double precision: R1, R2 functions for needle growth.

P - double precision

Péclet number.

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Error Indicators

None.

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Accuracy

The accuracy of the results can be set by modifying the code, but very large precision may cause a non-convergent soluton.

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Further Comments

The program is set to write the results to files 'res1.d', 'res2.d', a sample version those files is provided.
The variation of N1 and N2 with Péclet number is tabulated in `res1.d', and the variation of R1 and R2 with Péclet number is tabulated in `res2.d'.
The program is set to calculate the values of N1, N2, R1, R2 for values of Péclet number between 1.0 and 3.0.

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