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Program MAP_KINETIC_NEEDLE3

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

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 small values of dimensionless supersaturation with Péclet number and the ratio of the plate tip radius and the critical radius for nucleation.

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Specification

This program reads the value of Q, and a table with the variation of N1 and N2 with Péclet number from the input data file 'indat12.d' (see MAP_KINETIC_PARAMETER_R1), and writes the output in the file 'res1.d'.
Language:FORTRAN
Product form:Source code

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Description

The program obtains the variation of small values of dimensionless supersaturation with Péclet number and the ratio of the plate tip radius and the critical radius for nucleation by simultaneously solving the diffusion equation expressed in parabolic coordinates and an equation to account for mass balance at the parabolic interface. The equations can be found in the references.

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References

  1. 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.
  2. P. E. J. Rivera Díaz del Castillo, Kinetics of Precipitation Reactions, Ph.D. Thesis, University of Cambridge.
  3. R. Trivedi, 'Growth of dendritic needles from a supercooled melt', Acta Metallurgica, 18 287-296 1970.
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Parameters

Input parameters

Q - double precision
parameter to characterise the relative importance of interface kinetics and diffusion effects.

PEC - double precision array of size 10010
Péclet number.

N1, N2 - double precision arrays of size 10010
N1, N2 functions for plate growth.

Output parameters

O - double precision
Dimensionless supersaturation.

RRR - double precision
Ratio between needle tip radius and critical radius for nucleation.

P - double precision
Péclet number.

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

The program is set to write the results to files 'res1.d', a sample version of that file is provided.

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Example

The example is for Q=0.02.

1. Program data

See input data file 'indat12.d'.

2. Program results

See sample results file 'res1.d'.
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Auxiliary Routines

The subroutines called by this program are :-

ERROR

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Keywords

capillarity, interface kinetics, needle, growth, Trivedi, small supersaturations

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Download

Download source code

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