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  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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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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This is a self-contained program.
Product form:Source code

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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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  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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Input parameters


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


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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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See files `res1.d' and `res2.d'.

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Auxiliary Routines

The subroutines called by this program are :-


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capillarity, interface kinetics, needle, growth, Trivedi

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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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