Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials

Rifa J. El-Khozondar; Dana Zӧllner; Klaus Kassner

doi:doi:10.11648/j.ijmsa.20140306.26

| Peer-Reviewed

Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials

Rifa J. El-Khozondar, Dana Zӧllner, Klaus Kassner

Published in International Journal of Materials Science and Applications (Volume 3, Issue 6)

Received: 16 November 2014 Accepted: 28 November 2014 Published: 2 December 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Numerical simulations based on the Monte Carlo Potts model are used to study the temporal change of the grain size distribution of two-phase polycrystalline materials, where both phases grow simultaneously. After a sufficiently long time, grain growth in such two-phase systems can be characterized by a self-similar scaled grain size distribution function and an associated growth law. In particular, the grain size distribution is analyzed for a broad range of second phase volume fractions and found to vary with the volume fraction such that the size distribution becomes narrower and higher peaked with decreasing volume fraction of the second phase, where particularly the normal distribution function describes the simulation results very well. On the other hand, for one-phase systems the grain size distribution is in excellent agreement with an analytical grain size distribution function based on a statistical mean-field theory of grain growth that is completely compatible with the principal physical condition of total volume conservation.

Published in	International Journal of Materials Science and Applications (Volume 3, Issue 6)
DOI	10.11648/j.ijmsa.20140306.26
Page(s)	381-390
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Monte Carlo, Grain Growth, Grain Size Distribution, Grain Structure, Polycrystalline Materials

References

[1]	K.W. Mahis, K. Hanson and J.W. Morrid Jr., "Comparative analysis of the cellular and Johnson-Mahl microstructures through computer simulation," Act Metall., Vol. 28, pp. 443-453, 1980.
[2]	H.J. Frost and C.V. Thompson, "The effect of nucleation conditions on the Topology and Geometry of two-dimensional grain structures," Act Metall., vol. 35, pp. 529-540, 1987.
[3]	O. Ito and E.R. Fuller Jr., "Computer modeling of anisotropic grain microstructure in two-dimensions," Act Metall., vol. 41, pp. 191-198, 1993.
[4]	E. Schule, "A justification of the Hillert distributions by spatial grain growth simulation performed by modifications of Laguerre tessellations," Comput. Mater. Sci., vol. 5, pp. 277-285, 1996.
[5]	H.J. Frost, C.V. Thompson, C.L. Howe, and J. Whang, "A two-dimensional computer simulation of capillarity-driven grain growth: Preliminary results," Scr. Metal., vol. 22, pp. 65-70, 1988.
[6]	E.A. Ceppi and B.O.Nasello, "Computer simulation of bidimensional grain growth," Scr. Metal., vol. 12, pp. 1221-1225, 1984.
[7]	D. Kinderlehrer, J. Lee, I. Livshits, A. Rollett and S. Ta'asan, "Mesoscale simulation of grain growth," Materials Science Forum, Vol. 467, pp. 1057-1062, 2004.‏
[8]	L. A. Barrales-Mora, V. Mohles, P. J. Konijnenberg and D. A. Molodov, "A novel implementation for the simulation of 2-D grain growth with consideration to external energetic fields," Comput. Mater. Sci., Vol. 39, pp. 160-165, 2007.
[9]	D. Fan and L.Q. Chen, "On the possibility of spinodal decomposition in zirconia-yittria alloys-A theoretical investigation," J. Am. Ceram., vol. 78, pp. 1680-1686, 1995.
[10]	Z. Nikolic and W. Huppmann, "Computer simulation of chemically driven grain growth during liquid phase sintering," Acta Metall., vol. 28, pp. 475-479, 1980.
[11]	P.W. Voorhees and M.E. Glicksman, "Solution to the multi-particle diffusion problem with applications to Ostwald-ripening-II. Computer simulation," Acta Metall., vol. 32, pp. 2013-2030, 1984.
[12]	J. Geiger, A. Roosz and P. Barkoczy, "Simulation of grain coarsening in two dimensions by cellular-automaton," Acta Mater., Vol. 49, pp. 623-629, 2011.
[13]	M.P. Anderson, D.J. Srolovitz, G.S. Grest, and P.S. Sahni, "Computer simulation of grain gowth-I. Kinetics," Acta Metall. Vol. 32, pp. 783-791, 1984.
[14]	M.P. Anderson, G.S. Grest, D.J. Srolovitz, "Computer simulation of grain gowth in three dimensions," Phil. Mag. Vol. 59B, pp. 293-329, 1989.
[15]	X. Song and G. Liu, "A simple and efficient three-dimensional Monte Carlo simulation of grain growth," Scr. Mater., Vol. 38, pp. 1691-1696, 1998.
[16]	P. Blikstein and A. P. Tschiptschin, "Monte Carlo simulation of grain growth, " Materials Research, Vol. 2, 133-137, 1999.
[17]	‏ Q. Yu and S.K. Esche, "A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency," Comput. Mater. Sci., Vol. 27, pp. 259-270, 2003.
[18]	L. Hui, W. Guanghou, D. Feng, B. Xiufang, and F. Pederiva, "Monte Carlo simulation of three-dimensional polycrystalline material," Materials Science and Engineering: A, Vol. 357, pp. 153-158, 2003.
[19]	Q. Yu and S.K. Esche, "Three-dimensional grain growth modeling with a Monte Carlo algorithm," Materials Letters, Vol. 57, pp. 4622-4626, 2003.
[20]	C. Ming Huang, C.L. Joanne, B.S.V. Patnaik, and R. Jayaganthan, "Monte Carlo simulation of grain growth in polycrystalline materials," Applied Surface Science, Vol. 252, pp. 3997-4002, 2006.
[21]	D.Zöllner and P. Streitenberger, "Monte Carlo Simulation of Normal Grain Growth in Three Dimensions," Materials Science Forum, Vol. 567, pp. 81-84, 2008.
[22]	V. Tikare and J.D. Gawlez, "Applications of the Potts model to simulation of Ostwald ripening," J. Am. Ceramic Soc., vol. 81, pp. 485-491, 1998.
[23]	R. M. German, P. Suri, and S.J. Park, "Review: liquid phase sintering," Journal of materials science, Vol. 44, pp. 1-39, 2009.‏
[24]	R. El-Khozondar, H. El-Khozondar, G. Gottstein, A. Rollet, "Microstructural Simulation of Grain Growth in Two-phase Polycrystalline Materials," Egypt. J. Solids, vol. 29(1), pp. 35-47, 2006.
[25]	R. El-Khozondar and H. El-Khozondar, "Numerical simulations of coarsening of lamellar structures: applications to metallic alloys," Egypt. J. Solids, vol. 27(2), pp.189-199, 2004.
[26]	V.S. Solomatov, R. El-Khozondar, and V. Tikare, "Grain size in the lower mantle: constraints from numerical modeling of grain growth in two-phase systems," Phys. Earth. Planet. Inter., vol. 129, pp. 265-282, 2002.
[27]	R. El-Khozondar and H. El-Khozondar, "Numerical modeling of microstructural evolution in three-phase polycrystalline materials," Arabian Journal for Science and Engineering, vol. 34(1A), pp. 241-252, 2009.
[28]	J.E. Burke, D. Turnbull, "Recrystallization and grain growth," Prog. Metal. Phys., vol. 3, pp. 220-292, 1952.
[29]	P. Felthman, "Grain growth in metals," Acta Metall., vol. 5, pp. 97-105, 1957.
[30]	N.P. Louat, "On the theory of grain growth," Acta Metall., vol. 22, pp. 721-724, 1974.
[31]	M. Hillert, "On the theory of normal and abnormal grain growth," Acta Metall., vol. 13, pp. 227-238, 1965.
[32]	I.M. Lifshitz and V.V. Slyozov, "The kinetics of precipitation from supersaturated solid solution," J. Phys. Chem. Solids, vol. 19, pp. 35-50, 1961.
[33]	C. Wagner, "Theorio der altering von niederschlägen durch unlӧsen," Elektrochem., vol. 65, pp. 581-591, 1961.
[34]	A.J. Ardell, "On the coarsening of grain boundary," Acta Metall., vol. 20, pp. 601-609, 1972.
[35]	P. Streitenberger, "Generalized Lifshitz-Slyozov theory of grain and particle coarsening for arbitrary cut-off parameter," Scr. Mater., vol. 39, pp. 1719-1724, 1998.
[36]	M.W. Nordbakke, N. Ryum, and O. Hunderi, "Curvilinear polygons, finite circle packings, and normal grain growth," Materials Science and Engineering A., vol. 385, pp. 229-234, 2004.
[37]	D. Zӧllner and P. Streitenberger, "Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theory," Scr. Mater., vol. 54, pp. 1697-1702, 2006.
[38]	D. Zöllner and P. Streitenberger, "Grain size distributions in normal grain growth," Practical Metallography/Praktische Metallographie," vol. 47, pp. 618-639, 2010.
[39]	V. Tikare and J. D. Cawley, "Numerical simulation of grain growth in liquid phase sintered materials. II. Study if isotropic grain growth," Acta Mater., vol. 46, pp. 1343-1356, 1998.
[40]	D. Zöllner, "A new point of view to determine the simulation temperature for the Potts model simulation of grain growth," Comput. Mater. Sci., vol. 86, pp. 99-107, 2014.

Cite This Article

Plain Text BibTeX RIS

APA Style

Rifa J. El-Khozondar, Dana Zӧllner, Klaus Kassner. (2014). Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials. International Journal of Materials Science and Applications, 3(6), 381-390. https://doi.org/10.11648/j.ijmsa.20140306.26

Copy | Download

ACS Style

Rifa J. El-Khozondar; Dana Zӧllner; Klaus Kassner. Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials. Int. J. Mater. Sci. Appl. 2014, 3(6), 381-390. doi: 10.11648/j.ijmsa.20140306.26

Copy | Download

AMA Style

Rifa J. El-Khozondar, Dana Zӧllner, Klaus Kassner. Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials. Int J Mater Sci Appl. 2014;3(6):381-390. doi: 10.11648/j.ijmsa.20140306.26

Copy | Download

@article{10.11648/j.ijmsa.20140306.26,
  author = {Rifa J. El-Khozondar and Dana Zӧllner and Klaus Kassner},
  title = {Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials},
  journal = {International Journal of Materials Science and Applications},
  volume = {3},
  number = {6},
  pages = {381-390},
  doi = {10.11648/j.ijmsa.20140306.26},
  url = {https://doi.org/10.11648/j.ijmsa.20140306.26},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20140306.26},
  abstract = {Numerical simulations based on the Monte Carlo Potts model are used to study the temporal change of the grain size distribution of two-phase polycrystalline materials, where both phases grow simultaneously. After a sufficiently long time, grain growth in such two-phase systems can be characterized by a self-similar scaled grain size distribution function and an associated growth law. In particular, the grain size distribution is analyzed for a broad range of second phase volume fractions and found to vary with the volume fraction such that the size distribution becomes narrower and higher peaked with decreasing volume fraction of the second phase, where particularly the normal distribution function describes the simulation results very well. On the other hand, for one-phase systems the grain size distribution is in excellent agreement with an analytical grain size distribution function based on a statistical mean-field theory of grain growth that is completely compatible with the principal physical condition of total volume conservation.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials
AU  - Rifa J. El-Khozondar
AU  - Dana Zӧllner
AU  - Klaus Kassner
Y1  - 2014/12/02
PY  - 2014
N1  - https://doi.org/10.11648/j.ijmsa.20140306.26
DO  - 10.11648/j.ijmsa.20140306.26
T2  - International Journal of Materials Science and Applications
JF  - International Journal of Materials Science and Applications
JO  - International Journal of Materials Science and Applications
SP  - 381
EP  - 390
PB  - Science Publishing Group
SN  - 2327-2643
UR  - https://doi.org/10.11648/j.ijmsa.20140306.26
AB  - Numerical simulations based on the Monte Carlo Potts model are used to study the temporal change of the grain size distribution of two-phase polycrystalline materials, where both phases grow simultaneously. After a sufficiently long time, grain growth in such two-phase systems can be characterized by a self-similar scaled grain size distribution function and an associated growth law. In particular, the grain size distribution is analyzed for a broad range of second phase volume fractions and found to vary with the volume fraction such that the size distribution becomes narrower and higher peaked with decreasing volume fraction of the second phase, where particularly the normal distribution function describes the simulation results very well. On the other hand, for one-phase systems the grain size distribution is in excellent agreement with an analytical grain size distribution function based on a statistical mean-field theory of grain growth that is completely compatible with the principal physical condition of total volume conservation.
VL  - 3
IS  - 6
ER  -

Copy | Download

Author Information

Rifa J. El-Khozondar

Physics Department, Al-Aqsa University, Gaza, Palestine
Dana Zӧllner
Klaus Kassner

Institute for Theoretical Physics, Otto von Guericke University Magdeburg, Magdeburg, Germany

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Rifa J. El-Khozondar, Dana Zӧllner, Klaus Kassner. (2014). Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials. International Journal of Materials Science and Applications, 3(6), 381-390. https://doi.org/10.11648/j.ijmsa.20140306.26

Copy | Download

ACS Style

Rifa J. El-Khozondar; Dana Zӧllner; Klaus Kassner. Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials. Int. J. Mater. Sci. Appl. 2014, 3(6), 381-390. doi: 10.11648/j.ijmsa.20140306.26

Copy | Download

AMA Style

Rifa J. El-Khozondar, Dana Zӧllner, Klaus Kassner. Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials. Int J Mater Sci Appl. 2014;3(6):381-390. doi: 10.11648/j.ijmsa.20140306.26

Copy | Download

@article{10.11648/j.ijmsa.20140306.26,
  author = {Rifa J. El-Khozondar and Dana Zӧllner and Klaus Kassner},
  title = {Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials},
  journal = {International Journal of Materials Science and Applications},
  volume = {3},
  number = {6},
  pages = {381-390},
  doi = {10.11648/j.ijmsa.20140306.26},
  url = {https://doi.org/10.11648/j.ijmsa.20140306.26},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20140306.26},
  abstract = {Numerical simulations based on the Monte Carlo Potts model are used to study the temporal change of the grain size distribution of two-phase polycrystalline materials, where both phases grow simultaneously. After a sufficiently long time, grain growth in such two-phase systems can be characterized by a self-similar scaled grain size distribution function and an associated growth law. In particular, the grain size distribution is analyzed for a broad range of second phase volume fractions and found to vary with the volume fraction such that the size distribution becomes narrower and higher peaked with decreasing volume fraction of the second phase, where particularly the normal distribution function describes the simulation results very well. On the other hand, for one-phase systems the grain size distribution is in excellent agreement with an analytical grain size distribution function based on a statistical mean-field theory of grain growth that is completely compatible with the principal physical condition of total volume conservation.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Numerical Simulation of Grain Size Distribution in Two-Phase Polycrystalline Materials
AU  - Rifa J. El-Khozondar
AU  - Dana Zӧllner
AU  - Klaus Kassner
Y1  - 2014/12/02
PY  - 2014
N1  - https://doi.org/10.11648/j.ijmsa.20140306.26
DO  - 10.11648/j.ijmsa.20140306.26
T2  - International Journal of Materials Science and Applications
JF  - International Journal of Materials Science and Applications
JO  - International Journal of Materials Science and Applications
SP  - 381
EP  - 390
PB  - Science Publishing Group
SN  - 2327-2643
UR  - https://doi.org/10.11648/j.ijmsa.20140306.26
AB  - Numerical simulations based on the Monte Carlo Potts model are used to study the temporal change of the grain size distribution of two-phase polycrystalline materials, where both phases grow simultaneously. After a sufficiently long time, grain growth in such two-phase systems can be characterized by a self-similar scaled grain size distribution function and an associated growth law. In particular, the grain size distribution is analyzed for a broad range of second phase volume fractions and found to vary with the volume fraction such that the size distribution becomes narrower and higher peaked with decreasing volume fraction of the second phase, where particularly the normal distribution function describes the simulation results very well. On the other hand, for one-phase systems the grain size distribution is in excellent agreement with an analytical grain size distribution function based on a statistical mean-field theory of grain growth that is completely compatible with the principal physical condition of total volume conservation.
VL  - 3
IS  - 6
ER  -

Copy | Download