Skip to main content Skip to main navigation menu Skip to site footer

Quantifying the differences in properties between polycrystals containing planar and curved grain boundaries

  • Robert M. Forrest
  • Emanuel A. Lazar
  • Saurav Goel
  • Jonathan J. Bean


There are several methods in which grain boundaries can be made for modelling, but most produce planar (flat) grains. In this study, we investigated the difference in materials properties between polycrystalline systems comprised of planar grain and curved grain boundaries. Several structural and mechanical properties for both systems were determined. For systems with curved grain boundaries, it was found that the elastic moduli are all larger in magnitude, the excess volumes are comparable, and the plastic properties are smaller. In addition, a grain tracking algorithm was used to determine the differences in the numbers of triple junctions detected between polycrystalline systems with planar and curved grain boundaries. This can be theoretically determined and compared to a simple model system. We find that planar systems of grain boundaries possess significantly more triple junctions than systems of curved grain boundaries by a factor of two. There are also systematic differences between the two types of a system when they undergo grain growth, when there is an anomalous close-packed hexagonal phase which grows in the system of planar grain boundaries.



  1. Ashby, M. F., & Jones, D. R. (2011). Engineering materials 1: an introduction to properties, applications and design (Vol. 1): Elsevier.
  2. Ashby, M. F. J. M. I. (1994). Materials selection in mechanical design. 86, 475-475.
  3. Barber, C. B., Dobkin, D. P., & Huhdanpaa, H. J. A. T. o. M. S. (1996). The quickhull algorithm for convex hulls. 22(4), 469-483.
  4. Bean, J. J., & McKenna, K. P. J. A. M. (2016). Origin of differences in the excess volume of copper and nickel grain boundaries. 110, 246-257.
  5. Bean, J. J., Saito, M., Fukami, S., Sato, H., Ikeda, S., Ohno, H., . . . McKenna, K. P. J. S. r. (2017). Atomic structure and electronic properties of MgO grain boundaries in tunnelling magnetoresistive devices. 7(1), 1-9.
  6. Carlton, C., & Ferreira, P. J. A. M. (2007). What is behind the inverse Hall–Petch effect in nanocrystalline materials? , 55(11), 3749-3756.
  7. Cheng, Y., Ma, E., & Sheng, H. J. P. r. l. (2009). Atomic level structure in multicomponent bulk metallic glass. 102(24), 245501.
  8. Cheng, Y., & Ma, E. J. P. i. m. s. (2011). Atomic-level structure and structure–property relationship in metallic glasses. 56(4), 379-473.
  9. Gruber, J., Lim, H., Abdeljawad, F., Foiles, S., & Tucker, G. J. J. C. M. S. (2017). Development of physically based atomistic microstructures: the effect on the mechanical response of polycrystals. 128, 29-36.
  10. Gruber, J., Zhou, X., Jones, R., Lee, S., & Tucker, G. (2017). Molecular dynamics studies of defect formation during heteroepitaxial growth of InGaN alloys on (0001) GaN surfaces. Journal of Applied Physics, 121(19), 195301.
  11. Hall, E. J. P. o. t. P. S. S. B. (1951). The deformation and ageing of mild steel: III discussion of results. 64(9), 747.
  12. Hirth, J. J. M. T. A. (1985). A brief history of dislocation theory. 16(12), 2085-2090.
  13. Jones, D. R., & Ashby, M. F. (2012). Engineering materials 2: an introduction to microstructures and processing: Butterworth-Heinemann.
  14. Kambe, K. J. P. R. (1955). Cohesive energy of noble metals. 99(2), 419.
  15. Kelchner, C. L., Plimpton, S., & Hamilton, J. (1998). Dislocation nucleation and defect structure during surface indentation. Physical Review B, 58(17), 11085.
  16. Lazar, E. A., Mason, J. K., MacPherson, R. D., & Srolovitz, D. J. J. A. M. (2011). A more accurate three-dimensional grain growth algorithm. 59(17), 6837-6847.
  17. MacPherson, R. D., & Srolovitz, D. J. J. N. (2007). The von Neumann relation generalized to coarsening of three-dimensional microstructures. 446(7139), 1053-1055.
  18. Mason, J. K., Lazar, E. A., MacPherson, R. D., & Srolovitz, D. J. J. P. R. E. (2015). Geometric and topological properties of the canonical grain-growth microstructure. 92(6), 063308.
  19. Mendelev, M., Kramer, M., Ott, R., Sordelet, D., Yagodin, D., & Popel, P. J. P. M. (2009). Development of suitable interatomic potentials for simulation of liquid and amorphous Cu–Zr alloys. 89(11), 967-987.
  20. Mendelev, M., Sordelet, D., & Kramer, M. J. J. o. A. P. (2007). Using atomistic computer simulations to analyze x-ray diffraction data from metallic glasses. 102(4), 043501.
  21. Orowan, E. J. Z. P. (1934). The crystal plasticity. III: about the mechanism of the sliding. 89, 634-659.
  22. Panzarino, J. F., & Rupert, T. J. J. J. (2014). Tracking microstructure of crystalline materials: a post-processing algorithm for atomistic simulations. 66(3), 417-428.
  23. Pearson, W. B. (2013). A handbook of lattice spacings and structures of metals and alloys: International series of monographs on metal physics and physical metallurgy, Vol. 4 (Vol. 4): Elsevier.
  24. Plimpton, S. (1995). Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of Computational Physics, 117, 1-19.
  25. Prakash, A., Hummel, M., Schmauder, S., & Bitzek, E. J. M. (2016). Nanosculpt: A methodology for generating complex realistic configurations for atomistic simulations. 3, 219-230.
  26. Prakash, A., Weygand, D., & Bitzek, E. J. I. J. o. P. (2017). Influence of grain boundary structure and topology on the plastic deformation of nanocrystalline aluminum as studied by atomistic simulations. 97, 107-125.
  27. Saylor, D. M., El Dasher, B. S., Rollett, A. D., & Rohrer, G. S. J. A. M. (2004). Distribution of grain boundaries in aluminum as a function of five macroscopic parameters. 52(12), 3649-3655.
  28. Saylor, D. M., Morawiec, A., & Rohrer, G. S. J. A. m. (2003). The relative free energies of grain boundaries in magnesia as a function of five macroscopic parameters. 51(13), 3675-3686.
  29. Stukowski, A. (2010). Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modelling and Simulation in Materials Science and Engineering, 18(1).
  30. Sutton, A. P. J. M. o. t. P., & Materials, C. o. (1995). Interfaces in crystalline materials. 414-423.
  31. Tschopp, M., & McDowell, D. J. P. M. (2007). Structures and energies of Σ 3 asymmetric tilt grain boundaries in copper and aluminium. 87(22), 3147-3173.
  32. Xu, T., & Li, M. J. P. M. (2010). Geometric methods for microstructure rendition and atomic characterization of poly-and nano-crystalline materials. 90(16), 2191-2222.
  33. Zhao, B., Verhasselt, J. C., Shvindlerman, L., & Gottstein, G. J. A. m. (2010). Measurement of grain boundary triple line energy in copper. 58(17), 5646-5653.
  34. Zhao, L., Chan, K. C., & Chen, S. J. I. (2018). Atomistic deformation mechanisms of amorphous/polycrystalline metallic nanolaminates. 95, 102-109.

How to Cite

Forrest, R. M. ., Lazar, E. A. ., Goel, S. ., & Bean, J. J. . (2022). Quantifying the differences in properties between polycrystals containing planar and curved grain boundaries. Nanofabrication, 7, 11–23.


112 3


Search Panel


Article Details

Most Read This Month


Copyright (c) 2022 Robert M. Forrest, Emanuel A. Lazar, Saurav Goel, Jonathan J. Bean

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.