Description of Crystallographic Morphologies of Product Phases with Singularity and Δg Distribution

Abstract:

Product phases from various phase transformations often exhibit fascinating morphologies. Facets of unique crystallographic orientations are characteristic of the morphologies. Based on a comparison of facets in the surfaces and interfaces of crystals, this paper proposes to use singularity as the common features of facets on a crystal. While association of facets with energy singularity has been established from the Wulff construction, we defined singularity in structure with an absence of one or more types of defects common to a vicinal surface or interface. Singularity in an interfacial structure is described in terms of both ledges and dislocations. When dislocations are involved, the candidates of the singular interfaces derive mainly from the principal O-lattice planes. The orientations of these planes are defined by Δg’s, which are measurable in diffraction patterns. Singularity with respect to the orientation relationship results from further eliminating defects, which is permitted by a special arrangement of Δg’s. The candidates of singular interface confined by the arrangement of discrete Δg’s are helpful for understanding the crystallographic morphology. One example from an Mg alloy is provided to show the association of the singular interfaces with Δg’s. The effect of the potential presence of a long-range strain and kinetic effects are briefly discussed.

• Periodical: Solid State Phenomena (Volumes 172-174)
• Pages: 1096-1105
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.172-174.1096
• Online since: June 2011
• Authors: Wen Zheng Zhang, Zhang Zhi Shi
• Keywords: Crystallographic Morphology, Facet, O-Lattice, Singularity Argument, Δg Distribution

References

[1] J. W. Christian: The Theory of Transformation in Metals and Alloys, (Pergamon Press, Oxford, UK 2002).

[2] C. M. Wayman: Introduction to the crystallography of martensitic transformations, (MacMillan, New York 1964).

[3] M. -X. Zhang, and P. M. Kelly: Prog. Mater. Sci. Vol. 54 (2009), p.1101.

[4] W. -Z. Zhang, and G. C. Weatherly: Progress in Materials Science Vol. 50 (2005), p.181.

[5] A. P. Sutton, and R. W. Balluffi: Interfaces in crystalline materials, (Oxford University Press, Oxford 1995).

[6] J. M. Howe: Interfaces in materials, (John Wiley and Sons, New York 1997).

[7] D. A. Porter, and K. E. Easterling: Phase transformations in metals and alloys, (Chapman and Hall, New York 1992).

[8] L. Vitos, A. V. Ruban, H. L. Skriver, and J. Kollar: Surface Science Vol. 441 (1998), p.186.

[9] J. G. Che, and C. T. Chan: Physical Review B Vol. 57 (1998), p.1875.

[10] S. C. Erwin, L. Zu, M. I. Haftel, A. L. Efros, T. A. Kennedy, and D. J. Norris: Nature letter Vol. 436 (2005), p.91.

DOI: 10.1038/nature03832

[11] W. A. Tiller: The Science of Crystallization: Microscopic Interfacial Phenomena, (Cambridge University Press, New York 1991).

[12] T. Furuhara, J. M. Howe, and H. I. Aaronson: Acta Metallurgica et Materialia Vol. 39 (1991), p.2873.

DOI: 10.1016/0956-7151(91)90104-9

[13] T. Furuhara, T. Ogawa, and T. Maki: Philosophical Magazine Letters Vol. 72 (1995), p.175.

[14] W. Bollmann, and H. -U. Nissen: Acta Cryst. Vol. 24A (1968), p.546.

[15] W. Bollmann: Crystal lattices, interfaces, matrices, (Bollmann, Geneva 1982).

[16] A. P. Sutton, and V. Vitek: Philos. Trans. R. Soc. Lond. Vol. 309 A (1983), p.1.

[17] W. Bollmann: Crystal defects and crystalline interfaces, (Springer, Berlin 1970).

[18] W. -Z. Zhang, and G. R. Purdy: Phil. Mag. Vol. 68A (1993), p.279.

[19] W. -Z. Zhang, and G. R. Purdy: Phil. Mag. Vol. 68A (1993), p.291.

[20] F. Ye, W. -Z. Zhang, and D. Qiu: Acta Materialia Vol. 54 (2006), p.5377.

[21] D. Qiu, and W. -Z. Zhang: Acta Materialia Vol. 55 (2007), p.6754.

[22] F. Ye, and W. -Z. Zhang: Acta Materialia Vol. 54 (2006), p.871.

[23] D. Qiu, and W. -Z. Zhang: Acta Materialia Vol. 56 (2008), p. (2003).

[24] X. -F. Gu, and W. -Z. Zhang: Phil. Mag. Vol. 90 (2010), p.4503.

[25] F. Ye, and W. Z. Zhang: Acta Materialia Vol. 50 (2002), p.2761.

[26] M. Zhang, W. -Z. Zhang, and F. Ye: Metall. Mater. Trans. Vol. 36A (2005), p.1681.

[27] W. -Z. Zhang, F. Ye, C. Zhang, Y. Qi, and H. S. Fang: Acta Materialia Vol. 48 (2000), p.2209.

[28] W. -Z. Zhang: Scripta Materialia Vol. 37 (1997), p.187.

[29] H. Grimmer: Scripta Metallurgica Vol. 8 (1974), p.1221.

[30] Q. Liang, and W. T. Reynolds, Jr.: Metallurgical and Materials Transactions A (Physical Metallurgy and Materials Science) Vol. 29A (1998), p. (2059).

[31] X. -P. Yang, and W. -Z. Zhang: Poster in iib2007 (2007).

[32] M. Zhang, W. -Z. Zhang, G. -Z. Zhu, and Y. Kun: Trans. Nonferrous Met. Soc. China Vol. 17 (2007), p.1428.

[33] W. -Z. Zhang, and J. Wu: Mater. Sci. and Eng. Vol. A438-440 (2006), p.118.

[34] J. W. Cahn: Acta Metallurgica Vol. 8 (1960), p.554.

[35] J. W. Cahn, and G. Kalonji. Symmetry in solid state transformation morphology., Solid to Solid Phase Transformations. Eds. Aaronson, H. I., D. E. Laughlin, R. F. Sekerka and C. M. Wayman. Warrendale, USA: TMS, 1981. 3.

[36] M. G. Hall, H. I. Aaronson, and K. R. Kinsma: Surface Science Vol. 31 (1972), p.257.

[37] P. M. Kelly, and M. X. Zhang: Material Forum Vol. 23 (1999), p.41.