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| THE UNDERSTANDING AND CALCULATION OF MISORIENTATION BETWEEN VARIANTS BASED ON THE PHASE TRANSFORMATION |
| WU Jing; ZHANG Wenzheng |
| Laboratory of Advanced Materials; Department of Materials Science and Engineering; Tsinghua University; Beijing 100084 |
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Cite this article:
WU Jing ZHANG Wenzheng. THE UNDERSTANDING AND CALCULATION OF MISORIENTATION BETWEEN VARIANTS BASED ON THE PHASE TRANSFORMATION. Acta Metall Sin, 2009, 45(8): 897-905.
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Abstract Misorientation between crystalline grains generated from a solid state phase transformation can be understood according to the orientation relationship (OR) between the parent and product phases, when such an OR is reproducible and unique. Due to the symmetry of the parent phase, the product phase can be related to the parent phase by various crystallographically equivalent variants of the same OR. When a pair of product particles with different variants meet at a grain boundary, the misorientation between the adjacent grains can be determined based on the OR and the symmetry of the parent phase. Misorientations for ideal rational ORs of phase transformations in some systems have been tabulated in literatures, and also, irrational ORs have been reported, with an increasing tendency because of the improvement of measurement technologies. This paper describes in details how to calculate the misorientation of different variants with a general OR. It starts from constructing the transformation matrix for the phase transformation with a rational or irrational OR, from either measurements or calculations. By applying the symmetry operators in the parent phase with the matrix manipulation, the misorientations between different variants have been derived. Since the misorentations are due to the symmetry of the parent phase, the determined values of misorientation nles between different vriants are firstly independent of the OR, but the misorientations axes are dependent on the OR. Nevertheless, the final results of the minimum rotation angles usually vary with the OR when the symmetry of the product phase is taken into consideration to derive misorientation angle/axis. The present approach elaborates the quantitative relationship between the OR of a phase transformation and the misorientation between product particles of different variants. It contributes to a better understanding of the cause of the misorientation, and provides simple formulas to determine the misorientations for a general OR. For simplicity, an example of applications of the present approach is given to an fcc→bcc phase transformation system with the N–W OR. The calculated results are consistent with thosgot from othr approaches. In additin, the nuber of indepndent variants with different ORs, such as the N–W, K–S, Bain ORs in the fcc/bcc system is analyzed, by following Cahn and Kaloji approacof uperimposing point groups of te parent and product phases. The relationship betweethe transformation matrix, the orintation relationship matrix and the correspondinmatrix in cuic systems is also discussed.
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Received: 05 January 2009
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| Fund: Supported by National Natural Science Foundation of China (No.50671051) |
| [1] Furuhara T, Maki T. Mater Sci Eng, 2001; A312: 145
[2] Gey N, Humbert M, Gautier E, Bechade J L. J Nucl Mater, 2004; 328: 137
[3] Glavicic M G, Kobryn P A, Semiatin S L. Mater Sci Eng, 2004; A385: 372
[4] Stanford N, Bate P S. Acta Mater, 2004; 52: 5215
[5] Gourgues A F, Flower H M, Lindley T C. Mater Sci Technol, 2000; 16: 26
[6] Guo Z, Morris Jr J W. Scr Mater, 2005; 53: 933
[7] Morito S, Huang X, Furuhara T, Maki T, Hansen N. Acta Mater, 2006; 54: 5323
[8] Kitahara H, Ueji R, Tsuji N, Minamino Y. Acta Mater, 2006; 54: 1279
[9] Kitahara H, Ueji R, Ueda M. Mater Charact, 2005; 54: 378
[10] Humbert M, Wagner F, Moustahfid H, Esling C. J Appl Crystallogr, 1995; 28: 571
[11] Gey N, Humbert M. J Mater Sci, 2003; 38: 1289
[12] Glavicic M G, Kobryn P A, Bieler T R, Semiatin S L. Mater Sci Eng, 2003; A346: 50
[13] Glavicic M G, Kobryn P A, Bieler T R, Semiatin S L. Mater Sci Eng, 2003; A351: 258
[14] Karthikeyan T, Saroja S, Vijayalakshmi M. Scr Mater, 2006; 55: 771
[15] Cayron C, Artaud B, Briottet L. Mater Charact, 2006; 57: 386
[16] Cayron C. Acta Crystallogr Sect, 2006; 62A: 21
[17] Morito S, Tanaka H, Furuhara T, Maki T. In: Sakata T eds, The Fourth International Conference on Recrystallization and Related Phenomena, Japan: The Japan Institute of Metals, 1999: 295
[18] Morito S, Tanaka H, Konishi R, Furuhara T, Maki T. Acta Mater, 2003; 51: 1789
[19] Zhang W Z, Purdy G R. Acta Metall, 1993; 41: 543
[20] Ye F, Zhang W Z, Qiu D. Acta Mater, 2004; 52: 2449
[21] Qiu D, Zhang W Z. In: Johnson W C, Howe J M eds, Proceeding of an International Conference on Solid–Solid Phase Transformations in Inorganic Materials, Phenix: Warrendale, 2005: 123
[22] Wayman C M. Introduction to the Crystallography of Martensitic Transformations. New York: Macmillan, 1964: 134
[23] Nolze G. Cryst Res Technol, 2008; 43: 61
[24] Bowles J S, Mackenzie J K. Acta Metall, 1954; 2: 129
[25] Wechsler M S, Lieberman D S, Read T A. Trans AIME, 1953; 197: 1503
[26] Bollmann W. Crystal Defects and Crystalline Interfaces. Berlin: Springer, 1970: 254
[27] Zhang W Z, Purdy G R. Philos Mag, 1993; 68A: 279
[28] Zhang W Z, Weatherly G C. Prog Mater Sci, 2005; 50: 181
[29] Qiu D, Zhang W Z. Philos Mag, 2003; 83A: 3093
[30] Wu J, Zhang W Z, Gu X F. Acta Mater, 2009; 57: 635
[31] Zhang W Z, Purdy G R. Philos Mag, 1993; 68A: 291
[32] Bollmann W. Crystal Lattices, Interfaces, Matrices. Geneva: Bollmann, 1982: 360
[33] Christian J W. The Theory of Transformation in Metals and Alloys. 3rd Ed., Oxford: Pergamon Press, 2002: 586
[34] Altmann S L, Bradley C J. Philos Trans R Soc, 1963; 255A: 199
[35] Frank F C. Metall Mater Trans, 1988; 19A: 403
[36] Bradley C J, Cracknell A P. The Mathematical Theory of Symmetry in Solids. Oxford: Clarendon Press, 1972: 37
[37] Cahn J W, Kalonji G M. In: Aaronson H I eds, Proceedings of an International Conference on Solid–Solid Phase Transformations, Pittsburgh: AIME Press, 1982: 3 |
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