Abstract
We consider periodic good matching bands (which are centered at the O-lines) as the characteristic feature of the structures in irrational singular interfaces in the primary preferred state. This feature is shared by various structures described by different models for irrational singular interfaces, and it can be used to consolidate different descriptions. We have made a quantitative analysis on the distribution of good matching zones (GMZs) in a relationship with plane matching geometry. This analysis emphasizes that matching of one set of principal planes does not represent good lattice matching. Good lattice matching is possible only at the locations of 0-d intersections, where three sets of nonlinearly related Moiré planes intersect. Matching of one or more sets of principal planes in an interface usually implies the possible presence of periodic GMZs in the interface. The analysis also explains why and in what condition a dislocation configuration can be described by the traces of Moiré planes. The distribution of exact 0-d intersections can be determined based on the O-lattice theory. The approximate 0-d intersections can be used for determining a possible interfacial structure when periodic O-elements do not exist.
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W.-Z. Zhang and G.C. Weatherly: Progr. Mater. Sci., 2005, vol. 50, pp. 181–292.
J.W. Christian: The Theory of Transformation in Metals and Alloys, 3rd ed., Pergamon Press, Oxford, United Kingdom, 2002, pp. 106–377.
T. Furuhara, J.M. Howe, and H.I. Aaronson: Acta Metall. Mater., 1991, vol. 39, pp. 2873–86.
G.C. Weatherly, A. Perovic, N.K. Mukhopadhyay, D.J. Lloyd, and D.D. Perovic: Metall. Mater. Trans. A, 2001, vol. 32A, pp. 213–18.
C.P. Luo and U. Dahmen: Acta Metall. Mater., 1998, vol. 46, pp. 2063–81.
S. Das, J.M. Howe, and J.H. Perepezko: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 1623–34.
H. Jiao, M. Aindow, and R. Pond: Phil. Mag., 2003, vol. 83, pp. 1867–87.
V. Radmilovic, R. Kilaas, U. Dahmen, and G.J. Shiflet: Acta Mater., 1999, vol. 47, pp. 3987–97.
W.-Z. Zhang and G.R. Purdy: Acta Metall. Mater., 1993, vol. 41, pp. 543–51.
F. Ye, W.-Z. Zhang, and D. Qiu: Acta Mater., 2004, vol. 52, pp. 2449–60.
H.I. Aaronson and J.K. Lee: in Lecture on the Theory of Phase Transformation, H.I. Aaronson, ed., TMS, Warrendale, PA, 1999, pp. 165–229.
M.G. Hall, H.I. Aaronson, and K.R. Kinsman: Surf. Sci., 1972, vol. 31, pp. 257–74.
R.C. Ecob and B. Ralph: Acta Metall., 1981, vol. 29, pp. 1037–46.
K.M. Knowles and D.A. Smith: Acta Cryst., 1982, vol. A38, pp. 34–40.
C.P. Luo and G.C. Weatherly: Acta Metall., 1987, vol. 35, pp. 1963–72.
G.C. Weatherly and W.-Z. Zhang: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1865–74.
W.-Z. Zhang and G.R. Purdy: Phil. Mag., 1993, vol. 68A, pp. 291–303.
Q. Liang and W.T. Reynolds, Jr.: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 2059–72.
P.M. Kelly and M.-X. Zhang: Mater. Forum, 1999, vol. 23, pp. 41–62.
R.C. Pond: in Dislocations in Solids, F.R. N. Nabarro, ed., North-Holland, Amsterdam, 1989, vol. 8, pp. 1–66.
J.F. Nie and B.C. Muddle: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2381–90.
J.M. Howe, W.T. Reynolds, Jr., and V.K. Vasudevan: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2391–412.
W.T. Reynolds, Jr., J. F. Nie, W.-Z. Zhang, J.M. Howe, H.I. Aaronson, B.C. Muddle, and G. R. Purdy: Scripta Mater., 2003, vol. 49, pp. 405–09.
W.-Z. Zhang and G.R. Purdy: Mater. Sci. Forum, 1993, vols. 126–128, pp. 563–66.
R.W. Balluffi and T. Schober. Scripta Metall., 1972, vol. 6, pp. 697–706.
W. Bollmann: Crystal Lattices, Interfaces, Matrices, Bollmann, Geneva, 1982, pp. 173–200.
W.-Z. Zhang and G.R. Purdy: Phil. Mag., 1993, vol. 68A, pp. 279–90.
F.C. Frank: Acta Metall., 1953, vol. 1, pp. 15–21.
J.S. Bowles and J.K. Mackenzie: Acta Metall., 1954, vol. 2, pp. 129–37.
C.M. Wayman: Introduction to the Crystallography of Martensitic Transformations, MacMillan, New York, NY, 1964, pp. 112–22.
U. Dahmen: Ultramicroscopy, 1989, vol. 30, pp. 102–15.
A.G. Khachaturyan: Theory of Structural Transformations in Solids, John Wiley & Sons, New York, NY, 1983, pp. 1–25.
W. Bollmann: Crystal Defects and Crystalline Interfaces, Springer, Berlin, 1970, pp. 1–254.
P.H. Pumphrey: Scripta Metall., 1972, vol. 6, pp. 107–14.
P.H. Pumphrey: Scripta Metall., 1973, vol. 7, pp. 893–98.
G. Baro and H. Gleiter: Acta Metall., 1973, vol. 21, pp. 1405–08.
J.F. Nie: Acta Mater., 2004, vol. 52, pp. 795–807.
R.W. Balluffi and A.P. Sutton: Mater. Sci. Forum, 1996, vols. 207–209, pp. 1–12.
U. Dahmen: Acta Metall., 1982, vol. 30, pp. 63–73.
F. Ye and W.-Z. Zhang: Acta Mater., 2002, vol. 50, pp. 2761–77.
M. Zhang, W.-Z. Zhang, and F. Ye: Metall. Mater. Trans. A, 2005, vol. 36A.
J.M. Howe, H.I. Aaronson, and J.P. Hirth: Acta Mater., 2000, vol. 48, pp. 3977–84.
W. Lojkowsk and H.-J. Fecht: Progr. Mater. Sci., 2000, vol. 45, pp. 339–568.
W.-Z. Zhang: Appl. Phys. Let., 2005, vol. 86, p. 121919.
D. Qiu and W.-Z. Zhang: Phil. Mag., 2003, vol. 83, pp. 3093–3116.
T. Furuhara, K. Wada, and T. Maki: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 1971–78.
J.K. Chen, G. Chen, and W.T. Reynolds, Jr.: Phil. Mag., 1998, vol. 78A, pp. 405–22.
U. Dahmen: Scripta Metall., 1981, vol. 15, pp. 77–81.
G.J. Shiflet and J.H. Van der Merwe: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1895–903.
D. Qiu, Y.-X. Shen, and W.-Z. Zhang: Tsinghua University, Beijing, China, unpublished research, 2004.
U. Dahmen: Scripta Metall., 1987, vol. 21, pp. 1029–34.
J.M. Howe and D.A. Smith: Acta Metall. Mater., 1992, vol. 40, pp. 2343–50.
D. Qiu and W.-Z. Zhang: Scripta Mater., 2005, vol. 52, pp. 683–86.
D. Qiu and W.-Z. Zhang: Acta Mater., in press.
J.P. Hirth and R.C. Pond: Acta Metall., 1996, vol. 44, pp. 4749–63.
J.M. Rigsbee and H.I. Aaronson: Acta Metall., 1979, vol. 27, pp. 351–63.
M.G. Hall, J.M. Rigsbee, and H.I. Aaronson: Acta Metall., 1986, vol. 34, pp. 1419–31.
T. Furuhara and H.I. Aaronson: Acta Metall. Mater., 1991, vol. 39, pp. 2857–72.
J.H. Van der Merwe, G.J. Shiflet, and P.M. Stoop: Metall. Trans. A, 1991, vol. 22A, pp. 1165–75.
J.H. Van der Merwe and G.J. Shiflet: Acta Metall. Mater., 1994, vol. 42, pp. 1173–87.
F. Ye: Ph.D. Thesis, Tsinghua University, Beijing, China, 2004.
R.W. Balluffi, A. Brokman, and A.H. King: Acta Metall., 1982, vol. 30, pp. 1453–70.
P. Li, J.M. Howe, and W.T. Reynolds, Jr.: Acta Mater., 2004, vol. 52, pp. 239–48.
D.A. Smith and R.C. Pond: Int. Met. Rev., 1976, vol. 21, pp. 61–74.
W.-Z. Zhang: Proc. Microscopy and Microanalysis, G.W. Bailey, M.H. Ellisman, R.A. Hennigar, and N.J. Zaluzec, eds., MSA, New York, 1995, pp. 100–01.
W.-Z. Zhang and G.R. Purdy: Scripta Metall., 1997, vol. 37, pp. 543–48.
W.-Z. Zhang: Ph.D. Thesis, McMaster University, Hamilton, Canada, 1991.
P. Hirsch, A. Howie, R. Nicholson, D.W. Pashley, and M.J. Whelan: Electron Microscopy of Thin Crystals, Robert E. Krieger, Malabar, FL, 1977, p. 169.
W.-Z. Zhang, V. Perovic, A. Perovic, G.C. Weatherly, and G.R. Purdy: Acta Mater., 1998, vol. 46, pp. 3443–53.
W.-Z. Zhang: Phil. Mag., 1998, vol. 78A, pp. 913–33.
C.P. Luo, U. Dahmen, and K.H. Westmacott: Acta Metall. Mater., 1994, vol. 42, pp. 1923–32.
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This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee.
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Zhang, W.Z., Qiu, D., Yang, X.P. et al. Structures in irrational singular interfaces. Metall Mater Trans A 37, 911–927 (2006). https://doi.org/10.1007/s11661-006-0065-3
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DOI: https://doi.org/10.1007/s11661-006-0065-3