Abstract
This article identifies singular interfaces according to singularity in terms of structural defects, including dislocations and ledges. Defect singularities are defined by the elimination of one or more classes of defects, which must be present in the vicinal interfaces. In addition to the three commonly classified structural interfaces, a new type of interface—the CS-coherent interface—is introduced. Singularities in dislocation and ledge structures have been integrated in the study of orientation relationships (OR). The dislocation structures are determined through the O-lattice theory, originally proposed by Bollmann. The basic concepts of the O-lattice and related formulas from the original theory and extended studies are briefly reviewed. According to the theory, singular interfaces exhibiting singularity in the dislocation structures have been identified. An interface that is singular with respect to the interface orientation must be normal to at least one Δg, a vector connecting two reciprocal points from different lattices. An interface that is singular also with respect to the OR must obey one or more Δg parallelism rules. The selection of proper Δgs for different preferred states of interfaces are explained. Identification of singular interfaces with measurable Δgs provides a convenient and effective approach to the interpretation of the observed facets and ORs. The ambiguity about the selection of the deformation matrix (A) for the O-lattice calculation and the advantage of the O-lattice approach over the approach using the Frank–Bilby equation for the calculation of the interfacial dislocations are clarified. Limitations of the present approach and further study are discussed.
Similar content being viewed by others
Notes
Σ is the ratio of the unit cell volume of the CSL to that of a crystal lattice.
The O-lattice has been defined as a lattice of origins according to Bollmann [9, 11]. In this sense, the “O” is the abbreviation of origin. However, it can also be considered as the abbreviation of “zero” [11], as used in early publications by Bollmann, e.g. [9]. In this article, the letter O is adopted, since it is well-accepted pronunciation in the community with the O-lattice applications.
References
Howe JM (1997) Interfaces in materials. Wiley, New York
Sutton AP, Balluffi RW (1995) Interfaces in crystalline materials. Oxford University Press, Oxford
Erwin SC, Zu L, Haftel MI, Efros AL, Kennedy TA, Norris DJ (2005) Nat Lett 436(7):91
Moll N, Kley A, Pehlke E, Scheffler M (1996) Phy Rev B 54(12):8844
Che JG, Chan CT (1998) Phys Rev B 57(3):1875
Zhang W-Z, Weatherly GC (2005) Prog Mater Sci 50(2):181
Zhang M-X, Kelly PM (2009) Prog Mater Sci 54:1101
Bollmann W, Nissen H-U (1968) Acta Cryst 24A(5):546
Bollmann W (1970) Crystal defects and crystalline interfaces. Springer, Berlin
Zhang W-Z, Shi Z-Z (2011) Solid State Phenom (in press)
Bollmann W (1982) Crystal lattices, interfaces, matrices. Bollmann, Geneva
Zhang W-Z, Purdy GR (1993) Philos Mag 68A(2):291
Zhang W-Z, Purdy GR (1993) Philos Mag 68A(2):279
Tiller WA (1991) The science of crystallization: microscopic interfacial phenomena. Cambridge University Press, New York
Ye F, Zhang WZ (2002) Acta Mater 50(11):2761
Zhang M, Zhang W-Z, Ye F (2005) Metall Mater Trans 36A(7):1681
Christian JW (2002) The theory of transformation in metals and alloys, 3rd edn. Pergamon Press, Oxford, UK
Porter DA, Easterling KE (1992) Phase transformations in metals and alloys. Chapman and Hall, New York
Frank FC (1950) In: Symposium on the plastic deformation of crystalline solids, pp 150
Bilby BA (1955) In: Report on the conference on defects in crystalline solids, The Physical Society, London, pp 124
Wayman CM (1964) Introduction to the crystallography of martensitic transformations. MacMillan, New York
Bollmann W (1974) Phys Stat Solid A21:543
Zhang W-Z (2005) Appl Phys Lett 86(12):121919
Hirth JP, Lothe J (1992) Theory of dislocations, 2nd edn. Krieger Publishing Company, Malabar, FL
Qiu D, Zhang W-Z (2008) Acta Mater 56:2003
Zhang W-Z (1998) Philos Mag 78(4):913
Pitsch W (1959) Philos Mag 4(41):577
Hirsch P, Howe A, Nicholson R, Pashley DW, Whelan MJ (1977) Electron microscopy of thin crystals, 2nd edn. Robert E. Krieger Publishing Company, Malabar, FL
Duly D, Zhang WZ, Audier M (1995) Philos Mag 71A(1):187
Khachaturyan AG (1983) Theory of structural transformations in solids. Wiley, New York
Ye F, Zhang W-Z, Qiu D (2006) Acta Mater 54:5377
Zhang W-Z, Qiu D, Yang XP, Ye F (2006) Metall Mater Trans A 37:911
Gu X-F, Zhang W-Z (2010) Philos Mag 90:4503
Hall MG, Aaronson HI, Kinsma KR (1972) Surf Sci 31:257
Wu J, Zhang W-Z, Gu X-F (2009) Acta Mater 57:635
Gu X-F, Zhang W-Z (2010) Philos Mag 90:3281
Xiao SQ, Howe JM (2000) Acta Mater 48(12):3253
Kelly PM, Zhang MX (1999) Mater Forum 23:41
Zhang W-Z (1997) Scripta Mater 37(2):187
Grimmer H (1974) Scripta Metall 8(11):1221
Zhang W-Z, Ye F, Zhang C, Qi Y, Fang HS (2000) Acta Mater 48(9):2209
Hirth JP, Pond RC (1996) Acta Mater 44(12):4749
Pond R, Ma X, Chai Y, Hirth J (2007) In: Nabarro FRN, Hirth JP (eds) Dislocations in solids, vol 13. Elsevier, Amsterdam
Olson GB, Cohen M (1979) Acta Metall 27(12):1907
Babcock SE, Balluffi RW (1987) Philos Mag 55:643
Acknowledgements
Financial support from National Nature Science Foundation of China (No. 50971076) and National Basic Research Program of China (No. 2009CB623704) from Chinese Ministry of Science and Technology are gratefully acknowledged. The Authors wish to thank Professors A.P. Sutton and R.C. Pond for valuable discussions during iib 2010, to Mr. X.-F. Gu and Mr. Z.-Z. Shi for kind assistance in preparation of the manuscript, and to Mr. C. Ocier and Ms. S. Hadian for helpful proof reading, and to the reviewers for kind helps in providing many useful corrections and suggestions especially in English writing.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to W. Bollmann, the inventor of the O-lattice.
Rights and permissions
About this article
Cite this article
Zhang, WZ., Yang, XP. Identification of singular interfaces with Δgs and its basis of the O-lattice. J Mater Sci 46, 4135–4156 (2011). https://doi.org/10.1007/s10853-011-5431-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10853-011-5431-x