Chance Occurrence of Orientation Relationships Between Phases in Solid Transformations and Distribution of Grain Misorie
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IN solid phase transformations there is frequently a crystallographic relationship between the product and parent phases e.g. the Kurdjumov-Sachs orientation relationship between Widmanstatten ferrite and austenite in steels) Conclusions on such orientation relationships are frequently made after only a handful of observations without considering the possibility that the orientations may have arisen fortuitously. What would be desirable would be an approach like that of Ryder, Pitsch, and Mehl 2 where an estimate of the probability of random occurrence of orientations within a certain ~h~rved proximity of a suspected special orientation is first made and shown to be too low for the observed orientations to have occurred by chance. In this paper a general method of determining the probability of an orientation falling at random within various proximities of a special orientation will be described and the results of the application of the method to some actual cases presented. Akin to orientation relationships between the lattices of product and parent phases in a solid state phase transformation is the relationship between the lattices of adjacent grains i.e. the misorientation between neighboring grains. The influence of grain misorientation on the nature and morphology of precipitates of a new phase which form on grain boundaries are established, t~ Within the larger framework of this misorientation undoubtedly the grain boundary and interphase boundary structures have their influences on the development of the grain boundary precipitates. The effects of relative lattice orientation on grain and interphase boundary structure are complex subjects (see e.g. the studies of Ashby et a l s and Rigsbee and Aaronson 6) beyond the scope of this work which will confine itself for its final task to obtaining the random proportion of grain misorientations of different degrees in a polycrystalline sample. This information will be useful e.g. in understanding the frequencies of occurrence of different grain boundary precipitate morphologies in a transformed material. H. S. FONG is Senior Lecturer, Department of Mechanical and Production Engineering, National University of Singapore, Kent Ridge, Singapore 0511, Republic of Singapore. Manuscript submitted January 26, 1981. METALLURGICAL TRANSACTIONS A
D E T E R M I N A T I O N OF R A N D O M PROBABILITY OF AN O R I E N T A T I O N RELATIONSHIP The frequency of occurrence of an orientation relationship taking as an example the Kurdjumov-Sachs orientation relationship between fcc and bcc lattices: (111)rr162[1 (1i-0)br162 [ll-0]f~r II [lll]bcc is best shown by a stereographic plot of the [ 1i-0]br162 and [111]bcc poles on a standard projection of the fcc lattice. For greater rigor since crystal orientations involve three dimensions a third direction perpendicular to these two directions, i.e. the f112]bcc direction should also be plotted, the idea being to establish whether three orthogonal directions in the bcc lattice lie within some small angle ~ of corresponding directions in
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