Orienting grains with{110} surface traces
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I.
INTRODUCTION 114-1314
T R A C E S or markings of crystallographic planes are often observed on the surfaces of crystals or grains in the form of twin boundaries, slip lines, Widmanst~itten precipitates, edge pit edges, etc. They provide for a simple, convenient, and an inexpensive means of determining the orientation of the crystals or grains. The method is extremely useful when crystal sizes are too small, as is often so in polycrystalline specimens, or when the orientation of grains of a former phase which has completely transformed is required, such as the case of austenite in steels. In the case of crystals of cubic lattice, analytical methods of determining their orientations from crystallographic traces on a surface have already been developed for {100}j and {111}24 traces, but not for {110} traces which are seen in a number of situations, e.g., as slip lines in bcc metals and edges of etch pits such as in tungsten. 7 The cleavage planes of the Ill-V semiconductor compounds such as GaAs are also {110}, and if such {110} cleavage traces can be produced by the recently reported pulsed laser method, then they provide an easy and cheap way of orienting such materials analogous to the case reported for silicon. 8 Presently, the only way of deducing the crystal orientation from {110} surface traces is the laborious Wulff net technique described by Barrett and Massalski, 9 or by reference to the combination of charts by Tsubaki and Nishiyama m which, however, employed rather broad intervals. Both methods are cumbersome and not very precise. The aim of this paper is to develop analytical equations and expressions for determining crystal orientations from data on {110} surface traces which would enable a computer to be easily programmed to do the orientation determination. The procedure then becomes rapid and as accurate as the raw data will permit, without further errors being added to the determination, as may happen in the Wulff net and Tsubaki and Nishiyama chart techniques.
II. D E V E L O P M E N T OF T H E ANALYTICAL T E C H N I Q U E Because there are six variants of {110}, a total of up to six nonparallel {110} traces may be seen on a surface. Figure 1 shows the six {110} trace directions computed for a (2 4 7) surface. At least four traces will be required for a unique H. S. FONG is Associate Professor in the Department of Mechanical and Production Engineering, National University of Singapore, Singapore 051 I, Republic of Singapore. Manuscript submitted September 20, 1985.
METALLURGICAL TRANSACTIONS A
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Fig. l - - T h e six {1101 trace directions on a (2 4 7) surface. Angles are taken anticlockwise from an arbitrary reference direction OX and are exact computed values.
surface orientation, as will be seen later. Four {110} planes producing four trace directions will always contain an orthogonal pair (say (110) and (110)). The other two planes will be either a second orthogonal pair (e.g.,
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