Orientation Mapping: 1987 MRS Fall Meeting Von Hippel Award Lecture
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I must support the judgment of the Materials Research Society in naming its principal award after von Hippel. His early work was on dielectrics, and that is the area in which my own introduction to materials science was made. In fact, I habitually claim that one of the inventors and fathers of the subject was E.B. Moullin, Reader in Electrical Engineering at Oxford and later Professor of Electrical Engineering at Cambridge. In 1933 he approached my chemistry tutor, Sidgwick, saying "I have this man Willis Jackson coming to do a D.Phil, with me. He knows how to measure dielectric loss. I think that if I can put a physical chemist to work alongside him we might make that cease to be just an engineering parameter to be measured and come to know what causes it—and then perhaps design new materials which are better." Sidgwick nominated me as the physical chemist, and as far as I am concerned that is where the subject of materials science begins. My subject is how you should display the statistics of orientations of polycrystals. For this subject I have several heroes from the past. They are Euler, of course, Rodrigues, Cayley and Klein. Of these the most unjustly neglected is Olinde Rodrigues, which is something I have only come to know in comparatively recent years. The whole subject is one to which I have returned on and off, learning a little more each time, since it was first put to me as a problem by C.G. Dunn just about 30 years ago. It was on one of my more recent returns to the subject that I came to know of and admire the work of Olinde Rodrigues by noticing some disparaging remarks about the Rodrigues parameters in Whittaker's Analytical Dynamics (1904) and deciding to find out what they were. Dunn had gone to the trouble of using a finely collimated x-ray beam to determine the orientations of 200 grains MRS BULLETIN/MARCH 1988
Orientation Mapping
in a steel specimen by back-reflection Laue diffraction. He asked my advice about how to plot these results as a map. He appreciated, of course, that since it takes three parameters to define the orientation of a rigid body in three dimensions, it would have to be a threedimensional map. The question was what would be the best mapping coordinates to use, and he proposed to use the Eulerian angles. I told him not to. What I did not know until many years later was that had he been able to put the question to Euler himself, he would have received the same answer. The representation of orientations and the representation of rotations are, of course, essentially one problem. Given a representation of rotations, we obtain a representation of orientations by adding to it the specification of one standard reference orientation. Euler presented the Eulerian angles for representation of rotations in his paper "Formulae Generales" (1775). For a crystallographer they are most simply specified as the settings of a three-circle goniometer, and the reference orientation is that for which these settings are (0, 0, 0). There are two grave disadvantages to the use of these mapping
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