The Many Facets of Interface Motion.
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THE MANY FACETS OF INTERFACE MOTION. John W. Cahn Materials Science and Engineering Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899
ABSTRACT Many dynamic growth processes are shown to involve changes in more than one of the nine geometric variable that describe the geometry of a planar interface between crystals. Even simple examples illustrating changes in each one of the nine are found to involve some of the others. A generalized concept of crystal-crystal interface motion, using all nine variables, is suggested. Introduction. Interface motion is a geometric concept; the interface location at a given time is given as a surface in some coordinate system, and the velocity is derived from the variation of this position in time. But for an interface between two solid phases, if the coordinate system is fixed relative to the lattice of one of the phases, and if, as often occurs, the two phases move relative to each other during interface motion, growth rates measured using the coordinate system fixed in one solid will differ from that measured from the other. A more general definition of growth rates should give a unique result for this simple process. This symposium, entitled "Interface Dynamics and Growth," presents an opportunity to reexamine "Growth" in the broader context of "Interface Dynamics" using a complete geometric description of the interface. Stationary planar interfaces between solids require nine geometric variables for their full specification.[11 (For chiral solids a tenth dichotomous one is sometimes needed.) These can be described in a variety of ways with some variables as translations and others that are angular. The descriptions of even simple dynamic processes rarely involve only one of these variables alone, and it may be useful to recognize their interrelations. In this paper a generalized concept of interface motion that considers all of them is examined. The nine variables. There are two equivalent ways of describing the nine variables: 1. Begin by locating a Cartesian coordinate system in each crystal. Then find the rotation -Q and a translation -r, that when applied to the second crystal will bring the two coordinate systems into coincidence. Three angular variables are required for Q and three more for r. Q might be specified by the three components of the Rodriguez[2j or Euler vectors which are vectors along the rotation axes with lengths that are a measure of the angle of rotation. Equivalently Q might be given by the components of a rotation matrix that are the cosines of the angles between axes of the two systems. Q and r are
Mat. Res. Soc. Symp. Proc. Vol. 237. ©1992 Materials Research Society
usually defined in terms of the reverse process: start with the coordinate systems of the two crystal coincident, then rotate and translate one of the crystals to create the actual bicrystal. The planar surface that locates the interface is then given by three more variables, either the three intercepts on the coordinate axes of one of the crystals, or by t
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