Institute of Metals Division - Relative Energies of Grain Boundaries in Silicon Iron

IN recent investigations1. a data on relative grain boundary energies in silicon iron have been obtained. The present investigation is a continuation of this work along similar lines for the purpose of obtaining additional information on boundary energies. One aim has been to extend the data for a (110) series, which was formerly studied,' to small differences in orientation, since a recent theory3,4 based on a dislocation model of grain boundaries predicts a E. ? (A-ln ? )* form of energy curve for small differences in orientation. Another aim has been to provide data for a (100) series—all grains having (100) planes parallel with the surface of sheet speci-mens—and to compare the results with the predicted form of energy curve. Finally, information on the nature of approach to equilibrium conditions was to be obtained through observations on the movements of grain boundaries. Recently published papers2,3,5 have treated the mathematical problem of expressing equilibrium conditions for grain boundaries for the general case when boundary energy depends upon boundary orientation. The equilibrium equations, which relate equilibrium angles and grain boundary -free energies, contain additional terms that express the variation of energy with boundary rotation. It has been necessary in the present investigation, however, to neglect these additional terms since no data for their evaluation were available. Dropping the additional terms leads to the following approximate equations which were used: E12/sin ?3 = E18/sin?2 =E28/sin?1 or those of the form: E28 + E13 cos ?3 + E12 cos ?2 = 0 Experimental Procedure Except for sample F1, all specimens were made from two lots of silicon iron called C and L respectively. The compositions of these are listed in table I. In the preparation of 12 three-grain specimens for the present investigation, a controlled grain growth technique, which has been described previously,' was used. After preparation, the specimens were notched at the boundaries to shorten them as a means of providing more rapid approach to equilibrium in the anneals. Initial grain boundary angles were determined from micrographs taken at X500. Seven anneals, totaling about two days at 1300°C and two to four days at 1400°C, were run in an atmosphere of pure dry argon as described in a previous paper.' Boundary changes generally could be followed without metallographic surface preparation, because thermal etching occurred during the anneals. These observations indicated angle changes of as much as 35" in some instances, with the major changes occurring during the first anneal. Annealing was discontinued when the angles reached stationary values. Fig. 1 gives a schematic diagram for purposes of defining crystallographic and boundary directions for three grains with common plane parallel with the sheet. Differences in orientations (expressed by A) are the angles between [00l] directions. They can be calculated with the aid of the ?'s. The grain boundary angles can be calculated from the w'S. Results Results are given in table 11. Types of crystal-lographic planes refer to those parallel with the sheet. Orientations are given in terms of [00l] direc-tions as shown in fig. 1. Except for grain 3 of specimen H6, which was unintentionally tilted 7" out of a (100) plane, all grains generally were within 1" or 2" of the plane specified. The directions of boundaries were measured generally to within 1" on both upper and lower surfaces, and the average direc- tions were determined for use in calculating the grain boundary angles. Variations in grain boundary directions refer to deviations from average directions. Boundaries near the junction point for all specimens generally were very close to perpendicu-