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Influence of faceting upon the equilibrium shape of nuclei at grain boundaries. II. Three-dimensions
Vol. 9, No. 4
ABSTRACTS OF ARTICLES TO APPEAR IN ACTA MET
representative conditions of relative interfacial free energy; AG* is found to be significantly less at small values of this angle under most circumstances, and also to be smaller at puckered than at planar grain boundaries, though often by negligible amounts. 6.
INFLUENCE OF FACETING UPON THE EOUILIBRIUM SHAPE OF NUCLEI AT GRAIN BOUNDARIES. II. THREEDIMENSIONS Jong K. Lee & H. I. Aaronson Department of Metallurgical Engineering Michigan Technological University Houghton, Michigan 49931 Received May 4, 1974 Revised October 24, 1974
Based on the exact equilibrium shapes of nuclei at a grain goundary in the presence of a facet at one orientation of the nucleus: matrix boundary determined in the twodimensional case, three-dimensional nucleus shapes are studied under the same conditions. These shapes are investigated under the assumptions that the grain boundary is constrained to remain planar and that the grain boundary puckers in order to allow equilibrium junction angles with the nucleus to be more closely approached. At planar grain boundaries, the "upper" portion of the nucleus is taken to be a faceted spherical cap, as delineated by a modified version of the Wulff construction. For the shape of the "lower" or unfaceted portion of the nucleus, a second-order non-linear elliptic partial differential equation was derived and numerically solved. In the case of the pucker mechanism, the entire nucleus is considered as a faceted spherical cap. A catenoid surface, which is a minimal surface, is used to calculate the additional grain boundary area introduced by the pucker. Calculation of the free energy of activation for nucleation, AG*, indicates that planar boundary mechanism is favored when ~, the
xiii
tilt angle between the facet and the grain boundary plane, exceeds 18 ° x ~cl (where ~cl = smallest at which the facet touches the grain boundary), while the pucker mechanism has a lower AG* when ~ is smaller. AG* increases rapidly with ~, particularly when the relative specific interfacial energy of the facet is small. Hence nucleation at a disordered grain boundary should normally occur with pronounced preference parallel to only one of n crystallographically equivalent habTt planes.
7.
CROSS-SLIP ON [iI0] PLANES IN ALUMINUM SINGLE CRYSTALS COMPRESSED ALONG ~I00> AXIS Roger Le Hazif & Jean-Paul Poirier Section de Recherches de Metallurgie Physique Centre D'Etudes Nuclearies De Saclay, France Received June 12, 1974
In order to investigate the {114 slip appears. Coarse bundles of slip lines fill the whole sample. The average consolidation is low. - State III: The consolidation increases again. All slip systems probably participate in the deformation. -
The stress dll 0 is thermally activated. The activation energy for E at constant d l l O is close to 28 kCal/mole. The results are interpreted in
ABSTRACTS OF ARTICLES TO APPEAR IN ACTA MET
representative conditions of relative interfacial free energy; AG* is found to be significantly less at small values of this angle under most circumstances, and also to be smaller at puckered than at planar grain boundaries, though often by negligible amounts. 6.
INFLUENCE OF FACETING UPON THE EOUILIBRIUM SHAPE OF NUCLEI AT GRAIN BOUNDARIES. II. THREEDIMENSIONS Jong K. Lee & H. I. Aaronson Department of Metallurgical Engineering Michigan Technological University Houghton, Michigan 49931 Received May 4, 1974 Revised October 24, 1974
Based on the exact equilibrium shapes of nuclei at a grain goundary in the presence of a facet at one orientation of the nucleus: matrix boundary determined in the twodimensional case, three-dimensional nucleus shapes are studied under the same conditions. These shapes are investigated under the assumptions that the grain boundary is constrained to remain planar and that the grain boundary puckers in order to allow equilibrium junction angles with the nucleus to be more closely approached. At planar grain boundaries, the "upper" portion of the nucleus is taken to be a faceted spherical cap, as delineated by a modified version of the Wulff construction. For the shape of the "lower" or unfaceted portion of the nucleus, a second-order non-linear elliptic partial differential equation was derived and numerically solved. In the case of the pucker mechanism, the entire nucleus is considered as a faceted spherical cap. A catenoid surface, which is a minimal surface, is used to calculate the additional grain boundary area introduced by the pucker. Calculation of the free energy of activation for nucleation, AG*, indicates that planar boundary mechanism is favored when ~, the
xiii
tilt angle between the facet and the grain boundary plane, exceeds 18 ° x ~cl (where ~cl = smallest at which the facet touches the grain boundary), while the pucker mechanism has a lower AG* when ~ is smaller. AG* increases rapidly with ~, particularly when the relative specific interfacial energy of the facet is small. Hence nucleation at a disordered grain boundary should normally occur with pronounced preference parallel to only one of n crystallographically equivalent habTt planes.
7.
CROSS-SLIP ON [iI0] PLANES IN ALUMINUM SINGLE CRYSTALS COMPRESSED ALONG ~I00> AXIS Roger Le Hazif & Jean-Paul Poirier Section de Recherches de Metallurgie Physique Centre D'Etudes Nuclearies De Saclay, France Received June 12, 1974
In order to investigate the {114
The stress dll 0 is thermally activated. The activation energy for E at constant d l l O is close to 28 kCal/mole. The results are interpreted in