A comparison between calculated and observed elastically induced precipitate shape transitions in a Cu-2 At. Pct Co allo
- PDF / 2,915,840 Bytes
- 13 Pages / 597 x 774 pts Page_size
- 29 Downloads / 184 Views
I.
INTRODUCTION
Two types of elastically induced precipitate shape transitions have been observed in coherent alloys with increasing particle size during growth and coarsening. The first is symmetry conserving, in that the symmetry of both the initial and final precipitate shapes are greater than or equal to that permitted by the intersection of the symmetry groups of the precipitate and matrix phases (symmetry of Wulff shape or variant morphology). I1,2] An example is the sphere-to-cube shape transition in the nickel-based superalloys, t3] The second type of shape transition is symmetry breaking.]4] In this case, the symmetry of the final precipitate shape is less than that of the Wulff shape. Sphere-to-ellipsoid and cube-to-cuboid transitions in isotropic or cubic materials are examples of such symmetry-breaking shape transitions. Cuboids are also commonly seen in the nickel-based superalloys.[5] Equilibrium precipitate shape transitions result from changes in the relative contributions of the interfacial and elastic energies to the total energy with increasing precipitate size. The particle shape that minimizes the interfacial energy is not necessarily the shape that minimizes the elastic energy. Since the ratio of the elastic to the interfacial energy scales with the precipitate size, there may be continuous or discontinuous elastically induced changes in the precipitate shape, from that which minimizes the interfacial energy at small particle sizes to that which minimizes the elastic energy at large particle sizes. [4] Earlier experimental and theoretical investigations of precipitate shape changes have been concerned with symmetry-conserving transitions between spheres and cubes ]6,7,8] or symmetry-breaking transitions within the class of ellipsoids or cuboids./4,9,1~ However, previous experimental work in the Cu-Co system tll-tnl indicates SUSUMU SATOH, formerly with the Department of Materials Science and Engineering, Carnegie Mellon University, is Manager, Technical Research Division, Kawasaki Steel Corporation, Kurashiki 712, Japan. WILLIAM C. JOHNSON, Professor, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890. Manuscript submitted August 2, 1990. METALLURGICALTRANSACTIONSA
that a larger class of precipitate shapes (octahedra and tetrakaidecahedra) may also be observable in this coherent face-centered cubic (fcc) system. Therefore, in order to extend our knowledge of symmetry-conserving shape transitions, we have undertaken both a theoretical and experimental examination of elastically induced shape transitions of Co-rich precipitates in a Cu-2 at. pet Co alloy. To do so, we present for the first time elastic energy calculations for cubical-, octahedral-, and tetrakaidecahedral-shaped particles that are correct to first order in the difference in elastic constants between precipitate and matrix phases. In Section II, we present the results of our elastic and interfacial energy calculations and, in Section III, our experimental observati
Data Loading...
