Materials Week '97: Tuesday PM Session

Focusing on physical metallurgy and materials, Materials Week '97, which incorporates the TMS Fall Meeting, features a wide array of technical symposia sponsored by The Minerals, Metals & Materials Society (TMS) and ASM International. The meeting will be held September 14-18 in Indianapolis, Indiana. The following session will be held Tuesday afternoon, September 16.

NON-LINEAR EFFECTS IN MATERIALS SCIENCE: Session II: Phase Transformations

Session Chair: L. Brush, Dept. of Materials Science and Engineering, University of Washington, Seattle, WA 98195

MODELS OF BOUNDARY MOTION DURING PHASE TRANSFORMATIONS: Robert F. Sekerka, University Professor, Physics and Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213

Modeling of the motion of the free boundaries that separate phases during a phase transformation is an intrinsically nonlinear problem. For a few simple shapes, namely quadric surfaces, analytical solutions are possible by the method of Ivantsov or equivalent. For shapes that depart only slightly from these simple shapes, one can obtain approximate solutions by means of perturbation theory, as is done in the linear theory of morphological stability. Some weakly nonlinear results can also be obtained by carrying out perturbation theory to second and third order. This leads to information about the nature of the bifurcation at the onset of instability, as will be illustrated for perturbations of spheres and circular cylinders. For more complicated growth forms, one must resort to numerical methods or computer simulations. Examples such as the boundary integral method and the phase field model will be discussed, along with typical results. Strengths, limitations and prognoses for future improvements of these methods will be discussed. This work is supported by the National Science Foundation under grant DMR 9634056.

2:30 pm INVITED

NON-LINEAR INFLUENCE OF CRYSTAL-MELT CAPILLARITY ON DENDRITE SHAPE AND GROWTH SPEED: M.E. Glicksman, M.B. Koss, Afina Lupulescu, J.C. LaCombe, L.T. Bushnell, Materials Science and Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590

Dendritic patterns depend on the transport of heat and solute from the crystal-melt interface, and on capillarity occurring at that interface. The planforms and 3D shapes of dendrites are affected non-linearly by the material and the growth direction of the prunary axis, both of which alter the interracial energy and its anisotropy. The kinetics of dendrite growth were studied under microgravity conditions in two space flight experiments, called Isothermal Dendrite Growth Experiment (IDGE), flown by NASA in March, 1994, and in March, 1996. Results from these space flight experiments will be discussed, including the relationship of tip shape and speed to the interfacial energy and its anisotropy.

3:00 pm INVITED

NUMERICAL SIMULATION OF DENDRITIC ALLOY SOLIDIFICATION USING A PHASE FIELD METHOD: W.J. Boettinger , J.A. Warren, Metallurgy Division, Materials Science and Engineering Laboratory, NIST, Gaithersburg, MD 20899

The phase field method provides a promising approach to the description of solidification phenomena. In binary alloys, realistic microsegregation patterns produced by dendritic growth have been obtained. The phase field method enjoys much of its success because it removes the difficult numerical problem of tracking the liquid-solid interface, by giving up the notion of a mathematically sharp interface. A benefit of the diffuse interface model is that it naturally allows for topology changes. Two such changes, the coalescence of dendritic sidebranches during growth and fragmentation of dendrites during melting, are examined here.

3:30 pm BREAK

3:40 pm INVITED

ANHARMONIC CONTRIBUTIONS TO THE VIBRATIONAL ENTROPY OF PHASES OF CO₃V: B.T. Fultz and Laura Nagel, California Institute of Technology, Pasadena, CA 91125; J.L. Robertson, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831

Inelastic neutron scattering was used to measure phonon density-of-states (DOS) curves of CO₃V with the L12, hP24, and fcc phases at temperatures from 625 to 1060 C. The phonon DOS curves showed a significant dependence on temperature owing to enharmonic lattice vibrations. At low temperatures, the difference in vibrational entropies of the L12 and hP24 phases is about (0.12±0.03) kB/atom, with the vibrational entropy of the L12 phase being larger. Phonon softening causes the entropy of the hP24 phase to increase by about 0.055 kB/atom per 100°C, however. Such large enharmonic effects are important in understanding the thermodynamics of phase transformations that occur at elevated temperatures. This work was supported by the U. S. Department of Energy under contract DE-FG0396ER45572.

4:10 pm INVITED

AN ANALYSIS OF THE MORPHOLOGY AND STRUCTURE OF G.P. ZONES: J.K. Lee, Dept. of Metallurgical and Materials Engineering, Michigan Technological University, Houghton, MI 49931; H.I. Aaronson, Dept. of Materials Science and Engineering, Carnegie Mellon, University, Pittsburgh, PA 15213

Using the Discrete Atom Method to examine the elastic strain energy associated with arbitrarily-shaped, elastically-inhomogeneous, coherent precipitates, the three-dimensional morphology and structure of Guinier-Preston zones in a model system similar to Al-Cu are investigated. As the anisotropy factor, A = 2C44/(C,C,2), increases, the shape of G. P. zones changes from globules (A = 0.4) to five-atomic-layer plates (A= 3.2), and then to three-layer plates (A = 10). The internal structure is found to depend on the Cu-A1 bond length; the smaller this length, the greater the volumetric misfit strain energy. At a given value of A, if the Cu-AI bond length is taken to be similar to that of Cu-Cu, the G. P. zones remain pure fcc Cu, whereas if this length is close to that of Al-AI, the zones form an ordered crystal with tetragonal symmetry, a structure reminiscent of the theta-double-prime phase in this alloy system.

4:40 pm

CRITICAL EVENTS IN EVOLVING MICROSTRUCTURES: John W. Cahn, W. Craig Carter, Jean E. Taylor, Mathematics Department, Rutgers University, Piscataway, NJ 08540; Materials Science and Engineering Laboratory, NIST, Gaithersburg, MD 20899

Symmetry considerations are important in a Landau-type of bifurcation theory for determining some characteristic features of higher order phase transitions and spinodals in multicomponent alloys, not only for phase diagrams, but also for critical parameters that determine major differences in how the microstructures evolve. Similar symmetry considerations affect interfacial phase transitions and their effect on microstructure evolution. Phase separation in ternary alloys will be compared with the onset of edge and corner formation and faceting in evolving crystal shapes in three dimensions. Ordering of fcc to L1₂ and L1₀ will be compared to ordering of bcc to B₂ and DO₃, not only with regard to major differences in phase diagram features, but also with respect to critical aspects of their respective interfaces and two-phase and domain microstructures.

5:00 pm INVITED

ORDER PARAMETER COUPLING AND KINETICS OF PHASE TRANSFORMATIONS: L.Q. Chen, Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802

The formation and sequence of various morphological patterns during phase transformations, as a result of nonlinear coupling between different order parameters, were investigated. Cases to be discussed include coupling between (I) a composition and a long-range order parameter, (II) a composition and the transformation strain, (m) a long-range order parameter and the transformation strain, and (V) the transformation strain and an applied stress. Examples to be presented include the kinetics of precipitation of ordered intermetallic precipitates, transformation-strain-induced morphological evolution, and microstructural evolution under an external applied stress. Where possible, the morphological patterns and their evolution predicted from our computer simulations will be compared with experimental observations in practical alloy systems.

5:30 pm

UNSTEADY CONVECTION AD LAYERED STRUCTUR FORMATION IN PERITECTIC SYSTEMS: P. Mazumder, R.K. Trivedi, Ames Laboratory U. S. Department of Energy and Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011

The solidification of two phase microstructures in peritectic systems has recently received quantitative examination. Both the diffusive and boundary layer models have been developed to predict the conditions under which a layered growth can occur. Experimental studies, however, have shown that neither of these models are operative in the experiments carried out in the Pb-Bi and Sn-Cd systems. The layered structure, in fact, is an oscillatory structure that is interconnected in three dimensions. We shall show that these interconnected structures evolve due to unsteady convection in the melt. A theoretical model, which includes oscillatory convection, has been developed that shows that the oscillatory behavior of the solute profile in the liquid can give rise to the simultaneous growth of the primary and peritectic phases in which the primary phase forms as a macroscopic Christmas tree. This unique structure forms in a nonlinear regime and the results of numerical computation based on the mass, momentum, and heat transport equations will be presented. The importance of oscillatory convection will be demonstrated through experimental results in the Pb-Bi and Sn-Cd system in which the oscillatory structures disappear when the alloy is solidified in finer tubes in which convection effects are minimized.