M.E. Glicksman

Ostwald ripening during liquid phase sintering—Effect of volume fraction on coarsening kinetics

Phase coarsening, also termed Ostwald ripening, is generally thought to be a slow, diffusion-controlled process which occurs subsequent to phase separation under extremely small under- or over-saturation levels. The theory due to Lifshitz, Slyozov, and Wagner (LSW), which predicts the coarsening kinetics and the particle distribution function, are applicable todilute systems only, in which particle-particle interactions are unimportant. Most liquid phase sintered systems, however, have large enough volume fractions of the dispersed phase to violate the essential assumptions of LSW theory. Recent progress will be described on simulating Ostwald ripening in randomly dispersed, high volume fraction systems. A fast algorithm for solving the multiparticle diffusion problem (MDP) will be described, permitting simulation of coarsening dynamics by cyclic time-stepping and updating the diffusion solution for large random particle arrays. The rate constants, controlling the growth of the average particle, and the particle distribution functions were obtained by numerical simulations up to a volume fraction of 0.55. A new statistical mean field theory has now been developed which reproduces the MDP simulation data accurately, and finally makes clear how the linear mean-field approximations employed by LSW theory must be modified to describe real systems. The predictions of the mean field are found to compare favorably with experimental measurements made over a wide range of volume fraction solid of the kinetics of Ostwald ripening in liquid phase sintered Fe-Cu alloys. The new theory provides a comprehensive approach to understanding microstructural coarsening in liquid phase sintered systems.

High-confidence measurement of solid/liquid surface energy in a pure material

Abstract A new method for measuring solid/liquid surface energies, with a total systematic and random error of well under 10%, is described. The surface energies are derived from measurements of grain-boundary grooves in solid/liquid interfaces which are maintained in shallow temperature gradients. The gradients are established by an axial heater wire in a cylindrical specimen chamber. Applying the method to highly-purified succinonitrile, a solid/liquid surface energy of 8·94±0·5 erg/cm2 was determined. This corresponds to 37% of the heat of fusion per surface molecule.

Kinetics of phase coarsening in dense systems

Diffusion-limited coarsening is formulated as a statistical description of the evolving particle size distribution. Diffusional interactions among dispersed particles are accounted for using a statistical field cell associated with each particle size class. The field cells correlate particle volumes with an averaged growth rate and the corresponding volume of the matrix phase associated with a particles transport field. The particle and matrix volumes obey a linear affine transformation, derived here from self-similar dynamics. The coarsening kinetics are determined by adding two global constraints on the distributional representation of the microstructure, which specify the volume fraction and critical (zero-growth) particle size in terms of explicit spatial and ensemble averages. Comparison of the theoretically predicted coarsening rates with those obtained from liquid-phase sintering experiments in binary alloys show agreement over a wide range of phase fractions.

Analysis of 3-D network structures

Integral geometry and topology are applied to the problem of space-filling in irregular network structures such as liquid and amorphous metals, polycrystals, and foams. The theory developed is based on representing cells in irregular polyhedral networks as “average -hedra”, where equals the number of faces between contacting neighbours. Average -hedra satisfy, at their edges and vertices, the networks angular averages for triple lines and quadrajunctions, as dictated by topology. Although they themselves are incapable of filling space as a contiguous network, average -hedra act as high-symmetry “proxies” for analysing the average metric, energetic, and kinetic behaviour of real irregular network cells of equivalent topologies. The analysis developed here accurately predicts the average behaviour of 3-dimensional network structures, such as polycrystals and foams, and may also be applicable to biological tissues. This approach should prove especially useful for constructing quantitative descriptions of ev...Integral geometry and topology are applied to the problem of space-filling in irregular network structures such as liquid and amorphous metals, polycrystals, and foams. The theory developed is based on representing cells in irregular polyhedral networks as “average -hedra”, where equals the number of faces between contacting neighbours. Average -hedra satisfy, at their edges and vertices, the networks angular averages for triple lines and quadrajunctions, as dictated by topology. Although they themselves are incapable of filling space as a contiguous network, average -hedra act as high-symmetry “proxies” for analysing the average metric, energetic, and kinetic behaviour of real irregular network cells of equivalent topologies. The analysis developed here accurately predicts the average behaviour of 3-dimensional network structures, such as polycrystals and foams, and may also be applicable to biological tissues. This approach should prove especially useful for constructing quantitative descriptions of evolving microstructures. The analytic relations derived here can provide precise benchmarks to test numerical simulations of the properties of constructible (irregular) network cells, and can guide future quantitative experiments and numerical modelling.

Determination of the mean solid-liquid interface energy of pivalic acid

Abstract A high-confidence solid-liquid interfacial energy is determined for an anisotropic material. A coaxial composite having a cylindrical specimen chamber geometry provides a thermal gradient with an axial heating wire. The surface energy is derived from measurements of grain boundary groove shapes. Applying this method to pivalic acid, a surface energy of 2.84 erg/cm2 was determined with a total systematic and random error less than 10%. The value of interfacial energy corresponds to 24% of the latent heat of fusion per molecule.

Simulations of experimentally observed dendritic growth behavior using a phase-field model

An anisotropic phase-field model is used to simulate numerically dendritic solidification for a pure material in two dimensions. The phase-field model has been formulated to include the effect of four-fold anisotropy in both the surface energy and interfacial kinetics. The computations presented here are intended to model qualitatively experimentally observed dendritic solidification morphology. In particular, we simulate the growth into an undercooled melt of two dendrite tips which have formed as the result of a splitting event. The computation exhibits the competition between the two growing dendrite branches and the eventual predominance of one branch. Also, we simulate the effect of time-periodic forcing of an isolated dendrite tip on the mechanism of sidebranch formation. Although it is not yet computationally feasible to adequately verify convergence of the phase-field solutions, the phase-field simulations presented show many of the qualitative features observed in dendritic growth experiments.

Effects of crystal-melt interfacial energy anisotropy on dendritic morphology and growth kinetics

Abstract Morphological and kinetic studies of succinonitrile, a BCC crystal with a low (0.5%) anisotropy and pivalic acid, and FCC crystal with relatively large (5%) anisotropy in solid-liquid interfacial energy, show clearly that anisotropy in the solid-liquid interfacial energy does not affect the tip radius-velocity relationship, but has a profound influence on the tip region and the rate of amplification of branching waves. Anisotropy of the solid-liquid interfacial energy may be one of the key factors by which the microstructural characteristics of cast structures reflect individual material behavior, especially crystal symmetry.

Dendritic growth kinetics and structure II. Camphene

Abstract Camphene is an organic “plastic crystal” which grows dendritically under the appropriate solute or temperature gradient conditions. This study provides the first reported body of such kinetic data for this material. Camphene was previously believed to be cubic; however, shape analysis of droplets in a solid matrix has shown it to be tetragonal. Results of dendrite radius and velocity measurements are presented, and compared to a combination of Ivantsovs transport theory and Langer and Muller-Krumbhaars stability theory. We show that, despite the crystallographic structure of camphene, its dendritic growth kinetics closely approximate theoretically predicted behavior.

Dendritic grown kinetics and structure I. Pivalic acid

Abstract Pivalic acid (PVA) is an organic, fcc, “plastic crystal” which has a relatively high degree of interfacial energy anisotropy. This study of PVA shows that dendrite growth velocity multiplied by the square of the tip radius is not constant with supercooling. The crystal growth kinetics of PVA differ, in this respect, from both previously observed succinonitrile behavior and theoretical scaling laws. This material displays a linear increase in υ r 2 with supercooling. We consider the possible effect of interfacial energy anisotropy, buoyancy-driven convection, and molecular polarity, as it affects interfacial attachment, on the dendritic growth behavior of PVA.

Isothermal Dendritic Growth A Proposed Microgravity Experiment

Dendritic growth is one of the most common forms of crystallization in supercooled metals or al-loys. The isothermal dendritic growth experiment (IDGE) is a microgravity flight-oriented scientific experiment aimed at testing and developing dendritic growth theory at small supercoolings. In the case of dendrites grown from pure, supercooled melts, growth is controlled by diffusion-limited transport of heat, which causes temperature gradients to be present in the liquid phase. Thermal gradients can excite anisotropic convection which affects the growth velocity, overall crystal mor-phology, and distribution of heat and solute. Dendritic growth, by its nature, does not permit inde-pendent manipulation of parameters which would reduce the vigor of melt convection under terrestrial conditions. The reduction of gravity through free fall is the only practical way to allow observation of “convection free” growth and thereby provide a test of dendritic growth theory. The IDGE is currently being developed at our laboratory, in collaboration with the NASA Lewis Research Center. The apparatus consists of a controlled thermostatic bath capable of millikelvin stability, a photographic data collection system, a crystal growth chamber ensuring “free” dendritic growth, and an optical RAM crystal growth detection system to initiate data collection. The ex-periment will be essentially autonomous, since it will be located aboard the Materials Science Laboratory in the cargo bay of the space shuttle, where direct astronaut intervention is not possible. Limited interaction from the ground is planned through a number of preprogrammed computer com-mands. Previously conducted ground based studies will be described and the current approach to performing these studies in low earth orbit will be discussed.