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Voorhees, P. W.

Publications and source records attributed to Voorhees, P. W..

Coarsening in Solid-liquid Mixtures: Overview of Experiments on Shuttle and ISS

The microgravity environment on the Shuttle and the International Space Station (ISS) provides the ideal condition to perform experiments on Coarsening in Solid-Liquid Mixtures (CSLM) as deleterious effects such as particle sedimentation and buoyancy-induced convection are suppressed. For an ideal system such as Lead-Tin in which all the thermophysical properties are known, the initial condition in microgravity of randomly dispersed particles with local clustering of solid Tin in eutectic liquid Lead-Tin matrix, permitted kinetic studies of competitive particle growth for a range of volume fractions. Verification that the quenching phase of the experiment had negligible effect of the spatial distribution of particles is shown through the computational solution of the dynamical equations of motion, thus insuring quench-free effects from the coarsened microstructure measurements. The low volume fraction experiments conducted on the Shuttle showed agreement with transient Ostwald ripening theory, and the steady-state requirement of LSW theory was not achieved. More recent experiments conducted on ISS with higher volume fractions have achieved steady-state condition and show that the kinetics follows the classical diffusion limited particle coarsening prediction and the measured 3D particle size distribution becomes broader as predicted from theory.

Ostwald ripening

Morphological instability in epitaxially strained dislocation-free solid films - Linear stability theory

The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.

Spencer, B. J.

On the morphological development of second-phase particles in elastically-stressed solids

We examine the equilibrium shape and the dynamics of the morphological evolution of a coherent misfitting particle in an elastically anisotropic medium. No a priori assumptions are made on the possible particle morphologies; the particle evolves in a manner consistent with both the diffusion and elastic fields surrounding the particle and the thermodynamics of interfaces in stressed solids. Through these calculations we find the thermodynamically stable equilibrium shape of a misfitting particle. By thermodynamically stable we mean that all the equilibrium conditions, elastic, chemical and interfacial are satisfied simultaneously, in contrast to previous treatments which determined the equilibrium shape by minimizing the sum of the elastic and interfacial energies for certain classes of particle shapes. We find that the equilibrium particle morphologies are not simple geometric shapes, have fourfold symmetry and a continuously varying interfacial curvature with position along the interface. Furthermore, the results show that the times required for a particle to evolve to its equilibrium morphology are likely to be within those which are accessible experimentally. In addition, we develop a general approach for determining the equilibrium shape of a particle in an elastically stressed solid.

Voorhees, P. W.

The effect of compositionally-generated elastic stresses on morphological instability during directional solidification

The effect of compositionally-generated elastic stresses on the conditions for morphological instability during directional solidification of a dilute, ideal binary alloy is investigated using the Gibbs-Thomson equations for an elastically-stressed solid with zero surface stress in equilibrium with a liquid. It is found that these stresses lead to a small stabilization of the Mullins and Sekerka cellular mode of instability. The steady mode is stabilized by a stress-induced modification to the interfacial concentration of the solid, which in turn alters the amount of solute rejected to inhibit the growth of perturbations. The presence of elastic stresses could generate a new oscillatory instability which is most likely to be found in experiments near absolute stability for materials with segregation coefficients near unity and large solute expansion coefficients.

Spencer, B. J.

Measurement and analysis of grain boundary grooving by volume diffusion

Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1/3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Gamma associated with the interfacial free energy of the crystal-melt interface. The small-slope theory of Mullins is generalized to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and excellent agreement with experimental groove shapes is obtained. By using the diffusivity measured by Jordon and Hunt, the present measured values of Gamma are found to agree to within 5 percent with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.

Hardy, S. C.

Coarsening in binary solid-liquid mixtures

A theory of Ostwald ripening has been developed for a solid-liquid mixture cosisting of a low volume fraction array of spherical solid particles in a liquid wherein the coarsening process proceeds via the transport of both heat and mass. It is found that the simultaneous transport of heat and mass during ripening does not alter the exponents of the temporal power laws governing the ripening process from their classical values but does alter the amplitudes of these power laws. The growth rate of the cube of the average particle radius, the rate constant, is found to depend both on the alloy solute concentration and the ratio of the thermal to solutal diffusivities. In most metallic systems, a large decrease in the rate constant can be expected with small additions of solute to a pure metal. Possible extensions of this theory to the analogous problem of ripening in isothermal ternary alloys are also discussed.

Voorhees, P. W.

Ostwald ripening in a system with a high volume fraction of coarsening phase

The coarsening of Sn-rich and Pb-rich solid phases in contact with eutectic liquid in the volume fraction solid range above approximately 0.6, where the development of a solid skeletal structure inhibits sedimentation, is investigated. Particle intercept distributions are shown to be time independent when scaled by the average intercept. It is noted that the coarsening rate constants obtained exceed the values calculated from theory by factors ranging from about 2 to 5.

Hardy, S. C.

Initial conditions implied by t exp 1/2 solidification of a sphere with capillarity and interfacial kinetics

The paper explores the initial conditions implied by t exp 1/2 growth of a spherical crystal solidifying from a pure, undercooled melt, including the effects of both capillarity and interface kinetics, and relates the findings to initial conditions that would be expected on the basis of classical nucleation theory. For crystal sizes near the nucleation radius, the calculated temperature profiles show a cold region ahead of the advancing interface that is even more undercooled than the undercooled bath. This cold region acts as a local heat sink that compensates for the reduced growth speed that would otherwise result from capillarity and kinetics, leading to precisely the same t exp 1/2 growth law that would have been obtained had both capillarity and kinetics been neglected.

Sekerka, R. F.

Numerical simulation of morphological development during Ostwald ripening

The morphological evolution of a small number of particles undergoing Ostwald ripening in two dimensions was investigated using a boundary integral technique. The numerical calculations show that, in many cases, interparticle diffusional interactions do not induce large distortions in particle morphology from a circle, due to the strong local interaction between regions of different curvature on the same particle. Particle migration due to interparticle diffusional interactions was observed, with the migration distance larger than the initial radius of a particle, which is linked to the particle spatial arrangement. As diffusion is the mechanism for the migration, it is expected that particle movement is a generic aspect of the coarsening process at high volume fractions of coarsening phase and, possibly, at low volume fractions. The calculations support unambiguously the Ostwald ripening mechanism for flat formation during liquid-phase sintering. As such, the appearance or regions of low interfacial curvature is a dynamic phenomenon dependent on interparticle diffusion.

Voorhees, P. W.

The effect of anisotropic crystal-melt surface tension on grain boundary groove morphology

The shape of a stationary solid-liquid interface in a temperature gradient near a grain boundary in a pure material is calculated for anisotropic crystal-melt surface tension and equal thermal conductivities of crystal and melt. Results are compared with those for the well-known problem of the two-dimensional equilibrium shape of a crystal. For small anisotropy, the resulting interface shapes have continuously turning tangents but differ in detail from the grain boundary groove shapes that have been calculated for isotropic surface tension. For larger anisotropy, the interface shapes have discontinuities in slope as a result of missing orientations.

Voorhees, P. W.