Biomedical subjects

P W Voorhees

Publications and source records attributed to P W Voorhees.

7 recordsLinked to original sources

PubMed2006

Orientation dependence of strained-Ge surface energies near (001): role of dimer-vacancy lines and their interactions with steps.

Recent experiments and calculations have highlighted the important role of surface-energy (gamma) anisotropy in governing island formation in the Ge/Si(001) system. To further elucidate the factors determining this anisotropy, we perform atomistic and continuum calculations of the orientation dependence of gamma for strained-Ge surfaces near (001), accounting for the presence of dimer-vacancy lines (DVLs). The net effect of DVLs is found to be a substantial reduction in the magnitude of the slope of gamma vs orientation angle, relative to the highly negative value derived for non-DVL, dimer-reconstructed, strained-Ge(001) surfaces. The present results thus point to an important role of DVLs in stabilizing the (001) surface orientation of a strained-Ge wetting layer.

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PubMed2005

Role of strain-dependent surface energies in Ge/Si(100) island formation.

Formation energies for Ge/Si(100) pyramidal islands are computed combining continuum calculations of strain energy with first-principles-computed strain-dependent surface energies. The strain dependence of surface energy is critically impacted by the presence of strain-induced changes in the Ge {100} surface reconstruction. The appreciable strain dependencies of rebonded-step {105} and dimer-vacancy-line-reconstructed {100} surface energies are estimated to give rise to a significant reduction in the surface contribution to island formation energies.

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PubMed2004

Topological complexity and the dynamics of coarsening.

Coarsening or Ostwald ripening occurs in a vast array of two-phase systems. Coarsening results in a decrease in the interfacial area per unit volume and a concomitant increase in the size scale of the interfacial morphology. Much is known about the coarsening process in two-phase mixtures consisting of a polydisperse array of spherical particles. In contrast, in many two-phase mixtures, such as those found in two-phase polymers, ceramics, dendritic solid-liquid mixtures and order-disorder transformations, the interfaces are both interconnected and have a spatially varying mean curvature. Here we show that the morphological evolution of these topologically complex systems during coarsening can be quantified by measuring the probability of finding a patch of interface with a given curvature tensor. We find that the morphological evolution is described by the flow of probability density in this curvature space that is induced by the coarsening process. The hallmark of our approach is a close coupling between experiment and theory; we use the experimentally measured three-dimensional microstructure as an input to a phase-field calculation that then determines the flow in curvature space. The methodology is general, and applicable to many systems undergoing coarsening, regardless of their topology.

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PubMed2003

Self-organization of quantum dots in epitaxially strained solid films.

A nonlinear evolution equation for surface-diffusion-driven Asaro-Tiller-Grinfeld instability of an epitaxially strained thin solid film on a solid substrate is derived in the case where the film wets the substrate. It is found that the presence of a weak wetting interaction between the film and the substrate can substantially retard the instability and modify its spectrum in such a way that the formation of spatially regular arrays of islands or pits on the film surface becomes possible. It is shown that the self-organization dynamics is significantly affected by the presence of the Goldstone mode associated with the conservation of mass.

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PubMed2003

Faceting of a growing crystal surface by surface diffusion.

Consider faceting of a crystal surface caused by strongly anisotropic surface tension, driven by surface diffusion and accompanied by deposition (etching) due to fluxes normal to the surface. Nonlinear evolution equations describing the faceting of 1+1 and 2+1 crystal surfaces are studied analytically, by means of matched asymptotic expansions for small growth rates, and numerically otherwise. Stationary shapes and dynamics of faceted pyramidal structures are found as functions of the growth rate. In the 1+1 case it is shown that a solitary hill as well as periodic hill-and-valley solutions are unique, while solutions in the form of a solitary valley form a one-parameter family. It is found that with the increase of the growth rate, the faceting dynamics exhibits transitions from the power-law coarsening to the formation of pyramidal structures with a fixed average size and finally to spatiotemporally chaotic surfaces resembling the kinetic roughening.

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PubMed2001

Dynamics of late-stage phase separation in crystalline solids.

The dynamics of Ostwald ripening in elastically stressed crystalline solids is determined through large-scale numerical simulations. Using the insight provided by the simulations, a theory for the dynamics of late-stage phase separation in elastically anisotropic homogeneous solids is developed. Both the theory and simulations show that for the systems considered elastic stress does not alter the exponent of the temporal power law for the average particle size but does affect the amplitude of the power law in a manner that is only a function of the symmetry of the particle morphology.

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PubMed2001

Quantitative serial sectioning analysis.

A method for serial sectioning is presented that allows one to take about 20 sections per hour with spacings in the range 1-20 microm between sections. The alignment of the cross-sections is done with a linear variable differential transformer; it is thus independent of the microstructure of the sample and does not rely upon markers implanted in the sample. The alignment errors as well as tilts and rotation errors between sections associated with the new method are found to be negligible. Once all the sections are captured in a computer a three-dimensional image can be constructed. This image can be viewed interactively and rotated, thus allowing the direct observation of three-dimensional shapes. It can further be used to determine a vast array of microstructural parameters including those that cannot be determined from planar sections. The technique is illustrated through the reconstruction of the microstructure of a cast standard aluminium alloy specimen.

Alloys↗