The solid-liquid interfacial free energy of close-packed metals: hard spheres and the Turnbull coefficient

Largely due to its role in nucleation and crystal-growth, the free energy of the crystal-melt interfacial free energy is an object of considerable interest across a number of scientific disciplines, especially in the materials-, colloid- and atmospheric sciences. Over fifty years ago, Turnbull observed that the interfacial free energies (scaled by the mean interfacial area per particle) of a variety of metallic elements exhibit a linear correlation with the enthalpy of fusion. This correlation provides an important empirical "rule-of-thumb" for estimating interfacial free energies, but lacks a compelling physical explanation. In this work we show that the interfacial free energies for close-packed metals are linearly correlated with the melting temperature, and are therefore primarily entropic in origin. We also show that the slope of this linear relationship can be determined with quantitative accuracy using a hard-sphere model, and that the correlation with the enthalpy of fusion reported by Turnbull follows as a consequence of the fact that the entropy of fusion for close-packed metals is relatively constant.Comment: 3 pages, 1 figure, to appear in J. Chem. Phy

The industrial processing of unidirectional fiber prepregs

Progress made in the industrial processing of preimpregnated composites with unidirectional fibers is discussed, with particular emphasis on applications within the aerospace industry. Selection of industrial materials is considered. Attention is given to the conditions justifying the use of composites and the properties required of industrial prepregs. The hardening cycle is examined for the cases of nonmodified and polymer modified resins, with attention given to the stabilization of flow, the necessary changes of state, viscosity control, and the elimination of porosity. The tooling necessary for the fabrication of a laminated plate is illustrated, and the influence of fabrication and prepreg properties on the mechanical characteristics of a laminate are indicated. Finally, the types of prepregs available and the processing procedures necessary for them are summarized

Direct calculation of the crystal-melt interfacial free energies for continuous potentials: Application to the Lennard-Jones system

Extending to continuous potentials a cleaving wall molecular-dynamics simulation method recently developed for the hard-sphere system [Phys.Rev.Lett 85, 4751 (2000)], we calculate the crystal-melt interfacial free energies, $\gamma$, for a Lennard-Jones system as functions of both crystal orientation and temperature. At the triple point, T* = 0.617, the results are consistent with an earlier cleaving potential calculation by Broughton and Gilmer [J. Chem. Phys. {\bf 84}, 5759 (1986)], however, the greater precision of the current calculation allows us to accurately determine the anisotropy of $\gamma$. From our data we find that, at all temperatures studied, $\gamma_{111} < \gamma_{110} < \gamma_{100}$. Comparison is made to the results from our previous hard-sphere calculation and to recent results for Ni by Asta, Hoyt and Karma [Phys. Rev. B, 66 100101(R) (2002)].Comment: 7 pages, 3 figures, 2 table

Preconditioned iterative solution of the 2D Helmholtz equation

Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow

Molecular dynamics simulation of binary hard-sphere crystal/melt interfaces

We examine, using molecular dynamics simulation, the structure and thermodynamics of the (100) and (111) disordered face-centered cubic (FCC) crystal/melt interfaces for a binary hard-sphere system. This study is an extension of our previous work, [Phys. Rev. E 54, R5905 (1996)], in which preliminary data for the (100) interface were reported. Density and diffusion profiles on both fine- and course-grained scales are calculated and analyzed leading to the conclusion that equilibrium interfacial segregation is minimal in this system.Comment: 7 pages, 7 figures, to appear in Molecular Physic

Preconditioning harmonic unsteady potential flow calculations

This paper considers finite element discretisations of the Helmholtz equation and its generalisation arising from harmonic acoustics perturbations to a non-uniform steady potential flow. A novel elliptic, positive definite preconditioner, with a multigrid implementation, is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1D Helmholtz test problem the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2D Helmholtz equation, grid independent convergence is achieved using a QMR Krylov solver, significantly outperforming the popular SSOR preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with non-stagnant mean flow and modal boundary conditions

Flexibly Instructable Agents

This paper presents an approach to learning from situated, interactive tutorial instruction within an ongoing agent. Tutorial instruction is a flexible (and thus powerful) paradigm for teaching tasks because it allows an instructor to communicate whatever types of knowledge an agent might need in whatever situations might arise. To support this flexibility, however, the agent must be able to learn multiple kinds of knowledge from a broad range of instructional interactions. Our approach, called situated explanation, achieves such learning through a combination of analytic and inductive techniques. It combines a form of explanation-based learning that is situated for each instruction with a full suite of contextually guided responses to incomplete explanations. The approach is implemented in an agent called Instructo-Soar that learns hierarchies of new tasks and other domain knowledge from interactive natural language instructions. Instructo-Soar meets three key requirements of flexible instructability that distinguish it from previous systems: (1) it can take known or unknown commands at any instruction point; (2) it can handle instructions that apply to either its current situation or to a hypothetical situation specified in language (as in, for instance, conditional instructions); and (3) it can learn, from instructions, each class of knowledge it uses to perform tasks.Comment: See http://www.jair.org/ for any accompanying file

Solid-liquid interfacial premelting

We report the observation of a premelting transition at chemically sharp solid-liquid interfaces using molecular-dynamics simulations. The transition is observed in the solid-Al/liquid-Pb system and involves the formation of a liquid interfacial film of Al with a width that grows logarithmically as the bulk melting temperature is approached from below, consistent with current theories of premelting. The premelting behavior leads to a sharp change in the temperature dependence of the diffusion coefficient in the interfacial region, and could have important consequences for phenomena such as particle coalescence and shape equilibration, which are governed by interfacial kinetic processes.Comment: 6 pages, 4 figure