The conditions for structural transitions at the core of a grain boundary separating two crystals was investigated with a diffuse interface model that incorporates disorder and crystal orientation ͓Kobayashi et al., Physica D 140, 141 ͑2000͔͒. The model predicts that limited structural disorder near the grain boundary core can be favorable below the melting point. This disordered material is a precursor to a liquid phase and therefore the model represents grain boundary premelting. This model is shown to be isomorphic to Cahn's critical point wetting theory ͓J.W. Cahn, J. Chem. Phys. 66, 3667 ͑1977͔͒ and predicts first-and higher-order structural grain boundary transitions. A graphical construction predicts the equilibrium grain boundary core disorder, the grain boundary energy density, and the relative stability of multiple grain boundary "complexions." The graphical construction permits qualitative inference of the effect of model properties, such as empirical homogeneous free energy density and assumed gradient energy coefficients, on properties. A quantitative criterion is derived which determines whether a first-order grain boundary transition will occur. In those systems where first-order transition does occur, they are limited to intermediate grain-boundary misorientations and to a limited range of temperatures below the melting point. Larger misorientations lead to continuously increasing disorder up to the melting point at which the disorder matches a liquid state. Smaller misorientation continuously disorder but are not completely disordered at the melting point. Characteristic grain boundary widths and energies are calculated as is the width's divergence behavior at the melting point. Grain boundary phase diagrams are produced. The relations between the model's predictions and atomistic simulations and with experimental observations are examined.
This paper discusses a digital library designed to help undergraduate students draw connections across disciplines, beginning with introductory discipline-specific science courses (including chemistry, materials science, and biophysics). The collection serves as the basis for a design experiment for interdisciplinary educational libraries and is discussed in terms of the three models proposed by Sumner and Marlino. As a cognitive tool, the library is organized around recurring patterns in molecular science, with one such pattern being developed for this initial design experiment. As a component repository, the library resources support learning of these patterns and how they appear in different disciplines. As a knowledge network, the library integrates design with use and assessment.
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