Indeed, fundamental and application-driven computational studies of surfaces in the literature are extensive 8, 32– 34. Computational techniques provide the means to precisely control the surface structure and composition. 27 and Keene 28.įirst principles computations such as those based on density functional theory (DFT) methods are important complementary tools to experimental techniques in characterizing surface properties of a material 29– 31. Reviews of such surface tension techniques have been compiled by Mills et al. References 26 and 20 have accumulated a large set of metallic elemental surface energy data by extrapolating surface tension of liquid phases for solid surfaces. Furthermore, experimentally observed Wulff shapes are often inconsistent across studies due to the sensitivity of high energy facets to temperature and impurities 25. Despite its importance, experimental determination of surface energies, especially for specific facets, is difficult and rare 20– 24. This fundamental quantity is important in understanding surface structure, reconstruction, roughening and the crystal’s equilibrium shape 19. The stability of a surface is described by its surface energy γ, a measure of the excess energy of surface atoms due to a variety of factors, such as the broken bonds yielding undercoordinated atoms. For example, the nanoscale stability of metastable polymorphs is determined from the competition between surface and bulk energy of the nanoparticle 15– 18. Surface effects are especially important in nanomaterials, where relatively large surface area to volume ratios lead to properties that differ significantly from the bulk material 10– 14. For instance, technologies such as fuel cells and industrial chemical manufacturing require the use of catalysts to accelerate chemical reactions, which is fundamentally a surface-driven process 1– 9. The surface properties of a crystal are crucial to the understanding and design of materials for many applications. We will describe the methodology used in constructing the database, and how it can be accessed for further studies and design of materials. The database is systematically improvable and has been rigorously validated against previous experimental and computational data where available. Well-known reconstruction schemes are also accounted for. This database contains the surface energies of more than 100 polymorphs of about 70 elements, up to a maximum Miller index of two and three for non-cubic and cubic crystals, respectively. In this work, we present the largest database of calculated surface energies for elemental crystals to date. Such surface phenomena are especially important at the nanoscale, where the large surface area to volume ratios lead to properties that are significantly different from the bulk. The book brings the reader through the entire development of the proof of this result.The surface energy is a fundamental property of the different facets of a crystal that is crucial to the understanding of various phenomena like surface segregation, roughening, catalytic activity, and the crystal’s equilibrium shape. Heuristically, the main result can be stated this way: a droplet of one phase immersed in the opposite one will be formed with the separation line following with high accuracy the shape yielded by the Wulff construction. Its value is chosen to lie in the interval between the spontaneous magnetizations of pure phases. Namely, the authors investigate the phenomenon of phase separation in a (small) canonical ensemble characterized by a fixed total spin in a finite volume. This research monograph considers the Wulff construction in the case of a two-dimensional Ising ferromagnet with periodic boundary conditions and at sufficiently low temperatures. Assuming that the anisotropic interfacial free energy (depending on the orientation of the interface with respect to the crystal axes) is known, the Wulff construction yields the shape of crystal in equilibrium and allows one to understand its main features. A theory of the equilibrium shape of crystal assuming minimal surface free energy was formulated at the beginning of the century by Wulff.
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