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One of the major goals of materials science is to relate the properties of materials to the potential functions that characterize the atomic and molecular interactions that hold the material together. Sharing this ambitious and ongoing quantum-mechanical program with students is usually beyond the scope of an introductory course in materials science. However, there are situations where an elementary approach to connecting atomic interactions to material properties is possible. One of these areas is the use of the lattice energies and bond energies of metals to predict the metal surface energies. These calculations are presented here at a level that is suitable for an introductory materials science course.Many phenomena of importance in solids depend on the properties of the surfaces or interfaces of the materials in question, rather than properties of the bulk material. Surface and interfacial tensions are key properties in understanding phenomena such as crystal faceting, grain structure, crack propagation, capillaritydriven mass transport, vacancy formation, wetting, and adhesion (1). The bonding concepts considered here are similar to those applied to the covalent bond energy that is a central idea in general, organic, inorganic, and physical chemistry courses (2). Once determined, the metallic bond strengths are seen to be somewhat smaller than the energies of the more familiar covalent bonds. For body-centered cubic (bcc), face-centered cubic (fcc), and hexagonalclosest-packed (hcp) metals, the bond energy and the lattice constant can then be used to make reasonably good estimates the surface energies of solid metals. Bond Energies for the Bcc and Fcc MetalsThe calculation of the bond energy in a metallic lattice is similar to that in gaseous molecules except that students find it a little more challenging to determine the number of bonds broken during atomization. The atomization of a crystalline metal, M(c), can be represented by the processwhere the molar energy of atomization of the metal lattice is Δ a U and the gaseous metal is assumed to be entirely monatomic. The atomization energy is also called the energy of sublimation, the cohesive energy, or the lattice energy. The calculation of bond energies from Δ a U will initially be limited to bcc and fcc metals. Each metallic crystal structure has its own coordination number, Z, which is the number of nearest neighbors surrounding a central atom. The crystal lattice is assumed to be composed entirely of "hard spheres" of identical radius so that all of the nearest neighbors "touch" the central atom they surround. The unit cell geometries for the bcc and fcc metals are shown in Figures 1A and 2A. The coordination numbers for these two crystal structures areZðfccÞ ¼ 12Because the removal of one atom from a metallic lattice causes the breaking of Z bonds, it is tempting, but not correct, to assume that Δ a U = Zε, where ε is the molar bond energy. It is true that the Z bonds surrounding this atom are broken during atomization; however, this process also brea...

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If a liquid is in contact only with immiscible solid or liquid phases which it wets completely, then the liquid can be heated isobarically until it reaches its limit of superheat where it vaporizes explosively.The liquid phase can likewise be "stretched" isothermally to this same limit, which is sometimes called the tensile strength of the liquid. A kinetic limit of superheat can be predicted from homogeneous nucleation theory. A thermodynamic limit of superheat can also be predicted from the liquid-phase spinodal which is that curve in PVT space which separates metastable states from unstable states at densities larger than the critical density. Along this spinodal the equation of state satisfies the conditions (BP/ BV)t -0 and (B2P/BV2)t > 0. Liquid spinodals for the normal alkanes from methane through nonane and for ether were derived from a variety of equations of state, including those of van der Waals, Berthelot, a modified Berthelot equation, and a generalized van der Waals equation based on scaled particle theory for rigid, convex molecules. Good agreement is obtained between experimental limits of superheat for these liquids and the liquid-phase spinodals calculated from the generalized van der Waals equation of state for rigid, cylindrical molecules with a size based on the molecular structure which they represent. Our estimate of the limit of superheat of water, based on significant structure theory, is 305°at atmospheric pressure. This exceeds superheatings observed thus far by 25°. Spinodals describing the limits of supersaturation of vapors and supercooling of liquids are briefly discussed.