enormous number of adjacent-crystal pairs and their respective orientations. Nanocrystalline, glassy, and normal crystalline properties of various metals are compared in Table 2.³⁷

By and large, properties that differ by less than 10 percent between the crystalline and glassy states will differ very much more from those of the nanocrystalline state. The phonon-dependent thermal-expansion and specific-heat differences in Table 2 have been interpreted to signify that the grain boundary structure in nanocrystalline metals constitutes a novel state of matter in solids. On the other hand, the remarkable strength of the nanocrystalline iron-carbon alloy is reasonably commensurate with the Hall-Petch strengthening to be expected from grain refinement alone; in fact, this magnitude of strengthening is also found with pure nanocrystalline iron.³⁸ The 1.8 weight percent carbon in the iron-carbon alloy shown in Table 2 is presumably present as nanocrystals of carbon—i.e., not atomically dissolved in the iron. Such “alloy mixtures” deserve detailed investigation of their structural changes on heating as well as their physical, chemical, and mechanical properties. Experiments along these lines, reaching into the nanoscale grain-size regime and generating a correspondingly high concentration of grain boundary material, represent a new research frontier not only for metals and alloys but for other classes of materials as well. Moreover, the evaporation and con-