Holes in lattices in liquids

In their feature article in the February 2019 issue of Physics Today (page 38 ), Robert Evans, Daan Frenkel, and Marjolein Dijkstra quote from “About liquids,” an essay in which Victor Weisskopf discusses the mysterious nature of liquids. ¹

Around 1960, when I was a graduate student at the University of Washington, the thesis project of one of my fellows was to calculate the entropy of a hole in a crystal lattice. The seemingly quixotic nature of the assignment—“A hole is a nothing. How can it have an entropy?”—led to much merry banter in our group. Today, the idea of holes in lattices is well established.

Evaporation (or sublimation) occurs when molecules on the surface of a condensed phase acquire enough energy to break free, enter the gas phase, and thus achieve unconstrained mobility. Similarly, for crystalline solids, there is a characteristic temperature—the melting temperature—at which the holes become mobile and move freely throughout the lattice. Noncrystalline solids such as rubber and plastics have a range of hole and dislocation types that reach mobility at various temperatures; they soften gradually rather than exhibiting a sharp melting point.

I find that the molecule/hole analogy provides a satisfying way to visualize the phenomenon of melting and the nature of liquids.