“Die heterogenen gleichgewichte (The Heterogeneous Equilibria)” a century later

Abstract

Hendrik Willem Bakhuys Roozeboom’s “Die Heterogenen Gleichgewichte vom Standpunkte der Phasenlehre” (The Heterogeneous Equilibria from the Points of View of the Phase Rule) was a monumental work that established and taught many fundamental principles that have since found unexpected uses in many fields. The principles were based on thermodynamic laws that will always be valid, but the development of some depended on nineteenth century concepts about the physical world. Bakhuys Roozeboom also shed light on many issues of his time that have remained with us throughout this century. This paper will explore the present status of some of these issues. In the nineteenth century, solids were thought to be inert and of definite chemical proportions. Bakhuys Roozeboom participated in the first discoveries that the composition of solids could vary continuously. The chemistry of the solid state is still undergoing rapid development. For example, equilibria of solids under nonhydrostatic stress are very different from what is seen for fluids under pressure, and defects in solids often play important parts. Surfaces are a pervasive presence in heterogeneous equilibria, whose effects were long ignored. Their effect on the equilibria of three-dimensional phases becomes more pronounced as the scale of subdivision by surfaces becomes smaller. Surfaces, as two-dimensional phases, have equilibria of their own, which can be described by another kind of geometrical thermodynamics. The theory of Van der Waals about the continuity between a liquid and its vapor was still new in Bakhuys Roozeboom’s time. It gave an explanation for the critical point that can occur when these two phases become identical, and raised the hope that critical points would occur between other pairs of phases. The theory relied implicitly on the fact that the symmetry of a liquid is the same as that of a vapor. For pairs of phases with differing symmetries, the matter is more complex. A critical point is impossible when the symmetries of the phases are as different as that of a crystal and its melt. Although Bakhuys Roozeboom argued convincingly and correctly that there cannot be a critical point where an equilibrated liquid and a crystal become identical, the belief was slow to die. However, continuity at the interface is another matter. It is an important assumption of the phase field theory of the interface between a liquid and a crystal, which has many interesting and useful predictions.