Grains, Phases, And Interfaces: An Interpretation Of Microstructure

THE art of metallography is mature and the forms in which various micro-constituents appear are well known. Investigations almost without end have disclosed the importance of the exact manner of distribution of phases on the physical properties and usefulness of an alloy. Surprisingly, however, relatively little attention has been paid to the forces that are responsible for the particular and varied spatial arrangements of grains and phases that are observed. Like the anatomist, the metallurgist has been more concerned with form and function than with origins. In this paper it is proposed to develop the simple concept that many microstructures result from an attempted approach to equilibrium between phase and grain interfaces whose surface tensions geometrically balance each other at the points and along the lines where they meet. From this follows a number of principles which may prove to be of interest to the metallographer and of practical use in explaining failures and in designing alloys for particular service. In general, the discussion will be limited to structures obtained after full annealing. The simple principles do not apply to structures resulting from Widmanstatten mechanisms in precipitation, or to other structures not in local equilibrium and in which lattice coherency is a determining factor. INTERFACIAL TENSION Much has been written by physical chemists about the free energy of surfaces, which manifests itself as a measurable surface tension. Two- and three-phase interfaces in fluids seek a condition of minimum energy and approach a geometrical configuration in which the various forces are in vectorial balance.* Measurement of the angles established between the interfaces when in equilibrium provides a quantitative value for the relative value of the surface forces involved. The case of two fluids meeting at the surface of a solid (of great importance in connection with the flotation of minerals) has often been studied, but there have been few investigations of the equally definite interface between two or more crystals of a single solid phase, or the more complex cases where crystal grains of more than one phase are involved. The principles are best illustrated by considering first the case of two and three immiscible liquids. If, as in Fig I, a liquid, 2, is dropped into a less dense liquid, I, it will form a sphere-if gravity and viscosity can be ignored-for in this shape the interface has the smallest possible area. If these two phases should together encounter a third phase in which they are both immiscible, the geometry will change to become that which gives the lowest total energy for all three interfaces. Thus, if the spherical drop of liquid, falling through r, eventually reaches the interface between liquids 3 and I (we are assuming that the density of 3 is greater than 2, and 2 than I), it will assume the shape of a lens, the angle