The geometry of two-phase aggregates in which the shape of the second phase is determined by its dihedral angle

Abstract

A theoretical examination is made of the equilibrium geometry of an aggregate composed of second-phase β-particles located at α-cell corners. For the host α-cells. two cases are considered. In the first case nonuniform cells correspond to those in a real cellular or polycrystalline aggregate, and only a limited description of the α + β mixture is possible. In the second case uniform cells, represented by a modification of Kelvin's tetrakaidecahedron, give an ideal aggregate which allows a more complete quantitative treatment of the geometry. For example, relationships between the volume fraction, β v , the fraction of cell-boundary area covered, β A , and the dihedral angle, θ, have been determined. In addition, θ t- β v space and the corresponding composition-temperature space can be divided according to the various structures possible in the two-phase mixture. Recognition of these structural domains is useful when considering the mechanical behavior of the mixtures.