Determination of the interface energies of spherical, cuboidal and octahedral face-centered cubic precipitates in Cu–Co, Cu–Co–Fe and Cu–Fe alloys

Abstract

The coarsening theory of a spherical particle in a ternary alloy developed by Kuehmann and Voorhees (KV) has been generalized to any centro-symmetric particle. A classical thermodynamic analysis reveals that the generalized KV theory enables us to estimate the interface energy of a particle with a fixed shape, even if the shape of the particle is not

Morphological and Crystallographic Characteristics of Incoherent Octahedral FCC Co Precipitates in a Cu Matrix

“…The origin of the {111} octahedral shape has been explained by the lowest energy density of the incoherent {111} Co/Cu interface. 8,12,1820,25) However, some deviations of the shape from the regular {111} octahedron seem to exist for the Co precipitates observed in previous studies. 12,15) The equilibrium shapes of small particles controlled by the particle/matrix interface energy are known in many alloy systems.…”

Coarsening of cuboidal Al3Sc precipitates in an Al–Mg–Sc alloy

“…The GKV theory also predicts that the solute concentration C in solid solution after coarsening time t varies as [5] ,…”

“…The GKV mathematical treatment of coarsening predicts that the cube of the average size of precipitates, 3 λ , increases with ageing time t, as follows [5]:…”

“…Moreover, we have shown in the previous study [5] that the coarsening rate of second-phase precipitates at a given temperature is dependent upon the interface energy alone, even when the precipitates have internal stress and corresponding elastic strain energy: that is, the Wluff construction [x] that the shape of a particles is determined by minimization of the interface energy does not hold true in actual systems. Therefore, the relation γ s = g 001 γ 001 must be satisfied.…”

“…Recently, Watanabe et al have extended the KV theory to a general case of second-phase particle with any centro-symmetric shape [5]. They applied the generalized KV (GKV) theory to the experimental data on the coarsening of spherical, {001}-faceted cuboidal and {111}-faceted octahedral Co, Fe and Co-Fe precipitates with a face-centred cubic (fcc) structure in a Cu-Co alloy, a Cu-Fe alloy, and three Cu-Co-Fe alloys with different Co and Fe contents during ageing at 873 to 973 K, and then estimated the values of γ for sphere, {001}…”