Effects of temperature and ferromagnetism on the γ-Ni/γ′- Ni₃Al interfacial free energy from first principles calculations

The temperature dependencies of the γ(f.c.c.)-Ni/γ′- Ni₃Al(L1₂) interfacial free energy for the {100}, {110}, and {111} interfaces are calculated using first-principles calculations, including both coherency strain energy and phonon vibrational entropy. Calculations performed including ferromagnetic effects predict that the {100}-type interface has the smallest free energy at different elevated temperatures, while alternatively the {111}-type interface has the smallest free energy when ferromagnetism is absent; the latter result is inconsistent with experimental observations of γ′-Ni₃Al-precipitates in Ni-Al alloys faceted strongly on {100}-type planes. The γ(f.c.c.)-Ni/ γ′-Ni₃Al interfacial free energies for the {100}, {110}, and {111} interfaces decrease with increasing temperature due to vibrational entropy. The predicted morphology of γ′-Ni₃Al(L1 ₂) precipitates, based on a Wulff construction, is a Great Rhombicuboctahedron (or Truncated Cuboctahedron), which is one of the 13 Archimedean solids, with 6-{100}, 12-{110}, and 8-{111} facets. The first-principles calculated morphology of a γ′-Ni ₃Al(L1₂) precipitate is in agreement with experimental three-dimensional atom-probe tomographic observations of cuboidal L1₂ precipitates with large {100}-type facets in a Ni-13.0 at.% Al alloy aged at 823 K for 4096 h. At 823 K this alloy has a lattice parameter mismatch of 0.004 ± 0.001 between the γ(f.c.c.)-Ni-matrix and the γ′-Ni₃Al-precipitates.