FIRST PRINCIPLES COMPUTATIONS Effects of temperature and ferromagnetism on the c-Ni/c-Ni3Al interfacial free energy from first principles calculations

The temperature dependencies of the c(f.c.c.)Ni/c-Ni3Al(L12) interfacial free energy for the {100}, {110}, and {111} interfaces are calculated using firstprinciples 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 c-Ni3Al-precipitates in Ni–Al alloys faceted strongly on {100}-type planes. The c(f.c.c.)-Ni/c-Ni3Al interfacial free energies for the {100}, {110}, and {111} interfaces decrease with increasing temperature due to vibrational entropy. The predicted morphology of c-Ni3Al(L12) 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 c-Ni3Al(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 c(f.c.c.)-Ni-matrix and the c-Ni3Alprecipitates. Introduction The c(f.c.c.)-Ni/c-Ni3Al(L12 structure) interfacial free energy is of technological importance, since it affects the coarsening resistance of c-Ni3Al precipitates in commercial nickel-based superalloys used for turbine blades in aerospace (commercial and military) and land-based turbine engines [1]. The c-Ni/c-Ni3Al interfacial free energy enters directly in all coarsening theories used to model microstructural stability at elevated temperatures, and is needed to predict the reliability of existing superalloys and to further improve them. The exact value of the c-Ni/c0Ni3Al interfacial free energy is controversial, since values determined from different experiments and computational research range from 6.9 to 46 mJ m [2–9]. Experimentally, these interfacial free energies are frequently evaluated using Lifshitz–Slyozov–Wagner (LSW) coarsening theory and its variants [2–9], which yield average values of the interfacial free energy over all the {hkl} facets of Al3Ni(L12) precipitates. Prior calculations of the values of the c-Ni/c-Ni3Al interfacial energy are somewhat similar to experimentally determined ones [10–14], but are inconsistent with experimental findings of precipitate morphologies. For example, Ni3Al(L12) precipitates have been observed to evolve upon aging from spheroids to {100}-faceted cuboids, indicating that the {100}-interfacial free energy has the smallest value [4, 6, 8, 9]. Whereas, prior first-principles calculations and Monte Carlo simulations using embedded-atom method potentials (EAM), which did not include ferromagnetism, demonstrated that the {111}-planes have the smallest interfacial energy [4, 8], which is inconsistent with experimental observations. To address these discrepancies, and to obtain physically meaningful values of the interfacial free energies of the {100}, {110}, and {111} interfaces, we employ density Z. Mao C. Booth-Morrison E. Plotnikov D. N. Seidman (&) Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, IL 60208-3108, USA e-mail: [email protected] 123 J Mater Sci (2012) 47:7653–7659 DOI 10.1007/s10853-012-6399-x