A1-L12 interfacial free energies from data on coarsening in five binary Ni alloys, informed by thermodynamic phase diagram assessments

Abstract

The data on coarsening of c 0 -type precipitates (Ni 3 X, with the L1 2 crystal structure) in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, and Ni-Ti alloys are re-evaluated in the context of recent (TIDC) and classical (LSW) theories of coarsening, with the objective of ascertaining the best values possible of interfacial free energies, r, of the c/c 0 interfaces in these five alloy systems. The re-evaluations include fitting of the particle size distributions, reanalyzing all the available data on the kinetics of particle growth and kinetics of solute depletion, and using thermodynamic assessments of the binary alloy phase diagrams to calculate curvatures of the Gibbs free energies of mixing. The product of the work is two sets of interfacial free energies, one set for the analysis using the recent TIDC theory and the other for the analysis using the classical LSW theory. The TIDC-based analysis yields lower values of r by about a factor of 2/3. All the interfacial energies are considerably larger, by factors ranging from *4 to 10, than those previously reported, which were for the most part calculated from data on coarsening assuming idealsolution thermodynamics. In the TIDC theory the width of the interface, d, is allowed to increase with particle size, r. A simple equation relating r to the ratio of the gradient energy and d is used to show that r can remain constant even though d increases with r. Published work supporting this contention is presented and discussed.

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

“…(16), the magnitude of the interfacial free energy, r, can be derived as shown previously [37]. The work presented in this paper provides a semi-empirical, but rigorous, explanation for the non-integer temporal exponents that allow the kinetics of coarsening of c 0 precipitates in Ni-based alloys, and the PSDs, to be explained by the TIDC theory.…”

“…To calculate M fromD; it is necessary to know the thermodynamic factor U. These were obtained using the formula U ¼ R g T G 00 mc (R g is the gas constant) after calculating G 00 mc using the procedures described in [37], which are based on the thermodynamic model of Ansara et al [86]. The vacancy wind factor, S, is ignored in these calculations.…”

“…Ardell and Ozolins [14] briefly considered the possibility that d might actually vary with r, arguing that precipitates approaching the dimensions of several unit cells of the L1 2 structure would lose their identity as a distinct phase unless the interface sharpened for very small values of r. In subsequent papers [35][36][37][38][39], this conjecture was made quantitative by assuming a relationship of the form d µ r m , with m satisfying 0 B m B 1, ultimately leading to a temporal exponent of n = m ? 2.…”

“…Analysis of previously published experimental data on the c 0 PSDs Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, and NiTi alloys [37] confirms the efficacy of the TIDC Figure 1 a The dependencies of the rate constant for particle growth during coarsening, k(f e ), normalized by the rate constant of the LSW theory, k(0), predicted by 5 theories: MLSW [6], DNS [7], MR [8], BW [9], and VG [10]. b The experimentally measured values of k(f e ) for the coarsening of c 0 Ni 3 Si precipitates in different Ni-Si alloys aged at 650°C.…”

The development of phase-based property data using the CALPHAD method and infrastructure needs

“…More recently, Shi and Luo [105] developed a method to estimate the interfacial energy associated with a grain boundary between two phases. Combining these and other methods with data available from coarsening experiments [106,107] and single-sensor DTA nucleation cooling experiments [101] a CALPHAD based databases could be established, where the interfacial energies are defined by two phases.…”