Temperature Dependence of the γ/γ′ Interfacial Energy in Binary Ni–Al Alloys

Abstract

Published data on the coarsening kinetics of γ′ (Ni3Al) precipitates in binary Ni–Al alloys aged at 12 temperatures ranging from 773 K to 1073 K are analyzed to provide a comprehensive evaluation of the temperature dependence of the γ/γ′ interfacial free energy, σ. The data are analyzed using equations of the trans-interface-diffusion-controlled (TIDC) theory of coarsening, with temporal exponent n = 2.4. The results show that σ decreases with increasing temperature, T. A linear empirical equation is fitted to the data on σvsT; it extrapolates to σ = 0 in the liquid region of the Ni–Al phase diagram, as it should do. A quantitative temperature-dependent transition radius, rtrans, is calculated; it depends on the product of the interface width and the ratio of the chemical diffusion coefficients in the γ phase and interface regions. Applying the TIDC coarsening equations to calculate σ is justified when the average radius, 〈r〉, satisfies the condition 〈r〉 < rtrans, which is valid for all the data used in the fit. The data on σvsT are compared with theoretical predictions. The results are discussed in the context of previous work, as well as with values of σ obtained through analyses using the equations of traditional LSW coarsening kinetics, n = 3.

Interfacial Energy of Strained Coherent Interfaces and a New Design Rule To Select Phase Combinations for In Situ Coherent Nanocomposites

“…"Experimental" data mentioned above are obtained by Ardell from the comparison of experimental data on kinetics of grain coarsening in the Ni−Al alloy with his improved kinetic model. 80 The reason why the interface between the Ni 3 Al and Ni−Al matrix remains in a strained-coherent state follows from Figure 2. This is because σ s−c * is smaller compared to σ se and because Nature prefers states with minimum possible energy.…”

“…Now, let us substitute eq into eq : σ normals − normalc * = σ normalc + k 54 · Y cu − nm · z normalo 3 Eq with parameters listed in Table is compared to “experimental” data and by the least square method an optimum value is found: k ≅ 2400 nm (see Figure ), being in the middle of the possible interval found above (1000 ... 5000 nm). “Experimental” data mentioned above are obtained by Ardell from the comparison of experimental data on kinetics of grain coarsening in the Ni–Al alloy with his improved kinetic model . The reason why the interface between the Ni 3 Al and Ni–Al matrix remains in a strained-coherent state follows from Figure .…”

“…Temperature dependence of the interfacial energy of the gamma/gamma-prime interface in the Ni–Al alloy. Data points: “experiments”, the top dotted theoretical line represents the strain-free semi-coherent interface calculated by eq , the bottom theoretical dotted line represents the strain-free coherent interface, and the bold line represents the estimated coherent strained interface calculated by eq with parameters of Table and k = 2400 nm.…”

“…70,81−83 As follows from above, strained-coherent NPs remain stable even after they are coarsened if σ s−c * < σ se . Substituting eqs 5a and "experiments", 80 the top dotted theoretical line represents the strainfree semi-coherent interface 45 calculated by eq 5a, the bottom theoretical dotted line represents the strain-free coherent interface, 45 and the bold line represents the estimated coherent strained interface calculated by eq 9e with parameters of Table 1 and k = 2400 nm. 9e and k =2400 nm into this condition, the following criterion is obtained to select cubic metallic phase combinations that ensure nanocomposites with coherent NPs: SSC 4.9…”

A „capillaritási tünemények”, azaz Eötvös kapilláris egyenlete és annak háttere • The “Capillarity Phenomena”: On Eötvös’s Capillary Equation and Its Historical Background

“…Az ugyanis általánosan érvényes minden határfelület-típusra, hogy azon a hőmérsékleten, amikor a határfelület eltűnik (mert például feloldódik egymásban a határfelületet definiáló korábbi két fázis), akkor a határfelületi energia zérussá válik. Ez egy nagyon hasznos határérték, amit én többek között a szuperötvözetek élettartama szempontjából fontos koherens szilárd/szilárd határfelületi energia hőmérsékletfüggésének leírására használtam a közelmúltban (Kaptay, 2020), és amit azóta amerikai kutatók is átvettek (Ardell, 2021).…”