Lattice misfits in four binary Ni-Base γ/γ¹ alloys at ambient and elevated temperatures

Abstract

High-temperature X-ray diffractometry was used to determine thein situlattice parameters,a _γ anda _γ′, and lattice misfits, δ = (a _γ′, -a _γ)/a _γ, of the matrix (γ) and dispersed γ′-type (Ni₃X) phases in polycrystalline binary Ni-Al, Ni-Ga, Ni-Ge, and Ni-Si alloys as functions of temperature, up to about 680 °C. Concentrated alloys containing large volume fractions of theγ′ phase (∼0.40 to 0.50) were aged at 700 °C to produce large, elastically unconstrained precipitates. The room-temperature misfits are 0.00474 (Ni-Al), 0.01005 (Ni-Ga), 0.00626 (Ni-Ge), and -0.00226 (Ni-Si), with an estimated error of ± 4 pct. The absolute values of the lattice constants of theγ andγ′ phases, at compositions corresponding to thermodynamic equilibrium at about 700 °C, are in excellent agreement with data from the literature, with the exception of Ni₃Ga, the lattice constant of which is much larger than expected. In Ni-Ge alloys, δ decreases to 0.00612 at 679 °C, and in Ni-Ga alloys, the decrease is to 0.0097. In Ni-Si and Ni-Al alloys, δ exhibits a stronger temperature dependence, changing to-0.00285 at 683 °C (Ni-Si) and to 0.00424 at 680 °C (Ni-Al). Since the times required to complete the high-temperature X-ray diffraction (XRD) scans were relatively short (2.5 hours at most), we believe that the changes in δ observed are attributable to differences between the thermal expansion coefficients of theγ andγ′ phases, because the compositions of the phases in question reflect the equilibrium compositions at 700 δC. Empirical equations are presented that accurately describe the temperature dependences ofa _γ,a _γ′, and δ over the range of temperatures of this investigation.