Interdependence among kinetics, morphology, spatial correlations and volume fraction on coarsening behavior in binary nickel-titanium, nickel-germanium and nickel-gallium alloys

The coarsening behavior of coherent γ′ Ni ₃Ti, Ni₃Ge and Ni₃Ga precipitates in binary 10.31, 11.84, 13.72 at% Ni-Ti, 12.15, 13.01, 14.03 at% Ni-Ge and 14.89, 18.31 at% Ni-Ga alloys was investigated to study the interdependence among kinetics, morphology, spatial correlations and volume fractions. The Ni-Ti, Ni-Ge and Ni-Ga alloys were aged at 724, 720 and 628°C, respectively. At these aging temperatures, the volume fractions were 0.017, 0.117, 0.240 in the Ni-Ti alloys, 0.022, 0.105, 0.202 in the Ni-Ge alloys and 0.058, 0.363 in the Ni-Ga alloys. These alloy systems were chosen because they provide different lattice mismatches, varying from an intermediate value of 0.0063 in the Ni-Ge system to a higher value of 0.0085 in Ni-Ti system to the highest one, 0.0101, in the Ni-Ga system at room temperature. Measurements were made of the particle growth kinetics and particle size distributions using transmission electron microscopy. The solute depletion kinetics were investigated using measurements of the ferromagnetic Curie temperature in the Ni-Ti, Ni-Ge and Ni-Ga alloys. From both kinetic measurements, estimates of the precipitate-matrix interfacial free energy, σ, and the diffusion coefficient, D, were obtained. Values of σ were about 14.1, 16.1 and 4.8 mJ/m2, and values of D were about 4.98 × 10−18, 2.10 × 10−17 and 4.59 × 10−19 m2/s for the Ni-Ti, Ni-Ge and Ni-Ga alloys, respectively. These data are in reasonably good agreement with previously reported values. The coarsening rates in these alloys decreased with increasing volume fraction. These results are totally contrary to all the theories of the volume-fraction dependence of the coarsening rate. The morphological evolution was also studied experimentally and compared with several theoretical predictions. In particular, rod-shaped Ni₃Ga precipitates were found in aged Ni-Ga alloys for the first time in a binary Ni-base alloy system. Furthermore, the precipitation of matrix solid solution γ in γ′ (Ni₃Ge) precipitates was also observed in a Ni-Ge alloy. This result is consistent with a recently published Ni-Ge phase diagram.; Finally, it is demonstrated that the anomalous dependence on volume fraction, the sizes at which shape transitions occur, and the strength of spatial correlations does not simply correlate with the magnitude of the lattice mismatch, $3$. Instead, these tendencies are found to correlate better with the reciprocal of the length scale parameter , where is an elastic constant.