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The morphology and kinetics evolution of γ′ and γ phases in Ni-xAl-(20‒x)Cr at% (x = 7.5–13.7) alloys aged at 700 °C were studied by utilizing the phase-field simulation. The separated γ′ phases from γ matrix in low Al content (x 13) alloys, and long-time aging produced near cubic γ′ phase. The coarsening rate of γ′ phase declined firstly when the Al content x = 7.5–9.0, then increased sharply as x ranges from 9 to 12, while the coarsening rate of γ phase declined directly. Additionally, the average edge-to-edge distance of neighboring γ′ phases showed a three-stage variation when Al content x

The morphology and kinetics evolution of the γ′(Ni3Al) phase during re-dissolution are studied in Ni-15 at% Al alloy, the changes of volume fraction and average particle radius of the γ′ phase were clarified with phase-field simulation. During isothermal aging, the interdistance of the neighboring γ′ phase affects the interface concentration gradient of Al, which dominates the growth or re-dissolution of the γ′ phase particle. After isothermal aging at 700 K, the alloy is continuously heated to 900 K with different heating rates, the re-dissolution lag happens, meaning the coalescence coarsening of adjacent γ′ phase particles still proceeds at the initial heating stage. The pre-dissolution of γ′ phase with cubic shape is re-dissolved firstly at the edges and corners, in continuous heating to 900 K or by second-order aging from 700 to 900 K. Different from continuous heating, in the second-order aging process, the connected particles with band shape are broken initially by re-dissolving. At different heating rates, the similar dynamic relationships are abstracted for the volume fraction and the heating rates, and the average particle radius and the heating rates.

The early precipitation of γ'-Co3(Al, W) phase affects the spatial distribution and kinetic evolution of precipitates for the morphology transmission effect, but the nucleation and concomitant growth are not studied still by aging experiments due to the expeditious precipitation of γ' phase in Co-Al-W alloy. By using the phase-field simulation with sublattice free energy, the early-stage kinetics evolution of γ'-Co3(Al, W) phase in a medium supersaturation Co-9Al-8W (at.%) alloy aged from 1023 K to 1173 K is investigated. The influences of aging temperature on the evolution of morphology and composition of γ' phase, and the kinetics of nucleation and growth to coarsening are clarified. It is found that the rates of composition evolution of W in γ phase are two or three times that of γ' phase, and the W compositions in γ and γ' phases show a linear relationship with time t–1/3, which means that the coarsening takes place earlier at high temperature. In addition, the equilibrium partitioning ratios indicate Al and W partition into the γ' phase and the ratios decrease with elevated temperature. The compositional variations across the γ/γ' phase interfaces suggest that low aging temperature makes the stoichiometric ratio closer to 3:1. Moreover, the precipitation evolutions from early nucleation to growth and coarsening in Co-Al-W alloy are distinguished, and the rate constants of square and cube of average particles radius increase with temperature. In later growth stage, the relationship of the square of average particles radius and time is obeyed, while the steady-state coarsening stage follows the cube law. The time exponents of particles number density at the coarsening stage are close to –1 of Kuehmann-Voorhees (KV) theory. The study demonstrates that the early-stage evolution of γ' phase which is undiscovered in the experiment can be captured by the phase-field simulation, and the resultant kinetics laws agree well with the experimental and theoretical results.

The two-dimensional phase-field simulation coupled with the sublattice model is utilized to simulate the γ′ precipitation in Ni-12 Al-x Cr at.% (x = 8, 9, 10) alloys aged at 1073 K for 831 h. The compositional evolution of Cr and Al, and the precipitation kinetics of γ′ phase are studied. At the nucleation and growth stage, the concentration distribution of Cr and Al is characterized by an Al enrichment and Cr depletion at the γ/γ′ interface. As Cr content increases from 8 to 10 at.%, the partition ratio of Al and Ni into γ′ phase is promoted, and the equilibrium volume fraction of γ′ phase is increased, while the Al and Ni atoms at the corner site of L12-Ni3(Al, Cr) sublattice are replaced by Cr atoms partly. Besides, the coarsening rate constants of steady-state coarsening (166.2

Phase separation of the Cr-enriched nanoscaleα′phase in the Fe-38 at.% Cr-10 at.% Al alloy is studied by utilizing phase-field simulation. The partition of elements in theαandα′phases is clarified with the composition evolution through theα/α′phase interface, and the separation kinetics is quantitatively investigated by the temporal evolution of the size and volume fraction of theα′phase. Aluminum partitions into the Fe-enrichedαphase and depletes in theα′phase, and the partition coefficient decreases as the temperature changes from 720 K to 760 K for the steady-state coarsening stage. As the temperature increases, the initial change rate of the volume fraction of theα′phase is faster, indicating an accelerated phase separation. At the coarsening stage, the average particle distance and coarsening rate constant of theα′phase increase with increased temperature, and the ratio of the Ostwald ripening is dominating compared with coalescence coarsening. The element partition and kinetics evolution of theα′phase with temperature are helpful for the morphology and property predication of nanoscale precipitates.

The morphological evolution and precipitation kinetics of γ′ phase in Ni–Al alloys with the variation of volume fraction are studied by using phase-field simulation. The variation of morphology, particles number density and coarsening rate constants are quantitatively clarified with increased volume fraction. The shape of γ′ phase changes from square to rectangular and then to connected strip structure, so the average aspect ratio of γ′ phase increases. The change rate of particles number density has an uniformly increase at the nucleation and growth stage, while it increases firstly and then decreases for volume fraction greater than 30% at the coarsening stage. The coarsening rate constants decrease for the volume fraction less than 20%, while increase when the volume fraction is greater than 30%. In addition, the width of the particles size distribution (PSD) broadens and the peak value decreases, the peak position shifts from 1.0 to 0.5, the PSDs deviate from the theoretical value by the Lifshitz-Slyozov-Wagner for the large volume fraction.