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We study the contributions from solute segregation to rafting in CMSX4 and CMSX6 superalloys. For this purpose, we use a phase-field model that takes into account the cross interaction between all solutes in Ni-base superalloys. The thermodynamic formulation in the phase-field model is validated by comparing phase-field simulations to ThermoCalc equilibrium calculations and DICTRA sharp interface simulations. Additionally, an elastic term is coupled to the model to account for the misfit, elastic inhomogeneity and applied loading. A technique to quantify the kinetics of microstructures with anisotropic γ′γ′-precipitates is integrated in the model. Our simulations reveal that the rafting process is considerably slower in CMSX4 than in CMSX6. The presence of slow diffusing elements in CMSX4, particularly the refractory element Re, plays a major role in reducing the rate of rafting. The results suggest that Re slows interface mobility by accumulating along the growth path, a behavior we attribute to its low diffusivity and low solubility in the γ′γ′-precipitate.