The principal length scales associated with dendritic solidification, which being the dendritic tip-radius (R-tip) and the primary dendritic arm spacing, are functions of the relative solutal interdiffusivities of the different components in a multi-component alloy. In this paper, we firstly derive marginal stability based theories to predict R(tip )during isothermal free growth in any generic multi-component alloy for any generic diffusivity matrix. Here, we extend the Ivanstov solution of the diffusion problem in the liquid with a parabolic solid-liquid interface and propose the closure conditions between the The principal length scales associated with dendritic solidification, which being the dendritic tip-radius (R-tip) and the primary dendritic arm spacing, are functions of the relative solutal interdiffusivities of the different components in a multi-component alloy. In this paper, we firstly derive marginal stability based theories to predict R(tip )during isothermal free growth in any generic multi-component alloy for any generic diffusivity matrix. Here, we extend the Ivanstov solution of the diffusion problem in the liquid with a parabolic solid-liquid interface and propose the closure conditions between the R-tip and the selected dendrite tip velocity (V) based on modification of the classical marginal stability criteria for multi-component situations. Additionally, we derive the constant Rtip(2)V from phase-field simulations and using the Ivantsov parabola as the approximate interface shape compute the R-tip and the V, which we term as "Approximate microsolvability prediction (AMP)". Thereafter, we compare our predictions of R-tip, V as well as phase compositions with independent phase-field simulation results for different choices of the diffusivity matrix, where we show that the analytical theories based upon the marginal stability theory are unable to accurately predict variations of the dendrite tip velocity V and the R-tip. We thereby utilize the phase-field simulation results to investigate the tip selection in multi-component alloys and derive an appropriate solvability constant sigma*. We find that the sigma* in a multi-component alloy is a function of the diffusivity ratios of the components for the case of a diagonal diffusivity matrix. and the selected dendrite tip velocity (V) based on modification of the classical marginal stability criteria for multi-component situations. Additionally, we derive the constant Rtip(2)V from phase-field simulations and using the Ivantsov parabola as the approximate interface shape compute the R-tip and the V, which we term as "Approximate microsolvability prediction (AMP)". Thereafter, we compare our predictions of R-tip, V as well as phase compositions with independent phase-field simulation results for different choices of the diffusivity matrix, where we show that the analytical theories based upon the marginal stability theory are unable to accurately predict variations of the dendrite tip velocity V and the R-tip. We thereby utilize the phase-field simulation results to investigate the tip selection in multi-component alloys and derive an appropriate solvability constant sigma*. We find that the sigma* in a multi-component alloy is a function of the diffusivity ratios of the components for the case of a diagonal diffusivity matrix.
