Scaling Theory of Two-Phase Dendritic Growth in Undercooled Ternary Melts

Two-phase dendrites are needlelike crystals with a eutectic internal structure growing during solidification of ternary alloys. We present a scaling theory of these objects based on Ivantsov's theory of dendritic growth and the Jackson-Hunt theory of eutectic growth. The additional introduction of the relationship rho similar to lambda (rho: dendrite tip radius; lambda: eutectic interphase spacing) suggested by recent experimental results [S. Akamatsu et al., Phys. Rev. Lett. 104, 056101 (2010)] leads to a complete solution of the selection problem and to the scaling rule rho similar to nu(-1/2) (nu: dendrite tip growth rate).