title: Scaling theory of two-phase dendritic growth in undercooled ternary melts.
abstract: 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 ρ∼λ (ρ: dendrite tip radius; λ: eutectic interphase spacing) suggested by recent experimental results [S. Akamatsu et al., Phys. Rev. Lett. 104, 056101 (2010)] leads to a complete solution of theselection problem and to the scaling rule ρ∼λ -1/2 (v: dendrite tip growth rate).
authors.affiliation: Institut des Nanosciences de Paris, UMR 7588, Sorbonne Universités/UPMC, 4 place Jussieu, 75005 Paris, France and INSP, UMR 7588, CNRS, 4 place Jussieu, 75005 Paris, France.
authors.forename: Silvère
authors.initials: S
authors.lastname: Akamatsu
authors.affiliation: Institut des Nanosciences de Paris, UMR 7588, Sorbonne Universités/UPMC, 4 place Jussieu, 75005 Paris, France.
authors.forename: Sabine
authors.initials: S
authors.lastname: Bottin-Rousseau
authors.affiliation: Institut des Nanosciences de Paris, UMR 7588, Sorbonne Universités/UPMC, 4 place Jussieu, 75005 Paris, France and INSP, UMR 7588, CNRS, 4 place Jussieu, 75005 Paris, France.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Faivre
authors.affiliation: Peter Grünberg Institut, Forschungszentrum Jülich, D-52425 Jülich, Germany.
authors.forename: Efim A
authors.initials: EA
authors.lastname: Brener