Similarity law for the tilt angle of dendrites in directional solidification of non-axially-oriented crystals

We report on an experimental and numerical study of tilted dendrites observed in thin-film directional solidification of a CBr4-8 mol % C2Cl6 alloy for an arbitrary orientation of the crystal with respect to the plane of the sample and the pulling direction. The drift velocity V-d, or, equivalently, the tilt angle alpha (defined as tan alpha=V-d/V, where V is the pulling velocity) of the dendrites is an increasing function of V and the dendritic spacing lambda. We show that alpha scales like the Peclet number P=lambda V/D (D is diffusion coefficient in the liquid). In the limit of large P values (P>7), alpha tends to a constant, crystallographically determined value. We show that the alpha versus P master curve is insensitive to the temperature gradient as long as V is not too close to the cellular-threshold velocity. The tilt dynamics of dendrites in directional solidification is thus essentially deter mined by the interactions between neighboring dendrites within the approximately periodic pattern. We also show that the shape of the master curve only slightly depends on the value of the interfacial anisotropy, as long as it is not too small.