Growth and pinch-off of sidearm necks: a model of dendrite fragmentation

Dendrite fragmentation commonly occurs by pinch-off of sidearms at the narrow neck with the parent stem. Comprehensive measurements of the local neck dynamics are performed using in-situ synchrotron radiography experiments in which a flat sample of a Ga–35wt%. In alloy is solidified under both steady and transient growth conditions with minimal effects of melt convection. The measurements reveal two characteristic limits where the neck radius follows universal self-similar t 1 / 3 power laws, with a positive rate constant in the limit of steady growth and a negative rate constant in the isothermal pinch-off limit. The temporal power law for steady growth found here relates the sidearm neck radii to the tip radius of the primary dendrite stem, and the neck radius probability density distribution is shown to be symmetric. For the more general case of decelerated growth, it is observed that the neck initially widens along the steady growth limit, is then increasingly limited by the pinching tendency, and for sufficiently large decelerations converges ultimately to the pinch-off limit. A dynamical model is derived that predicts the behavior of the sidearm neck radius under arbitrary decelerating growth conditions. The highly variable nature of dendrite fragmentation is explained by the stochastic properties of the initial sidebranch development process. The model can be used to estimate the number of dendrite fragments forming during a certain time interval at any location behind the primary tips.