Stability criterion for determination of primary arm spacing

Abstract

A new expression of the primary arm spacing is analytically evaluated assuming that the observed cell/primary arm spacing defines a stable cell/dendrite configuration. Two mechanisms determining the existence of a stable configuration have been previously identified. In the lower cell/dendrite spacing range, there is the mechanism of overgrown which limits inferiorly the stable cell dendrite spacing. In the upper cell/dendrite spacing range, the mechanism of dendrite division is identified. One expects at the intersection of these two unstable regimes to find a stable dendrite array configuration defined by the primary arm spacing λ1. A quasi-steady state columnar dendrite array, whose one dendrite is slightly perturbed, is considered. Using this particular configuration, it is possible to derive a characteristic time for each mechanism described above. The primary arm spacing is derived assuming that stability of the dendritic array is insured only if these both characteristic times are of the same order of magnitude. The value of λ1 is confronted with experimental results. The comparison is excellent and improves previous models predictions.