Primary Arm Spacing Λ1 Research Articles

Stability criterion for determination of primary arm spacing

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.

The dendrite arm spacings of aluminum-copper alloys solidified under steady-state conditions

Aluminum-copper alloys of different composition have been solidified under steady-state conditions with known growth velocities and temperature gradients. Specimens were quenched during solidification to reveal the dendrite growth morphology and to allow the solute content at dendrite tips to be analyzed. Primary and secondary arm spacings have been measured as a function of the distanced behind the growing dendrite tips, the tip velocityR the temperature gradient in the liquid Gl and the solute content. The primary arm spacing λ1 is described for each alloy by the empirical relation: λ1 = kGL-aR-b wherek is a constant, and both a and b are close to 1/2; λ1 is also found to increase with solute content. The secondary arm spacing λ2 for each alloy increases with timeθ spent in the liquid/solid region, being directly proportional to θn where n is close to 1/3; increasing solute content however causes a reduction in λ2. It is suggested that the observed “coarsening” of the secondary arms is primarily a coalescence phenomenon.