Dendrite spacing in unidirectionally solidified Al-Cu alloy

Directional solidification experiments have been carried out to study the variation in primary and secondary arm spacings with solidification parameters in the Al-Cu system. It is found that the primary arm spacing Z₁ obeys the common correlation Z₁ = KG^-aV^-b in the high velocity regime or low temperature gradient regime, where a and b are constants, the value of K included the composition dependence, G is the temperature gradient in the liquid and V the growth rate; however, it does not obey this correlation for the low velocity regime or high temperature gradient regime but goes through a maximum or a catastrophe as a function of V or G at V = V_cs/k or G = kG_cs, where k is the equilibrium distribution coefficient, and V_cs and G_cs are the critical velocity and temperature gradient at the limit of constitutional undercooling respectively. The initial secondary arm spacings Z₂₀ are nearly independent of G and mainly depended on V, Z₂₀ = 0.016 V^-0.54 (mm). The secondary arm spacing Z₂ tends to c oarsen with time and thus is a function of coarsening time t_f, Z₂ = 0.016t^0.34_f (mm). Theoretical analyses of the primary arm spac ing and the initial secondary arm spacing have been proposed, and the derived relationships agree reasonably well with the above experimental results.