Solidification thermal variables, i.e., transient metal/mold heat transfer coefficient and tip cooling rate, and tertiary dendrite arm spacings have been measured in Sn-Pb and Al-Cu alloys directionally solidified under unsteady-state heat flow conditions. The tertiary arms seem to initiate from the secondary branches only when a certain value of a parametric factor (delta = (T) over dot/CO) relating cooling rate and alloy solute content is attained. It was observed that a -0.55 power law characterizes the tertiary spacing variation with the cooling rate, for any hypoeutectic alloy experimentally examined. The influence of initial alloy composition on tertiary dendritic spacing is also analyzed. The insertion of analytical expressions for cooling rate into the resulting experimental equations permitting to establish empirical formulae relating tertiary dendrite spacing with unsteady-state solidification parameters like: melt superheat, type of mold and transient metal/mold heat transfer coefficient is proposed. (C) 2004 Elsevier B.V. All rights reserved.37341671131138