**2. Materials and methods**

36 Corrosion Resistance

However, a quantitative understanding of the CET requires a thorough comprehension of

In 1984, Hunt first developed an analytical model to describe steady-state columnar and equiaxed growth, and to qualitatively reveal the effects of alloy composition, nucleation density and cooling rate on the CET. On the other hand, he used a very simple empirical relationship to describe the variation of the undercooling with alloy composite and solidification rate. Cockcroft et al. (1994) used a more recent growth theory for the columnar and equiaxed growth but without considering high velocity non-equilibrium effects under rapid solidification. Recently, based on Hunt's CET model, Gäumann et al. (1997, 2001) developed a more comprehensive model by combining KGT model (Kurtz et. al., 1986) for directional solidification with LKT model (Lipton et. al., 1987) for the undercooling melt growth, with high velocity non-equilibrium effects to be taken into account. Gäumann et al. (2001) succeeded in applying their model to epitaxial laser metal forming of single crystal. In previous research, the authors of this work carried out experiments in which the conditions of columnar to equiaxed transition (CET) in directional solidication of dendritic alloys were determined The alloy systems in this work include Pb–Sn (Ares & Schvezov, 2000), Al–Cu (Ares et. al., 2011), Al–Mg (Ares et. al., 2003), Al–Zn and Zn-Al alloys (Ares & Schvezov, 2007). These experiments permit to determine that the transition occurs gradually in a zone when the gradient in the liquid ahead of the columnar dendrites reaches critical and minimum values, being negative in most of the cases. The temperature gradients in the melt ahead of the columnar dendrites at the transition are in the range of -0.80 to 1.0 ºC/cm for Pb–Sn, -11.41 to 2.80 ºC/cm for Al–Cu, -4.20 to 0.67 ºC/cm for Al–Si, -1.67 to 0.91 ºC/cm for Al–Mg, -11.38 to 0.91 ºC/cm for Al–Zn. Two interphases are dened; assumed to be macroscopically at, which are the liquidus and solidus interphases. After the transition, the speed of the liquidus front accelerates much faster than the speed of the solidus front; with values of 0.004 to 0.01, 0.02 to 0.48, 0.12 to 0.89, 0.10 to 0.18 and 0.09 to 0.18 cm/s, respectively. Also, the average supercooling of 0.63 to 2.75 1C for Pb–Sn, 0.59 to 1.15 1C for Al–Cu, 0.67 to 1.25 1C for Al–Si, 0.69 to 1.15 1C for Al–Mg, 0.85 to 1.40 1C for the Al–Zn and was measured, which provides the driving force to surmount the energy barrier required to create a viable solid–liquid interface (Ares et al., 2005). A semi-empirical model to predict the columnar to equiaxed transition is developed based on experimental results obtained from measurements during solidication of lead–tin alloys directly upwards (Ares et al., 2002). The measurements include the solidication velocities of the liquidus and solidus fronts, and the temperature gradients along the sample in the three regions of liquid, mushy and solid. The experimental data was coupled with a numerical model for heat transfer. With the model, the predicted positions of the transition are in agreement with the experimental observations which show that the transition occurs when the temperature gradient reaches values below 1ºC/cm and the velocity of the liquidus front increases to

In addition, the thermal parameters, type of structure, grain size and dendritic spacing with the corrosion resistance of Zn-4wt%Al, Zn-16wt%Al and Zn-27wt%Al alloys were correlated (Ares et al., 2008). The polarization curves showed that the columnar structure is the most susceptible structure to corrosion, in the case of the alloy with only 4wt%of Al. The rest of the structures presented currents of peaks in the same order which were independent to the

all physical mechanisms involved.

values around 0.01cm/s.

concentration of Al composition presenting in the alloy.
