Fig. 1 Vertical upward directional solidification casting assembly and its devices

Fig. 2 Schematic representation of a, c transverse, b longitudinal sections with methods used to measure dendritic and interphase spacings: intercept method for λ, λ2 and λ3 and triangle method for λ1

Fig. 3 a Experimental time-temperature curve allowing transformation temperatures to be determined; b experimental thermal profiles obtained along the length of the Sn-9 wt%Zn-2 wt%Cu alloy DS casting

Fig. 4 Experimental profiles obtained for the Sn-Zn-Cu alloy corresponding to a position versus time taken by the liquidus front to reach each thermocouple; b growth rate, c cooling rate as a function of position

Fig. 5 Macrostructure of the ternary Sn-9 wt%Zn-2 wt%Cu alloy DS casting with indications of three relative positions at 5, 20 and 70 mm from the cooled surface of the casting and their corresponding transverse and longitudinal microstructures

Fig. 6 a Primary/tertiary dendritic arm spacing as a function of cooling rate (T˙T˙), b secondary dendritic spacing as a function of growth rate (v) for the Sn-Zn-Cu alloy. R2 is the coefficient of determination

Fig. 7 Interphase spacing as a function of growth rate (v) for the Sn-9 wt%Zn-2 wt%Cu alloy

Fig. 8 SEM images of transverse sections detailing the morphological evolution of α-Zn eutectic phase surrounded by the Sn-rich dendritic matrix in the Sn-9 wt%Zn-2 wt%Cu alloy. P is the position from the metal/mold interface The resulting eutectic microstructure of the Sn-9 wt% Zn-2 wt%Cu alloy, close to the bottom of the casting, is formed by a mixture of globular-like Zn particles embedded in a Sn-rich matrix, as can be observed in Fig. 8. However, at positions farther away from the cooled surface of the casting, needle-like particles of the α-Zn phase start to prevail. Regions within the DS casting associated with v > 0.5 show prevalence of globules, while the needle-like α-Zn phase particles are restricted to v < 0.3 mm/s. These limits regarding the different eutectic morphologies of the Sn-Zn-Cu alloy apply also to the binary Sn-9 wt%Zn alloy, as reported by Garcia et al. [14].

Fig. 9 Experimental Zn and Cu macrosegregation profile along the length of the DS Sn-9 wt%Zn-2 wt%Cu alloy DS casting

Fig. 10 Elemental SEM-EDS mappings obtained along the transverse specimen at the positions P = 10 mm, P = 20 mm and P = 70 mm from the metal/mold interface of the vertically solidified Sn-9 wt%Zn-2 wt%Cu alloy casting

Fig. 11 XRD patterns of the Sn-9 wt%Zn-2 wt%Cu alloy for specific positions along the length of the DS casting: aP = 5 mm, bP = 90 mm

Fig. 12 Evolution of Vickers hardness as a function of the inverse of the square root of the interphase spacing for the Sn-9 wt%Zn-2 wt%Cu solder alloy