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Zn-0.7wt.%Cu hypoperitectic alloys were directionally solidified upwards with different temperature gradients (3.85 K/mm to 9.95 K/mm) at a constant growth rate (0.042 mm/s), and with different growth rates (0.0083 mm/s to 0.436 mm/s) at a constant temperature gradient (3.85 K/mm), using a Bridgman-type growth apparatus. Measurements of microhardness of the directionally solidified samples were carried out. The dependence of microhardness (HV) on growth rate (V) and temperature gradient (G) was analyzed. According to these results, it has been found that, for increasing values of G and V, the value of HV increases. Variations of electrical resistivity (q) and electrical conductivity (r) for cast samples with temperature from 300 K to 670 K were also measured by using a standard direct-current (DC) four-point probe technique. The variation of the Lorenz coefficient with temperature for the Zn-0.7wt.%Cu hypoperitectic alloy was determined using the measured values of electrical conductivity and thermal conductivity. The enthalpy of fusion for the same alloy was determined by means of differential scanning calorimetry (DSC) from the heating trace during the transformation from liquid to solid.