Coagulation and solidification of the copper droplets suspend in the liquid slag are usually accompanied by the appearance of the Cu-Cu2O eutectic. Locally, this eutectic is created in the stationary state. Therefore, frequently it has a directional morphology. Since the E = (Zn) + Zn16Ti – eutectic is similar in the asymmetry of the phase diagram to the Cu-Cu2O – eutectic, the (Zn) single crystal strengthened by the E = (Zn) + Zn16Ti precipitate is subjected to directional growth by the Bridgman’s system and current analysis. Experimentally, the strengthening layers (stripes) are generated periodically in the (Zn) – single crystal as a result of the cyclical course of precipitation which accompanies the directional solidification. These layers evince diversified eutectic morphologies like irregular rods, regular lamellae, and regular rods. The L – shape rods of the Zn16Ti – intermetallic compound appear within the first range of the growth rates when the irregular eutectic structure is formed. Next, the branched rods transform into regular rods and subsequently the regular rods into regular lamellae transitions can be recorded. The regular lamellae exist only within a certain range of growth rates. Finally, the regular rods re-appear at some elevated growth rates. The entropy production per unit time and unit volume is calculated for the regular eutectic growth. It will allow to formulate the entropy production per unit time for both eutectic structure: rod-like and lamellar one.