The copper and copper alloys’ ingots have been subjected to structural observation in order to estimate the Peclet Number at which these ingots were solidifying. It was stated that the formation of columnar structure within the ingots occurred at a high Peclet Number, higher than the threshold value of this parameter, Pe = 500. The formulated relationships of the Growth Law correspond to a high Peclet Number due to application of the adequate development in series of the Ivantsov’s function. The Growth Law has been developed on the basis of the definition of the wavelength of perturbation which leads to the dispersion of the planar s/l interface. New definition of the index of stability connected with the behavior of solute concentration at the s/l interface has been delivered. The current definition is related to non-equilibrium solidification. The index can be easily calculated using some parameters delivered by a given Cu-X phase diagram. Physical meaning of the formulated Growth Law has also been presented.

Experimental observations of the steel morphology as well as measurements of the solutes concentration in the macro-scale were made on the basis of the vertical cut at the mid-depth of the 15-tons steel forging ingot serially produced in one of the steel plant in Poland. Experimental observations of the morphology accompanied by the measurements of the Peclet Number were also made on the cross-section of the continuously cast brass ingots serially produced in the copper / brass industry in Poland. The performed measurements allowed to work out some maps of the alloying elements segregation for the longitudinal section of the steel static ingot and a Growth Law for the columnar grains formation in the brass ingots. The marginal stability criterion has been applied to the last mentioned development / description. Some suggestions for the micro-segregation measurement mode in the columnar structure are derived.

The (Zn) – single crystal strengthened by the E = (Zn) + Zn16Ti eutectic 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.

A new solution to the diffusion equation is provided to describe the micro-field of the solute concentration in the liquid adjacent to the front of the growing eutectic structure. The solution is based on the mass balance in the considered system. Moreover, the existence of the protrusion of the leading eutectic phase over the wetting one is required by the mass balance. The appearance of the d – protrusion in the growing eutectic is well confirmed by the experimental observations of the frozen solid/liquid interface. The mentioned solution satisfies the concept of the eutectic coupled growth according to which undercooling of the leading phase is less than undercooling of the wetting eutectic phase. Also, the Ti – solute micro-segregation / redistribution is analyzed within the matrix of the single crystal. The micro-segregation is described as a result of the solution to the adequate, newly developed differential equation. The definition for the solute redistribution is given by the subsequently / separately formulated relationship. This definition takes into account both extent -, and intensity of the solute redistribution.

Finally, the entropy production is calculated for the regular lamellae -, and for the regular rods formation, respectively. The entropy production is a function of some parameters which define the eutectic phase diagram, coefficient of the diffusion in the liquid, and some capillary parameters connected with the mechanical equilibrium located at the triple point of the solid/liquid interface. Branches formation is related to the marginal stability. A new criterion is formulated and subjected to successful verification. It is: in the structural – thermodynamic competition the winner is this kind of the pattern for which minimum entropy production has a lower value.