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.