The fine-scale precipitates, that occurs during aging, the supersaturated Al–1.0 at.% Mg–x at.% Si (x = 0.6, 1.0 and 1.6) alloys have been investigated by differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and X-ray diffraction (XRD) techniques. The strength of the alloys increases as a high density of very fine β″ coherent and β′ semicoherent precipitates nucleate. The precipitates compositions have been determined by analyzing the X-ray diffraction (XRD) charts, by using Scherrer equation. The obtained results showed that the β″ and β′ precipitates size lies in the nanometer range (from 5 nm to 32 nm). In addition, increasing Si concentration has exhibited an increase in the density of the precipitates, which fortifies the physical properties.

The main aim of this paper is to define and study a new confluent hypergeometric matrix function, say, (m,n)-Kummer's matrix function of two complex variables. The radius of regularity and recurrence relation on this function is established. The effect of differential operator on this function is investigated. We study the operation of a differential operator on the Hadamard product of two (m,n)-Kummer's matrix functions. Finally, we define the composite (m,n)-Kummer's matrix functions and the effect of differential operator on this function is investigated