*4.1. Particle Morphology*

The SEM data show that the particle fragmentation process is not the same in Al-2Fe and Al-4Fe alloys, presumably due to the morphology of the intermetallic particles in the as-cast state. The difference in the alloys' properties could be explained by the difference in the fragmentation process. To evaluate this difference, we take the overall interphase area parameter total surface of the "aluminum–particle" interface.

Corresponding calculations and measurements have been undertaken in order to find the overall interphase area between aluminum and intermetallic particles. The following assumption has been made: all particles have the shape of perpendicular prisms with a base of *AP* (area of particle) and a height of *h* (Figure 6).

**Figure 6.** Particle morphology model describing the terms necessary for the calculations.

The area of interest (*AI*) is calculated via the markers on the SEM images. For statistical purposes, acquisition of data has been performed over multiple SEM images for each of the alloys.

The interphase area (*IA*) is calculated as a perimeter ( *P*) multiplied by the *h*:

$$IA = P \times h \tag{3}$$

Relative interphase area (*RIA*) is calculated as the interphase area divided by the studied volume (area of interest multiplied by the *h*):

$$RIA = \frac{IA}{AI \times h} = \frac{P}{AI} \tag{4}$$

Table 2 represents the results of the statistical analysis of the data, collected from the Al-Fe alloys SEM images. The average particle size (area) in the as-cast state is smaller in the Al-2Fe alloy 0.26 μm<sup>2</sup> against 2.55 μm<sup>2</sup> in the Al-4Fe alloy.


**Table 2.** Analysis data of Al-Fe alloys' intermetallic particles, obtained from the SEM images.

> HPT leads to particle refinement, and thus to a decrease of their average area of 13 times for the Al-2Fe and of 10 times for the Al-4Fe alloy.

> The average perimeter of particles is bigger in the Al-4Fe alloy in both the as-cast (0.49 μm against 0.26 μm) and HPT (1.24 μm against 0.49 μm) conditions, indicating the presence of the coarser particles in Al-4Fe both before and after deformation. It can be seen (Table 2) that the total perimeter of the particles increases by about two times for the Al-2Fe alloy after HPT, and decreases by about two times for the Al-4Fe alloy. For us, the perimeter-to-area ratio (*PtA*) is of greater importance, since it considers both of these parameters.

> The perimeter-to-area ratio (*PtA*) can be more informative, since it combines these two parameters. The value of the *PtA* is the same for the alloys in the as-cast state, but changes drastically after HPT from 1 to 24.5 μm<sup>−</sup><sup>1</sup> for the Al-2Fe alloy and from 1.1 to 4.96 μm<sup>−</sup><sup>1</sup> for the Al-4Fe alloy. The higher the value of the *PtA*, the smaller the particles in the studied volume. Hence, the particle refinement in the Al-4Fe alloy is five times less intensive than in the Al-2Fe alloy.

> Figure 7 shows the area distribution of particles in Al-Fe alloys depending on their size. In the as-cast state in the Al-2Fe alloy, the area distribution is close to normal, while the Al-4Fe alloy plot has a plateau, pointing to the presence of coarser particles. After HPT, both curves for the Al-2Fe and Al-4Fe alloys become skewed left, showing the decrease in the average area size of the particles. While the distribution of the particle size is characterized by a single peak, for the Al-2Fe alloy, the curve for the Al-4Fe alloy exhibits a second peak, signifying bimodal distribution.

> The *RIA* parameter shows how many interphase boundaries are presented at a given volume. The higher the value of *RIA*, the higher the density of the interphase boundaries. In the as-cast state, *RIA* in the Al-2Fe alloy is higher than in the Al-4Fe alloy 0.396 μm<sup>−</sup><sup>1</sup> against 0.234 μm<sup>−</sup>1. The difference is even more notable after HPT—the *RIA* in the HPT state in the Al-2Fe alloy is more than three times greater than in the Al-4Fe alloy.

> The *RIA* parameter and the level of electrical conductivity in the as-cast Al-2Fe alloy are higher than in the Al-4Fe alloy. This means that in the as-cast condition, the surface amount of the interphase boundaries is not as significant as the total amount of the intermetallic phase. During the HPT, however, we observe a much more intense change of properties (Section 3.2), making the interphase area (and, thus, the morphology of the intermetallic phase in the as-cast state) more significant for the physical properties than its total amount.

**Figure 7.** Particle area distribution: (**a**) in as-cast state, (**b**) after HPT. Histogram for Al-2Fe alloy is marked by blue color, for Al-4Fe alloy is marked by orange color. μm2.

#### *4.2. Formation of the Solid Solution*

The differences in mechanical strength and electrical conductivity are linked to different structural parameters, such as dislocation density, grain size, size and density of particles and so on.

Among all, the negative effect of solid solution on the conductivity is much higher than that of the other crystal lattice defects [1]. A sharp decrease in the electrical conductivity after the HPT (Table 1) can indirectly indicate the strain-induced formation of supersaturated solid solution of Fe in Al.

The lattice parameters of the Al-2Fe and the Al-4Fe alloys in the as-cast condition are close to that of pure Al. It allows suggesting that nearly all Fe atoms are stored within the intermetallic phases which is consistent with the results presented in [25,36]. After HPT, the lattice parameter of both Al-2Fe and Al-4Fe alloys decreases. This change can be associated with the dissolution of Fe in Al [16,25,36]. Al-4Fe alloy, where the decrease of the lattice parameter is smaller than in Al-2Fe alloy, exhibits a tendency to form solid solution with a smaller concentration of Fe.

The discussion in Section 4.1 supports the HPT-induced dissolution of Fe in Al. Since Fe could only migrate to Al from intermetallic particles, and the *RIA* parameter after HPT is 3 times higher in the Al-2Fe alloy than in the Al-4Fe alloy, the microstructure of the as-cast Al-2Fe alloy provides wider opportunities for Fe to diffuse into the Al matrix by the higher density of interphase boundaries.

The difference in the lattice parameter, electrical conductivity, and density of the interphase boundaries before and after HPT in both alloys indicates more intensive formation of the strain-induced solid solution of Fe in Al in Al-2Fe alloy. Since intermetallic particles are still present after the HPT, we can safely assume that the concentration of Fe in the supersaturated solid solution is far less than 1 at. % (which is the total amount of Fe in Al-2Fe alloy). The solid solution is formed due to the partial dissolution of intermetallic particles. This observation is consistent with the previous studies, focused on the intermetallic phase transformation in Al-Fe alloys [14,15,25,36].

Higher dissolution rate of Fe in Al matrix in Al-2Fe alloy than in Al-4Fe alloy during HPT proves that the total amount of alloying element is not as important for the formation of the solid solution as the morphology of the intermetallic phase in the initial state.
