3.1. Microstructural Analysis
Figure 1a,b display TEM bright-field and dark-field images, respectively. The corresponding selected area diffraction (SAD) patterns (visible in the inset) reveal the distribution of the Al4C3 phase within the Al matrix.
The microstructural, morphological phase and dislocation strain distribution characteristics are revealed through the TEM-HRTEM imaging study.
Figure 2a-c present the brightfield TEM images, illustrating the distribution of Al4C3 nanoparticles within the Al matrix, adopting a nanorod morphology (some of the nanorods are indicated by arrows for clarity).
Histograms with overlaid distribution curves of nanorod sizes, determined from TEM images for Al-22, Al-24, and Al-26 samples, are graphically represented in
Figure 3a-c, respectively. The graphs also display the mean and standard deviation parameters obtained from histograms fitted to a log-normal function.
High-resolution transmission electron microscopy (HRTEM) analyses were conducted in the vicinity of Al4C3 nanorods in samples with 2 wt. % of Mix sintered at intervals of 2, 4, and 6 hours.
Figure 4a,
Figure 5a and
Figure 6a illustrate the selected region adjacent to the Al4C3 nanorod, along with the associated digital diffraction pattern based on the results of the Fast Fourier Transform (FFT) (obtained using GATAN software). The digital diffraction pattern conducted in Zone A on Al-22 sample, shows the Al phase oriented along the [011] direction. Using Geometric Phase Analysis (GPA), we determined the projected 2D strain tensor component, represented by ε, with the assistance of CrysTBox software (version 1.10) [
16]
To calculate the geometric phase using the methodology proposed by M.J. Hytch and colleagues [
17], we selected two primary reciprocal lattice vectors (g
1(111) and g
2(200)) corresponding to the Al phase from the digital diffraction pattern.
The strain field (ε
xy) distribution within the specified region A is depicted in
Figure 4b. This image reveals how the strain fields are influenced by the presence of dislocations within the examined region. In
Figure 4c, we observe the enlarged FFT-filtered image obtained from the selected region B (see
Figure 4b). The image shows the fringes associated to the (111) Al lattice plane.
Figure 4d provide an enhanced view of the strain field (ε
xy) distribution within the specified region B. The detailed relationship between lattice defects and strain fields (dislocations and stacking faults) is observed in
Figure 4c,d.
The HRTEM image at the interface of a Al4C3 nanorod corresponding to the Al24 sample is shown in
Figure 5a. The digital diffraction pattern inset obtained via FFT from region A indicates that this region corresponds to the aluminum Al phase, which is oriented along the [011] zone axis. The FFT filtered image of region A using the (111) plane of the digital diffraction pattern, is shown in
Figure 5b. This image illustrates the distribution of dislocations within the examined region. For calculating the geometric phase, two primary vectors in reciprocal space were chosen: g1 = 111 and g2 = 200 from de digital diffraction pattern. Strain field distribution (ε
xy) within the specified region A is depicted in
Figure 5c.
Figure 5d provide an enhanced view of the specific area B of both Fourier-filtered and strain fields images, detailing how the deformation fields are influenced by the presence of dislocations.
In
Figure 6a, we observe the HRTEM image of an Al4C3 nanorod taken from the Al26 sample. The digital diffraction patterns corresponding to a region inside the nanorod (region A) and a region outside the nanorod (region B) are visible. Area A correspond to the Al4C3 phase oriented along the [100] zone axis, while area B corresponds to the Al phase, oriented along the [101] zone axis. The Fourier-filtered images using the (015) plane for the Al4C3 phase (area A) and the (101) plane for the Al phase (area B), are shown in
Figure 6b and 6c respectively. The images display the dislocation distribution within the examined regions. For calculating the geometric phase, two primary vectors in reciprocal space of the FFT image, were chosen: g1 = 015 and g2 = 006 and g1 = 021 and g2 = 101 for the Al4C3 and Al phase, respectively. The distribution of strain fields (ε
xy) localized at the dislocations for Al4C3 and Al is depicted in
Figure 6d and 6e, respectively.
Table 2 provides the following values obtained from X-ray diffraction patterns using the CMWP technique for each sample: the average dislocation density, ρ, the area average mean crystallite size, <x> area and the median and variance, m and σLN, of the log-normal size distribution function, the q experimental parameter, the average character number, M and the effective outer cut-off radius Re of dislocations.
The size distribution curve of crystallites was modeled using the log-normal distribution function, f(x), defined by Equation (7) [
18]:
This function depends on the median,
m, and the variance,
σ parameters determined from X-ray analyses (see Table 2). The results corresponding to the concentration of 1 and 2% by weight of Mix and subjected to 0, 2, 4 and 6 h of sintering, are shown in
Figure 3a,b, respectively.
3.3. Results Discussion
During mechanical milling, numerous linear defects are induced in the aluminum matrix. These defects include dislocations generated by shear forces resulting from the impact of the milling media. In the early stages of milling, dislocations organize and form small-angle sub-boundaries. As the milling process advances, a nanostructured state composed of fine crystallites develops [
21]. Based on the results obtained from the CMWP, the logarithmic distribution of the normal grain size (as shown in
Figure 7a,b) reveals a significant difference between the curves of the samples in the green state and those sintered for 2, 4, and 6 hours (for both samples 1 and 2 wt. % of Mix). The findings indicate that the dispersion of crystallite size values increases with longer sintering times. On the other hand, the behavior of dislocation density concerning sintering time and the samples in the green state can be observed in Table 2. Specifically, in the green samples, relatively high dislocation density values were observed (~28x10
14 m
-2), however, in the sintered samples, a significant decrease is evident, with dislocation density values around ~1.8x10
14 m
-2 after 6 hours of sintering in the samples containing 1 wt. % of Mix. Similar trends were observed in samples with 2 wt. % of Mix. In this study, the strengthening of the Al matrix was attributed to a combination of various mechanisms, including Peierls–Nabarro and solid solution strengthening (H
L), dislocation density strengthening (H
D), grain boundary strengthening (H
D), and the Orowan effect (HP). Based on the results obtained from the individual hardening contributions calculated (refer to Table 3), the value of the experimental microhardness is equated to the sum of three main contributions to hardening: H
L + H
D + H
C values. For more clarity, the graph in
Figure 8 depicts the microhardness as a function of sintering time for samples containing 1 wt.% and 2 wt.% of Mix. The columns specify the calculated strengthening contribution, denoted as H
L + H
D + H
C, as well as the contribution from particle dispersion, represented by HP. The latter is determined as the difference between the experimental microhardness (H
EXP) and the sum of H
L + H
D + H
C (refer to Table 3). According to these findings, during mechanical milling, fine and irregular particles of Al
4C
3 disperse within the aluminum matrix, primarily contributing to the generation of dislocation density and reduction in crystallite size in the green state. It is noteworthy that for the samples in the green state (Al-10 and Al-20), an important contribution to hardening is attributed to dislocation density (H
D) and crystallite size (H
C), while a smaller contribution to hardening is observed due to Al4C3 nanoparticle dispersion, H
P (see
Figure 8). These nanoparticles particles were observed using TEM conducted on the Mix powder, which was used to reinforce the Al matrix.
Figure 1a,b present TEM bright-field and dark-field images, respectively, accompanied by the corresponding selected area diffraction (SAD) pattern (inset). These images reveal the distribution of the Al4C3 phase, which exhibits an irregular shape and ranges in size from approximately 5 nm to 20 nm.
On the other hand, after 2 hours of sintering in both samples with 1 and 2 wt.% of Mix, a noticeable reduction in the combined effect of contributions (H
L + H
D + H
C) was observed. Subsequently, a gradual decrease occurs at 4 and 6 hours of sintering, as shown in the graph in
Figure 8. However, the strengthening effect from particle dispersion (HP) intensifies after 2 hours of sintering, reaching a dispersion strengthening value (HP) of approximately 160 HV (~80% higher than the green state sample, Al-10) in samples with 1 wt.% of Mix. In samples with 2 wt.% of Mix, a similar behavior was observed, with an increase of ~100% over the green state sample, Al-20. Moreover, a reduction was observed as the sintering time extended from 4 to 6 hours, resulting in hardness values (HP) of approximately 60 HV for both samples with Mix contents of 1 and 2 wt.%. The results indicate second phase precipitation with sintering, significantly influence the Al matrix strengthening. Brightfield TEM images of the Al22, Al24, and Al26 samples in Figs. 2a, b, and c, respectively, reveal a homogeneous dispersion of nanorod-like Al4C3 particles, which are responsible for the increase in hardness. On the other hand, the decrease in hardness of the aluminum matrix with sintering time is associated with the increase in nanorod size. Based on the histograms with overlaid distribution curves of nanorod sizes shown in
Figure 3a-c, it becomes evident that as sintering time increases, there is an enlargement in the size of nanorods. The average media and standard deviation values obtained from histograms fitted to a log-normal function (values inset in each graph), increases from 57.5 (0.220) for the Al22 sample to 70.5 (0.315) for the Al24 sample, and finally to 64.2 (0.339) for the Al26 sampleIn summary, during the mechanical milling (MM) process, fine and irregular Al₄C₃ particles are dispersed within the Al matrix. During the initial 2 hours of sintering, these particles transform into Al₄C₃ nanorods, which continue to grow as the sintering period extends from 4 to 6 hours. According to Lee et al., smaller particles grow at the expense of larger ones. [
22]. Consequently, this leads to an increase in the interparticle distance. The Orowan strengthening equation predicts a decrease in yield stress as the interparticle mean free path for dislocation motion increases [
23]. The reduction in the strengthening dispersion effect (H
P) particles with increasing sintering time, as depicted in
Figure 8, can be reasonably attributed to the formation of larger particles, as expressed above.
On the other hand, one of the issues encountered in metal matrix composites reinforced with ceramic particles is the generation of lattice dislocations near the interface, which can lead to the failure of a weak interface [
24,
25]. Various authors have reported the fragility of Al-Al
4C
3 composites [
26]. The residual stresses is attributed to the mismatch of coefficient of thermal expansion (CTE) between the reinforcement and the Al matrix during the heating/cooling fabrication process and is directly related to the level of expansion coefficient mismatch between the matrix and reinforcement [
27,
28]. Previous investigations have reported various types of defects at the metal-ceramic interface, including edge and screw dislocations, planar defects such as twin boundaries and stacking faults, and low-angle twist boundaries, among others. [
29]. Other researchers have reported low-angle twist boundaries, which consist of a network of screw dislocations with the Burgers vector lying within the boundary plane [
30,
31,
32].
From the analyses conducted using HRTEM and the GPA method near and at the nanorod interfaces, we observed strain field distributions primarily associated with partial screw dislocations accompanied by stacking faults. Additionally, edge dislocations with opposite signs, known as edge dislocation dipoles, were observed. The formation of edge dislocation dipoles is associated with the motion of screw dislocations containing dislocation jogs [
33,
34,
35].
The HRTEM image analysis of the Al-22 sample revealed strain fields resulting from dislocations within the aluminum matrix near the nanorod (region A), as shown in
Figure 4a,b. The image shows that the presence of these strain fields increased in areas near the nanorod interface. In the filtered image of
Figure 4c we observe a typical dissociated screw dislocations composed of partial dislocations connected by an intrinsic stacking fault in the (111) plane.
Figure 4d depicts the strain field corresponding to the filtered image, revealing the presence of dislocation dipoles.
Similar results were obtained from the HRTEM image analysis of the Al24 sample. In
Figure 5b and 5c is observed the Fourier-filtered and strain fields of a specific area B, respectively. The filtered Fourier image (see
Figure 5b) reveals the presence of dipoles in the Al phase near the nanorod, while
Figure 5c illustrates the distribution of strain fields in this same region.
Figure 5d,e present magnified views of the filtered Fourier image and the strain fields in area B, respectively. The image details the presence of partial dislocations connected by a stacking fault.
Figure 6 presents a comparative view of the Fourier-filtered and the strain field distribution images of the Al4C3 and Al phases at the Al-nanorod interface region of the Al-26 sample. In the filtered image of
Figure 6b, there are virtually no defects observed in the atomic planes corresponding to the Al4C3 phase. In contrast, the Al phase region (
Figure 6c) shows an intrinsic stacking fault in the (111) plane, resulting from dissociated screw dislocations.
Figure 6d,e compare the strain fields in the Al4C3 and Al phases, respectively. A greater presence of deformation fields including dislocation dipoles is observed in the Al phase region. However, for the Al4C3 phase region, the strain fields are mainly located near the Al4C3-Al interface. Dislocation dipoles are better observed in the images of the strain field distribution. Dislocation dipoles were typically identified by a localized point of deformation, visible as a small region blue and red area, connected by a thin red or orange band. In the strain field distribution, the green color in the strain images corresponds to the unstrained lattice plane, strains are positive and tensile in the red region, while the lattice is negative and compressive in the blue region.
These results are consistent with the parameters values derived from the CMWP adjustment. The experimental
q parameter value, presented in Table 2, ranges between 1.03 and 1.58, while the calculated
q, following the methodology described by T. Ungar et al.,
q = 1.31 is for pure screw dislocations and
q = 0.33 for pure edge dislocations. This data leads to the interpretation that the predominant dislocation character within the samples is primarily of the screw type. Conversely, most samples exhibit an average M value of less than one, indicating a pronounced dipole character in the dislocations. This suggests a strong correlation with adjacent dislocations, leading to strain fields that are predominantly short-range due to the screening effect [
36]. These results align with the analysis of the HRTEM images, in which closely correlated dipole dislocations are observed in close proximity to each other.
Figure 9a,b illustrate the relationship between dislocation density and the dipole parameter, M, as derived from the CMWP adjustment results for 1 and 2 wt. % of Mix by weight, respectively. For most samples in both the green and sintered states, the dipole character parameter, M, is observed to be below 1. This indicates a strong correlation between the dislocation dipoles in these samples. However, the sample sintered for 6 hours (A-16) showed a notable increase in the M value to 1.4, suggesting that the dislocation dipoles are no longer closely correlated and instead display random dispersion. On the other hand, the dislocation density remains virtually unchanged after 6 hours of sintering. This is attributed to the competition between recrystallization and grain growth mechanism and the potential generation of dislocations due thermal mismatch between the matrix and the nanorods during sintering.
Therefore, it is assumed that samples with a lower weight percentage of Mix and longer sintering times (Al-16) may exhibit reduced brittleness in the Al/Al4C3 composites. This occurs because, under these conditions, the dislocation dipoles lack close correlation and are randomly dispersed at the metal-ceramic interface. Other authors have noted that the density of dislocation dipoles is often very high, which can significantly impact the mechanical properties of crystalline materials. The reduction in elastic moduli, for instance, may be attributed to the polarization of these dipoles [
37].