## 3 Results and Discussion  
### Structural and Morphological Properties of the Power Particles  
#### 3.1.1 X-ray Diffraction  
Figure 1 shows the X-ray diffraction results of the powder particles after 25, 50, and 75 h at 500 rpm in a low-energy ball mill. The peak with the highest intensity corresponded to the graphite (002) plane. When grinding time increased, the (002) graphite peak decreased in the XRD spectrum after 25-50 h of milling. This decrease corresponded to a 62.71% reduction of the peak intensity, and from 50 to 75 h, a reduction of 45.14% of intensity. By increasing the milling time, all the peaks decreased; this is related to the microstructural refinement and the formation of crystallographic defects caused by mechanical impacts during the MA process. These events allow the formation of new phases. The synthesis of theMoW phase can form a solid solution for different compositions and temperatures [12]. Section 3.1.2 explains more in detail the thermodynamic calculation of the formation of this solid solution phase. The formation of the MoW solid solution phase is possible when Hume-Rothery rules are satisfied as follows: (1) Size factor: W and Mo atoms should be of similar size (with no more than 15% difference in their atomic radii). The atomic radii of W and Mo are 0.1386 nm and 0.1394 nm [25], respectively, with a size difference of 0.57%; this is a much smaller value than 15%. (2) Crystal structure: The raw materials must have the same crystal structure; in this case, both materials show a bcc crystalline structure. (3) Valence: Atoms must have the same valence; in this case, both elements show valences of 2, 3, 4, 5, and 6. According to this previous explanation, the MoW solid solution phase is feasible through MA. The MoW alloy was indexed with the characteristic peak of this phase at 40.46\({}^{\circ}\), a value that coincides perfectly with the 071-9828 JCPDS card. However, at 50 and 75 h of milling, a new peak of greater intensity located between 40.6\({}^{\circ}\) and 40.8\({}^{\circ}\) was observed (shown in Figure 2). This phenomenon was related to the decreasing of (002) peak (graphite phase) caused by the introduction of carbon to the MoW lattice to produce the MoWC bimetallic nanostructured carbide in a solid solution. Figure 1: X-ray diffraction (XRD) patterns of the MoWC mixture at different grinding times at 500 rpm of a low-energy ball mill. Figure 2: A zoom between 40\({}^{\circ}\) and 41\({}^{\circ}\) of XRD patterns of the MoWC mixture at different grinding times in a low-energy mill. One advantage of using a low-energy ball mill is that this process can produce a small amount of cross contamination caused by media milling and vial [17]. Nevertheless, to transform the elemental powder particles to the nanostructured carbide phases in a solid solution, at least, it needs between 120 and 240 h in this kind of process (low energy) [7; 26]. As observed in Figure 1, a low-energy ball mill was not enough to introduce a major quantity of carbon into the MoW lattice, so it needed a longer milling time to transform Mo, W, and C elemental materials to the MoWC phase. To avoid extended milling times until 240 h, the use of a high-energy ball mill at 1500 rpm was an option to produce the MoW nanostructured bimetallic carbide. Figure 3 shows the X-ray diffraction of the powder particles by a high-energy ball mill at 125 and 150 h. The intensity of the peak corresponding to the graphite (002) showed a drastic decrease from 125 to 150 h of milling, which corresponded to a 99.74% reduction. This behavior was attributed to the incorporation of C into the MoW matrix, occupying the interstitial sites, thus producing the WMoC bimetallic carbide of the interstitial solid solution due to the increasing of (110) plane with a value of 42.44% between 125 and 150 h of milling. Modeling the interstitial atom as a hard sphere, it yields that the radius ratio of the interstitial atom/radius of the host metal atom must be less than 0.59 for an interstitial structure [25].