## 3 Results and Discussion
### Structural and Morphological Properties of the Power Particles
#### Thermodynamic Analysis for MoW Synthesis during Mechanical Alloying
\(f(C^{5})\) Equation (8) is the concentration function for solid solutions, and it can be calculated by the following equation:  
\[f\big{(}C^{5}\big{)}=\Bigg{(}\frac{x_{\text{Mo}}V_{\text{Mo}}^{2/3}}{x_{\text {Mo}}V_{\text{Mo}}^{2/3}+x_{\text{W}}V_{\text{W}}^{2/3}}\Bigg{)}\Bigg{(}\frac {x_{\text{W}}V_{\text{W}}^{2/3}}{x_{\text{Mo}}V_{\text{Mo}}^{2/3}+x_{\text{W} }V_{\text{W}}^{2/3}}\Bigg{)} \tag{8}\]  
Then, by substituting the concentration function in (7), \(\Delta H_{chem}\) is calculated as:  
\[\Delta H_{chem}=\frac{2x_{\text{Mo}}V_{\text{Mo}}^{4/3}x_{\text{W}}V_{\text{ W}}^{4/3}}{\Big{[}\Big{(}n_{\text{us}}^{\text{Mo}}\Big{)}^{-1/3}+\Big{(}n_{ \text{us}}^{\text{W}}\Big{)}^{-1/3}\Big{]}\Big{[}x_{\text{Mo}}V_{\text{Mo}} ^{2/3}+x_{\text{W}}V_{\text{W}}^{2/3}\Big{]}^{3}}\times\Big{[}-P(\Delta\phi* )^{2}+Q(\Delta n_{\text{us}})^{2/3}\Big{]} \tag{9}\]  
The elastic contribution of enthalpy \(\Delta H_{elas}\) is calculated as:  
\[\Delta H_{elast}=x_{\text{Mo}}x_{\text{W}}\Bigg{(}x_{\text{Mo}}\underbrace{ \frac{2K_{\text{Mo}}G_{\text{W}}(\Delta V)^{2}}{3K_{\text{Mo}}V_{\text{W}}+4G _{\text{W}}V_{\text{Mo}}}}_{\Delta E_{\text{Mo in W}}}+x_{\text{W}}\underbrace{ \frac{2K_{\text{W}}G_{\text{Mo}}(\Delta V)^{2}}{3K_{\text{W}}V_{\text{Mo}}+4G _{\text{Mo}}V_{\text{W}}}}_{\Delta E_{\text{W in Mo}}}\Bigg{)} \tag{10}\]  
where \(\Delta E_{\text{Mo in W}}\) and \(\Delta E_{\text{W in Mo}}\) are the elastic energies caused by Mo dissolving in W and W dissolving in Mo, respectively. \(K\) and \(G\) are the bulk and shear moduli, respectively. The structure contribution of enthalpy is related to the fact that transition metals show preferential crystallization in one of three simple crystallographic phases (bcc) depending on the number of valence electrons Z (summation of \(s\) and \(d\) electrons) [24]. \(\Delta H_{struct}\) is a small positive value, and it can be neglected in the estimation of the enthalpy of mixing [32]. For the case of an amorphous phase, since there is no crystal structure and the atoms can arrange themselves in such a manner that mismatch is avoided, the elastic and structural enthalpies can be neglected [32]. The enthalpy of the amorphous phase can be obtained as follows:  
\[\Delta H_{\text{amorphous}}=\Delta H_{chem}+\beta T_{f} \tag{11}\]  
where \(T_{f}=x_{\text{Mo}}\ Tm^{\text{Mo}}+x_{\text{W}}\ Tm^{\text{W}}\) and \(\beta=0.0035\) kJ mol\({}^{-1}\) K\({}^{-1}\). \(T_{m}\) is the melting temperature of the raw materials (Mo and W). The parameters to obtain the enthalpy for the MoW system are listed in Table 2. For the crystalline and amorphous phases in Equations (4) and (9)-(11), an entropy change of 3.5 J kmol\({}^{-1}\) was considered, owing to the disordered nature of the amorphous phase compared to the crystalline phase [33]. During MA, a maximum process temperature of 473 K has been reported in the powder particles [34]. At this temperature, the Gibbs free energy for the solid solution and amorphous MoW phase was calculated and the results are shown in Figure 4. The results indicated that, for the crystalline solid solution, the Gibbs free energy was positive in almost all the ranges of the composition except on the interval of \(x_{\text{Mo}}\) = 0.9125-1.00 (Figure 4). This meant that, at room temperature, there was limited solubility for the formation of the MoW phase, so it required external energy for transforming the raw materials to the MoW alloy. In this work, initially W\({}_{1.5}\)Mo\({}_{6}\)C\({}_{2.5}\) wt.% was mixed, considering only the Mo and W composition, and then, it was equivalent to a composition of \(x_{\text{o}}\) = 0.80 and the Gibbs free energy was +19.82 kJ mol\({}^{-1}\) which indicated that this phase cannot be formed at 473 K of temperature and atmospheric pressure because of the positive energy.