**3.4 Melting temperatures (***T***m) of A15 Ru-based alloys**

To assess the potential of high-temperature application of X3Ru structures, we have calculated their melting temperatures based on the elastic constants Cij, [30, 32] as presented in **Table 3**. It is evident that Ti3Ru (6824 K) structure possesses high melting point whereas Fe3Ru (7295 K) has a low melting point. This attributes to the elastic constant C11 factor in these structures that leads to variation in melting temperatures. The calculated melting temperatures (*Tm*) of several studied X3Ru are in the same range as Nb3Al (2333 K) [1] and Ni3Al (1668 K) [44] which are obtained experimentally and theoretically. The calculated Tm of V3Ru (1983 K), Cr3Ru (2539 K), Co3Ru (5074 K) and Ti3Ru (6824) are greater than the Tm of Ni3Al (1668 K).

#### **3.5 Elastic anisotropy**

If the anisotropic index A is close to 1 (unity) respectively, the solid materials are predicted to be isotropic. Otherwise, it will be anisotropic. The anisotropic factors (A) of X3Ru (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) ranges from 4.7 to 2.2 respectively. It is clear that all the X3Ru (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) values have deviated away from unity; thus, the structures are anisotropic.

### **4. Conclusion**

Using first principles density functional theory calculations, we have investigated the structural, electronic, magnetic and elastic properties of X3Ru (X = Sc, Ti, V, Cr, Fe, Co, Cu and Zn) binary alloys in search of potential materials for high temperature structural application. The negative heat of formation in Mn3Ru has been observed, indicating that the system is thermodynamically stable compared to other studied X3Ru alloys that exhibited positive heats of formation. The total partial density of states show a strong overlap between the valence and conduction bands in Sc3Ru, Ti3Ru, V3Ru, Cr3Ru Fe3Ru, Cu3Ru and Zn3Ru indicating that these systems are metallic, whilst X3Ru (X = Mn, Co and Ni) are found to be half-metallic. Furthermore, Cr3Ru is known to exist experimentally, on the other hand, no experimental data has been reported on all the remaining X3Ru systems. The elastic constants and related mechanical parameters such as bulk modulus, shear modulus, Young's modulus, B/G ratio and Poisson's ratio, melting temperatures and anisotropy factor are calculated. According to the elastic stability criteria, all X3Ru structures are mechanically unstable except Cr3Ru with highest B/G ratio of 19.6. The calculated anisotropic factor indicates that all the X3Ru (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) are anisotropic. Co3Ru, Fe3Ru, Ni3Ru and Mn3Ru possess magnetic moments of 1.70, 1.58, 0.97 and 2.59 uB, respectively, while Sc3Ru, Ti3Ru, V3Ru, Cu3Ru, Cr3Ru and Zn3Ru are non-magnetic. The results for stable Mn3Ru with high magnetic moment could pave way for experimental realization (synthesis) of this material. Finally, the thermodynamic stable alloy Mn3Ru is predicted to be a good candidate for high temperature and spintronic applications.

#### **Acknowledgements**

This work was supported by the National Research Foundation (grant number: 121479) and UNISA Masters and Doctoral Bursary. The computational work was

performed using High-Performance Computing (HPC) facilities at the University of South Africa. Special thanks to Mr. Brian Nyandoro (PhD student) for fruitful discussions related to this work.
