## 3 Results and Discussion

Table 2: The X-ray diffraction (XRD) data of Cu\({}_{2}\)SnTi\({}_{3}\) using Cu K\(\alpha\) radiation (\(\lambda\) = 0.1541 nm). is approximately Cu\({}_{2}\)SnTi\({}_{3}\), in agreement with results of the EPMA measurement in SEM. To expand our insight into the new ternary compounds Cu\({}_{2}\)SnTi\({}_{3}\) for determining the crystalline structure, we carried out a brief comparative study of the structural, electronic, and energetic properties in the CaCu\({}_{5}\)-like and InNi\({}_{2}\)-like Cu\({}_{2}\)SnTi\({}_{3}\). Six Cu\({}_{2}\)SnTi\({}_{3}\) models denoted by model number m (wherem = 1-6) with specific Wyckoff positions of the Cu, Sn, and Ti. Models 1, 2, and 3 are close to CaCu\({}_{5}\)-like Cu\({}_{2}\)SnTi\({}_{3}\). In Model 1, Cu, Sn, and Ti were assigned to the atomic positions of 2c (x = 1/3, y = 2/3, z = 0), 1a (x = 0, y = 0, z = 0), and 3g (x = 1/2, y = 0, z = 1/2), respectively. In Model 2, two Cu, one Sn, and three Ti were assigned to the atomic positions of (x = 1/2, y = 1/2, z = 1/2), (x = 1/2, y = 0, z = 1/2), 1a (x = 0, y = 0, z = 0), (x = 1/3, y = 2/3, z = 0), (x = 2/3, y = 1/3, z = 0), and (x = 0, y = 1/2, z = 1/2), respectively. In Model 3, two Cu, one Sn, and three Ti were assigned to the atomic positions of (x = 1/2, y = 0, z = 1/2), (x = 0, y = 1/2, z = 1/2), (x = 1/2, y = 1/2, z = 1/2), (x = 1/3, y = 2/3, z = 0), (x = 2/3, y = 1/3, z = 0), and (x = 0, y = 0, z = 0), respectively. Models 4, 5, and 6 are similar to InNi\({}_{2}\)-like Cu\({}_{2}\)SnTi\({}_{3}\). In Model 4, two Cu, one Sn, and three Ti were assigned to the atomic positions of (x = 1/3, y = 2/3,z = 3/4), (x = 2/3, y = 1/3, z = 1/4), 1a (x = 0, y = 0, z = 0), (x = 0, y = 0, z = 1/2), (x = 2/3, y = 1/3, z = 3/4), and (x = 1/3, y = 2/3, z = 1/4), respectively. In Model 5, two Cu, one Sn, and three Ti were assigned to the atomic positions of (x = 0, y = 0, z = 1/2), (x = 2/3, y = 1/3, z = 3/4), 1a (x = 0, y = 0, z = 0), (x = 2/3, y = 1/3, z = 3/4), and (x = 1/3, y = 2/3, z = 3/4), respectively. In Model 6, two Cu, one Sn, and three Ti were assigned to the atomic positions of (x = 2/3, y = 1/3, z = 1/4), (x = 1/3, y = 2/3, z = 3/4), (x = 0, y = 0, z = 1/2), (x = 0, y = 0, z = 0), (x = 2/3, y = 1/3, z = 3/4), and (x = 1/3, y = 2/3, z = 1/4), respectively. We conduct first-principles density functional theory (DFT) calculations based on the generalized gradient approximation (GGA) using the Vienna Ab Initio Simulation Package (VASP) [17; 18; 19]. A plane wave cutoff of 355 eV (350 eV) was used in conjunction with a \(7\times 7\times 7\) (\(7\times 7\times 8\)) Gamma centered grid to achieve a force accuracy of 0.01 eV/A for CaCu\({}_{5}\)-like (InNi\({}_{2}\)-like) Cu\({}_{2}\)SnTi\({}_{3}\). Under these conditions, the atomic coordinates were completely relaxed to their zero-force positions, resulting in the optimized six structures shown in Figure 3.  
Figure 2: Transmission electron microscope (TEM) bright field image (**a**) and its corresponding selected area diffraction (SAD) pattern (**b**) of Phase A. Table 3 shows the space groups, lattice constants, and total energies of Models 1-6. Model 6 has the lowest total energy of \(-\)35.239 eV for InNi\({}_{2}\)-like Cu\({}_{2}\)SnTi\({}_{3}\) and Model 2 has the lowest total energy of \(-\)33.926 eV for CaCu\({}_{5}\)-like Cu\({}_{2}\)SnTi\({}_{3}\). Model 1 follows closely the model proposed by the literature [12] and has the highest total energy of \(-\)33.094 eV. We have plotted the three plausible models describing the transformation path for ternary intermetallic phases of Cu\({}_{2}\)SnTi\({}_{3}\) shown in Figure 4. It can be clearly seen that the hexagonal Cu\({}_{2}\)SnTi\({}_{3}\) (space group: 191 _P6/mmm_) is metastable phase. The hexagonal Cu\({}_{2}\)SnTi\({}_{3}\) tends to a more stable phase or transition phase of the orthorhombic structure. Figure 4: Energy profile of Models 1, 2, and 6. Red, gray, and dark green spheres represent the atoms Cu, Ti, and Sn, respectively. Figure 3: Models 1–6 showing the most favorable atomic structures.