# Ferroelectric Transition in Sr- and W-Doped BaTiO3 Solid Solutions
## 3 Results and Discussion  
BTO has a perovskite structure with the chemical formula of ABO\({}_{3}\). In this case, the Sr\({}^{2+}\) atoms are located at the eight corners (A sites) of the cuboid, and the Ti\({}^{4+}\) atoms are located at the center (B sites) of the cuboid, as seen in Figure 1a. BTO has two different phases, each of which exhibits a cubic (high-temperature phase, above the T\({}_{\text{C}}\)) or tetragonal (room-temperature phase, below the T\({}_{\text{C}}\)) structure. Both crystal structures are perovskite structures with different ratios between the lattice constants (c/a) (i.e., 1 for the cubic structure and >1 for the tetragonal structure). The Ti atoms are surrounded by six O\({}^{2-}\) atoms, which form an octahedral shape, thereby occupying the B sites. In cubic BTO, all of the lattice constants are identical, leading to a paraelectric condition with no polarization. On the other hand, tetragonal BTO exhibits an elongation of the lattice along the c-axis. Thus, the Ti-O octahedrons have down-shifted O\({}^{2-}\) atoms and up-shifted Ti\({}^{4+}\) atoms, resulting in permanent electrical polarization. Therefore, the polarization curves of tetragonal BTO can have hysteresis curves as a function of the applied electric field (E-field), and they can retain a certain amount of polarization after removing the E-field. The X-ray diffraction patterns of the BTO doped with Sr and W atoms are shown in Figure 1b. The BTO systems with Sr and W substitutions retained the tetragonal structure when the dopant content was x = 0.1 for Sr and y = 0.06 for W. The Sr-doped BTO had a single phase (tetragonal structure) for all values of the Sr content, but with high W content (y = 0.06). W-doped BTO has several small secondary peaks that correspond to TiO\({}_{2}\) and SrO [23]. This indicates that Sr atoms have a greater solubility than W atoms in the BTO  
Figure 1: **(a)** Two crystal structures of BaTiO\({}_{3}\); the cubic structure has a paraelectric behavior with \(p=0\), and the tetragonal structure has a ferroelectric behavior with \(p\
eq 0\). **(b)** X-ray diffraction patterns of the Sr- and W-doped BTO systems with tetragonal BTO as a reference (black bars). The green asterisks indicate the XRD peaks of unintentionally formed secondary phases. **(c)** SEM images of the Sr- and W-doped BTO systems. system. The SEM images revealed that the influence of Sr and W doping on the morphology and particle size was insignificant, as shown in Figure 1c. To see the changes in the BTO lattice, we analyzed the diffraction peaks located around 32.0\({}^{\circ}\) and 45.0\({}^{\circ}\), which corresponded to the diffractions of the (101), (110), (002), and (200) planes in tetragonal BTO. The diffraction angles of these XRD peaks (as marked with black and red bars in Figure 2a) were deduced from the Rietveld refinement results, which are summarized in Table 1. As the Sr content x increased from 0.025 to 0.1, all of the diffraction peaks of (101), (110), (002), and (200) shifted to higher diffraction angles (see Figure 2b). This indicated that the lattice constants of a and c in the Sr-doped BTO became smaller. However, with the increase in the W content y from 0.02 to 0.06, the diffraction peaks of (101), (110), (002), and (200) shifted, but the tendency of these shifts was different from that in the case of the Sr-doped BTO. With y = 0.02 and 0.04, the peaks of (101) and (002) were shifted to higher angles, while the peaks of (110) and (200) were shifted to lower angles, as seen in Figure 2c. This indicated that the lattice constant of a became larger while that of c became smaller in the case of W-doped BTO. Above y = 0.04, the diffraction angles of (101), (110), (002), and (200) were saturated without significant changes, indicating that BTO has a solubility limit for W doping at around y = 0.04.