# Ferroelectric Transition in Sr- and W-Doped BaTiO3 Solid Solutions
## 3 Results and Discussion
Considering the ionic radii of Ti\({}^{4+}\) (60.5 pm) and W (66 pm, 62 pm, and 60 pm for W\({}^{4+}\), W\({}^{5+}\), and W\({}^{6+}\)), Ti\({}^{4+}\) atoms might be replaced by hexavalent W\({}^{6+}\) atoms because they have similar effective ionic radii [24]. However, as mentioned before, hexavalent W\({}^{6+}\) doping creates a significant charge imbalance in the system, leading to an unstable system with considerable numbers of vacancies and interstitials. Therefore, we could also consider doping a BTO system with W\({}^{4+}\) or W\({}^{5+}\). The oxygen vacancies could not be expected in the BTO system doped with W\({}^{4+}\) or W\({}^{5+}\) for the charge compensation. Considering that the amount of oxygen was larger than the stoichiometric values in the W- and Sr-doped BTO systems (the value of 3-8 was roughly 3.08 according to the EDS measurements), we could not exclude the possibility of excess oxygen in the W-doped BTO system. Figure 2: (**a**) X-ray diffraction peaks of the (101), (110), (002), and (200) (**b**) planes of Ba\({}_{1-}\)Sr\({}_{x}\)Ti\({}_{x-y}\)WyO\({}_{3-8}\) with x = 0.025, 0.05, and 0.10 and y = 0.02, 0.04, and 0.06. (**c**) The shifts of the XRD peaks as a function of the Sr (x) or W (y) content. Figure 3a shows the changes in the BTO lattice constants a and c caused by substitution with Sr and W atoms at the A and B sites. With the increase in the Sr content x, the values of the lattice constants a and b simultaneously decreased. The volume of the tetragonal structure of Sr-doped BTO also decreased from 64.36(1) to 63.88(2) A\({}^{3}\) (0.74%). Considering that the ionic radius of Sr\({}^{2+}\) (118 pm) is smaller than that of Ba\({}^{2+}\) (135 pm), the decreases in the lattice constants and the volume were reasonable. However, with the increase in the dopant content (W) in BTO, the lattice constant a increased while the lattice constant c decreased. With y = 0.06, the change in the lattice constants seemed to be saturated because a = 4.001(1) A and c = 4.023(5) A. The volume of W-doped BTO slightly increased with the increase in y from 64.36(1) to 64.41(4) A\({}^{3}\), indicating that W\({}^{4+}\) or W\({}^{5+}\) atoms could also be candidates as substitutional atoms at the B sites in a BTO system. In the tetragonal BTO, the lattice constants a and c had different values. We obtained the ratio of a and c to study the effects of doping at the A and B sites on the crystal structure of BTO. Initially, the BTO had a c/a ratio of 1.008, as seen in Figure 3b. The B-site doping with W atoms resulted in a c/a ratio of about 1.005-1.006, regardless of the W dopant content, while the A-site doping with Sr atoms gradually decreased the c/a ratio from 1.008 (BTO) to 1.006 (x = 0.1) as a function of x. Because the differences between a and c in the tetragonal structure became smaller, the crystal structures of the BTO doped with Sr and with W became similar to the cubic structure. This could result in an indistinct transition between the tetragonal and cubic structures in a doped BTO system with large amounts of Sr and W atoms. To study the effects of A- and B-site doping on the transition between the tetragonal and cubic BTO structures, the DSC curves of BTO, Ba1-xSrTiO\({}_{3}\) (x = 0.025, 0.05, and 0.1), and BaTi1-yV\({}_{3}\)O\({}_{3}\) (y = 0.02, 0.04, and 0.06) were taken with increasing and decreasing temperatures (from room temperature to 200 \({}^{\circ}\)C), as seen in Figure 4a,c. With the Sr and W substitutions, the endothermic and exothermic peaks in the DSC curves were flattened and the transition ranges were broadened. The transition temperature, T\({}_{\rm C}\), was obtained from the positions of the peaks in the DSC curves, and the latent heat--the enthalpy at T\({}_{\rm C}\)--was calculated from the integrated area of the DSC curves. The T\({}_{\rm C}\) of BTO was found at 123.1 \({}^{\circ}\)C with heating and 114.7 \({}^{\circ}\)C with cooling.