Phase content and tetragonal unit cell distortion

The results from XRD pattern fitting of the tetragonal/rhombohedral phase content and distortion of the tetragonal unit cell are presented in this section. XRD patterns of prepared compositions are shown in Figure 6-16 and Figure 6-17. The patterns from all compositions could be indexed entirely on the peaks expected from a pure perovskite phase. Restrictions placed on pattern fitting were discussed in section 4.1.3. Due to the purely graphical and mathematical nature of peak fitting and the significant overlap of some peaks which was observed, absolute calculated values of phase content may contain significant error. However, the deconvolution was performed in a consistent manner and should allow observation of trends.

Error bars could not be estimated for the calculated phase content as the software only calculates the standard error of the peak position, height and half width at half maximum. The error bars for the tetragonal cell distortions computed from values given by the software were below 0.0002 units (smaller than the datapoints shown in the graphs). Therefore, the unit cell distortions should be considered representative as it only relies on positions of (200) and (002) tetragonal peaks, which was clear in most cases.

Figure 6-16 X-ray diffraction patterns of (Pb1−x Srx)(ZryTi1−y)O3 (0 at% Fe). Values of variable factors are shown above each pattern. When the variable is not shown, It assumes that y(Zr) = 0.52, Tsint = 1310 °C and x(Sr) = 0.05.

Figure 6-17 X-ray diffraction patterns of(Pb1−x Srx)(ZryTi1−y)1−zFezO3. Values of variable factors are shown above each pattern. When the variable is not shown, It assumes that z(Fe) = 0.014, y(Zr) = 0.52 , Tsint = 1310 °C and x(Sr) = 0.05.

The phase content did not show significant variation with increasing sintering temperature as shown in Figure 6-18. Fe-doped samples contained slightly more rhombohedral content. This has been observed in other studies [63, 80, 162] and attributed to either an MPB shift by Fe doping or a decrease in the micro-/nanohomogeneity of the material induced by Fe doping. It was previously suggested that Fe inhibits diffusion, therefore Zr-rich rhombohedral microregions take longer to mix with Ti-rich tetragonal microregions. Phase content reaches the same value for doped/undoped samples at 1360 °C, which supports this theory as increasing temperature facilitates diffusion.

The phase content may be also influenced by grain size. Previous research has shown that the width of the phase coexistence region increases as the grain size decreases [163, 164]. Fe-doped samples exhibit much smaller grain size, therefore, their phase coexistence range should be wider, and they should contain more rhombohedral phase. This theory does not agree well with the data presented in Figure 6-18 a), because for a sintering temperature of 1360 °C, both compositions regardless of Fe doping and difference in grain size show the same amount of both phases. On the other hand, one must consider that possible inaccuracies in the data as discussed above.

The tetragonal distortion of the unit cell decreased for the samples at 1360 °C (Figure 6-18 b), which has also been observed previously [165, 166] and could be explained by compositional fluctuations. When Zr-rich regions mix with Ti-rich regions at the highest sintering temperature, overall distortion of tetragonal phase decreases. The effect is more pronounced in Fe-doped compositions, which agrees with the previous reasoning that Fe inhibits diffusion.

a) b)

Figure 6-18 Dependence of a) phase content, b) tetragonal cell distortion (cT/aT−1) on sintering temperature of (Pb0.95Sr0.05)(Zr0.52Ti0.48)1−zFezO3 with z(Fe) = 0.000 or 0.014.

Incorporation of Sr²⁺ into the PZT lattice increased the tetragonal content and decreased tetragonal cell distortion as shown in Figure 6-19. Ikeda showed that substituting Pb²⁺ with Sr²⁺

up to approximately 15 at% continuously shifts the MPB towards a higher Zr/Ti ratio, which is illustrated in Figure 6-20 [167]. This agrees with results from other studies [50, 154, 168-170].

In the experiment reported in this thesis, compositions with a constant Zr/Ti ratio of 52/48 were used and only the Pb/Sr fraction was varied from 100/0 to 95/5 (as illustrated by points C1 and C2 in Figure 6-20). It is apparent, that the shift of MPB should have increased the tetragonal content, as was observed. Reduction of cell distortion is associated with the replacement of Pb²⁺

ion by smaller Sr²⁺ ion. With an increasing fraction of Sr/Pb, the cell distortion decreases until the material becomes cubic [50, 167].

1260 1310 1360

a) b)

Figure 6-19 Dependence of a) phase content, b) tetragonal cell distortion (cT/aT−1) on strontium content of (Pb1−x Srx)(Zr0.52Ti0.48)1−zFezO3 with z(Fe) = 0.000 or 0.014, sintered at 1310 °C.

Figure 6-20 Room temperature quaternary phase diagram of the (Pb-Sr)(Ti-Zr)O3 system published by Ikeda [167]. FT = tetragonal, FR rhombohedral ferroelectric phases; AT = tetragonal, AO = orthorhombic anti-ferroelectric phases. Points C1 and C2 show locations of

compositions investigating effects of Sr content in this work.

The dependence of phase content on Zr/Ti ratio is plotted in Figure 6-21 a). Regardless of Fe content, both series show a decrease of tetragonal phase and eventual transition into a majority rhombohedral phase as the y in (Pb1−x Sr^x)(Zr^yTi1−y)1−zFe^zO3 is increased. The position of the MPB appears to lie between y = 53 and 55 at%. However, this should be treated with caution as the phase content values are likely to be less accurate near the MPB due to the severe peak

0 2 4 6

overlap, especially on the rhombohedral side, where maxima of the tetragonal peaks could not be distinguished. Fe-doped samples seem to show an increased amount of rhombohedral phase in all compositions and their phase content variation with y(Zr) is less pronounced. Increased presence of rhombohedral phase in all Fe-doped compositions suggests that the coexistence region widened, rather than a shift in MPB position. This can be rationalised either by the phase coexistence width dependence on grain size or by the local inhomogeneities in Fe-doped samples as suggested earlier.

The tetragonal cell distortion exhibited a linear decrease with increasing y(Zr) (see Figure 6-21 b), which agrees well with previous research [27, 140]. Fe-doped samples generally show lower distortion, which will be further discussed in next paragraphs. It should be noted that unlike tetragonal distortion, phase content did not show a linear dependence on Zr/Ti fraction as one would expect, and which was demonstrated in other studies [49, 169, 171]. It suggests that phase content measurements may not be accurate enough possibly due to the resolution of the diffractometer or the peak fitting process.

a) b)

Figure 6-21 Dependence of a) phase content, b) tetragonal cell distortion (cT/aT−1) on Zr/Ti ratio of (Pb0.95Sr0.05)(ZryTi1−y)1−zFezO3 with z(Fe) = 0.000 or 0.014, sintered at 1310 °C.

Figure 6-22 a) shows the dependence of tetragonal and rhombohedral phase content on Fe doping. The rhombohedral phase content increased by ~10 % with 0.4 at% Fe but then remained constant with further Fe content up to 2.0 at%. Increase of the rhombohedral phase content with Fe doping has been reported in other studies [63, 80, 162, 172]. Weston et al. implied that the phase content ratio continuously changes with increasing Fe doping as the material switched from being predominantly tetragonal to being predominantly rhombohedral at a certain Fe content (2 at% Fe in [80]). This trend is not reflected in Figure 6-22 a), although this might be due to inaccuracy of the measurement as discussed previously. An increase in rhombohedral content may be explained by several reasons: 1) Fe shifted the location of the MPB, 2) width of the phase coexistence region widened due to grain growth inhibition or 3) width of the phase coexistence region widened due to a decrease in homogeneity caused by the presence of Fe.

Tetragonal distortion continuously decreased with increasing Fe content as shown in Figure 6-22 b). This general trend has been previously observed [63, 172] and is mostly related to the substitution of Zr⁴⁺/Ti⁴⁺ by Fe³⁺. The ionic radius of Fe³⁺(VI) is 0.55 or 0.65∙10^-10 m depending on its spin, which is lower than that of Zr⁴⁺(VI) (0.86∙10^-10 m) [36], and the Fe³⁺ doping introduces oxygen vacancies, which result in reduction of the cell volume [26]. The presence of Fe³⁺ is expected to distort the surrounding oxygen octahedra and decrease the B-O-B coupling as well as the Curie temperature [172]. Additional factors affecting the tetragonal distortion may include the previously suggested decrease in micro-/nanohomogeneity, or an effect of grain size, where smaller grains were reported to enhance clamping of the unit cell distortion [51].

The distortion would be expected to decrease only up to the dopant’s solubility limit, which should be < 2.0 at% in the case of Fe³⁺ as discussed previously in section 5.2. Contrary to this, the distortion is seen to decrease monotonously (Figure 6-22 b). This can be rationalised by

considering that the distribution of Fe³⁺ may not be perfectly homogeneous on a nanoscale level and therefore the dopant may not be fully incorporated even at lower doping concentrations due to its local saturation. Another possibility is that the distortion is affected by a newly-formed secondary phase containing the excess Fe³⁺.

a) b)

Figure 6-22 Dependence of a) phase content, b) tetragonal cell distortion (cT/aT−1) on Fe content of (Pb0.95Sr0.05)(Zr0.52Ti0.48)1−zFezO3 sintered at 1310 °C.