Crystal symmetry in single domains of ${\text{PbZr}}_{0.54}{\text{Ti}}_{0.46}{\text{O}}_3$

This work focuses on the crystal symmetry of morphotropic ${\text{PbZr}}_x{\text{Ti}}_{1-x}{\text{O}}_3$ (PZT). The crystal symmetry is investigated within single domains of $\approx 30–100\text{nm}$ width by convergent beam electron diffraction (CBED). The composition ${\text{PbZr}}_{0.54}{\text{Ti}}_{0.46}{\text{O}}_3$ was chosen for experiments at room temperature and $\approx 300°\text{C}$. The observed zone axis symmetry at room temperature was a $\left(\overline{1}10\right)$ mirror in some domains whereas symmetry was broken in neighboring domains. Therefore the highest crystal symmetry that can be attributed with certainty to the probed volume is monoclinic. The local symmetry of single cells might be lower due to disordered displacements of the cations. At $\approx 300°\text{C}$ the zone axis symmetry had changed to a ${\left(100\right)}_{pc}$ mirror that only occurs in the tetragonal phase of PZT.

Figure 1

(a) Unit cells for the three space groups $P4mm$, $Cm$, and $R3m$ with symmetry elements. (b) The mirror planes in stereographic projections along ${\left[001\right]}_{pc}$. Both visualize zone axis symmetries observable with convergent beam electron diffraction (CBED).

Figure 2

(a) Image of an ${⟨100⟩}_{pc}$ oriented area in sample $A$ at $20°\text{C}$. Mainly domain wall with tracks running along [010] are visible with some additional inner domain walls. The spots index the position for convergent beam electron diffraction (CBED) and were reconstructed from double exposures. (b) The ${\left[100\right]}_{pc}$ zone axis pattern (ZAP) of domain 2 shows no symmetry according to ${\left[1\overline{1}0\right]}_m$ orientation. (c) ${\left[100\right]}_{pc}$ ZAP of domain 8 with intensity distribution close to $\left(1\overline{1}0\right)$ symmetry. (d) The simulated ${\left[1\overline{1}0\right]}_m$ ZAP with an orientation matching to domain 2 with a sample thickness of 65 nm.

Figure 3

(a) Bright-field (BF) image of domain configuration in sample $A$ viewed along ${⟨111⟩}_{pc}$. The spots correspond to the positions the CBED patterns in Figs. 4, 5 were taken from. The indexing was chosen to $\left[\overline{1}\overline{1}1\right]$ as can be seen from the inset. (b) Sketched configuration with indexed domain walls. For the inclined domain walls with tracks along [011], two planes are possible as shown in (c) (100) and (d) $\left(0\overline{1}1\right)$. (c) Model 1 showing the orientations of monoclinic cells in domain 3 and 2 as indexed in Figs. 4a, 4b with a (100) wall. (d) Model with domain 2 in ${\left[0\overline{1}\overline{1}\right]}_m$ orientation and a $\left(0\overline{1}1\right)$ wall.

Figure 4

Projected whole patterns (proj. ${\left[111\right]}_{pc}$ WPs) of domain 3(a) and domain 2(b) and whole pattern (WP) from domain 3(c) and 2(d). In (a) and (c) for domain 3(a) horizontal mirror plane is present. No symmetry is found in the patterns of domains 2(b) and 2(d).

Figure 5

The ${\left[111\right]}_{pc}$ dark-field patterns (DPs) of domain 3(a) and domain 2(b). The horizontal mirror plane is also found in the DP of domain 3(a). (b) The mirror expected from proj. WP of domain 2 is not found in the DP. [(c) and (d)] The orientations could be determined by comparison to simulations. Simulations were done using monoclinic structural model and 75 nm thickness for domain 3(c) and 70 nm for domain 2(d).

Figure 6

(a) The ${\left[100\right]}_{pc}$ ZAP at $20°\text{C}$ and (b) $\approx 300°$ taken from an area without domain contrast point out the change in symmetry. No symmetry was found at room temperature while a ${\left(010\right)}_t$ mirror is present at $\approx 300°\text{C}$. (c) The ${\left[110\right]}_{pc}$ ZAP of a nanodomain at room temperature shows no symmetry. (d) In the tilted pattern of the neighboring domain at $\approx 300°\text{C}$, a ${\left(010\right)}_t$ mirror plane is present. The double exposures (e) and (f) reveal the disappearance of nanodomains with increasing temperature and the beam positions for the ${\left[110\right]}_{pc}$ patterns in (c) and (d).