The effect of dislocations on phase transition in PbZrO₃-based antiferroelectrics

Materials synthesis

PLZS ceramics were obtained using traditional high-temperature solid-phase sintering methods. The raw materials for sintering PLZS are Pb₃O₄, La₂O₃, ZrO₂ and SnO₂ powders with purity higher than 99.0%. Because Pb volatilizes during sintering, a small amount of excess PbO (0.5 wt%) was added. The preparation process of PLZS was as follows: firstly, the raw material powders were mixed and ball milled for 6 h, dried at 120 °C, and then calcined at 900 ^oC for 2 h. The obtained PLZS powders were ball milled again for 24 h, dried at 120 °C, mixed with 6 wt% PVA as a binder, and then pressed into disks with a diameter of 13 mm at 150 MPa. Lastly, the binder was burned out at 800 °C for 2 h, and the disks were sintered at 1,300 °C for 2 h.

Materials characterizations

The TEM specimens were prepared from ceramic bulk by mechanical thinning, polishing, and Ar⁺ ion-milling in a gatan precision ion polishing System (PIPS) II, and finally, a thin carbon film was sprayed with a thickness of 3 nm. In order to decrease ion-beam damage during ion-milling, the ion-beam voltage was gradually decreased from 3 to 0.5 keV. TEM investigation was performed on a JEM-2100F equipped with a heating holder (Gatan Model 652). In situ X-ray diffraction (XRD) experiment was conducted on a Rigaku D/max 2,550 V diffractometer using Cu-Kα radiation in the 2θ range of 10°-110° with a scanning speed of 10° per minute and a step of 0.2°. This temperature range measured in the in situ XRD experiment is 25 to 350 °C, with a rate of 10 °C per minute.

Characterization of dislocations

Extensive TEM examinations indicate universal appearance of dislocations in PLZS AFE ceramics, as shown in Figure 1. Compared with those reported in other perovskite oxides, the most notable feature of dislocations in PLZS AFE ceramics is that they manifest themselves as dislocation arrays and networks, which mainly distribute within grains and always across the domain walls. Individual dislocations could also be observed, but in very small amounts. They usually project along the <110> and <001> directions (all crystallographic indices refer to the simple pseudocubic unit cell in this work), similar to those reported in SrTiO₃^[21].

Figure 1. Dislocations in different grains of the present PLZS sample. The green arrows indicate the individual dislocations. PLZS: (Pb_0.97La_0.02)(Zr_0.50Sn_0.50)O₃.

The Burgers vector b and line direction l are the main parameters for the characterization of dislocations. From the two parameters, the possible slip system of dislocations can be deduced. Figure 2 shows the characterization of Burgers vector b of dislocations, determined by invisibility criteria g · b = 0. The condition g · b = 0 signifies the reflection vector g is normal to b, and dislocations meeting this criterion are displayed out of contrast in the two- or weak-beam dark-field (DF) micrographs. Figure 2A and B was acquired using two reflection vectors g = [$$ 10\bar{1} $$] and g = [020], respectively, after large-angle tilting of the sample to near the [101] zone axis, while Figure 2C was attained using g = [121] near the [$$ 3\bar{2} 1 $$] zone axis. It can be seen that the contrast of the dislocation array in Figure 2B and C was weak, which is similar to the contrast of dislocations in alloys when g · b = 0^[22]. Their strong residual contrasts are due to the large magnitude of the Burgers vector and the strong free surface relaxation. That is to say, the dislocation array is out of contrast under reflection vectors g = [020] and g = [121], while it is visible under g = [$$ 10\bar{1} $$]. Thus, the Burgers vector of the present dislocation array could be determined as [$$ 10\bar{1} $$], belonging to the <110>-type. In oxide perovskites, including SrTiO₃^[23] and BaTiO₃^[9], dislocations with Burgers vector of <110> have been widely reported.

Figure 2. Characterization of dislocation arrays in PLZS. (A-C) The two-beam dark-field micrographs of the identical area using an operating vector of g = [$$ 10\bar{1} $$], [020] and [121], respectively; (D) the selected-area electron diffraction pattern; (E) the corresponding bright-field micrograph; (F) the schematic drawing of dislocation arrays. The blue and yellow arrows in (E) indicate the directions of dislocation lines and array layout, respectively. The orange arrow and blue lines in (F) denote the electron-beam direction and dislocations. PLZS: (Pb_0.97La_0.02)(Zr_0.50Sn_0.50)O₃.

The line direction l is determined by performing a trace analysis during tilting. The line contrast of dislocations indicates a projection of the dislocation lines along the [101] viewing direction [Figure 2D]. With the line projections parallel to [$$ 10\bar{1} $$] [Figure 2E], the line direction l of dislocations could refer to [$$ 10\bar{1} $$] ± n[101], which means the possible direction includes [$$ 10\bar{1} $$], [100] and [001]. As shown in Figure 2A-C and 2F, when this grain is rotated around the g = [$$ 10\bar{1} $$] or g = [010] in order to obtain a two-beam condition for DF imaging, the length of dislocations varies accordingly. Via tracing the dislocation length variation during tilting, it is found that the projected line length of dislocations in Figure 2A is similar to that in Figure 2E, while that in Figure 2B is significantly shortened. Therefore, we finally determine that the line direction l is along the [$$ 10\bar{1} $$] direction.

Based on the above analyses, it can be inferred that these dislocation arrays have the glide system of the <110>{$$ 1\bar{1} 0 $$}, whose characteristic is pure screw. The Peierls-Nabarro model suggested that this is the easiest system for slipping in perovskite oxides^[24]. In addition, the system is responsible for the plasticity in SrTiO₃ single crystals at room temperature^[25]. Kondo et al. observed in real-time the formation of this system under the action of nanoindentation in SrTiO₃^[23].

Most dislocations in perovskite oxides, including SrTiO₃^[21], BaTiO₃^[9] and KNbO₃ single crystals^[4], are activated by a compressive stress at high temperatures. For PLZS ceramics, the stress to activate the dislocations most likely comes from the strain generated during cooling in the synthesis. Figure 3A shows the in situ XRD examination upon decreasing the temperatures. At a high temperature of 350 °C, PLZS exhibits a simple cubic perovskite structure of the PE phase, which is evidenced by non-split {h00}, {hh0} and {hhh} peaks. After cooling to room temperature, the PLZS spontaneously transits from the PE to AFE phase, accompanied by significant volume shrinkage up to -1.33%. Therefore, it is believed that large volume shrinkage arising from temperature-induced phase transition has induced considerable strains and provided enough driving force for forming dislocations in PLZS. A similar phenomenon has been widely reported in alloys^[26,27].

Figure 3. (A) XRD patterns of PLZS at 25 C and 350 C. At 350 C, the lattice parameters are a = b = c = 4.1164 Å, and the unit volume is V = 69.75 ų. At 25 C, the lattice parameters are a = b = 4.113 Å, c = 4.085 Å, and the unit volume is V = 68.82 ų. So, the volume shrinkage during cooling is ∆V = (V_{25 °C} – V_{350 °C}) / V_{350 °C} = -1.33%; (B-E) nucleation of dislocation array at the grain boundaries in PLZS. The white dashed lines indicate the grain boundary. The blue and yellow arrows represent the directions of dislocation lines and array layout, respectively. PLZS: (Pb_0.97La_0.02)(Zr_0.50Sn_0.50)O₃.

Because the strain is usually concentrated at the bends or steps, grain boundaries should have accumulated the largest strain and consequently behave as nucleation sites for dislocations^[28,29]. As seen in Figure 3B and C, Figure 3D and E dislocation arrays have indeed been emitted from the grain boundaries. This phenomenon makes sense because when a screw dislocation moves along the <001> direction, the required Peierls stress to overcome the energy barrier is minimal^[24]. The gliding vectors of the dislocation arrays in Figure 2E and Figure 3C and E are along the [010] and [001] directions, respectively; the dislocation is emitted in the <001> direction, consistent with the moving direction of screw dislocations, as has been observed in the literature^[23].

Effect of dislocations on the phase transition

In situ TEM via changing the temperatures has been employed to investigate the effect of dislocations on the phase transition. The selected zone axis for the present in situ TEM examination is along the [001] direction at which the AFE and PE phases could be explicitly discriminated. The red framed region in Figure 4A (corresponding electron diffraction is shown in Figure 4B) was enlarged and monitored during the in situ heating [Figure 4C] and cooling [Figure 4D] processes. At 20 °C, satellite reflections in the fast Fourier transform (FFT) are both visible in areas 1 (near the dislocation) and 2 (away from the dislocation). Upon heating to 120 °C, the satellite reflections disappear in area 2 while they remain in area 1. The satellite reflections are associated with antiparallel alignment of A-site cations in the AFE phase^[30], and its disappearance indicates that the AFE phase has transformed to the PE phase. Therefore, dislocations could stabilize the AFE phase during heating. Until the sample is heated to 160 °C, all satellite reflections disappear in area 1, suggesting full transition to the PE phase. Upon cooling from 160 °C and when the temperature reached 135 °C, interestingly, satellite reflections started to appear on the FFT of area 1 while they were still absent in area 2 [Figure 4D]. This suggests that the AFE phase preferentially nucleates near the dislocations during the PE-AFE phase transition. The present reversible in situ TEM investigation indicates that dislocations favor the stabilization of the AFE phase.

Figure 4. (A) The bright-field micrograph at room temperature showing a dislocation array near the domain boundary. The green arrows indicate the dislocations; (B) the [001] selected-area electron diffraction pattern obtained from framed area in (A), showing the modulated wave along the [110] direction. The modulation period N is counted by: N = d₁₁₀/λ, where d₁₁₀ and λ are the distance measured in selected-area electron diffraction pattern; (C and D) present the in situ TEM of the green framed area in (A) during heating and cooling, respectively. The scale bar is 20 nm. Dislocations are indicated by green arrows. Areas 1 and 2 refer to dislocation and non-dislocation areas, respectively; (E and F) show the temperature dependence of FFT patterns in areas 1 and 2, respectively. TEM: Transmission electron microscopy; FFT: fourier transform.

PbZrO₃-based AFEs demonstrate a distorted perovskite structure with antiparallel Pb-cation displacements. Such a structure is equivalent to a perovskite with modulated structure of 1/N {110}, i.e., a wavelength of N layers of its pseudocubic {110} plane^[31-33], and N is termed as modulation period. It is similar to our previous discovery of the electric devil’s staircase phenomenon^[34], i.e., the modulation period shows a step-like change with temperature. In the present in situ study, the modulated structure of the AFE phase in PLZS again exhibits a stepwise variation during heating but shows difference between dislocation [Figure 4E] and non-dislocation areas [Figure 4F]. As shown in Figure 4B, the modulation period N of PLZS at room temperature could be obtained as four multiples by: N = d₁₁₀/λ. Multiple characterization methods, including XRD^[35], electron diffraction^[34-36] and aberration-corrected TEM^[34,35], have confirmed this previously. Therefore, based on the shape and position of satellite reflections, it can be inferred that the modulation period referred to by the purple lines is around 4 [Figure 4E and F], by the orange lines is around 4.5, and by the red lines is around 5. It can be seen that a certain modulation period can be maintained within a comparatively wide temperature range. Moreover, the dislocations [Figure 4E] are found to further expand the temperature range of the stages, especially for stages 2 and 3. The ranges of stages 2 and 3 in area 2 (non-dislocation area) are 62-72 °C and 82-92 °C, respectively, while they expand to 62-82 °C and 92-120 °C, respectively, in area 1 (dislocation area) along with the duration of the AFE phase at higher temperatures. The AFE phase has transformed to the PE phase at 120 °C in the non-dislocation area [stage 4 in Figure 4F] while it remains available in the dislocation area [stage 3 in Figure 4E]. As a result, dislocations slow the transition rate among different modulated structures by extending the temperature range of stages in the electric devil’s staircase, thus stabilizing the AFE phase during heating. Such discovery further indicates that the existence of dislocations disperses the phase transition of the whole system in a wider temperature range, potentially avoiding abrupt volume changes.

Compared to area 2, the lattice parameters in area 1 are significantly reduced [Table 1]. The previous atomistic simulation study on <110> screw dislocations in oxide perovskites considered that the dislocation causes distortion of the BO₆ octahedra and, especially, the AO₁₂ cub-octahedra and, thus, generates local electric dipole moments inside the core^[37]. Thereafter, we infer that the large electric dipole moments of A-site atoms around the dislocation core are responsible for stabilizing the AFE phase.

Besides stabilizing the AFE phase near dislocations, it is found that the dislocation array, in the meantime, plays a specific role in the evolution of AFE domains. Figure 5 demonstrates a large-field view of both domain and dislocation arrays subject to an in situ heating and cooling process in TEM. Here, the domain marked by yellow dash lines is pinned by a dislocation array, resulting in a controlled motion of domain walls, hence regulating the domain size. As shown in Figure 5A-C and Supplementary Materials Video 1, upon increasing the temperature, the domain started to shrink from dislocation array β because of its wedge tip and eventually disappeared at the dislocation array α [see yellow-arrowed site in Figure 5C]. As shown in Figure 5D and E and Supplementary Materials Video 2, upon cooling, highlighted by yellow arrows in Figure 5E, domain walls nucleated at dislocation array α, then crossed the whole dislocation array α and terminated at dislocation array β. It seems that the dislocation array can provide a strong stress field nearby, which is evidenced by the following three phenomena during domain growth [Figure 5D-F]: (1) the width of domain is similar to that of the dislocation array α and was not further broadened; (2) the domain cannot grow as a lamellar shape but form wedged shape when it approaches close to the dislocation array β; (3) the domain wall can pass through the dislocation array α with a smaller crossing angle but terminate at one side of dislocation array β which is nearly perpendicular to the domain growth direction. These phenomena indicate that dislocation arrays can be critical in manipulating domain size and orientation.

Figure 5. The bright-field observations of the evolution of AFE domains during (A-C) heating and (D-F) cooling in PLZS. The yellow dashed lines and arrows in (A, C, and E) indicate the AFE domain wall. The green arrows depict dislocation arrays. AFE: Antiferroelectric; PLZS: (Pb_0.97La_0.02)(Zr_0.50Sn_0.50)O₃.

According to the theoretical calculations in KNbO₃ FE perovskite oxide^[4], the strong axial elastic field of linear screw dislocations^[38,39] exerts a long-range influence on the polarization, which not only cause a rotation of the polarization vector around the dislocation line but also significantly increase the magnitude of polarization at the cores of dislocations. As a result, if a domain nucleates at the dislocation, the axial elastic field of the screw dislocation seems to preferentially promote its growth in a direction at a smaller angle to the direction of the dislocation array [see Figure 5E]. Nevertheless, the detailed reasons should be further investigated in the future.