The 4d transition metal oxide BaZrO₃ is widely used throughout the industry. The high proton conductivity of BaZrO₃ enables its use as an electrolyte material for proton-conducting fuel cells[1, 2]. The low dielectric loss also provides advantages for widespread application in wireless communication technologies[3]. Also, BaZrO₃ plays a significant role as a material for a perovskite substrate. With a lattice constant of 4.189 Å, this value significantly surpasses those of other perovskite substrates such as SrTiO₃ (3.905 Å), LaAlO₃ (3.792 Å), and DyScO₃ (3.944 Å)[4-7]. BaZrO₃ has a cubic perovskite structure (space group Pm3¯m), in which Ba​2+, Zr​4+, O​2- ions are located at the unit cell corners, at the body center, and at the face centers, respectively[8]. It has been presumably known that no phase transitions exist down to the absolute zero temperature. On the other hand, recently, it has been reported that there exists a ZrO​6 octahedra rotation under 80 K while maintaining the cubic structure[8]. Under high pressure of up to 45 GPa[9] and 42 GPa[10], BaZrO₃ undergoes structural phase transitions. In this paper, we report the temperature dependence of the dielectric properties for the BaZrO₃ single crystal, which was grown by the optical floating zone method. The crystallographic properties were investigated by the X-ray diffraction (XRD) experiments and the Rietveld refinement analysis. The atomic force microscopy (AFM) imaging shows atomically flat surface states of the BaZrO₃ single crystal. Finally, the temperature dependences of the dielectric constant and tanδ reveal several dielectric anomalies of BaZrO₃ below the room temperature.

Single crystals of BaZrO₃ were grown using the optical floating zone furnace method[11, 12], where the seed and feed rod of the polycrystalline BaZrO₃ was prepared by solid state reaction method. In the first step, polycrystalline BaZrO₃ was fabricated with BaCO₃ (Alpha Aesar 99.99%) and ZrO​2 (Alpha Aesar 99.99%) powders as starting materials, mixed well with the stochiometric ratio and were pelletized. These pellets were sintered at 1050 °C for 12 hours in air followed by two additional heat treatments at 1200 °C and 1400 °C with intermediate grindings. After the third heating the pellets were ground, molded in a cylindrical shapes and were given the final heating treatment at 1600 °C for 24 hours. Finally, BaZrO₃ single crystals were grown by optical floating zone furnace (FZ-T-12000-X-VII-VPO-PC, Crystal System) equipped with the Xenon lamp. In order to minimize molten zone instability due to evaporation of BaO, the pulling speed of the seed and feed rods were kept different such as the seed rod was pulled down with a speed of 8–60 mm/hr, and feed rod pulling speed was 10–70 mm/hr. The optimal rotational speed for the seed and feed were found to be 30 rpm. The XRD for powder BaZrO₃ prepared from crushing single crystal was performed by Bruker D7 Advance. The crushed powder was annealed at 1300 °C for 12 hours to avoid any strain induced effect during the crushing process. The Rietveld refinement for the experimental powder XRD data of BaZrO₃ was performed using Fullprof package. The crystallinity and orientation of the grown single crystals were determined by high-resolution four circle X-ray diffractometer (D8 Discover, Bruker). Atomic surface flatness was checked by atomic force microscopy (Multimode V, Bruker) in tapping mode. Temperature dependent measurements for the dielectric constant and dissipation of the BaZrO₃ single crystal were performed with oscillating electric fields applied along the [100] direction using a General Radio Capacitance Bridge 1615A and a Stanford Research SR830 Lock-in Amplifier at various frequencies.

Figure 1(a) compares experimental and calculated powder XRD patterns of the crushed BaZrO₃ single crystals. It confirms that impurity phase peaks were not detected. The Rietveld refinement results in complete agreement with a cubic ABO₃ type structure with the lattice constant a = 4.189 Å and Rwp factor of 9.91. Since our Rietveld refinement results produced lattice constant value of 4.189 Å for BaZrO₃ crystals, in this range above 4 Å, LaLuO₃ (4.18 Å) is the only perovskite oxides close to our BaZrO₃ single crystal with the cubic structure, although LaLuO₃ has pseudocubic structure. We analyzed the crystallographic orientation of the cleaved surface of BaZrO₃. Figure 1(b) represents the XRD on the cleaved surface which shows only the (00l) reflections indicating (00l) orientation of the out-of-plane alignment of the cleaved surface. The rocking curve of (002) Bragg peak in Fig. 1(c) demonstrates that the Full Width at Half Maximum (FWHM) reaches 0.0074°. This small value of FWHM is the indication of good crystallinity of our crystals. Detailed crystallographic data are listed in Table 1.

Figure 1. (Color online) (a) Experimental powder X-ray diffraction (XRD) data and calculated XRD pattern for crushed BaZrO​3 single crystal. (b) High-resolution XRD for the cleaved (001) plane. The peaks correspond to Bragg peaks of (001), (002), (003). (c) Rocking curve for the (002) Brag peak. The full width at half maximum (FWHM) of the (002) rocking curve is estimated as the value of 0.0074​∘.

Table 1 . Crystal and structure refinement data.

Chemical Formula	BaZrO3
Structure	Cubic
Space Group	Pm3¯m
a=b=c (Å)	a=4.1899
Rp (%)	18.0
Rwp (%)	15.7
Rexp (%)	9.82
χ2	2.56
Ba(x,y,z)	(0, 0, 0)
Zr(x,y,z)	(0.5000, 0.5000, 0.5000)
O(x,y,z)	(0, 0.5000, 0.5000)

Using the AFM, we investigated the topography of the cleaved (00l) surfaces of the BaZrO₃ single crystal. The ab initio calculations reported that surface energies for BaO and ZrO₂ surface termination are very close each other[13]. The atomically clear step terraces in the AFM image have been used as an indication for the application of the high-quality single crystal for the substrate. Figure 2 shows AFM topographic images of the cleaved (00l) surface of the as-grown BaZrO₃ single crystal. Figure 2(a) shows AFM topographic images of the cleaved surfaces of BaZrO₃ measured from about 5 μm × 5 μm scale. At this scale, it is observed that the surface is composed of steps and atomically flat terraces at atomic level scanning. In the line profile (Fig. 2(c)), a single step is estimated as about 0.5 nm, which is approximately close to the lattice constant (a = 4.189 Å) of BaZrO₃. Furthermore, Fig. 2(b) presents an AFM topographic image resulting from a scanning area of 50 μm × 50 μm which shows successively and atomically smooth step terrace structures. In the line profile of Fig. 2(d), the width of a step is ∼10 μm across the surface for 50 μm × 50 μm scanning scale which is very wide enough for the substrate applications.

Figure 2. (Color online) Atomic force microscope (AFM) topography images of the cleaved (001) surfaces of BaZrO​3 single crystal with (a) 5 μm × 5 μm scale and (b) 50 μm × 50 μm scale. Topographic line profiles in (c) and (d) correspond to white dotted lines in (a) and (b), respectively. The step terrace structures appear.

Figure 3 displays the temperature dependence of the dielectric response at various frequencies of 0.5 kHz, 1 kHz, 2 kHz, 5 kHz, and 10 kHz. In Fig. 3(a), the overall values of the dielectric constant of the BaZrO₃ are approximately within ranges of 3–47.5 from 2 K to 400 K. As decreasing the temperature from ∼370 K, the dielectric constant gradually increases from 43.4 to 47.3. In addition, four step-like anomalies in the dielectric constant appear around temperatures of ∼240 K, ∼135 K, ∼110 K, and ∼30 K, which are exhibited as corresponding peak-features in the tanδ (Fig. 3(b)). Such plateau has already been observed in the incipient ferroelectrics KTaO₃[14, 15], and SrTiO₃[16, 17], and was attributed to zero-point vibrations. On the contrary, it was reported that this behavior of permittivity in polycrystalline BaZrO₃ is not a result of suppression of ferroelectricity since BaZrO₃ does not have any instabilities in ferroelectric ground-state even in the classical regime[18]. They have proposed that the anomaly in the dielectric response at low temperature ∼15 K is due to the activation of the oxygen octahedra rotation in BaZrO₃. However, the dielectric response at high temperature is frequency dependent with decreasing frequency the anomaly is shifted to low temperature. It is possible that defects, such as oxygen vacancies and/or unavoidable impurity ions, could be attributed to the frequency dependent tiny dielectric anomaly. For in detailed, further comprehensive studies are required. Although such step-like anomalies in the dielectric constant have been reported in the polycrystalline BaZrO₃[18], the existing temperatures and the number of anomalies have discrepancies with our observation. The theoretical calculations for the BaZrO₃ predict the antidistortive ground states in BaZrO₃[19] so that the dielectric anomalies in BaZrO₃ are still under debate, and further investigation is required.

Figure 3. (Color online) Temperature dependence of (a) dielectric constant and (b) dissipation for BaZrO​3 single crystal at oscillating frequencies of 0.5 kHz, 1.0 kHz, 2.0 kHz, 5.0 kHz, and 10.0 kHz.

In conclusion, we have successfully grown the BaZrO₃ single crystals by the optical floating zone method. Through the X-ray diffraction experiments and Rietveld refinement, we confirmed that the BaZrO₃ single crystal has a cubic perovskite structure with the lattice constant of 4.189 Å. The AFM measurement on the cleaved (00l) surface reveals the atomically flat and step terrace structures. The temperature dependence of the dielectric constant and tanδ from 2 K to 400 K represents the four step-like and peak-featured anomalies, respectively, around ∼240 K, ∼135 K, ∼110 K, and ∼30 K. The ground state of BaZrO₃ is theoretically and experimentally under debate. So, further investigations for the microstructure at low temperatures are required.

This work is supported from the Basic Science Research Programs through the National Research Foundation of Korea (NRF) (No. RS-2023-00244404).