Fabrication and properties of non-stoichiometric Tb2(Hf1−xTbx)2O7−x magneto-optical ceramics

Non-stoichiometric Tb2(Hf1−xTbx)2O7−x (x = −0.07–0.45) magneto-optical ceramics were fabricated by solid-state reactive sintering in vacuum combined with hot isostatic pressing (HIP) post-treatment without any sintering aids. The phase composition, densification process, microstructure, optical transmittance, and Verdet constant of Tb2(Hf1−xTbx)2O7−x ceramics were investigated. The in-line transmittance of (Tb0.93Hf0.07)2Hf2O7.07 ceramics with a thickness of 2.0 mm reaches 74.6% at 1064 nm. The Verdet constant of Tb2(Hf1−xTbx)2O7−x ceramics is −153.4, −155.8, and −181.2 rad/(T·m) at the wavelength of 633 nm when x = −0.07, 0, and 0.1, respectively. The Verdet constant increases with the increase of Tb content, and these values are higher than that of the commercial Tb3Ga5O12 crystal, indicating that non-stoichiometric Tb2(Hf1−xTbx)2O7−x ceramics have a great potential for the application in Faraday isolators.

Transparent Tb 2 Hf 2 O 7 ceramics show high Verdet constant and high optical quality [41][42][43]. The Verdet constant of Tb 2 Hf 2 O 7 ceramics reaches about −159 rad/(T·m) at 633 nm and −50 rad/(T·m) at 1064 nm, which is 18.7% and 38.9% higher than that of commercial TGG crystal, respectively. The required length of Tb 2 Hf 2 O 7 ceramics is 28% shorter than that of TGG crystal when they are applied at 1064 nm under the same magnetic field intensity. Short magneto-optical elements have big advantages because they contribute to limiting the light absorption, minimizing the effects of self-focusing and other thermal-related effects [15].
Generally, the Verdet constant of the material increases with the increasing volume concentration of the paramagnetic metal ions according to Van Vleck et al.'s theory [44,45] where V is the Verdet constant, N is the volume concentration of the paramagnetic ions, g is the Lande splitting coefficient, C n denotes the transition moments, ν is the frequency, ν n is the frequency corresponding to the splitting of excited states, J is the total angular momentum quantum number, k is the Boltzmann constant, and μ B is the Bohr magneton number, c is the speed of light in vacuum, h is the Plank constant, T is the absolute temperature. Considering the large solid solution range of the cubic phase shown in the phase diagram of HfO 2 -Tb 2 O 3 systems [46], transparent nonstoichiometric Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics can be fabricated in theory. The non-stoichiometric Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics with excess Tb will possess higher Verdet constants than the stoichiometric Tb 2 Hf 2 O 7 ceramics because of the higher volume concentration of the paramagnetic ions, N value in Eq. (1). In our previous work [43], high-optical-quality Tb 2 (Hf 1−x Tb x ) 2 O 7−x magneto-optical ceramics with x = 0.1 were fabricated successfully, while the properties of Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics across a wider stoichiometric range are under expectation.
In this work, non-stoichiometric Tb 2 (Hf 1−x Tb x ) 2 O 7−x (x = −0.07-0.45) magneto-optical ceramics were fabricated by solid-state reactive sintering in vacuum combined with hot isostatic pressing (HIP) post-treatment without any sintering aids. The phase composition, densification process, microstructure, optical transmittance, and Verdet constant of Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics were discussed for the first time.

Experimental
Detailed information of the raw powders and experimental procedures were presented in our previous work [43]. Briefly, high-purity Tb 4 O 7 powders and HfO 2 powders were mixed and ball-milled without any sintering aids. The milled slurry was dried and sieved through a screen. The mixed powders were calcined in a muffle furnace at 800 ℃ for 4 h and then uniaxially pressed into pellets. These pellets were treated at 800 ℃ for 10 h in NH 3 atmosphere to remove Tb 4+ , preventing the ceramics from cracking during sintering. The pellets were cold isostatically pressed at 250 MPa for 5 min. These green bodies were pre-sintered at 1450-1750 ℃ for 3 h in vacuum and HIP post-treated at 1750 ℃ for 3 h under 176 MPa argon atmosphere. At last, the Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics were mirrorpolished on both surfaces to 2.0 mm.
Microstructure of the fracture and thermally etched surfaces, and energy-dispersive X-ray spectrometry (EDS) mapping were analyzed by field emission scanning electron microscopy (FESEM, SU-8220, Hitachi, Japan). Ceramic samples were thermally etched at 1300 ℃ for 10 h in high-purity argon atmosphere in a tube furnace. Linear intercept method was used to measure the grain sizes of the ceramics. Phase identification was performed by X-ray diffraction (XRD, D8 Advance, Bruker, Germany) equipped with a copper target X-ray tube in the 2θ range of 10°-80°. Bulk densities of the ceramic samples were measured using the Archimedes method. In-line transmittance of the ceramics with the wavelength range from 200 to 1800 nm was measured with ultravioletvisible-near infrared (UV-vis-NIR) spectrophotometry (Cary-5000, Varian, USA). The Verdet constant at 633 nm of ceramics was determined at room temperature by an instrument consisting of a He-Ne laser, two polarizers, and an electromagnet.  (space group Fd3m, No. 227) can be seen at about 28.4° when x = 0 shown in Fig. 1(a), confirming the pyrochlore phase of Tb 2 Hf 2 O 7 . No pyrochlore characteristic peaks can be detected when x ≠ 0 in this work. Thus, the main crystal phase of the nonstoichiometric ceramics can be regarded as a defect fluorite phase (space group Fm3m, No. 225) [47][48][49], and this result is consistent with the phase diagram of HfO 2 -Tb 2 O 3 binary systems [46]. An obvious peak shifting can be seen in the partial enlarged XRD patterns in Fig. 1(a) (the peak splitting in high angle is caused by Cu Kα 2 ). As the radius of Hf 4+ is smaller than that of Tb 3+ when six-coordinated, the lattice spacing increases with the increase of the x value, and the peak will shift to the low angle from the Bragg equation. No obvious peaks of the secondary phase can be found when x ≤ 0.4. However, when x = 0.45, the full width at half-maximum (FWHM) of diffraction peaks increases evidently, and some diffraction peaks of a secondary phase can be detected, which is a solid solution of bixbyite Tb 2 O 3 phase with diffused HfO 2 . Based on the XRD data, the lattice parameters (or 1/2 of lattice parameter in pyrochlore crystal) and theoretical densities of Tb 2 (Hf 1−x Tb x ) 2 O 7−x (x = −0.07 -0.45) are calculated and shown in Fig. 1(b). The calculated lattice parameters increase, and the theoretical densities decrease with the increase of Tb content. When −0.07 ≤ x ≤ 0.45, the lattice parameters and theoretical densities change almost linearly. Figure 2 shows the relative densities of Tb 2 (Hf 1−x Tb x ) 2 O 7−x (x = −0.07-0.45) ceramics pre-sintered at different temperatures for 3 h in vacuum. With the elevating pre-sintering temperature, the relative densities of Tb 2 (Hf 1−x Tb x ) 2 O 7−x (−0.07 ≤ x ≤ 0.3) ceramics increase basically, indicating the densification process. When −0.07 ≤ x ≤ 0.3, with the increasing x value except x = 0, the required pre-sintering temperature for achieving 95% relative density decreases. This suggests that excess Tb is favorable for the densification of Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics because the oxygen vacancy (for charge compensation of Tb 3+ replacing Hf 4+ ) can promote the lattice diffusion [50]. The densification process of Tb 2 Hf 2 O 7 (x = 0) ceramics is singular in this work, which may be attributed to the different diffusion mobility in different phases as the Tb 2 Hf 2 O 7 (x = 0) ceramics are the only specimens with pyrochlore phase shown in Fig. 1. After pre-sintered at 1650 ℃ for 3 h, the relative densities of Tb 2 (

Results and discussion
3) ceramics are higher than 92%, and hence these pre-sintered specimens can be further densified during HIP post-treatment. The relative densities of Tb 2 (Hf 0.7 Tb 0.3 ) 2 O 6.7 ceramics decrease slightly with the increase of pre-sintering temperature after 1650 ℃. Furthermore, when x = 0.4 and 0.45, the relative densities decrease abnormally with the increase of pre-sintering temperature. This converse densification phenomenon may associate with the complex behavior of the secondary phase during sintering. In order to find out the cause of the converse densification when x = 0.4 and 0.45, XRD and FESEM were used to characterize the Tb 2 (Hf 0.55 Tb 0.45 ) 2 O 6.55 ceramics pre-sintered at different temperatures for 3 h, as shown in Figs. 3 and 4. It is clear that defect fluorite is the major crystal phase, and the secondary phase is observed shown in Fig. 3. It should be noted that the secondary phase is a Tb-rich solid solution with cubic bixbyite structure (space group Ia3, No. 206) [46]. The bixbyite secondary phase cannot be eliminated even after sintered at 1750 ℃ for 3 h. The diffraction peak of bixbyite phase shifts to a higher angle with the increase of pre-sintering temperature, and the peak of defect fluorite phase shifts slightly to the lower angle, as shown in the partial enlarged patterns in Fig. 3. This phenomenon demonstrates the interdiffusion between defect fluorite phase and bixbyite phase. However, peak intensity of the secondary phase shows no sign of decrease, as shown in Fig. 3(a), implying that the bixbyite phase may be thermodynamically stable in Tb 2 (Hf 0.55 Tb 0.45 ) 2 O 6.55 ceramics during 1450 and 1750 ℃. This result is inconsistent with the phase diagram in which Tb 2 (Hf 1−x Tb x ) 2 O 7−x compound is a single cubic phase with x = 0.14-0.47 over 1700 ℃, and little phase diagram data below 1700 ℃ is available till now. Low diffusion rate between Tb 2 O 3 and HfO 2 may be one of the causes for this inconsistence [46]. Figure 4 shows the FESEM images of the thermally etched surfaces of Tb 2 (Hf 0.55 Tb 0.45 ) 2 O 6.55 ceramics presintered at different temperatures for 3 h. The grain size of the ceramics pre-sintered at a certain temperature is not uniform. Fine grains and larger grains are present in the ceramics. With the increase of pre-sintering temperature, all the grains grow up evidently but still nonuniformly. Meanwhile, the sizes of pores increase evidently. In general, grains grow up, and pores are gradually removed during the sintering process. The evolution of the pores shown in Fig. 4 is not the same with the usual sintering phenomenon. Figure 5 shows the EDS patterns of the Tb 2 (Hf 0.55 Tb 0.45 ) 2 O 6.55 ceramics pre-sintered at 1450 ℃ (unindexed peaks belong to Tb, Hf, and O). EDS patterns confirm that the fine grains are Tb-rich secondary phase, and the composition of larger grains is near the designed composition. Here we provide a hypothesis about the converse densification and microstructure evolution process. During the sintering process, the secondary phase particles with small grain size have high sintering activity, and they cause rapid grain boundary migration. The grain boundary migration is more sensitive to the temperature than the elimination rate of pores [51]. As a result, the grain boundary migration accelerates when the sintering temperature raises and the grain boundary closes, leading to the difficulty for pores to remove continually. The hindered pore removal process causes the abnormal densification shown in Fig. 2, and the porous ceramics with both intergranular and intragranular pores are formed as shown in Fig. 4. Further studies are eagerly needed to understand the causes of abnormal densification as well as the exact phase composition in Tb 2 O 3 -HfO 2 binary system under 1700 ℃.
FESEM images of the thermally etched surfaces of Tb 2 (Hf 1−x Tb x ) 2 O 7−x (x = −0.07-0.45) ceramics presintered at 1650 ℃ for 3 h in vacuum are shown in Fig. 6. There are many pores in the pre-sintered specimens. The pores in the ceramics with x = −0.07, 0, and 0.1 are mainly intergranular pores and can be eliminated in the following HIP post-treatment, shown in Figs. 6(a)-6(c). The numbers of pores shown in FESEM images are in good agreement with the relative densities shown in Fig. 2. Tb 2 Hf 2 O 7 (x = 0) ceramics have the highest relative density and the fewest pores shown in Fig. 6(b) because of the distinct phase composition and diffusion mobility. A remarkable phenomenon shown in Figs. 6(c)-6(g) is that the excessive Tb 2 O 3 can significantly promote the grain boundary migration and grain growth in Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics. The fast migration of grain boundaries results in larger grains and intragranular pores shown in Figs. 6(d)−6(g). Generally, intragranular pores are hard to be eliminated during HIP post-treatment, and those pores will remain in the ceramics becoming the optical scattering center [52], which brings a serious adverse effect on the optical quality of ceramics. In addition, some dark, small scattered  points can be seen in the pre-sintered ceramics when x ≥ 0.1, which are Tb-rich secondary phases. Some particles can be seen in Figs. 6(f) and 6(g), and they are impurities caused during the polishing process.  [52]. In general, pre-sintered ceramics with the relative densities of 92%-95% are suitable for the following HIP post-treatment to obtain pore-free ceramics [53,54]. Most of the intergranular pores in the specimens shown in Fig. 6(a) are eliminated after HIP post-treatment. There are no obvious pores or secondary phase found in Fig. 7(a), implying the relatively high optical quality of the ceramics with x = −0.07. However, when x = 0, some small intergranular pores still exist because the sinterability of the pre-sintered Tb 2 Hf 2 O 7 ceramics is too low, resulting from the inappropriate pre-sintering temperature. When x = 0.1, shown in Fig.  7(c), no secondary phase can be found, which means that Tb-rich secondary phase diffuses and is mostly eliminated during HIP post-treatment. As the presintering temperature is lower than that of the HIP post-treatment, this phenomenon indicates that enough sintering temperature and holding time may be needed for the diffusion between Tb 2 O 3 and HfO 2 to obtain Tb 2 (Hf 1−x Tb x ) 2 O 7−x with composition homogeneity. Some residual pores can be seen in grains when x ≥ 0.1, proving that intragranular pores are hard to be eliminated during HIP post-treatment. Pre-sintering and HIP post-treatment temperatures can be further optimized to obtain fully dense Tb 2 (Hf 1−x Tb x ) 2 O 7−x (x = −0.07-0.45). Figure 8 shows the EDS patterns of the Tb 2 (Hf 0.8 Tb 0.2 ) 2 O 6.8 ceramics pre-sintered at 1650 ℃ with HIP post-treatment. The EDS patterns show that Tb-rich secondary phase remains in the ceramics when x = 0.2 even after HIP post-treatment, so the existence of secondary phase in Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics when x > 0.2 is predictable. Both pores and secondary phases scatter the incident light, so it is foreseeable that the Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics with x ≥ 0.2 have relatively low optical quality.   x value, the anti-site Tb increases, the concentration of Tb 4+ can be higher, and the brown color becomes deeper. The color of the Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics with x = 0.4 and 0.45 is lighter than that of the ceramics with x = 0.3, which may be attributed to the low relative density and high porosity because the light will be scattered and reflected more easily rather than absorbed in the ceramics. Figure 9(b) shows the in-line transmittance of the specimens. The transmittance of the ceramics is in good accordance with the microstructures shown in Fig. 7. When x = −0.07, the (Tb 0.93 Hf 0.07 ) 2 Hf 2 O 7.07 ceramics show a relatively high optical quality. The in-line transmittance of (Tb 0.93 Hf 0.07 ) 2 Hf 2 O 7.07 ceramics (2.0 mm thick) is higher than 70% at 600-1500 nm, and reaches 74.6% at 1064 nm. As a reference, the theoretical in-line transmittance of stoichiometric Tb 2 Hf 2 O 7 is 77.8% [41]. When x = 0 and 0.1, the in-line transmittance of the ceramics is 40.1% and 65.0% at 1064 nm, respectively. The main cause of the relatively low transmittance when x = 0 and 0.1 is the optical scattering from pores remained in ceramics, which can be improved promisingly by adjusting the pre-sintering and HIP schedule in the future [43]. However, when x ≥ 0.1, the in-line transmittance of Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics decreases with the increase of Tb content, which can be interpreted to the increase of secondary phase and pores as they both scatter the light severely. From the phase diagram of the binary system with hafnia and terbia [46], Tb 2 (Hf 1−x Tb x ) 2 O 7−x can maintain single cubic phase (pyrochlore or defect fluorite phase) when −0.74 ≤ x ≤ 0.47 from 1700 to 2300 ℃. However, the extremely low diffusion mobility in Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics limits the fabrication of single-phase ceramics by reactive sintering method. Hence, it is challenging to fabricate Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics with both high Tb content (x > 0.1) and high optical quality by this method. Improving the powder homogeneity and using non-reactive sintering may be an optional way, e.g., using the co-precipitation or combustion method to prepare the raw powder as the element distribution can be more uniform, so the diffusion distance can be reduced greatly. In addition, supplements are needed in the phase diagram of HfO 2 -Tb 2 O 3 , especially the phase composition under 1700 ℃.
The Verdet constant is one of the most important magneto-optical parameters. For paramagnetic materials, the Verdet constant can be calculated by Eq. (2): where V is the Verdet constant, θ is the Faraday rotation angle, B is the magnetic field intensity, and d is the thickness of the sample. We measured the Faraday rotation angle under certain magnetic field intensity and sample thickness.

Conclusions
In summary, non-stoichiometric Tb 2 (Hf 1−x Tb x ) 2 O 7−x (x = −0.07-0.45) magneto-optical ceramics were fabricated by solid-state reactive sintering in vacuum combined with HIP post-treatment without any sintering aids. The phase composition and lattice parameters change with the change of Tb content. The densification process of Tb 2 (Hf 1−x Tb x ) 2 O 7−x ceramics was discussed, and the existence of Tb-rich bixbyite secondary phase was confirmed.