Optical Properties and Band Gap of Ternary PSN-PMN-PT Single Crystals

: This study investigated the optical properties and the interband transition of a ternary [100]-oriented 6PSN-61PMN-33PT relaxor ferroelectric single crystal. Compared with the binary [100]-oriented PMN-32PT crystal, the [100]-oriented 6PSN-61PMN-33PT crystal exhibited excellent optical properties, including high transmittance, low refractive index, weak frequency dispersion, and low reﬂection and absorption coefﬁcients. All these differences can be attributed to the structural changes of the 6PSN-61PMN-33PT crystal, such as its large lattice size and increased band gap. The crystal’s transmittance was signiﬁcantly improved after alternating current electric ﬁeld poling due to the increased domain size and the order domain structure. The largest transmittance for the 6PSN-61PMN-33PT crystal was up to 66%. Our experimental results indicate that the ternary 6PSN-61PMN-33PT ferroelectric single crystal has great application potential in the optical ﬁeld.


Introduction
Multifunctional materials with acoustic, optical, electrical, and magnetic properties are considered the mainstream of the future development in the materials science field. Ferroelectric crystals integrated with excellent optical and electrical properties have great application prospect in advanced devices such as electro-optic switches, electro-optic modulators, and light valves.
To overcome these shortcomings and improve the Tc and the Tr-t, Pb(Sc 1/2 Nb 1/2 )O 3 (PSN) was introduced into the PMN-PT because its Tc that is much quite higher than that of PMN [11][12][13][14][15][16]. A relatively high phase transition temperature (Tc > 200 • C) has been reported in PSN-PMN-PT single crystals at the MPB, with good piezoelectric d 33 (1260~1550 pC/N) [16]. On the other hand, the introduction of Sc 3+ into LiNbO 3 ferroelectric crystal has been reported to increase the crystal's optical damage-resistance properties [17]. Therefore, we speculate that ternary PSN-PMN-PT crystal will have higher optical damage-resistance properties than PMN-PT crystal, indicating its potential application prospect in the optical field. At present, most studies focus on these crystals' electrical properties [11][12][13][14][15][16]. No study has yet focused on the optical properties of the ternary PSN-PMN-PT crystal, which are detrimental to the design of optical devices and the development of multifunctional materials.
This study investigates the optical properties and the interband transitions of a [100]oriented ternary 6PSN-61PMN-33PT crystal. The effects of the polarization method on the optical transmittance are analyzed by domain configuration. The differences of the optical properties between the [100]-oriented 6PSN-61PMN-33PT and the [100]-oriented PMN-32PT are compared. The band gaps are calculated based on the optical spectra. Sellmeier optical coefficients are determined by fitting the Wemple and DiDomenico (WDD) single oscillator equation.
Crystals 2021, 11, x FOR PEER REVIEW 2 of 10 (1260~1550 pC/N) [16]. On the other hand, the introduction of Sc 3+ into LiNbO3 ferroelectric crystal has been reported to increase the crystal's optical damage-resistance properties [17]. Therefore, we speculate that ternary PSN-PMN-PT crystal will have higher optical damage-resistance properties than PMN-PT crystal, indicating its potential application prospect in the optical field. At present, most studies focus on these crystals' electrical properties [11][12][13][14][15][16]. No study has yet focused on the optical properties of the ternary PSN-PMN-PT crystal, which are detrimental to the design of optical devices and the development of multifunctional materials. This study investigates the optical properties and the interband transitions of a [100]oriented ternary 6PSN-61PMN-33PT crystal. The effects of the polarization method on the optical transmittance are analyzed by domain configuration. The differences of the optical properties between the [100]-oriented 6PSN-61PMN-33PT and the [100]-oriented PMN-32PT are compared. The band gaps are calculated based on the optical spectra. Sellmeier optical coefficients are determined by fitting the Wemple and DiDomenico (WDD) single oscillator equation.
The room-temperature optical transmission and absorption coefficient spectra of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals were measured in the wavelength range of 200-2500 nm through a UV-Vis-NIR spectrophotometer (Agilent, Cary 5000, Egilent, NM, USA). The refraction parameters were tested using a spectroscopic ellipsometer (SE-VM, Eoptics, Wuhan,China) in the wavelength range of 380-1000 nm. The incident light angle was 65° during the measurement process. Silver paste was Laue diffraction was used to analyze the crystal orientation. Two crystals were cut into the slices of 5 × 5 × 0.8 mm 3 perpendicular to the [100] direction. The crystalline structure was examined by X-ray diffraction (XRD, Bruker D2 focus). For the optical measurements, the 740 µm-thick specimens were polished using diamond-polishing compounds. The samples were then annealed to remove the residual stress derived from the polishing process (350 • C, 30 min).
The room-temperature optical transmission and absorption coefficient spectra of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals were measured in the wavelength range of 200-2500 nm through a UV-Vis-NIR spectrophotometer (Agilent, Cary 5000, NM, USA). The refraction parameters were tested using a spectroscopic ellipsometer (SE-VM, Eoptics, Wuhan, China) in the wavelength range of 380-1000 nm. The incident light angle was 65 • during the measurement process. Silver paste was used to cover both sides of the (100) crystal face to load the external electric field on the single crystals. The samples were dried at 70 • C for 20 min to ensure good electrical conductivity. The crystal samples were then poled at room-temperature for 15 min under a direct current electric field (20 kV/cm) and an alternating current electric field with a triangular waveform at 20 kV/cm and 5 Hz. The domain configurations were observed using a polarized light microscope (PLM, LEICADM2500P+7HMS, Leica, Germany) after the silver electrodes were removed using acetone.

Results and Discussions
The single crystal orientation has an effect on the optical properties due to various domain structures. Figure 2a,c shows the XRD pattern of the 6PSN-61PMN-33PT and 68PMN-32PT square slices. Only two diffraction peaks of (100) and (200) at 22 • and 45 • were obtained, indicating that the orientation of the two square slices was the [100] direction. We performed powder XRD to prove whether or not the two crystals were of perovskite structure (Figure 2b,d). As compared to Pb(Mg 1/3 Nb 2/3 )O 3 (PDF#81-0861), standard perovskite structure peaks were obtained, indicating that the selected samples were of pure perovskite structure without any pyrochlore phase. Compared to those shown in Figure 2d, the diffraction peaks in Figure 2b slightly shifted towards a low angle, suggesting an increase of the lattice size in the 6PSN-61PMN-33PT crystals, which can be attributed to the large-ion Sc 3+ (r ion = 0.0745 nm) occupying the B-site to substitute the small-ion Mg 2+ (r ion = 0.072 nm) and Nb 5+ (r ion = 0.064 nm). Crystal lattice parameters (a = b = c = 4.0257 Å for 6PSN-61PMN-33PT, and a = b = c = 4.0226 Å for PMN-32PT) calculated by the software Jade further certify the increase of lattice size.
Crystals 2021, 11, x FOR PEER REVIEW 3 of 10 used to cover both sides of the (100) crystal face to load the external electric field on the single crystals. The samples were dried at 70 °C for 20 min to ensure good electrical conductivity. The crystal samples were then poled at room-temperature for 15 min under a direct current electric field (20 kV/mm) and an alternating current electric field with a triangular waveform at 20 kV/mm and 5 Hz. The domain configurations were observed using a polarized light microscope (PLM, LEICADM2500P+7HMS, Leica, Germany) after the silver electrodes were removed using acetone.

Results and Discussions
The single crystal orientation has an effect on the optical properties due to various domain structures. Figure 2a,c shows the XRD pattern of the 6PSN-61PMN-33PT and 68PMN-32PT square slices. Only two diffraction peaks of (100) and (200) at 22° and 45° were obtained, indicating that the orientation of the two square slices was the [100] direction. We performed powder XRD to prove whether or not the two crystals were of perovskite structure (Figure 2b,d). As compared to Pb(Mg1/3Nb2/3)O3 (PDF#81-0861), standard perovskite structure peaks were obtained, indicating that the selected samples were of pure perovskite structure without any pyrochlore phase. Compared to those shown in Figure 2d, the diffraction peaks in Figure 2b slightly shifted towards a low angle, suggesting an increase of the lattice size in the 6PSN-61PMN-33PT crystals, which can be attributed to the large-ion Sc 3+ (rion = 0.0745 nm) occupying the B-site to substitute the smallion Mg 2+ (rion = 0.072 nm) and Nb 5+ (rion = 0.064 nm). Crystal lattice parameters (a = b = c = 4.0257 Å for 6PSN-61PMN-33PT, and a = b = c = 4.0226 Å for PMN-32PT) calculated by the software Jade further certify the increase of lattice size. Excellent transmittance is a key factor in nonlinear optical materials. Figure 3 shows the transmittance spectra of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT crystals at different poled states, including the alternate current electric field-poled (AC-poled) state, direct current electric field-poled (DC-poled) state, and green state (unpoled) to explore the effects of the polarization process on the optical properties. All samples were transparent in the visible light and near-infrared regions in the wavelength range from 450 to 2500 nm. However, the transmittance rapidly decreased near 400 nm, showing an optical absorption edge in the ultraviolet region. The inset in Figure 3 shows the amplified plot of the transmittance spectra near the optical absorption edge. The wavelength of the absorption edge of the 6PSN-61PMN-33PT crystal was smaller than that of the binary PMN-32PT crystals, indicating a slight blue shift in the maximum absorption. The crystal transmittance after the AC poling sharply increased in the visible light region and obtained large values compared with the unpoled and DC-poled samples. In particular, for the [100]-oriented 6PSN-61PMN-33PT crystal, the highest transmittance of approximately Excellent transmittance is a key factor in nonlinear optical materials. Figure 3 shows the transmittance spectra of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT crystals at different poled states, including the alternate current electric field-poled (AC-poled) state, direct current electric field-poled (DC-poled) state, and green state (unpoled) to explore the effects of the polarization process on the optical properties. All samples were transparent in the visible light and near-infrared regions in the wavelength range from 450 to 2500 nm. However, the transmittance rapidly decreased near 400 nm, showing an optical absorption edge in the ultraviolet region. The inset in Figure 3 shows the amplified plot of the transmittance spectra near the optical absorption edge. The wavelength of the absorption edge of the 6PSN-61PMN-33PT crystal was smaller than that of the binary PMN-32PT crystals, indicating a slight blue shift in the maximum absorption. The crystal transmittance after the AC poling sharply increased in the visible light region and obtained large values compared with the unpoled and DC-poled samples. In particular, for the [100]oriented 6PSN-61PMN-33PT crystal, the highest transmittance of approximately 63% in the visible light range was obtained after the AC poling along the [100] direction. This value was higher than that of the DC-poled (<50%) and unpoled (<37%) samples. These results provide an effective means of optimizing the optical performance of the ferroelectric crystal.
63% in the visible light range was obtained after the AC poling along the [100] direction. This value was higher than that of the DC-poled (<50%) and unpoled (<37%) samples. These results provide an effective means of optimizing the optical performance of the ferroelectric crystal. For ferroelectrics, the domain wall scattering is another main factor of the optical loss, except for the optical band gap [2,8]. Figure 4a-c shows the domain structure of the [100]oriented 6PSN-61PMN-33PT crystal pretreated by different electric fields. For the unpoled sample (Figure 4a), most of the domains showed blurred margins and discontinuities, except for a few tiny domain bands, indicating a large domain wall density caused by the relatively small domain size. After the crystal was poled using the DC electric field, the domain size increased and the discontinuous domains showed an obvious decrease (Figure 4b). According to a previous report by Liu [18], this is a typical '4R' engineering domain configuration with 71° and 109° domain walls. For the AC-poled sample in Figure  4c, the domain configuration underwent amazing changes. The domain walls almost disappeared, suggesting the emergence of a monodomain state. Our experimental results are consistent with the theorical calculation results reported by Xu et al. [2,3,18,19]. Therefore, we propose that the decrease of domain walls density and ordered domain structure is beneficial to improve the crystal transmittance. For ferroelectrics, the domain wall scattering is another main factor of the optical loss, except for the optical band gap [2,8]. Figure 4a-c shows the domain structure of the [100]-oriented 6PSN-61PMN-33PT crystal pretreated by different electric fields. For the unpoled sample (Figure 4a), most of the domains showed blurred margins and discontinuities, except for a few tiny domain bands, indicating a large domain wall density caused by the relatively small domain size. After the crystal was poled using the DC electric field, the domain size increased and the discontinuous domains showed an obvious decrease (Figure 4b). According to a previous report by Liu [18], this is a typical '4R' engineering domain configuration with 71 • and 109 • domain walls. For the AC-poled sample in Figure 4c, the domain configuration underwent amazing changes. The domain walls almost disappeared, suggesting the emergence of a monodomain state. Our experimental results are consistent with the theorical calculation results reported by Xu et al. [2,3,18,19]. Therefore, we propose that the decrease of domain walls density and ordered domain structure is beneficial to improve the crystal transmittance.
Crystals 2021, 11, x FOR PEER REVIEW 4 of 10 63% in the visible light range was obtained after the AC poling along the [100] direction. This value was higher than that of the DC-poled (<50%) and unpoled (<37%) samples. These results provide an effective means of optimizing the optical performance of the ferroelectric crystal. For ferroelectrics, the domain wall scattering is another main factor of the optical loss, except for the optical band gap [2,8]. Figure 4a-c shows the domain structure of the [100]oriented 6PSN-61PMN-33PT crystal pretreated by different electric fields. For the unpoled sample (Figure 4a), most of the domains showed blurred margins and discontinuities, except for a few tiny domain bands, indicating a large domain wall density caused by the relatively small domain size. After the crystal was poled using the DC electric field, the domain size increased and the discontinuous domains showed an obvious decrease (Figure 4b). According to a previous report by Liu [18], this is a typical '4R' engineering domain configuration with 71° and 109° domain walls. For the AC-poled sample in Figure  4c, the domain configuration underwent amazing changes. The domain walls almost disappeared, suggesting the emergence of a monodomain state. Our experimental results are consistent with the theorical calculation results reported by Xu et al. [2,3,18,19]. Therefore, we propose that the decrease of domain walls density and ordered domain structure is beneficial to improve the crystal transmittance.  The refractive index is an important factor for material applications in the optical field. Figure 5 depicts the refractive indices of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals. Similar to those in most ABO3-type perovskite compounds, the significant dispersion relationship and the rapid decrease of the refractive index with increasing wavelength from 375 nm to 1000 nm are presented in Figure 5a,b, indicating normal dispersion characteristics [20]. The ternary [100]-oriented 6PSN-61PMN-33PT crystal showed a smaller refractive index (n = 2.85 -2.6) than PMN-32PT (n = 3.05 -2.63) in the low wavelength range from 375 nm to 600 nm. This result indicates that the light with a wavelength between 375 nm and 600 nm had a higher propagation speed in the 6PSN-61PMN-33PT crystal than in the PMN-32PT crystal. Upon further increasing the wavelength above 600 nm, the refractive index values of both crystals gradually tended to become similar. In the same wavelength range, the change in the refractive index in the 6PSN-61PMN-33PT crystal was smaller than that in the PMN-32PT crystal. This shows the weaker dispersion in the 6PSN-61PMN-33PT crystal compared to that in the PMN-32PT crystal, which is conducive for improving the image quality. For ferroelectrics with a perovskite structure, lattice dynamical theories indicate that the optical properties are mainly determined by the coupling of the d orbits in the B-site cation and the 2p orbits in the O anions related to each BO6 octahedron [21], suggesting The refractive index is an important factor for material applications in the optical field. Figure 5 depicts the refractive indices of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals. Similar to those in most ABO 3 -type perovskite compounds, the significant dispersion relationship and the rapid decrease of the refractive index with increasing wavelength from 375 nm to 1000 nm are presented in Figure 5a,b, indicating normal dispersion characteristics [20]. The ternary [100]-oriented 6PSN-61PMN-33PT crystal showed a smaller refractive index (n = 2.85-2.6) than PMN-32PT (n = 3.05-2.63) in the low wavelength range from 375 nm to 600 nm. This result indicates that the light with a wavelength between 375 nm and 600 nm had a higher propagation speed in the 6PSN-61PMN-33PT crystal than in the PMN-32PT crystal. Upon further increasing the wavelength above 600 nm, the refractive index values of both crystals gradually tended to become similar. In the same wavelength range, the change in the refractive index in the 6PSN-61PMN-33PT crystal was smaller than that in the PMN-32PT crystal. This shows the weaker dispersion in the 6PSN-61PMN-33PT crystal compared to that in the PMN-32PT crystal, which is conducive for improving the image quality.  The refractive index is an important factor for material applications in the optical field. Figure 5 depicts the refractive indices of the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals. Similar to those in most ABO3-type perovskite compounds, the significant dispersion relationship and the rapid decrease of the refractive index with increasing wavelength from 375 nm to 1000 nm are presented in Figure 5a,b, indicating normal dispersion characteristics [20]. The ternary [100]-oriented 6PSN-61PMN-33PT crystal showed a smaller refractive index (n = 2.85 -2.6) than PMN-32PT (n = 3.05 -2.63) in the low wavelength range from 375 nm to 600 nm. This result indicates that the light with a wavelength between 375 nm and 600 nm had a higher propagation speed in the 6PSN-61PMN-33PT crystal than in the PMN-32PT crystal. Upon further increasing the wavelength above 600 nm, the refractive index values of both crystals gradually tended to become similar. In the same wavelength range, the change in the refractive index in the 6PSN-61PMN-33PT crystal was smaller than that in the PMN-32PT crystal. This shows the weaker dispersion in the 6PSN-61PMN-33PT crystal compared to that in the PMN-32PT crystal, which is conducive for improving the image quality. For ferroelectrics with a perovskite structure, lattice dynamical theories indicate that the optical properties are mainly determined by the coupling of the d orbits in the B-site cation and the 2p orbits in the O anions related to each BO6 octahedron [21], suggesting For ferroelectrics with a perovskite structure, lattice dynamical theories indicate that the optical properties are mainly determined by the coupling of the d orbits in the B-site cation and the 2p orbits in the O anions related to each BO 6 octahedron [21], suggesting that the BO 6 octahedron plays a dominant role in the refractive index behavior in perovskite structure ferroelectrics. Based on the results in Figure 2, we propose that the decrease of the refractive indices in the ternary 6PSN-61PMN-33PT crystals are related to the expansion of the BO 6 oxygen octahedron because the Sc 3+ (r ion = 0.0745 nm) ions enter into the B-site to replace the Mg 2+ (r ion = 0.072 nm) and Nb 5+ (r ion = 0.064 nm) ions [20,22].
Most ferroelectrics with oxygen octahedron as the basic structural unit are well known to have similar optical properties. Wemple and DiDomenico (WDD) introduced the singleoscillator dispersion model to study the relationship between the internal structure and the optical properties [23][24][25]: where n, λ 0 , S 0 , E 0 , E d , λ, and E are the refractive index, average oscillator position, average oscillator strength of the dipole oscillator, oscillator energy, dispersion energy, wavelength, and energy of the incident light, respectively. The oscillator energy E 0 is directly related to the energy band gap of the material. The dispersion energy E d is closely related to the structural order of the material. The parameters in Equation (1) can be obtained by plotting (n 2 − 1) −1 versus λ −2 and E 2 , as shown in Figure 6. The perfect linear relationship in Figure 6 shows that it is reasonable to use the WDD dispersion model to study the 6PSN-61PMN-33PT and PMN-32PT ferroelectric crystals. Table 1 lists the calculated values of the Sellmeier optical coefficients for the 6PSN-61PMN-33PT and PMN-32PT crystals. E 0 and E d of the PMN-32PT crystal were 5.6038 eV and 28.0141 eV, respectively. For the 6PSN-61PMN-33PT crystal, E 0 was 5.8288 eV, and E d was 29.0784 eV, respectively. Our results are similar to those of the other PT-based materials with a ABO 3 perovskite structure [26][27][28].
The E 0 is considered the energy difference between the centers of gravity of the valence and conduction bands [29]. It is related to the direct bandgap E gd , and a large bandgap E gd corresponds to a large E 0 . E d is associated with the change in the chemical and structural order of a material, and a large order structure corresponds to a large E d . Compared with the PMN-32PT, the 6PSN-61PMN-33PT crystal showed larger E 0 and E d values (see Table 1). Therefore, we suggest that the 6PSN-61PMN-33PT crystal had a larger band gap and structure order than the PMN-32PT crystal [20,21].
Crystals 2021, 11, x FOR PEER REVIEW 6 of 10 that the BO6 octahedron plays a dominant role in the refractive index behavior in perovskite structure ferroelectrics. Based on the results in Figure 2, we propose that the decrease of the refractive indices in the ternary 6PSN-61PMN-33PT crystals are related to the expansion of the BO6 oxygen octahedron because the Sc 3+ (rion = 0.0745 nm) ions enter into the B-site to replace the Mg 2+ (rion = 0.072 nm) and Nb 5+ (rion = 0.064 nm) ions [20,22]. Most ferroelectrics with oxygen octahedron as the basic structural unit are well known to have similar optical properties. Wemple and DiDomenico (WDD) introduced the single-oscillator dispersion model to study the relationship between the internal structure and the optical properties [23][24][25]: where n, λ0, S0, E0, Ed, λ, and E are the refractive index, average oscillator position, average oscillator strength of the dipole oscillator, oscillator energy, dispersion energy, wavelength, and energy of the incident light, respectively. The oscillator energy E0 is directly related to the energy band gap of the material. The dispersion energy Ed is closely related to the structural order of the material. The parameters in Equation (1) can be obtained by plotting (n 2 − 1) −1 versus λ −2 and E 2 , as shown in Figure 6. The perfect linear relationship in Figure 6 shows that it is reasonable to use the WDD dispersion model to study the 6PSN-61PMN-33PT and PMN-32PT ferroelectric crystals. Table 1 lists the calculated values of the Sellmeier optical coefficients for the 6PSN-61PMN-33PT and PMN-32PT crystals. E0 and Ed of the PMN-32PT crystal were 5.6038 eV and 28.0141 eV, respectively. For the 6PSN-61PMN-33PT crystal, E0 was 5.8288 eV, and Ed was 29.0784 eV, respectively. Our results are similar to those of the other PT-based materials with a ABO3 perovskite structure [26][27][28].
The E0 is considered the energy difference between the centers of gravity of the valence and conduction bands [29]. It is related to the direct bandgap Egd, and a large bandgap Egd corresponds to a large E0. Ed is associated with the change in the chemical and structural order of a material, and a large order structure corresponds to a large Ed. Compared with the PMN-32PT, the 6PSN-61PMN-33PT crystal showed larger E0 and Ed values (see Table 1). Therefore, we suggest that the 6PSN-61PMN-33PT crystal had a larger band gap and structure order than the PMN-32PT crystal [20,21].    Figure 7 shows the change in optical absorption coefficient α of the 6PSN-61PMN-33PT and PMN-32PT crystals as a function of the wavelength. A sharp absorption was observed near 500 nm, which can be interpreted by the mechanism of the band-to-band transition. Compared to that of the binary PMN-32PT crystal, the absorption wavelength of the ternary 6PSN-61PMN-33PT crystal was lower, indicating a larger optical band gap. In addition, the 6PSN-61PMN-33PT crystal showed a smaller light absorption (marked in ellipse) in the visible light region compared to the PMN-32PT crystal. The inset of Figure 7 shows the change in the reflection R as a function of the wavelength. R is calculated by Equation (2) under normal incidence, where the n is the refractive index. The R of the PMN-32PT crystal was higher than that of the 6PSN-61PMN-33PT crystal with the wavelength increasing from 350 nm to 1000 nm. This result indicates a larger optical loss in the PMN-32PT crystal compared to the 6PSN-61PMN-33PT crystal.

crystals-1322448
1) The manufacturer, city and country from where software or equipment has been sourced need to be stated in the experimental section. Thank you for your understanding.
Response: I accept this decision. However, the word "Egilent"must be deleted because we mistakenly wrote "Agilent" as "egilent". Thank you! 2) In Figure 7, the words "Visible light", arrows and ellipses are double. Please provide the correct Figure and we will help update it.
Response: The correct figure 7 is as follows Near the basic absorption edge, the absorption coefficient of the electron band-to-band transitions follows the following law [30]: where hν is the photon energy; E g is the allowed optical energy gap; and m is the exponent characterizing the optical transition mechanism. In the allowed direct transition, m = 1/2, and the valence band transits vertically to the conduction band only under the action of photons. In the indirect transition, m = 2, the electrons transit from the top of the valence band to the bottom of the conduction band with the participation of photons and suitable phonons. The photon energy dependence of (αhν) 2 and (αhν) 1/2 for the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals is shown in Figure 8a,b to investigate the absorption characteristics of the relaxor PT-based ferroelectric single crystal. The direct band gap energy (E gd ) of the samples was determined by extrapolating the linear portion of the curve to zero. The E gd of the 6PSN-61PMN-33PT single crystal (i.e., 3.22 eV) was higher than that of the PMN-32PT single crystal (i.e., 3.18 eV), which is in agreement with the results shown in Figure 3. For the indirect band gap energy (E gi ), Equation (3) becomes where E gi is the indirect band gap energy, and E p is the phonon energy. The E g1 and E g2 values were obtained by extrapolating (αhν) 1/2 versus hνcurves to zero (Figure 8b). Therefore, the indirect band gap energy E gi = 1/2(E g1 + E g2 ) and the phonon energy E p = 1/2(E g1 − E g2 ) could be obtained. The photon energy dependence of (αhν) 2 and (αhν) 1/2 for the [100]-oriented 6PSN-61PMN-33PT and PMN-32PT single crystals is shown in Figure 8a,b to investigate the absorption characteristics of the relaxor PT-based ferroelectric single crystal. The direct band gap energy (Egd) of the samples was determined by extrapolating the linear portion of the curve to zero. The Egd of the 6PSN-61PMN-33PT single crystal (i.e., 3.22 eV) was higher than that of the PMN-32PT single crystal (i.e., 3.18 eV), which is in agreement with the results shown in Figure 3. For the indirect band gap energy (Egi), Equation (3) becomes where Egi is the indirect band gap energy, and Ep is the phonon energy. The Eg1 and Eg2 values were obtained by extrapolating (αhν) 1/2 versus hνcurves to zero (Figure 8b). Therefore, the indirect band gap energy Egi = 1/2(Eg1 + Eg2) and the phonon energy Ep = 1/2(Eg1 − Eg2) could be obtained. Table 2 lists the direct band gap Egd = 3.2228 eV, indirect band gap Egi = 3.066 eV, and phonon energy Ep = 0.0697 eV for the 6PSN-61PMN-33PT single crystal; and Egd = 3.1838 eV, Egi= 2.952 eV, and Ep = 0.0913 eV for the PMN-32PT single crystal. The 6PSN-61PMN-33PT crystal evidently showed a larger direct bandgap energy and indirect bandgap energy compared to the PMN-32PT crystal, which may lead to differences in their optical properties. Our results are similar to the PZN-7PT and 24PIN-43PMN-33PT crystals in [27,31].

Conclusions
This study systematically investigated the optical properties and band gap of [100]oriented 6PSN-61PMN-33PT and PMN-32PT relaxor-based ferroelectric single crystals using the transmission spectra, refractive indices, WDD single-oscillator dispersion relation, and Tauc law. Consequently, the 6PSN-61PMN-33PT crystal showed superior optical properties, such as high transmittance, low refractive index, low reflection coefficient, and low light absorption compared to the 68PMN-32PT crystal. This outstanding performance makes the 6PSN-61PMN-33PT crystal a candidate optical material. The optical properties of a crystal can be controlled by the polarization process. The improvement in the transmittance through AC poling was more obvious than that in the DC polarization, which is related to the increased domain size and the order domain structure. The 6PSN-61PMN-33PT crystal showed an enlarged lattice size, a larger bandgap energy, and structure order compared to the PMN-32PT crystal, leading to differences in their optical properties.