Effects of the MnO additives on the properties of Pb Fe 2/3 W 1/3 PbTiO 3 relaxors: Comparison of empirical law and experimental results
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1 JOURNAL OF APPLIED PHYSICS 101, Effects of the MnO additives on the properties of Pb Fe 2/3 W 1/3 PbTiO 3 relaxors: Comparison of empirical law and experimental results Cheng-Shong Hong Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China and Department of Electrical Engineering, Chienkuo Technology University, Changhua, Taiwan, Republic of China Sheng-Yuan Chu a Department of Electrical Engineering and Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan, Taiwan, Republic of China Wen-Chang Su and Ren-Chuan Chang Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China Hsiau-Hsian Nien Department of Electrical Engineering, Chienkuo Technology University, Changhua, Taiwan, Republic of China Yung-Der Juang Department of Material Science, National University of Tainan, Tainan, Taiwan, Republic of China Received 16 October 2006; accepted 9 January 2007; published online 15 March 2007 In this paper, pure and 0.15 wt %MnO additives of 1 x Pb Fe 2/3 W 1/3 O 3 xpbtio 3 1 x PFW x PT with x=0.1, 0.2, 0.3, and 0.4 were synthesized by the conventional solid state reaction method. The dielectric diffusion properties were investigated with the empirical law. The lattice structure was found to transfer from tetragonal to pseudocubic and the diffusion phase characteristic is more notable as decreasing PbTiO 3 compositions or adding MnO additives. Moreover, the dielectric loss is improved and the space charge polarization effect is vanished as adding MnO additives in 0.7PFW-0.3PT compounds. We suggested it was probably due to the lead vacancy which is substituted by the manganese ions or the interstitial manganese ions intervene into the interstice between the positive and negative ions American Institute of Physics. DOI: / I. INTRODUCTION a Author to whom correspondence should be addressed; electronic mail: chusy@mail.ncku.edu.tw The complex perovskite-type relaxor ferroelectric FRE materials show the ABO 3 structure where the A site and B site can be occupied by different metal cations which cause the compositional fluctuation effect. With the heterogeneous properties, FRE have the abnormal characteristics of dielectric, piezoelectric, and pyroelectric, and can be used as multilayer capacitors, piezoelectric actuators, pyroelectric detectors, and nonvolatile memories. 1 5 In FRE materials, the polarization microregions have slightly different compositions which cause different polarization natures. Hence, the peculiar dielectric physical properties are induced by such dipoles and their interactions. 6 The superparaelectric model was proposed by Cross who suggested that the polar nanoregions do not interact in the paraelectric regions as the temperature is higher enough far above Curie region and the dielectric behavior obey the Curie-Weiss law. 1 The dielectric behaviors deviate from the Curie-Weiss law as the temperature decreases which result from the coupling interactions between the polar nanoregions. 7,8 The diffusion nature was described by Smolensky who suggested that the microregions have different Curie temperatures T C due to compositional fluctuation and that the broad peak dielectric permittivity is induced and the T C distribution is broader. 9,10 Also, the dielectric-temperature dependence and the phase transition behaviors depend on the short range order SRO or the long range order LRO of cations in FRE materials. 4,11,12 Pb Fe 2/3 W 1/3 O 3 PFW is one of the classical FRE materials which can be easily obtained at lower sintering temperature due to a relatively high tolerance factor However, the dielectric loss is high because of the p-type electron holes which are induced by the lead vacancy and the reduction of iron ions Besides, the Curie temperature is too low about 90 C for practical applications. 2,4,13 20 Mitoseriu et al. reported that the lattice structure and the dielectric properties can be adjusted by adding PbTiO 3 composition in PFW ceramics to form 1 x Pb Fe 2/3 W 1/3 O 3 xpbtio 3 1 x PFW xpt solid solution. 2,4,19,20 As increasing PbTiO 3 composition, the Curie temperature increases x=0.4, T C =109 C and the dielectric diffusion phase characteristics change from a broad relaxorlike to a sharp ferroelectric behaviors; the lattice structure also transfers from pseudocubic to tetragonal and the morphotropic phase boundary MPB is formed as 0.2 x ,4,19,20 Szwagierczak and Kulawik reported that the /2007/101 5 /054117/7/$ , American Institute of Physics
2 Hong et al. J. Appl. Phys. 101, dielectric loss is decreased, the dc resistivity is increased, and the second dielectric peak is vanished as adding with MnO 2 or Co 3 O 4 dopants for PFW ceramics which result from the charge compensation due to the oxygen vacancy and the iron reduction. 15 Zhou et al. reported the dielectric properties of Pb Fe 2/3 W 1/3 1 x Mn x O 3 ceramics with Mn NO 3 2 as dopants. 16,18 The diffusion phase characteristics are not obviously influenced by the manganese ions. As Pb Fe 2/3 W 1/3 1 x Mn x O 3 postannealing in air atmosphere, the sharp dielectric permittivity is obtained as the manganese ions increase, but it does not change as postannealing in oxygen atmosphere. 18 Zhou et al. reported that the Mn B V O dipole pairs are induced by oxygen vacancy and the ordering degree is enhanced by the interaction of neighboring polarization nanoregions. 18 Although the dielectric properties of the pure PFW doping with Mn NO 3 2 or adding with MnO 2 were investigated, 15,16,18 few papers reported the dielectric properties of 1 x PFW xpt system adding with MnO additives which is the motivation of present work. In present work, the dielectric properties are investigated for 1 x PFW xpt x=0.1,0.2,0.3,0.4 ceramics with and without adding MnO additives. The diffusion phase characteristics are described by using the empirical law and the roles of manganese ions in 1 x PFW xpt system are discussed. II. EXPERIMENTAL PROCEDURES Raw materials were mixed using pure reagent PbO, Fe 2 O 3,WO 3, TiO 2, and MnO powders 99.5% purity. The materials 1 x Pb Fe 2/3 W 1/3 O 3 xpbtio 3, x=0.1, 0.2, 0.3, and 0.4 with or without adding 0.15 wt. %MnO were synthesized by calcining at 750 C for 2 h, then followed by pulverization. After that, the powders were dried and milled with 8 wt. % of a 5% Polyvinyl alcohol PVA solution. Then, the samples were pressed into a disk of 12 mm diameter and 2 mm thickness at a pressure of 25 kg/cm 2. Specimens were sintered isothermally at a heating rate of 5 C/min at about 900 C for 2 h. A PbO-rich atmosphere was maintained to minimize the lead loss during sintering. In order to measure the electrical properties, silver paste was coated to form electrodes on both sides of the sample and then subsequently fired at 750 C for 25 min. The dielectric properties of the samples were measured using an impedance analyzer HP4294A in the temperature-controlled container. The dc resistivities were determined by using an ohmmeter TOADKK SM-8215 SUPER MEGOHMMETER at the room temperature. The phase relations for the sintered samples were identified using an x-ray diffractometer XRD. III. RESULTS AND DISCUSSIONS A. X-ray Figure 1 shows the x-ray patterns of 1 x PFW xpt and 1 x PFW xpt 0.15 wt. %MnO compounds with x =0.1, 0.2, 0.3, and 0.4. In Fig. 1 a, the pure perovskite structures are obtained and no pyrochlore phase has been detected. Besides, the 002 and 200 Bragg peaks split as x increases. The detailed representation of Bragg FIG. 1. Color online XRD patterns of 1 x PFW xpt and 1 x PFW xpt+0.15 wt %MnO ceramics with x=0.1, 0.2, 0.3, and 0.4. a The Bragg peaks of 2 in the range between 20 and 80. b Detailed representation of Bragg peaks. peaks is shown in Fig. 1 b. The split phenomenon represent that the lattice structure change from pseudocubic to tetragonal. 2,4,19,20 After adding MnO additives, 002 and 200 Bragg peaks merge into single peak for 0.7PFW-0.3PT ceramics; 002 and 200 Bragg peaks change from sharp to smoother for 0.9PFW-0.1PT and 0.8PFW-0.2PT and 002 and 200 Bragg peaks close to each other for 0.6PFW- 0.4PT. Since, the lattice structure slightly changes after adding with MnO additives and the second phase is not found, we suggest that the manganese ions dissolve into the lattice space. B. The dielectric properties for 0.7PFW-0.3PT adding with MnO additive Figures 2 and 3 show the dielectric-temperature behaviors for pure and 0.15 wt %MnO-additive 0.7PFW-0.3PT ceramics. As comparing Figs. 2 with 3, the sharper dielectric constant-temperature characteristics with larger peak dielec-
3 Hong et al. J. Appl. Phys. 101, FIG. 2. Color online The dielectric constant and dielectric loss as a function of temperature at different frequencies of 0.7PFW-0.3PT ceramics. tric constant m at higher temperature T m are obtained for pure 0.7PFW-0.3PT ceramics. The effects of MnO additives for 1 x PFW xpt with x=0.1, 0.2, and 0.4 are similar to those with x = 0.3. These results are different from Pb Fe 2/3 W 1/3 1 x Mn x O 3 solid solution reported by Zhou et al. for the pure PFW ceramics doping with Mn NO 3 2, 16 but are similar to Pb Fe 1 x Mn x 1/2 Nb 1/2 O 3 solid solution reported by Fang et al. for the pure Pb Fe 1/2 Nb 1/2 O 3 PFN ceramics doping with MnO Figure 4 shows the dependence of MnO on the 1 MHz maximum dielectric constant and the temperature T m for 1 x PFW xpt ceramics. The maximum dielectric constants are all depressed as adding MnO additives. T m slightly decreases as adding MnO which is similar to the report of Zhou et al.. 16 In Fig. 2, besides the maxima corresponding to the ferroelectric-paraelectric transition, the second peak is observed at higher temperature which is attributed to dielectric relaxation. 15,16,21 Zhou et al. suggested that the polarization mechanism of the second onset of peak dielectric is relative to the space charge polarization and the electron hole dc conduction. 16 As the frequency increases, the second dielectric peak is vanished, which is due to the relaxation time of the space charge polarization and the dc conduction. 15,16 According to Debye theory = s /1+ 2, is the dielectric constant, s is the static dielectric constant, is the angular frequency, and is the relaxation time of dipoles., 5,22 the dielectric constant decreases with increasing the frequency; the frequency dispersion of the dielectric constant evidently increases as the dipole relaxation time is larger. Inspecting the second dielectric peak in Fig. 2, the second peak depends on the frequency, obviously at lower frequency. According to FIG. 3. Color online The dielectric constant and dielectric loss as a function of temperature at different frequencies of 0.7PFW-0.3PT ceramic adding with 0.15 wt %MnO. FIG. 4. Color online The composition dependence of the maximum dielectric constant and the corresponding temperature T m for 1 x PFW xpt and 1 x PFW xpt+0.15 wt %MnO systems. the previous discussion, we can conclude that the relaxation time of the space charge polarization and dc conduction are larger and the distribution is broader. In Fig. 3, the second dielectric peak is vanished, which means that the polarization mechanism due to the space charge and the dc conduction is weakened by adding with MnO additives. Lead and iron based relaxors usually induce p-type conductive carriers because of the lead vacancy and the iron reduction according to the equation 15,18,21 V Pb V Pb + h, V Pb V Pb + h, Fe +3 Fe Fe +2 Fe + h, 3 where V Pb, V Pb, and V Pb are neutral, singly, and doubly ionized lead vacancies, h is the electron hole, and Fe Fe and Fe Fe are doubly and triply ionized iron ions. Zhou et al. 16,18 and Swagierczak and Kulawik suggested that the electron holes diminish with the electron compensation which is induced by the oxygen vacancy for pure PFW doping with Mn NO 3 2 or adding with MnO 2. 15,16,18 The resistivity increases, the dielectric loss decreases, and the space charge polarization is reduced because of the electron compensation according to the following equations: 15,16,18 Mn B Mn B +2V O, Mn B Mn B + V O, V O V O + e, V O V O + e, where V O, V O, and V O are neutral, singly, and doubly ionized oxygen vacancies, e is the free electron, and Mn B and Mn B are neutral and doubly ionized manganese which occupy on the B site. Furthermore, the dielectric properties change from a SRO state relaxor to a LRO state ferroelectric by the enhancement of the neighboring polarization correlation which results from the Mn B V O dipole pairs. 16,18 Also, Szwagierczak and Kulawik reported that the electron hole is reduced by decreasing the iron reduction as adding MnO 2 in PFW ceramics. 15 Fang et al. reported that the iron reduction concentrations are detected by using x-ray photoelectron spectrometry XPS for Pb Fe 1 x Mn x 1/2 Nb 1/2 O 3 ceram
4 Hong et al. J. Appl. Phys. 101, higher temperature as increasing frequency. The peak dielectric loss and the corresponding temperature-frequency dependence have different behaviors between the ferroelectric region and the paraelectric region which represent different polarization mechanisms according to the Debye theory and the Arrhenius law which will be investigated further. FIG. 5. Color online The composition dependence of the room temperature resistivity for 1 x PFW xpt and 1 x PFW xpt wt %MnO systems. ics with MnO 2 as dopants in pure PFN, the iron reduction concentrations increase as increasing the manganese ions. 21 Figure 5 shows the dependence of MnO 2 on the resistivity of 1 x PFW xpt ceramics. The resitivity evidently increases as adding with MnO additives. In the present work, 1 x PFW xpt ceramics are added with MnO additives and the B site cations are not substituted by manganese ions. In addition, lead vacancy is easily induced because the PbO lower volatile temperature is about 900 C. In previous discussion, we have suggested that the phenomenon of increasing resistivity as adding with MnO additives is the charge compensation by the manganese ion substitute the lead vacancy or intervene into the interstice the radii of Mn +2 and Mn +4 are 0.67 and 0.54 Å. The charge compensation effect can be described as below Mn Pb Mn Pb +2e, 8 Mn Pb Mn Pb +4e, Mn i Mn i +2e, 9 10 Mn i Mn i +4e, 11 where Mn Pb,Mn Pb, and Mn Pb are neutral, doubly, and tetravalent ionized manganese on the lead vacancy and Mn i, Mn i, and Mn i are neutral, doubly, and tetravalent ionized interstitial manganese. As comparing Figs. 2 and 3 again, the dielectric loss obviously decreases as adding with MnO, the space charge polarization decreases and the dc conduction reduces which are the reasonable mechanisms. Two dielectric loss peaks are observed at ferroelectric and paraelectric regions individually, which is similar to other reports. 15,16,21 In Figs. 2 and 3, the peak dielectric loss decreases as increasing the frequency in the ferroelectric region and increases with increasing the frequency in the paraelectric region individually. The temperature corresponding to the peak dielectric loss shifts to C. Discussion of the dielectric characteristic in terms of phenomenological model The diffusion phase transition DPT characteristics of FRE is relative to the ordering degree of cations. 4,11,12 The diffusion phase transition properties for relaxors were introduced by Smolensky 9 and Kirilov and Isupov 10 with the hetrogenous composition in the microregion. Moreover, the phase transition temperature T C is different in the individual microregion and the T C probability distribution is under the normal distribution. Although, the Smolensky s equation well describes the total DPT relaxor dielectric behaviors, it is not suitable in the incomplete DPT relaxor. Therefore, Clarke and Burfoot 23 and Santos and Eiras 24 proposed the modifying equation to describe the total DPT relaxor and the incomplete DPT relaxor. Recently, we have shown that the fitting curves are the same either using the law proposed by Clarke and Burfoot or by Snatos and Eiras. 25 Furthermore, the parameters of the law by Santos and Eiras are better than those of Clarke and Burfoot on the physical and mathematical meanings. 26 equation by Santos and Eiras can be written as m = 1+ T T m / 12 where m and T m are the maximum dielectric constant and corresponding temperature. value is in the range between 1 and 2, the dielectric material is the normal ferroelectric characteristic as the value near 1; 4,23 32 the dielectric material is the total DPT relaxor characteristic as the value near 2. represents the diffusive extension, and is larger if the diffusion characteristic is more obvious. 4,23 32 As mentioned before, the second dielectric peak is observed in 1 x PFW xpt ceramics and disappears at higher frequency because the space charge polarization is unswitchable under the higher frequency field. Furthermore, modified equation by Santos and Eiras has the adaptability to explain the diffusion phase transition behaviors for either the total DPT or the not complete DPT relaxors. Figure 6 shows the 1 MHz dielectric constant as a function of temperature experimental data and the fitting results using Eq. 12 for 1 x PFW xpt x=0.1, 0.2, 0.3, and 0.4 with and without 0.15 wt %MnO additives. In Fig. 6, the maximum dielectric constant is depressed and the temperature dependence of the dielectric constant is broadened as adding MnO in all samples. In Fig. 6, the fitting curves well describe the dielectric behavior at T T m but deviate at T T m, which are similar with other reports. 4,24 Figures 7 and 8 show the composition dependence of the value and the value of 1 x PFW xpt samples with and without MnO additives. In Figs. 7 and 8, the values of and decrease as increasing PbTiO 3 composition which represents the diffusion phase characteristic change from the total DPT relaxor to the nor-
5 Hong et al. J. Appl. Phys. 101, FIG. 6. Color online The experimental data and the fitting results of the dielectric constant-temperature dependence for 1 x PFW xpt and 1 x PFW xpt 0.15 wt %MnO ceramics with a x=0.1, b x=0.2, c x=0.3, and d x=0.4. mal ferroelectric behavior, which is consistent with those reported by Mitoseriu et al. 4 Beside, the values of and increase as adding with MnO additive in all samples, which means that the diffusion phase property changes from the more ferroelectric to the total DPT relaxor by MnO additives. D. DISCUSSION In previous discussion, lead and iron based relaxor materials can easily induce the space charge polarization and the electron hole due to lead vacancy and reduction of iron ions which can be diminished by charge compensation due to the dopants or thermal treatment ,21 The manganese atom is the transitive metal, the valence usually shows with +2, +3, or +4 on chemical equilibrium state. Adding with MnO additive for 1 x PFW xpt ceramics can induce the second phase or the manganese ions will enter into the lattice space. Zhou et al. synthesized Pb Fe 2/3 W 1/3 1 x Mn x O 3 ceramics where the pure PFW compounds were doped with Mn NO 3 2 : 16,18 the equivalent tetravalent B site cations are FIG. 7. Color online The composition dependence of the diffusion parameters for 1 x PFW xpt and 1 x PFW xpt 0.15 wt %MnO system.
6 Hong et al. J. Appl. Phys. 101, of the manganese ion is small. We conclude that the Mnsubstitute lead vacancy or the Mn-interstitial interstice are reasonable physical pictures to explain the roles of the manganese ion for 1 x PFW xpt ceramics. IV. CONCLUSION In this paper, the low field dielectric response of 1 x PFW xpt and 1 x PFW xpt 0.15 wt %MnO ceramics has been investigated. The roles of the manganese ions are examined with the Mn-substituent lead vacancy or the Mn-interstitial interstice. Thus, the charge compensation effect occurs and the interaction of neighboring polarization microregions reduces. The higher dielectric loss and the lower resistivity properties are changed by adding with MnO additive. The diffusion phase transition picture is transferred to the SRO state relaxor by adding with MnO additive or decreasing PbTiO 3 composition. FIG. 8. Color online The composition dependence of the diffusion parameters for 1 x PFW xpt and 1 x PFW xpt 0.15 wt %MnO system. substituted with the manganese ions for which the valence can be +2, +3, or +4, and the electron compensation is induced with the oxygen vacancy because of the charge balance. Fang et al. synthesized Pb Fe 1 x Mn x 1/2 Nb 1/2 O 3 ceramics where the pure PFN compounds were doped with MnO 2, 21 the Fe +3 B site cation is substituted with the Mn +4 ions which conduct the electron compensation, furthermore the Fe +3 ions reduce to Fe +2 as increasing the manganese ions. Szwagierczak et al. reported that the electron compensation in MnO 2 doped PFW ceramics is induced by increasing the oxygen vacancy and decreasing the iron reduction. 15 In this paper, 1 x PFW xpt ceramic adding and nonadding with MnO additive were synthesized, the resistivity increases, the dielectric loss decreases, and the space charge polarization vanishes as adding MnO additives. Observing the x-ray pattern, the lattice structure is changed as adding with MnO additives, but the second phase is not found. According to the effects of the electron compensation and the lattice structure changes, we suggest that the manganese ions enter the lattice space and probably induce with the oxygen vacancy, the Mn-substitutive lead vacancy, the Mnsubstitutive B site cations which is lower valency or the Mninterstitial interstice. Regarding the dielectric diffusion phase and the ordering characteristics, Zhou et al. reported that the diffusion phase property is poor in accordance with the LRO state due to the Mn B V O dipole pairs which result from postannealing Pb Fe 2/3 W 1/3 1 x Mn x O 3 in air atmosphere and inducing the oxygen vacancy, 16,18 Fang et al. reported that the diffusion phase property is more obvious in accordance with the SRO state because the iron ions are substituted with Mn +4 ions for Pb Fe 1 x Mn x 1/2 Nb 1/2 O 3 ceramic system. 21 In the present work, the dielectric picture of adding with MnO additive is different with the report Zhou et al. but is similar with the report Fang et al. the synthesis process of adding with MnO additive is different with the reports of Zhou et al. and Fang et al. The lead vacancy is easily induced as 1 x PFW xpt sintered at high sintering temperature, and the radius ACKNOWLEDGMENTS This research was supported by the National Science Council of Republic of China, under grant NSC E MY3, and made use of Shared Facilities supported by the Program of Top 100 Universities Advancement, Ministry of Education, Taiwan. 1 L. E. Cross, Ferroelectrics 76, L. Mitoseriu, P. M. Vilarinho, and J. L. Baptista, Appl. Phys. Lett. 80, Z. Y. Cheng, R. S. Katiyar, X. Yao, and A. Guo, Phys. Rev. B 55, L. Mitoseriu, A. Stancu, C. Fedor, and P. M. Vilarinho, J. Appl. Phys. 94, K. Uchino, Ferroelectric Devices Dekker, New York, Z.-Y. Cheng, R. S. Katiyar, X. Yao, and A. S. Bhalla, Phys. Rev. B 57, D. Viehland, S. J. Jang, L. E. Cross, and M. Wutting, Phys. Rev. B 46, D. Viehland, S. J. Jang, L. E. Cross, and M. Wutting, Phys. Rev. B 43, G. A. Smolenskii, J. Phys. Soc. Jpn. 28, V. V. Kirilov and V. A. Isupov, Ferroelectrics 5, N. Setter and L. E. Cross, J. Appl. Phys. 51, N. Setter and L. E. Cross, J. Mater. Sci. 15, G. A. Smolenskii, A. I. Agranovskaya, and V. A. Isupov, Sov. Phys. Solid State 1, T. R. Shrout and A. Halliyal, Am. Ceram. Soc. Bull. 66, D. Szwagierczak and J. Kulawik, J. Eur. Ceram. Soc. 25, L. Zhou, P. M. Vilarinho, and J. L. Baptista, J. Appl. Phys. 85, L. Zhou, P. M. Vilarinho, P. Q. Mantas, J. L. Baptista, and E. Fortunato, J. Eur. Ceram. Soc. 20, L. Zhou, P. M. Vilarinho, and J. L. Baptista, J. Mater. Sci. 33, L. Mitoseriu, P. M. Vilarinho, M. Viviani, and J. L. Baptista, Mater. Lett. 57, L. Mitoseriu, M. M. Carnasciali, P. Piaggio, and P. Nanni, J. Appl. Phys. 96, B. Fang, Y. Shan, and H. Imoto, Jpn. J. Appl. Phys., Part 1 43, L. L. Hench and J. K. West, Principles of Electronic Ceramics Wiley, New York, R. Clarke and J. C. Burfoot, Ferroelectrics 8, I. A. Santos and J. A. Eiras, J. Phys.: Condens. Matter 13, C.-S. Hong, S.-Y. Chu, W.-C. Su, R.-C. Chang, H.-H. Nien, and Y.-D. Juang, J. Appl. Phys. to be published. 26 C.-S. Hong, S.-Y. Chu, W.-C. Su, R.-C. Chang, H.-H. Nien, and Y.-D. Juang, J. Appl. Phys. submitted. 27 R. M. Piticescu, L. Mitoseriu, M. Viviani, and V. M. Poladian, J. Eur.
7 Hong et al. J. Appl. Phys. 101, Ceram. Soc. 25, L. Cao, X. Yao, Z. Xu, and Y. Feng, Ceram. Int. 30, R. Yimnirun, S. Ananta, and P. Laoratanakul, J. Eur. Ceram. Soc. 25, S. Huang, C. Feng, L. Chen, and X. Wen, Solid State Commun. 133, Y. Guo, K.-I. Kakimoto, and H. Ohsato, J. Phys. Chem. Solids 65, N. Vittayakorn, G. Rujijanagul, X. Tan, M. A. Marquardt, and D. P. Cann, J. Appl. Phys. 96,
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