- Email: [email protected]
Optoelectronic investigation of corundum Mg4Nb2O9 single crystal
Journal of Alloys and Compounds 619 (2015) 240–243
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Letter
Optoelectronic investigation of corundum Mg4Nb2O9 single crystal Liang Li a, Defang Duan a, Qiang Zhou a, Dapeng Xu a, Tian Cui a,⇑, Bingbing Liu a, Zhan Shi b, Hongming Yuan b a b
State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, China
a r t i c l e
i n f o
Article history: Received 19 June 2014 Received in revised form 7 September 2014 Accepted 8 September 2014 Available online 16 September 2014 Keywords: Mg4Nb2O9 crystal Refractive index Urbach tail Oscillator parameters
a b s t r a c t The Mg4Nb2O9 crystals grown by floating zone technology were used as prototypes to investigate optoelectronic parameters by measuring the absorption and transmittance spectra along the c-axis from 200 to 800 nm at room-temperature. The imaginary and real parts of the complex dielectric constants, extinction coefficient and refractive index for Mg4Nb2O9 were obtained. The Cauchy–Sellmeier equation for Mg4Nb2O9 was validated in the Urbach tail region (4.0–5.0 eV). The dispersion energy Ed and oscillator energy E0 were obtained via the single oscillator approximation. More interestingly, the self-trapped exciton and disorder of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons participating in the transition in the Urbach tail region were confirmed by the excitation spectrum. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Corundum Mg4Nb2O9 has a trigonal structure with space group of P-3c1 (1 6 5) with a = b = 5.1610 Å and c = 14.0280 Å [1,2]. The Mg4Nb2O9 is a promising candidate for microwave devices because of its high Q value and dielectric constant [3,4]. The rare-earth activated [5,6] and self-activated [7] emissions exhibit excellent luminescence properties. Mg4Nb2O9 is suitably applied in field emission display (FED) and high-definition television [5]. In addition, it is a key precursor in preparing lead magnesium niobate (PMN) ferroelectric ceramics, which are difficult to synthesize by using a conventional solid-state reaction process using oxides as starting materials [8]. Optical absorption with electronic transitions can clarify some basic physical properties of energy levels for applications in optical equipment [9,10]. The twin structure and crystal boundaries influence the material properties significantly. While high-quality crystals will assist to achieve the intrinsic properties of the samples [11–13]. However, the optical parameters of Mg4Nb2O9 have not been studied for absence of an appropriate single crystal. The Mg4Nb2O9 crystals have been grown by using floating zone technology recently [14]. Thus, the purpose of current work is to investigate the absorption and transmittance spectra, complex dielectric constant, refractive index and related useful parameters of Mg4Nb2O9 ⇑ Corresponding author. Tel.: +86 431 85167955; fax: +86 431 85167046. E-mail address: [email protected] (T. Cui). http://dx.doi.org/10.1016/j.jallcom.2014.09.081 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
for the first time. It is noteworthy that the self-trapped exciton and disorder of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons participating in the transition in the Urbach tail region are confirmed by the excitation spectrum. 2. Experimental details Colourless and transparent Mg4Nb2O9 crystals were fabricated by the floating zone technology [14]. For optical testament, a wafer of 3.1 5.2 0.8 mm was cut along the ab plane and polished to be optical standard, listed in the inset of Fig. 1. By using Bruker AXS D8 Discover with GADDS X-ray diffractometer (XRD2), the orientation of the wafers were measured in which a part of the Debye–Sherrer ring is two-dimensionally detected. As a result, orientation could be characterized easily. Room temperature spectra of absorption and transmittance for the crystal wafer were tested via Shimadzu UV–VIS-1700 spectrophotometer from 200 to 800 nm in an air atmosphere at room-temperature.
3. Result and discussion The orientation of the wafer was investigated by XRD2 as shown in Fig. 1. The peaks at 12.7°, 25.4° and 37.2° correspond to (0 0 2), (0 0 4) and (0 0 6) planes, respectively. These results suggest that the direction of the wafer is c-axis. We previously reported the ultraviolet–visible absorption coefficient and bandgap energy of Mg4Nb2O9 (Eg = 5.09 eV) with a direct transmission type [14]. The room-temperature absorption (Fig. 2a) and transmittance (T) spectrum (Fig. 2b) of Mg4Nb2O9 crystal wafer were obtained in this study. As shown in figure, Mg4 Nb2O9 is transparent (75%) from the visible to the near-infrared
L. Li et al. / Journal of Alloys and Compounds 619 (2015) 240–243
241
region (245–800 nm). However, transmittance is low in the ultraviolet region (<245 nm). T is related to the reflectance (R) and a in the transparent region of the crystal wafer as follows [15]:
T¼
ð1 RÞ2 expðadÞ 1 R2 expð2adÞ
ð1Þ
where d is thickness of the sample (d = 0.8) mm. Fig. 2 shows that the reflectance spectrum of Mg4Nb2O9 can be derived from Fig. 2 via Eq. (1). The refractive index (n) and extinction coefficient (K) should be obtained using the following equations [15]:
K¼
ak ; 4p
R¼
ðn 1Þ2 þ K 2 ðn þ 1Þ2 þ K 2
ð2Þ
where k represents the wavelength. The spectra of n and K were obtained from Eq. (2) with T and a. Fig. 3a plots the K and n of Mg4Nb2O9 against k from 245 to 800 nm. The n of Mg4Nb2O9 is large and rapidly decreases with increasing k, which is similar to those of other niobates reported in the literatures [16,17]. The energy band structure of niobates crystal usually depends on its NbO6 octahedron. In the corundum Mg4Nb2O9, the cations are ordered at twothirds of the octahedral sites in the hexagonal close packed oxygen array along the c axis. The cation is arranged in the form –Mg–(Mg, Nb)–(Mg, Nb)–Mg– along the c-axis. The MgO6 octahedron connected MgO6 octahedron by sharing faces and edges with the other MgO6 octahedron. The NbO6 octahedron connected NbO6 octahedron by sharing faces and connected MgO6 octahedron by sharing edges [18,19]. The face-shared NbO6 is the key contributor in the energy band structure and the refractive indices mainly relate to the 2p and 4d orbitals in O2- and Nb5+, respectively [20,21]. In the transparent region, the complex dielectric constant (e) can be obtained from n and K via equation [15]:
ei ¼ 2nK; er ¼ n2 K 2
Fig. 2. a: Absorption spectrum of the Mg4Nb2O9 wafer, and the inset shows the variations in transmission loss (db) and optical density versus photon energy for the Mg4Nb2O9 crystal and b: the measured transmittance and the reflectance spectra for the wafer.
ð3Þ
where ei and er are the imaginary and real parts of e, respectively. Fig. 3b illustrates the wavelength dependence of er and ei for Mg4Nb2O9 crystal obtained from Eq. (4) and Fig. 3a. The n and er of Mg4Nb2O9 gradually decrease from 2.4 to 1.8 and from 11.5 to 7.3, respectively, with increasing wavelength from 300 to 800 nm (ultraviolet region to infrared region). By contrast, K and ei respectively increase from 1.2 10–5 to 2.2 10–5 and from 0.7 10–4 to 1.2 10–4 with the same increase in wavelength.
Below the band gap (E < Eg), calling Urbach tail, the n against even energy (E) can be denoted by the Cauchy–Sellmeier function. The function can be approximated as [15]:
nðEÞ ¼ n0 þ a1 E2
ð4Þ
where n0 and a1 are constants. The n against E2 can be fitted linearly from 16.0 eV2 to 26.0 eV2 (Fig. 4a), indicating that the refractive index spectrum of the Mg4Nb2O9 crystal satisfies the Cauchy–Sellmeier function. The n0 and a1 were determined to be 0.62 and 0.10, respectively. Below the interband absorption edge, the refractive index dispersion corresponds to the fundamental electronic excitation spectrum, which can contribute to understand about the dielectric properties. Via the single-effective oscillator model, Wemple et al. [22,23] have validated more than 100 samples in liquid and solid forms. From relationship of Krammers–Kroning, er can be expressed as follows [15]:
er ¼ 1 þ
F ðE20 þ E2 Þ
ð5Þ
where E is photons energy. The F and single oscillator energy E0 are related to transition frequencies for all oscillators and the electric dipole strength. As defined by Wemple et al., parameters were special combined [22,23], Fig. 1. XRD2 pattern of the Mg4Nb2O9 crystal, the inset shows the Mg4Nb2O9 crystal wafer.
Ed ¼
F E0
ð6Þ
242
L. Li et al. / Journal of Alloys and Compounds 619 (2015) 240–243
where Ed is the dispersion energy. Neglecting K value from 4.0 to 5.0 eV, Eqs. (6) and (7) can be combined to express the relationship as follows [23]:
er ðEÞ ¼ n2 ðEÞ ¼ 1 þ
Ed E0 ðE20 E2 Þ
ð7Þ
For the Mg4Nb2O9 crystal, n and K were achieved directly from the tested a and T in the energy range of 4.0–5.0 eV (310–248 nm). Ed and E0 were evaluated as 6.31 and 15.82 eV, respectively, using linearly fitting (n2 1)1 versus E2 in Fig. 4b. Meanwhile, the static refractive index n(0) and static dielectric constant es = n2(0) were determined as1.58 and 2.50 from Eq. (8), respectively. Ed and E0 are correlated with er using the single-effective oscillator model. While the moments M3 and M1 of e can be expressed as follows [23]:
E20 ¼
M1 ; M3
E2d ¼
M31 M3
ð8Þ
where the nth moment of the optical spectra can be expressed as [22]:
Mn ¼
Fig. 3. a: Graphical variations of the refractive index and extinction coefficient and b: the dielectric constant and dielectric loss factor as a function of the incident wavelength for the Mg4Nb2O9 crystal.
2
p
Z
1
en ei ðEÞdE
ð9Þ
Et
where Et is the energy of absorption threshold. Then, E0, Ed, n(0), es, M1, and M3 for Mg4Nb2O9 were evaluated as 6.31 eV, 15.82 eV, 1.58, 2.50, 2.51 and 0.06, respectively, from Eqs. (8) and (9). Using an empirical formula, E0 corresponds to the bandgap energy: E0 = 2Eg. The optical band gap obtained from this formula is 3.16 eV, which is lower than the estimated value of 5.09 eV. Additionally, transmission loss (db) and optical density (q(E)) of the Mg4Nb2O9 crystal can be obtained by the relation [23]:
db ¼ 10qðEÞ;
qðEÞ ¼ log10
1 T
ð10Þ
db and q(E) versus energy E is shown in the inset of Fig. 2a. The maxima of the both spectra are 5.1 eV. a relate to the temperature of sample T0 can be expressed as [23]:
a ¼ a0 exp
Fig. 4. The relation of a: n and b: (n2 1)1 versus E2 in the range of 15.0–25.0 eV2.
r
kB T
ðh m h m Þ 0 0
ð11Þ
where ht0 and a0 are constants depending only on material properties [24], and r is the steepness parameter depending on the temperature (T0 ) which characterizes broadening of the absorption edge due to electron–phonon or exciton-phonon interactions in the lattice [25]. At room-temperature, ht versus ln a in the Urbach tail region (4.6–5.0 eV) was fitted to be a straight line (see Fig. 5a), achieving r = 0.014. At the bottom of Fig. 5a, we give the discrepancy between the measured ln a and the linear fitting curve. Worth noting, the discrepancy is small in the 4.60–4.87 eV. While the energy up to 4.87 eV, the discrepancy increased distinctly. To clarify the discrepancy, the spectrum of excitation, which is more sensitive than the absorption spectra, with monitoring fluorescence at 2.76 eV at room temperature of the crystal was tested, as shown in Fig. 5b. Three bands exist between 4.85 and 5.08 eV centered at 4.91, 4.94 and 5.01 eV, which were obtained from multiple peak fitting by Gaussian. The most intensity band at 5.01 eV can be attributed to the self-trapped exciton transition in the face-shared NbO6 octahedrons. The weaker ones can attribute to coexisting slight disorders of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons. More importantly, the energy of excitation bands in the excitation spectrum agrees with the energy of relatively larger discrepancy region between measured ln a and the linear fitting curve. Therefore, it is reasonable to believe that the self-trapped exciton and the slight disorders of Mg2+ and Nb5+ between MgO6 and NbO6
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the energy range of 4.0–5.0 eV (Urbach tail). Based on the singleeffective oscillator model, the moments of optical spectrum M1 and M3, oscillator energy E0 and dispersion energy Ed were determined as 4.10, 0.19, 26.88 eV, and 4.77 eV, respectively. The selftrapped exciton and disorder of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons participating in the transition in the Urbach tail were confirmed by the excitation spectrum. These results give an important basis for further theoretical study and practical device application based on Mg4Nb2O9 single crystals. Acknowledgements The financial support from the National Foundation for Fostering Talents of basic Science (Grant No. J1103202), the National Basic Research Program of China (No. 2011CB808200), the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), the National Natural Science Foundation of China (Grant No. 11274137, 11074090, 11304113), the open Project of State Key Laboratory of Superhard Materials (Jilin University) (No. 201302), and the open Project of State Key Laboratory of Inorganic Synthesis and Preparative Chemistry (Jilin University) (No. 2014-34) is greatly appreciated. References
Fig. 5. a: The ln a versus photon energy in the range of 4.6–5.0 eV and bottom shows the discrepancy between the measured ln a and the linear fitting curve and b: excitation spectrum of Mg4Nb2O9 crystal with monitoring fluorescence at 2.76 eV.
octahedrons participated in the transition in the Urbach tail region. These results also agree well with the theory developed by Sumi [26] that ascribes the exponential absorption shape to the coexistence of free exciton and momentarily self-trapped exciton. The theory is predominantly applicable to highly ionic crystals. Similar to most niobate, Mg4Nb2O9 should have an ionic character as the chemical bond [23]. 4. Conclusions The room-temperature absorption and transmittance spectra of Mg4Nb2O9 crystals fabricated by optical floating zone technology were measured from 200 to 800 nm. The extinction coefficient, complex dielectric constants and refractive index of the Mg4Nb2O9 crystals were obtained from the tested absorption and transmittance spectra. The Cauchy–Sellmeier equation was validated in
[1] T.H. Fang, Y.J. Hsiao, L.W. Ji, Y.S. Chang, S.S. Chi, J. Cryst. Growth 310 (2008) 3331–3334. [2] H. Ogawa, A. Kan, S. Ishihara, Y. Higashida, J. Eur. Ceram. Soc. 23 (2003) 2485– 2488. [3] C.L. Huang, C.H. Chu, F.S. Liu, P.C. Yu, J. Alloys Comp. 590 (2014) 494–499. [4] M.H. Sarrafi, H. Barzegar Bafrooei, M. Feizpour, T. Ebadzadeh, M. Harir Foroush, J. Mater. Sci.: Mater. Electron. 25 (2014) 946–951. [5] Y.C. You, N. Park, K.H. Jung, H.L. Park, K.C. Kim, S.I. Mho, T.W. Kim, J. Mater. Sci. Lett. 13 (1994) 1682–1683. [6] R. Cao, C. Cao, X. Yu, J. Qiu, Luminescence (2014). [7] A. Wachtel, J. Electrochem. Soc. 111 (1964) 534–538. [8] J.K. Park, K.H. Kim, I. Tanaka, K.B. Shim, J. Cryst. Growth 268 (2004) 103–107. [9] K.L. Young, M.B. Ross, M.G. Blaber, M. Rycenga, M.R. Jones, C. Zhang, A.J. Senesi, B. Lee, G.C. Schatz, C.A. Mirkin, Adv. Mater. 26 (2014) 653–659. [10] S. Ullah, H.U. Din, G. Murtaza, T. Ouahrani, R. Khenata, Naeemullah, S. Bin Omran, J. Alloys Comp. 617 (2014) 575–583. [11] H. Xu, Y. Jiang, S. Luo, Y. Ma, Y. Wang, J. Alloys Comp. 588 (2014) 42–45. [12] J.H. Lee, E.K. Lee, W.J. Joo, Y. Jang, B.S. Kim, J.Y. Lim, S.H. Choi, S.J. Ahn, J.R. Ahn, M.H. Park, Science 344 (2014) 286–289. [13] D. Xu, H. Yang, L. Li, Q. Zhou, H. Yuan, T. Cui, Cryst. Res. Technol. 49 (2014) 502–506. [14] L. Li, D. Duan, Q. Zhou, D. Xu, T. Cui, B. Liu, H. Yuan, J. Cryst. Growth 402 (2014) 109–112. [15] D. Xu, Y. Gu, L. Li, H. Shen, H. Yang, Q. Zhou, Z. Shi, H. Yuan, T. Cui, J. Phys. Chem. Solids 75 (2014) 1361–1364. [16] Z. Ruifeng, L. Jie, W. Qingpu, W. Yurong, W. Aijian, J. Jun, Y. Xiujie, C. Huanchu, H. Jianru, Cryst. Res. Technol. 41 (2006) 494–497. [17] S. Kundu, K.B.R. Varma, Cryst. Growth Des. 14 (2013) 585–592. [18] N. Kumada, K. Taki, N. Kinomura, Mater. Res. Bull. 35 (2000) 1017–1021. [19] A. Kan, H. Ogawa, A. Yokoi, Y. Nakamura, J. Eur. Ceram. Soc. 27 (2007) 2977– 2981. [20] A. Kahn, A. Leyendecker, Phys. Rev. 135 (1964) A1321. [21] S. Kurtz, F. Robinson, Appl. Phys. Lett. 10 (2004) 62–65. [22] S.H. Wemple, M. DiDomenico, Phys. Rev. Lett. 23 (1969) 1156–1160. [23] S.H. Wemple, M. DiDomenico, Phys. Rev. B 3 (1971) 1338–1351. [24] M.V. Kurik, Phys. Status Solidi A 8 (1971) 9–45. [25] H. Mahr, Phys. Rev. 125 (1962) 1510–1516. [26] H. Sumi, Y. Toyozawa, J. Phys. Soc. Jpn. 31 (1971) 342–358.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Letter
Optoelectronic investigation of corundum Mg4Nb2O9 single crystal Liang Li a, Defang Duan a, Qiang Zhou a, Dapeng Xu a, Tian Cui a,⇑, Bingbing Liu a, Zhan Shi b, Hongming Yuan b a b
State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, China
a r t i c l e
i n f o
Article history: Received 19 June 2014 Received in revised form 7 September 2014 Accepted 8 September 2014 Available online 16 September 2014 Keywords: Mg4Nb2O9 crystal Refractive index Urbach tail Oscillator parameters
a b s t r a c t The Mg4Nb2O9 crystals grown by floating zone technology were used as prototypes to investigate optoelectronic parameters by measuring the absorption and transmittance spectra along the c-axis from 200 to 800 nm at room-temperature. The imaginary and real parts of the complex dielectric constants, extinction coefficient and refractive index for Mg4Nb2O9 were obtained. The Cauchy–Sellmeier equation for Mg4Nb2O9 was validated in the Urbach tail region (4.0–5.0 eV). The dispersion energy Ed and oscillator energy E0 were obtained via the single oscillator approximation. More interestingly, the self-trapped exciton and disorder of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons participating in the transition in the Urbach tail region were confirmed by the excitation spectrum. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Corundum Mg4Nb2O9 has a trigonal structure with space group of P-3c1 (1 6 5) with a = b = 5.1610 Å and c = 14.0280 Å [1,2]. The Mg4Nb2O9 is a promising candidate for microwave devices because of its high Q value and dielectric constant [3,4]. The rare-earth activated [5,6] and self-activated [7] emissions exhibit excellent luminescence properties. Mg4Nb2O9 is suitably applied in field emission display (FED) and high-definition television [5]. In addition, it is a key precursor in preparing lead magnesium niobate (PMN) ferroelectric ceramics, which are difficult to synthesize by using a conventional solid-state reaction process using oxides as starting materials [8]. Optical absorption with electronic transitions can clarify some basic physical properties of energy levels for applications in optical equipment [9,10]. The twin structure and crystal boundaries influence the material properties significantly. While high-quality crystals will assist to achieve the intrinsic properties of the samples [11–13]. However, the optical parameters of Mg4Nb2O9 have not been studied for absence of an appropriate single crystal. The Mg4Nb2O9 crystals have been grown by using floating zone technology recently [14]. Thus, the purpose of current work is to investigate the absorption and transmittance spectra, complex dielectric constant, refractive index and related useful parameters of Mg4Nb2O9 ⇑ Corresponding author. Tel.: +86 431 85167955; fax: +86 431 85167046. E-mail address: [email protected] (T. Cui). http://dx.doi.org/10.1016/j.jallcom.2014.09.081 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
for the first time. It is noteworthy that the self-trapped exciton and disorder of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons participating in the transition in the Urbach tail region are confirmed by the excitation spectrum. 2. Experimental details Colourless and transparent Mg4Nb2O9 crystals were fabricated by the floating zone technology [14]. For optical testament, a wafer of 3.1 5.2 0.8 mm was cut along the ab plane and polished to be optical standard, listed in the inset of Fig. 1. By using Bruker AXS D8 Discover with GADDS X-ray diffractometer (XRD2), the orientation of the wafers were measured in which a part of the Debye–Sherrer ring is two-dimensionally detected. As a result, orientation could be characterized easily. Room temperature spectra of absorption and transmittance for the crystal wafer were tested via Shimadzu UV–VIS-1700 spectrophotometer from 200 to 800 nm in an air atmosphere at room-temperature.
3. Result and discussion The orientation of the wafer was investigated by XRD2 as shown in Fig. 1. The peaks at 12.7°, 25.4° and 37.2° correspond to (0 0 2), (0 0 4) and (0 0 6) planes, respectively. These results suggest that the direction of the wafer is c-axis. We previously reported the ultraviolet–visible absorption coefficient and bandgap energy of Mg4Nb2O9 (Eg = 5.09 eV) with a direct transmission type [14]. The room-temperature absorption (Fig. 2a) and transmittance (T) spectrum (Fig. 2b) of Mg4Nb2O9 crystal wafer were obtained in this study. As shown in figure, Mg4 Nb2O9 is transparent (75%) from the visible to the near-infrared
L. Li et al. / Journal of Alloys and Compounds 619 (2015) 240–243
241
region (245–800 nm). However, transmittance is low in the ultraviolet region (<245 nm). T is related to the reflectance (R) and a in the transparent region of the crystal wafer as follows [15]:
T¼
ð1 RÞ2 expðadÞ 1 R2 expð2adÞ
ð1Þ
where d is thickness of the sample (d = 0.8) mm. Fig. 2 shows that the reflectance spectrum of Mg4Nb2O9 can be derived from Fig. 2 via Eq. (1). The refractive index (n) and extinction coefficient (K) should be obtained using the following equations [15]:
K¼
ak ; 4p
R¼
ðn 1Þ2 þ K 2 ðn þ 1Þ2 þ K 2
ð2Þ
where k represents the wavelength. The spectra of n and K were obtained from Eq. (2) with T and a. Fig. 3a plots the K and n of Mg4Nb2O9 against k from 245 to 800 nm. The n of Mg4Nb2O9 is large and rapidly decreases with increasing k, which is similar to those of other niobates reported in the literatures [16,17]. The energy band structure of niobates crystal usually depends on its NbO6 octahedron. In the corundum Mg4Nb2O9, the cations are ordered at twothirds of the octahedral sites in the hexagonal close packed oxygen array along the c axis. The cation is arranged in the form –Mg–(Mg, Nb)–(Mg, Nb)–Mg– along the c-axis. The MgO6 octahedron connected MgO6 octahedron by sharing faces and edges with the other MgO6 octahedron. The NbO6 octahedron connected NbO6 octahedron by sharing faces and connected MgO6 octahedron by sharing edges [18,19]. The face-shared NbO6 is the key contributor in the energy band structure and the refractive indices mainly relate to the 2p and 4d orbitals in O2- and Nb5+, respectively [20,21]. In the transparent region, the complex dielectric constant (e) can be obtained from n and K via equation [15]:
ei ¼ 2nK; er ¼ n2 K 2
Fig. 2. a: Absorption spectrum of the Mg4Nb2O9 wafer, and the inset shows the variations in transmission loss (db) and optical density versus photon energy for the Mg4Nb2O9 crystal and b: the measured transmittance and the reflectance spectra for the wafer.
ð3Þ
where ei and er are the imaginary and real parts of e, respectively. Fig. 3b illustrates the wavelength dependence of er and ei for Mg4Nb2O9 crystal obtained from Eq. (4) and Fig. 3a. The n and er of Mg4Nb2O9 gradually decrease from 2.4 to 1.8 and from 11.5 to 7.3, respectively, with increasing wavelength from 300 to 800 nm (ultraviolet region to infrared region). By contrast, K and ei respectively increase from 1.2 10–5 to 2.2 10–5 and from 0.7 10–4 to 1.2 10–4 with the same increase in wavelength.
Below the band gap (E < Eg), calling Urbach tail, the n against even energy (E) can be denoted by the Cauchy–Sellmeier function. The function can be approximated as [15]:
nðEÞ ¼ n0 þ a1 E2
ð4Þ
where n0 and a1 are constants. The n against E2 can be fitted linearly from 16.0 eV2 to 26.0 eV2 (Fig. 4a), indicating that the refractive index spectrum of the Mg4Nb2O9 crystal satisfies the Cauchy–Sellmeier function. The n0 and a1 were determined to be 0.62 and 0.10, respectively. Below the interband absorption edge, the refractive index dispersion corresponds to the fundamental electronic excitation spectrum, which can contribute to understand about the dielectric properties. Via the single-effective oscillator model, Wemple et al. [22,23] have validated more than 100 samples in liquid and solid forms. From relationship of Krammers–Kroning, er can be expressed as follows [15]:
er ¼ 1 þ
F ðE20 þ E2 Þ
ð5Þ
where E is photons energy. The F and single oscillator energy E0 are related to transition frequencies for all oscillators and the electric dipole strength. As defined by Wemple et al., parameters were special combined [22,23], Fig. 1. XRD2 pattern of the Mg4Nb2O9 crystal, the inset shows the Mg4Nb2O9 crystal wafer.
Ed ¼
F E0
ð6Þ
242
L. Li et al. / Journal of Alloys and Compounds 619 (2015) 240–243
where Ed is the dispersion energy. Neglecting K value from 4.0 to 5.0 eV, Eqs. (6) and (7) can be combined to express the relationship as follows [23]:
er ðEÞ ¼ n2 ðEÞ ¼ 1 þ
Ed E0 ðE20 E2 Þ
ð7Þ
For the Mg4Nb2O9 crystal, n and K were achieved directly from the tested a and T in the energy range of 4.0–5.0 eV (310–248 nm). Ed and E0 were evaluated as 6.31 and 15.82 eV, respectively, using linearly fitting (n2 1)1 versus E2 in Fig. 4b. Meanwhile, the static refractive index n(0) and static dielectric constant es = n2(0) were determined as1.58 and 2.50 from Eq. (8), respectively. Ed and E0 are correlated with er using the single-effective oscillator model. While the moments M3 and M1 of e can be expressed as follows [23]:
E20 ¼
M1 ; M3
E2d ¼
M31 M3
ð8Þ
where the nth moment of the optical spectra can be expressed as [22]:
Mn ¼
Fig. 3. a: Graphical variations of the refractive index and extinction coefficient and b: the dielectric constant and dielectric loss factor as a function of the incident wavelength for the Mg4Nb2O9 crystal.
2
p
Z
1
en ei ðEÞdE
ð9Þ
Et
where Et is the energy of absorption threshold. Then, E0, Ed, n(0), es, M1, and M3 for Mg4Nb2O9 were evaluated as 6.31 eV, 15.82 eV, 1.58, 2.50, 2.51 and 0.06, respectively, from Eqs. (8) and (9). Using an empirical formula, E0 corresponds to the bandgap energy: E0 = 2Eg. The optical band gap obtained from this formula is 3.16 eV, which is lower than the estimated value of 5.09 eV. Additionally, transmission loss (db) and optical density (q(E)) of the Mg4Nb2O9 crystal can be obtained by the relation [23]:
db ¼ 10qðEÞ;
qðEÞ ¼ log10
1 T
ð10Þ
db and q(E) versus energy E is shown in the inset of Fig. 2a. The maxima of the both spectra are 5.1 eV. a relate to the temperature of sample T0 can be expressed as [23]:
a ¼ a0 exp
Fig. 4. The relation of a: n and b: (n2 1)1 versus E2 in the range of 15.0–25.0 eV2.
r
kB T
ðh m h m Þ 0 0
ð11Þ
where ht0 and a0 are constants depending only on material properties [24], and r is the steepness parameter depending on the temperature (T0 ) which characterizes broadening of the absorption edge due to electron–phonon or exciton-phonon interactions in the lattice [25]. At room-temperature, ht versus ln a in the Urbach tail region (4.6–5.0 eV) was fitted to be a straight line (see Fig. 5a), achieving r = 0.014. At the bottom of Fig. 5a, we give the discrepancy between the measured ln a and the linear fitting curve. Worth noting, the discrepancy is small in the 4.60–4.87 eV. While the energy up to 4.87 eV, the discrepancy increased distinctly. To clarify the discrepancy, the spectrum of excitation, which is more sensitive than the absorption spectra, with monitoring fluorescence at 2.76 eV at room temperature of the crystal was tested, as shown in Fig. 5b. Three bands exist between 4.85 and 5.08 eV centered at 4.91, 4.94 and 5.01 eV, which were obtained from multiple peak fitting by Gaussian. The most intensity band at 5.01 eV can be attributed to the self-trapped exciton transition in the face-shared NbO6 octahedrons. The weaker ones can attribute to coexisting slight disorders of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons. More importantly, the energy of excitation bands in the excitation spectrum agrees with the energy of relatively larger discrepancy region between measured ln a and the linear fitting curve. Therefore, it is reasonable to believe that the self-trapped exciton and the slight disorders of Mg2+ and Nb5+ between MgO6 and NbO6
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the energy range of 4.0–5.0 eV (Urbach tail). Based on the singleeffective oscillator model, the moments of optical spectrum M1 and M3, oscillator energy E0 and dispersion energy Ed were determined as 4.10, 0.19, 26.88 eV, and 4.77 eV, respectively. The selftrapped exciton and disorder of Mg2+ and Nb5+ between MgO6 and NbO6 octahedrons participating in the transition in the Urbach tail were confirmed by the excitation spectrum. These results give an important basis for further theoretical study and practical device application based on Mg4Nb2O9 single crystals. Acknowledgements The financial support from the National Foundation for Fostering Talents of basic Science (Grant No. J1103202), the National Basic Research Program of China (No. 2011CB808200), the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), the National Natural Science Foundation of China (Grant No. 11274137, 11074090, 11304113), the open Project of State Key Laboratory of Superhard Materials (Jilin University) (No. 201302), and the open Project of State Key Laboratory of Inorganic Synthesis and Preparative Chemistry (Jilin University) (No. 2014-34) is greatly appreciated. References
Fig. 5. a: The ln a versus photon energy in the range of 4.6–5.0 eV and bottom shows the discrepancy between the measured ln a and the linear fitting curve and b: excitation spectrum of Mg4Nb2O9 crystal with monitoring fluorescence at 2.76 eV.
octahedrons participated in the transition in the Urbach tail region. These results also agree well with the theory developed by Sumi [26] that ascribes the exponential absorption shape to the coexistence of free exciton and momentarily self-trapped exciton. The theory is predominantly applicable to highly ionic crystals. Similar to most niobate, Mg4Nb2O9 should have an ionic character as the chemical bond [23]. 4. Conclusions The room-temperature absorption and transmittance spectra of Mg4Nb2O9 crystals fabricated by optical floating zone technology were measured from 200 to 800 nm. The extinction coefficient, complex dielectric constants and refractive index of the Mg4Nb2O9 crystals were obtained from the tested absorption and transmittance spectra. The Cauchy–Sellmeier equation was validated in
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